One important difference between a candle flame and a natural gas flame: whereas the flame of a well-adjusted natural gas burner emits very little light (a dim blue glow), the flame of a candle is quite visible. That's because the wax vapor in a candle flame isn't mixed well with air before it begins to burn. Instead of burning quickly and completely, as natural gas does in a burner that premixes the gas with air, the wax vapor in a candle flame burns gradually as it continues to mix with air. The partially burned wax forms tiny carbon particles. Those carbon particles are so hot that they glow yellow-hot — they emit thermal radiation. In other words, they are "incandescent". It's those glowing carbon particles that produce the candle's yellowish light. Eventually the carbon particles burn away to carbon dioxide.

The color sensing cells in our eyes are known as cone cells and they can detect only three different bands of color. One type of cone cell is sensitive to light in the red portion of the spectrum, the second type is sensitive to the green portion of the spectrum, and the third type is sensitive to the blue portion of the spectrum.

Their sensitivities overlap somewhat, so light in the yellow and orange portions of the spectrum simultaneously affects both the red sensitive cone cells and the green sensitive ones. Our brains interpret color according to which of three cone cells are being stimulated and to what extent. When both our red sensors and our green sensors are being stimulated, we perceive yellow or orange.

That scheme for sensing color is simple and elegant, and it allows us to appreciate many of the subtle color variations in our world. But it means that we can't distinguish between certain groups of lights. For example, we can't distinguish between (1) true yellow light and (2) a carefully adjusted mixture of true red plus true green. Both stimulate our red and green sensors just enough to make us perceive yellow. Those groups of lights look exactly the same to us.

Similarly, we can't distinguish between (3) the full spectrum of sunlight and (4) a carefully adjusted mixture of true red, true green, and true blue. Those two groups stimulate all three types of cone cells and make us perceive white. They look identical to us.

That the primary colors of light are red, green, and blue is the result of our human physiology and the fact that our eyes divide the spectrum of light into those three color regions. If our eyes were different, the primary colors of light would be different, too.

Many things in our technological world exploit mixtures of those three primary colors to make us see every possible color. Computer monitors, televisions, photographs, and color printing all make us see what they want us to see without actually reproducing the full light spectrum of the original. For example, if you used a light spectrum analyzer to study a flower and a photograph of that flower, you'd discover that their light spectra are different. Those spectra stimulate our eyes the same way, but the details of the spectra are different. We can't tell them apart.

The two tubes within a pair operate in series: current flowing as a discharge through the gas in one tube also flows through the gas in the other tube. That's why they both go out simultaneously. Only one of them is actually dead, but since the dead one has lost its ability to sustain a discharge, it can't pass any current on to its partner. Replacing the dead tube is usually enough to get the pair working again, at least for while.

Leaving dead tubes in a fixture isn't the same as removing unnecessary tubes. Tubes often die slow, lingering deaths during which they sustain weak or flickering discharges that consume some energy without providing much light. Also, most fluorescent fixtures heat the electrodes at the ends of the tubes to start the discharge. During startup, the ballast runs an electric current through each electrode (hence the two metal contacts at each end of the tube) and the heated electrodes introduces electric charges into the gas so the discharge can start.

That heating current is only necessary during starting, but if the discharge never starts then the ballast may continue to heat the electrodes for days, weeks, or years. If you look at the ends of a tube that fails to start, you may see the electrodes glowing red hot. Because of that heater current, leaving a failed fluorescent tube in a fixture can be waste of energy and money. Be careful removing those tubes from the fixture—although they produce no light, they can still be hot at their ends.

Snap-together beads are a perfect model for many polymers. As individual beads, you can pour them like a liquid and move your hand through them easily. But once you begin snapping them together into long chains, they develop new properties that weren't present in the beads themselves. For example, they get tangled together and don't flow so easily any more.

That emergence of new properties is exactly what happens in many polymers. For example, ethylene is a simple gas molecule, but if you stick ethylene molecules together to form enormous chains, you get polyethylene (more specifically, high-density polyethylene, recycling number 2, milk-jug plastic). Ethylene molecules are called "monomers" and the giant chains that are made from them are called "polymers".

Polyethylene retains some of the chemical properties of its monomer units, namely that it doesn't react with most other chemicals and almost nothing sticks to it. But polyethylene also has properties that the monomer units didn't have: polyethylene is a sturdy, flexible solid. You can stretch it without breaking it. That happens because you can make its polymer molecules slide across one another, but you can't untangle the tangles.

To get an idea of what it's like to work with molecules that can slide through each other but may not be able to untangle themselves, shift over to cooked and drained spaghetti. If you dice the spaghetti up into tiny pieces, it's like the monomers—nothing to tangle. You can pour the tiny pieces like a liquid. But trying doing that with a bowl of long spaghetti noddles. They're so tangled up that they can't do much. In fact, if you let the water dry up to some extent, the stuff will become a sturdy, flexible solid, just like HDPE!

There is much more to say about polymers, for example, they're not all simple straight chains and some of them cross-link so that they can't untangle no matter what you do. But this should be a good start. Polymer molecules are everywhere, including in paper and hair. Paper is primarily cellulose, giant molecules built out of sugar molecules. Hair is protein polymer, giant molecules built out of protein monomer units. They're both sturdy, stretchy, flexible solids and they're both softened by water—which acts as a molecular lubricant for the polymer molecules. Not all polymers are sturdy, or stretchy, or flexible, but a good many are.

As for how your cell phone and the cell tower can communicate for miles despite all the intervening stuff, it's actually a challenge. The microwaves from your phone and the tower are partly absorbed and partly reflected each time they encounter something in your environment, so they end up bouncing their way through an urban landscape. That's why cell towers have multiple antennas and extraordinarily sophisticated transmitting and receiving equipment. They are working like crazy to direct their microwaves at your phone as effectively as possible and to receive the microwaves from your phone even though those waves are very weak and arrive in bits and pieces due to all the scattering events they experience during their passage. Indoor cell phone reception is typically pretty poor unless the building has its own internal repeaters or microcells.

There are times when you don't get any reception because the microwaves from the cell phone and tower are almost completely absorbed or reflected. For example, if you were to stand in a metalized box, the microwaves from your cell phone would be trapped in the box and would not reach the cell tower. Similarly, the microwaves from the cell tower would not reach you. Moreover, the box doesn't have to be fully metalized; a metal mesh or a transparent conductor is enough to reflect the microwaves. Transparent conductors are materials that conduct relatively low-frequency currents but don't conduct currents at the higher frequencies associated with visible light. They're used in electronic displays (e.g., computer monitors and digital watches) and in energy-conserving low-E windows. I haven't experimented with cell phone reception near low-E windows, but I'm eager to give it a try. I suspect that a room entirely walled by low-E windows will have lousy cell phone reception.

Light is a form of energy, so you can compare the visible light energy emitted by any lamp to the energy that lamp consumes. According to that comparison, an incandescent lightbulb is roughly 5% efficient—a 100-watt incandescent bulb emits about 5 watts of visible light. In contrast, a fluorescent lamp is typically about 20% energy efficient—a 25-watt fluorescent lamp emits about 5 watts of visible light.

Another way to compare incandescent and fluorescent lamps is via their lumens per watt. The lumen is a standard unit of usable illumination and it incorporates factors such as how sensitive our eyes are to various colors of light. If you divide a light source's light output in lumens by its power input in watts, you'll obtain its lumens per watt.

For the incandescent lightbulb appearing at the left of the photograph, that calculation yields 16.9 lumens/watt. For the "long life" bulb at the center of the photograph, it give only 15.3 lumens/watt. And for the color-improved bulb on the right of the photograph, the value is only 12.6 lumens/watt. Our grandchildren will look at this photograph of long forgotten incandescent bulbs and be amazed that we could squander so much energy on lighting.

The fluorescent lamp in the other photograph is far more efficient. It produces more useful illumination than any of the three incandescent bulbs, yet it consumes just over a quarter as much power. Dividing its light out in lumens by its power consumption in watts yields 64.6 lumens/watts. It is 4 times as energy efficient as the best of the incandescent lightbulbs. Some fluorescent lamps are even more efficient than that.

Another feature to compare is life expectancy. Even the so-called "long life" incandescent predicts a 1500 hour life, which is only 15% of the predicted life for the fluorescent lamp (10,000 hours). Although the fluorescent costs more, it quickly pays for itself in energy use and less frequent replacement. You should recycle a fluorescent lamp because it does contain a tiny amount of mercury, but overall it's a much more environmentally friendly light source.

First, the egg has its weight—it's being pulled downward by gravity. That weight force tends to make the egg sink. Second, the egg is being pushed upward by the water around it with a force known as "the buoyant force." The buoyant force tends to make the egg float. It's a battle between those two forces and the strongest one wins.

The buoyant force exists because the water that is now surrounding the egg used to be surrounding an egg-shaped blob of water and it was pushing up on that blob of water just hard enough to support the blob's weight. Now that the egg has replace the egg-shaped blob of water, the surrounding water is still pushing up the same amount as before and that upward force on the egg is the buoyant force.

Since the buoyant force on the egg is equal in amount to the weight of the water that used to be there, it can support the egg only if the egg weighs no more than the egg-shaped blob of water. If the egg is heavier than that blob of water, the buoyant force will be too weak to support it and the egg will sink.

It so happens that a hard-boiled egg weighs slightly more than an egg-shaped blob of pure water, so it sinks in pure water. But that egg weighs slightly less than an egg-shaped blob of very salty water. Adding salt to the water increases the water's weight significantly while having only a small effect on the water's volume. Salt water is heavier, cup for cup, than fresh water and it produces stronger buoyant forces.

In general, any object that weighs more than the fluid it displaces sinks in that fluid. And any object that weighs less than the fluid it displaces floats. You are another good example of this: you probably sink in fresh water, particularly after letting out all the air in your lungs. But you float nicely in extremely salty water. The woman in this photograph is floating like a cork in the ultra-salty water of the Dead Sea.

Below water's boiling temperature, bubbles of water vapor are unstable—they are quickly crushed by atmospheric pressure and vanish into the liquid. At or above water's boiling temperature, those water vapor bubbles are finally dense enough to withstand atmospheric pressure and they grow via evaporation, rise to the surface, and pop. At that point, I'd probably call the water vapor by its other name: steam. But where do those steam or water vapor bubbles come from in the first place?

Forming water vapor bubbles in the midst of liquid water, a process called nucleation, is surprisingly difficult and it typically happens at hot spots or non-wetted defects (places where the water doesn't completely coat the surface and there is trapped air). When you boil water in a metal pot on the stove, there are hot spots and defects galore and nucleating the bubbles is not a problem. When you boil water in a glass or glazed container using a microwave oven, however, there are no significant hot spots and few non-wetted defects. The water boils fitfully or not at all. The "not at all" possibility can lead to disaster.

Water that's being heated in a metal pot on the stove boils so vigorously that the stove is unable to heat it more than tiny bit above its boiling temperature. All the heat that's flowing into the water is consumed by the process of transforming liquid water into gaseous water, so the water temperature doesn't rise. Water that's being heated in a glass container in a microwave oven boils so fitfully that you can heat it above its boiling temperature. It's simply not able to use up all the thermal energy it receives via the microwaves and its temperature keeps rising. The water becomes superheated.

Most of the time, there are enough defects around to keep the water boiling a bit and it superheats only a small amount. When you remove the container of water from the microwave oven and toss in some coffee powder or a teabag, thus dragging air bubbles below the surface, the superheated water boils into those air bubbles. A stream of bubbles suddenly appears on the surface of the water. Most people would assume that those bubbles had something to do with the powder or teabag, not with the water itself. Make no mistake, however, the water was responsible and those bubbles are mostly steam, not air.

Occasionally, though, the water fails to boil at all or stops boiling after it manages to wet the last of the defects on the glass or glazed surface. I've made this happen deliberately many times and it's simply not that hard to do. It can easily happen by accident. With no bubbles to assist evaporation, the water's only way to get rid of heat is via evaporation from its top surface. If the microwave oven continues to add thermal energy to the water while it is having such difficulty getting rid of that energy, the water's temperature will skyrocket and it will superheat severely.

Highly superheated water is explosive. If something causes nucleation in that water, a significant fraction of the water will flash to steam in the blink of an eye and blast the remaining liquid water everywhere. That boiling-hot water and steam are a major burn hazard and the blast can break the container or blow it across the room. I've heard from a good number of people who have been seriously hurt by exploding superheated water produced accidentally in microwave ovens. It's a hazard people should take seriously.

After that long introduction, it's time to answer your question. Yes, I believe that the microwave makers are responsible for advising people of this hazard. Moreover, they know that they are responsible for doing it. If you look at any modern microwave oven user manual, you will find a discussion of superheating or overheating. Look at your manual, I'll bet it's in there.

But that discussion will almost certainly be buried in the middle of an long list of warnings. For example, in one manual, the discussion of overheated water appears as item 17 of 22, after such entries as "4. Install or locate this appliance only in accordance with the provided installation instructions" and "12. Do not immerse cord or plug in water". To be fair to the manufacturer, warning 17 is longest of the bunch and it suggests mostly reasonable precautions (although I'm not so happy with recommendation 17a: "Do not overheat the liquid."). No Duh.

I think the issue is this: most product warnings are provided not out of any sincere concern for the consumer, but out of fear of litigation. A manufacturer's goal when providing those warnings is therefore to be absolutely comprehensive so that they can point to a line in a user manual in court and claim to have fulfilled their responsibility. The number and order of the warnings makes no difference; they just have to be in there somewhere.

So all those warnings you ignore in product literature aren't really about consumer safety, they're about product liability. You ignore them because everything now comes with a thousand of them, ranging from the reasonable to the ridiculous. For my research, I ordered 99.999% pure sodium chloride (i.e., ultrapure table salt). It came with a 6-page Material Safety Data Sheet that identifies it as an "Xi Irritant", noting that it is "Irritating to eyes, respiratory system and skin" and recommending first aid measures that include:

"After inhalation: supply fresh air. If required, provide artificial respiration. Keep patient warm. Seek immediate medical advice.
After skin contact: Immediately wash with water and soap and rinse thoroughly. Seek immediate medical advice.
After eye contact: rinse opened eye for several minutes under running water. Then consult a doctor."

By design and by accident, our society has lost the ability to distinguish real risk from imaginary risk. We treat all risks as equal and spend way too much time worrying about the wrong ones. If you want to be safer around your cell phone, for example, you should worry more about driving with it in your hand than about the microwave radiation it emits. The current evidence is that your risk of injury or death due to a cell-phone related accident far outweighs your risk from cell-phone microwave exposure. Even if further research proves that cell phone microwave exposure is injurious, we should be acting according to our best current assessments of risk, not according to fears and beliefs.

That said, I'd like to see product literature rank their warnings according to risk and put the real risks in a separate place where they can't be overlooked or ignored. Put the real consumer safety stuff where the consumers will see it and put the product liability stuff somewhere else where the lawyers can find it. For a microwave oven, there are probably about half a dozen real risks that people should know about. Several of them are relatively obvious (e.g., don't heat sealed containers) and some are not obvious (e.g., liquids heated in the microwave can become superheated and explode).

Maybe we'll get a handle on risk someday. In the meantime, inform your friends and children that they should be careful about heating liquids in the microwave, particularly in glass or glazed containers. Just knowing that superheating is possible would probably halve the number of burns and other injuries that result from superheating accidents.

In all my years of experimenting with microwave ovens, I've only killed a magnetron once. But then again, I haven't run a microwave oven for more than a minute or two without anything inside it. If the oven works again after cooling down, then you're probably OK. The oven may have thermal interlocks in its microwave source to prevent that source from overheating and becoming a fire hazard. If the oven fails to work after an hour of cooling off, then you're probably out of luck. The magnetron and/or its power supply are likely to be fried and in need of replacement.

When a women stands on the floor, the floor must support her weight. Specifically, she isn't accelerating so the net force on her must equal zero. That implies that the floor must exert an upward force on her that exactly cancels her downward weight. She is motionless and stays motionless because there is no overall force on her.

Because the floor is pushing upward on her shoes, her shoes must be pushing downward on the floor. It's an example of the famous "action and reaction" principle known as Newton's third law: if you push on something, it pushes back equally hard in the opposite direction. Anyway, her shoes are pushing down hard on the floor.

But when she wears high heels, most of her weight is supported by a very small area of flooring. If the heels are narrow spikes with a contact area of 0.1 square inches (0.65 square centimeters) and she puts all of her weight briefly on one of the heels, she may exert a pressure of 1300 pounds-per-square-inch (9000 newtons-per-square-centimeter or 90 million pascals) on the floor. That's an enormous pressure that will permanently dent most wooden floors.

You can experiment with these ideas simply by supporting the weight of your right hand with the open palm of your left hand. If you lay your right fist on your left palm, you won't feel any discomfort in your left hand. The pressure on your left palm is very small. But if you instead point right index finger into your left palm and use that finger to support the entire weight of your right hand, it won't feel so comfortable. If you shift all of the weight to your fingernail, it'll start to hurt your left palm. What you're doing is reducing the area of your left palm that is supporting your right hand and as that area gets smaller, the pressure on your left palm increases. Beyond a certain pressure, it feels uncomfortable. Long before your palm dents permanently, you'll decide to stop the experimenting.

Each portion of cable responds to being pulled by accelerating, moving, and consequently pulling on the portion of cable adjacent to it. There will be a long series of actions—pulling, accelerating, moving, and pulling again—that propagates your influence along the cable. A wave will travel along the cable, a wave consisting of a local reduction in the cable's density. It's a stretching wave. In that respect, the wave is a type of sound wave—a density fluctuation that propagates through a medium.

How quickly the density wave travels along the cable depends on how stiff the cable is and on its average mass density. The stiffer the cable, the more strongly each portion can influence its neighboring portions and the faster the density wave will travel. The greater the cable's mass density, the more inertia it has and the slower it respond to pulls, so the density wave will travel slower.

A cable made from a stiff, low-density material carries sound faster than a soft, high-density material. A steel cable should carry your wave at about 6100 meters/second (3.8 miles/second). But a diamond cable would reach 12000 meters/second (7.5 miles/second) because of its extreme stiffness and a beryllium cable would approach 13000 meters/second (8.0 miles/second) because of its extremely low mass density.

Regardless of which material you choose, you're clearly not going to be able to send any signals faster than the speed of light. It would take a density wave more than 100,000 years to travel the 5-light year length of your cable. And sadly, friction-like dissipation effects in the cable would turn the density wave's energy into thermal energy in a matter of seconds, so it would barely get started on its journey before vanishing into randomness.

To begin with, plug-in power adapters are designed to keep their electromagnetic fields relatively well contained. They're engineered that way not because of safety concerns but because their overall energy efficiencies would diminish if they accidentally conveyed power to their surroundings. Keeping their fields inside keeps their energy inside, where it belongs. Moreover, any electric and magnetic fields emerging from an adapter probably don't propagate as waves and instead fall off exponentially with distance. As a result, it should be fairly difficult to detect electric or magnetic fields more than a few inches from the adapter.

Even if the adapter did project significant electric and magnetic fields all the way to where your dog sleeps, it's still unlikely that they would cause any harm. For years, researchers have been looking for a correlation between high-voltage electric power lines and a variety of human illnesses, notably childhood cancers such as leukemia. As far as I know, no such correlation has ever been demonstrated. In all likelihood, if there are any risks to being near 60-Hz electric or magnetic fields, those risks aren't large enough to be easily recognized.

In contrast to power adapters, cell phones deliberate emit electric and magnetic fields in order to communicate with distant receivers on cell phone towers. Those fields are woven together to form electromagnetic waves that propagate long distances and definitely don't vanish inches from a cell phone. Any electromagnetic hazard due to a power adapter pales in comparison to the same for cell phones.

Furthermore, cell phone operate at much higher frequencies than the alternating current power line. A typical cell phone frequency is approximately 1 GHz (1,000,000,000 Hz), while ordinary alternating current electric power operates at 60 Hz (50 Hz in Europe). Higher frequencies carry more energy per quanta or "photon" and are presumably more dangerous. But even though cell phones are held right against heads and radiate microwaves directly into brain tissue, they still doen't appear to be significantly dangerous. As unfond as I am of cell phones, I can't condemn them because of any proven radiation hazard. Their biggest danger appears to be driving with them; I don't understand why they haven't been banned from the hands of drivers.

Lastly, there are no obvious physical mechanisms whereby weak to moderate electric and magnetic fields at 60-Hz would cause damage to human or canine tissue. We're essentially non-magnetic, so magnetic fields have almost no effect on us. And electric fields just push charges around in us but that alone doesn't cause any obvious trouble. Research continues into the safety of electromagnetic fields at all frequencies, but this low-frequency stuff (power lines and cell phones) doesn't seem to be unsafe.

Actually, I could have registered this website as www.howeverythingworks.com, but I would have had to purchase that domain name from someone else. It is registered to a cybersquatter—someone who registers a domain name in hopes of selling it at a profit to someone else. Cybersquatting was hugely popular during the internet bubble, when companies were paying vast amounts of money for particular domain names. But these days, who wants to pay thousands of dollars for a name? I'm totally happy to be www.howeverythingworks.org and I'll let someone else pay the big bucks to purchase www.howeverythingworks.com. In the meantime, that domain is just a link to advertising and an offer to sell the domain name.

Even if the oven door has multiple layers of glass, those layers are there for your protection. If you touch the outside of the metal grid while the oven is on or get close enough to it through the last layer of glass, you'll be able to absorb some microwave power and it'll probably hurt. That's because while the holes in the grid are too small to allow the microwaves to propagate through them and truly escape from the oven, they do allow an "evanescent wave" to exist just outside each hole in the grid. That evanescent wave dies off exponentially with distance beyond the hole, so it won't travel around the room. But you don't want to put your finger in it.

For inexpensive microwave ovens, you're probably best off simply recycling the oven. I'm not happy about the modern everything-is-disposable state of appliances and equipment, but I can't say that it's cost effective to repair an oven that costs less than about $100. For more expensive microwave ovens, you can usually replace the window or the door. We have had a GE combination microwave and convection oven over our stove top for about 10 years and the door started to come apart about 18 months ago. I purchased a replacement microwave oven door over the web for $140 and installed it myself. It works beautifully. If you're not handy or are concerned about microwave leaks, you should probably have it replaced professionally. But you can look up the parts themselves online at a number of web sites and get an idea of what the cost will be.

In fact, turning off the power strip is likely to save energy as well. Many computer devices have two different "off" switches: one that stops them from doing their normal functions and one that actually cuts off all electrical power. Computers in particular don't really turn off until you reach around back and flip the real power switch on the computer's power supply. The same is true of television monitors and home theater equipment.

In general, any device that has a remote control or that can wake itself up to respond to a pretty button or to some other piece of equipment is never truly off until you shut off its electrical power. Our homes are now filled with electronic gadgets that are always on, waiting for instructions. Keeping them powered up even at a low level consumes a small amount of electrical power and it adds up. Last I heard, this always-on behavior of our gadgets consumes something on the order of 1% of our electrical power. Whatever it is, it's too much. So by turning off your power strip and completely stopping the flow of power to your computer, your speakers, your monitor, etc., you are saving energy. You lose the convenience of being able to turn everything on from your couch with a remote, but who cares. Energy is too precious to waste for such nonessential conveniences.

The idea of a wave that travels through space itself was a rather disorienting notion to scientists in the late 1800s. They were used to the idea that waves are disturbances in a tangible material or "medium": fluctuations in the density of air, ripples on the surface of water, vibrations of a taut string. Having observed that light and radio waves are electromagnetic waves, they set about looking for the medium that supported those waves. They were expecting to find this "luminiferous aether" but they failed. In fact, the absence of an aether led in part to Einstein's theory of special relativity.

The structure of a radio wave, or any electromagnetic wave, is quite simple. It consists only of a fluctuating electric field and a fluctuating magnetic field. An electric field is a structure in space that affects electric charge; it pushes on charge and causes that charge to accelerate. Similarly, a magnetic field is a structure that affects magnetic pole. Remarkably, changing electric fields produce magnetic fields and changing magnetic fields produce electric fields. That interrelatedness allows the wave's fluctuating electric field to produce its fluctuating magnetic field and vice verse. The wave's electric and magnetic fields endless recreate one another. Although electric charge or magnetic pole is needed to emit or receive a radio wave, that wave can travel perfectly well for billions of light years without involving any charge or pole. It travels through space itself.

An older oven would have used a heavy transformer, a capacitor, and a diode to convert ordinary household AC power to high-voltage DC power for its magnetron microwave tube. But since your oven was made recently, it probably uses a switching power supply to produce that high voltage. That supply contains a much more sophisticated electronic switching system to convert household AC power to high-voltage DC power. The new approach is cheaper and lighter, so it's taking over in microwave ovens. Just because it's more sophisticated, however, doesn't mean it's more reliable.

My guess is that the unit in your oven has a problem. If it has an intermittent contact in it or if there is a conducting path that is sparking somewhere in the power supply or in the unit as whole, they'll be randomly fluctuating currents present in the oven and those current fluctuations will produce radio waves. A sparking wire or carbonized patch on the power supply will start and stop the flow of current erratically and that can easily cause interference on the AM band. Ordinary AM radio is very susceptible to radio-frequency interference at around 1 MHz and sparking stuff tends to produce such radio waves. A car with a bad ignition system, a lawn mower, and a thunderstorm all interfere beautifully with AM reception. And I suspect that you've got a similar electrical problem in your oven. I doubt that your oven is a microwave hazard, but you should probably have a repair person to take a look at it. It shouldn't have anything sparking inside it.

Those YouTube videos were complete fakes; they didn't pop any popcorn while the camera was rolling. To make it appear that the cell phones were popping the corn, the people who produced the videos dropped already prepared popcorn into the frame and then photoshopped away the unpopped kernels. When you watch the video, it looks like the kernels are popping, but they're really just disappearing via video editing as precooked popcorn is sprinkle onto the set from above.

The reason they had to use video trickery is pretty clear: to pop popcorn with microwaves, those microwaves have to be extremely intense. Each kernel contains only a tiny amount of water and it's the water that heats up when the kernel is exposed to microwaves. If the microwaves aren't intense enough, the heat they deposit in the kernel's water will flow out to the rest of the kernel and into the environment too quickly for the kernel's water to superheat and then flash to steam.

Even when you put popcorn kernels in a closed microwave oven, it takes a minute or two for the kernels to accumulate enough thermal energy to pop. In that closed microwave oven, the microwaves bounce around inside the metal cooking chamber and their intensity increases dramatically. It's like sending the beam from a laser pointer into a totally mirrored room—the light energy in that room will build up until it is extremely bright in there. In the closed cooking chamber of the oven, the microwave energy also builds up until the microwave intensity is enough to pop the corn. How intense? Well, a typical microwave oven produces 700 watts of microwave power. Since the cooking chamber is nearly empty when you're popping popcorn, the cooking chamber accumulates a circulating power of very roughly 50,000 watts.

Although that power is spread out over the cross section of the oven, the microwaves are still seriously intense -- thousands of watts per square inch. To put that in perspective, a cell phone transmits a maximum of 2 watts and that power is spread out over at least 5 square inches so the intensity is less than 1 watt per square inch. When I saw those videos in Summer 2008, I realized that there was no way cell phones were ever going to pop popcorn. They certainly wouldn't do it while they are ringing, because that's when they are primarily receiving microwaves, not when they're transmitting them. It's when you're talking that your cell phone is regularly producing microwaves. It was all obviously just fun and games.

So what about your disassembled microwave oven? Since there is no metal box to trap the microwaves and accumulate energy, they'll only have one shot at popping the corn kernels. The microwaves will emerge from the magnetron's waveguide at high intensity, but they'll spread out quickly once there is nothing to guide them. You could probably pop kernel right at the mouth of the magnetron but not a few inches away. Unless you use microwave optics to focus those microwaves, they'll have spread too much by the time they get through the table and reach the kernels of popcorn and the kernels will probably never pop.

If that were the whole story, the worst that would happen with your experiment would be that it wouldn't cook popcorn. But there is a real hazard here. Sending about 700 watts of microwaves into the room isn't exactly safe. It's something like having a red hot coal emitting 700 watts of infrared light, except that you won't see anything with your eyes and this microwave "light" is coherent (i.e., laser-like) so it can focus really tightly. You'd hate to have some metal structure in the room or even inside the walls of the room focus the microwaves onto you. You absorb microwave much better than the corn kernels and you'll "pop" long before they do. Actually, your eyes are particularly sensitive to microwave heating and you might not notice the damage until too late. Without instruments to observe the pattern of microwaves in the room when the magnetron is on, I wouldn't want to be in the room.

When you cool a basketball, however, you reduce the pressure of its air. That's because the air molecules have less thermal energy at colder temperatures and thermal energy is responsible for air pressure. A basketball that was properly inflated at warm temperature becomes under-inflated when you cool it down. At the same time, the basketball's skin becomes less elastic and more leathery at cool temperatures. So the basketball suffers from under-inflation and from a leathery, not-very-bouncy skin.

If you cool a basketball to low enough temperature, its skin will freeze and become brittle. Just how low the temperature has to go depends on the material used in to make the basketball. I've never seen a basketball shatter on the court, even in pretty cold weather, so I doubt you can "freeze" one in a household freezer. But I'm sure that a dip in liquid nitrogen at -395 °F would do the trick. I often freeze rubber handballs in liquid nitrogen for my class and then shatter them on the floor.

If you look carefully at the string while it's vibrating in a mixture of several harmonics, you'll see that it has only one shape at any moment in time. It's just a jiggling string, after all. The parts of that shape, however, are evolving at different rates in time and those parts are actually the different harmonics going through their individual motions at their own frequencies.

But while the speed of light in vacuum is a constant, the speed of light in matter isn't. Light is an electromagnetic wave and consists of electric and magnetic fields. Electric fields push on electric charge and matter contains electric charges, so light and matter interact. That interaction normally slows light down; the light gets delayed by the process of shaking the electric charges. In air, this slowing effect is tiny, less than 1 part in a thousand. In glass, plastic, or water, light is slowed by about 30 or 40%. In diamond, the interaction is strong enough to slow light by 60%. In silicon solar cells, light is slowed by 70%. And so it goes.

To really slow light down, however, you need to choose a specific frequency of light and let it interact with a material that is resonant with that light. Because a resonant material responds extremely strongly to the light's electric field, it delays the light by an enormous amount. And by choosing just the right wavelength of light to match a particular collection of resonant atoms, Lene Hau and her colleagues managed to bring light essentially to a halt. The light lingers nearly forever with the atoms in their apparatus and it barely makes any headway.

To understand why light scatter depends on homogeneity, consider what happens when light pass through clear particles. Even though they are clear, light still interacts with them, as evidenced by rainbows, clouds, and even the blue sky. How best to think about that interaction depends on the size of the particles. If the particles are large, like smooth beads of glass or plastic, then they exhibit the familiar refraction and reflection effects of window panes and lenses. If the particles are small, like air molecules and tiny water droplets, then they exhibit a more antenna-like interaction with light. In effect, those tiny particles occasionally absorb and reemit the light waves, particularly at the short-wavelength (i.e., blue) end of the light spectrum.

Both types of interactions are quite familiar to us. Large particles scatter light about without any color bias and exhibit a white appearance. The more surface area a collection of particles has, the more light that collection scatters. For example, a large ice crystal is clear but crushed ice or snow is white. Similarly, a bowl of water is clear but a mist of water droplets is white. Lastly, a bowl of air is clear, but a froth of air bubbles in water is white. As you can see, the transparent particles don't have to be solids or liquids to scatter light, they can even be gases!

On the other hand, truly tiny particles scatter light about according to wavelength and color. In most cases, shorter-wavelength (blue) light scatters more than longer-wavelength (red) light. That effect, known as Rayleigh scattering, is responsible for the blue sky and the red sunset.

In a nutshell then, large transparent particles appear white and tiny transparent particles appear colored (typically bluish). And the more particles there are, the more light is scattered.

Returning to your question, a loose powder of transparent particles scatters light like crazy and appears white or possible colored, depending on particle size. As you pack the powder more and more tightly together, its surfaces join together and it starts to lose the ability to scatter light; it becomes less white and more translucent. When the consolidation is almost complete, the material acquires a slightly hazy look due to scattering by the occasional voids left inside the otherwise transparent material. Finally, when the material is fully consolidated and there is no internal surface left in the powder, it is homogeneous and clear. So sending light through a packed transparent powder and measuring the amount and color of the scattered light tells you a lot about how well consolidated that powder is.

A simple way to see why that's the case is to picture the gas as composed of many little bouncing balls inside the container. Those balls are perfectly elastic so they rebound from a stationary wall without changing their speeds at all. But the walls of the container aren't stationary, they move back and forth as you shake the container. Because of the moving walls, the balls change their speeds as they rebound. A ball that bounces off a wall that is moving toward it gains speed during its bounce, like a pitched ball rebounding from a swung bat. On the other hand, a ball that bounces off a wall that is moving away from it loses speed during its bounce, like a pitched ball rebounding from a bat during a bunt. If both types of bounces were equally common in every way then, on average, the balls (or actually the gas molecules) would neither gain nor lose speed as the result of bounces off the walls and the gas temperature would remain unchanged.

But the bounces aren't equally common. It's more likely that a moving ball will hit a wall that is moving toward it than that it will hit a wall that is moving away from it. It's a geometry problem; you get wet faster when you run toward a sprinkler than when you run away from the sprinkler. So, on average, the balls (or gas molecules) gain speed as the result of bounces off the walls and the gas temperature increases.

How large this effect is depends on the relative speeds of the gas molecules and the walls. The effect becomes enormous when the walls move as fast or faster than the gas molecules but is quite subtle when the gas molecules move faster than the walls. Since air molecules typically move at about 500 meters per second (more than 1000 mph) at room temperature, you'll have to shake the container pretty violently to see a substantial heating of the gas.

DC power also avoids the phase issues that make the AC power grid so complicated and fragile. It's not enough to ensure that all of the generators on the AC grid are producing the correct amounts of electrical power; those generators also have to be synchronized properly or power will flow between the generators instead of to the customers. Keeping the AC power grid running smoothly is a tour-de-force effort that keeps lots of people up at night worrying about the details. With DC power, there is no synchronization problem and each generating plant can concentrate on making sure that their generators are producing the correct amounts of power at the correct voltages.

Lastly, alternating currents tend to flow on the outsides of conductors due to a self-interaction between the alternating current and its own electromagnetic fields. For 60-cycle AC, this "skin effect" is about 1 cm for copper and aluminum wires. That means that as the radius of a transmission line increases beyond about 1 cm, its current capacity stops increasing in proportion to the cross section of the wire and begins increasing in proportion to the surface area of the wire. For very thick wires, the interior metal is wasted as far as power delivery is concerned. It's just added weight and cost. Since direct current has no skin effect, however, the entire conductor can be carry current and there is no wasted metal. That's a big plus for DC power distribution.

The great advantage of AC power transmission has always been that it can use transformers to convey power between electrical circuits. Transformers make it easy to move AC power from a medium-voltage generating circuit to an ultrahigh-voltage transmission line circuit to a medium-voltage city circuit to a low-voltage neighborhood circuit. DC power transmission can't use transformers directly because transformers need alternating currents to move power from circuit to circuit. But modern switching electronics has made it possible to convert electrical power from DC to AC and from AC to DC easily and efficiently. So it is now possible to move DC power between circuits by converting it temporarily into AC power, sending it through a transformer, and returning it to DC power. They can even use higher frequency AC currents and consequently smaller transformers to move that power between circuits. It's a big win on all ends. While I haven't followed the developments in this arena closely, I would not be surprised if DC power transmission started to take hold in the United State as we transition from fossil fuel power plants to renewable energy sources. Using those renewable sources effectively will require that we handle long distance transmission better than we do now and we'll have to develop lots of new transmission infrastructure. It might well be DC transmission.

The standard current limiter for fluorescent lamps and other discharge lamps that are powered from 60-cycle (or 50-cycle) alternating current has been an electromagnetic coil known as a ballast. When that coil is in series with the discharge, the coil's self-inductance limits how quickly the current flowing through the lamp can rise and therefore how much power the lamp can consume before the alternating current reverses direction. The discharge winks on and off with each current reversal and never draws more current than it can tolerate. Unfortunately, the lamp's light also winks on and off and some people can see that flicker, especially with their peripheral vision.

Actually, the ballast usually has another job to do in a traditional fluorescent lamp: it acts as a transformer to provide the current needed to heat the electrode filaments at the ends of the lamp. Heating those electrodes helps drive electrons out of the metal and into the lamp's gas so that the gas becomes electrically conducting. In total then, the ballast receives alternating current electric power from the power line and prepares it so that all the lamp filaments are heated properly and a limited current flows through the lamp from one electrode to the other.

In modern fluorescent lamps with heated electrodes, however, the role of the ballast has been usurped by a more sophisticated electronic power conditioning device. That device converts 60-cycle alternating current electric power into a series of electrical energy pulses, typically at about 40,000 pulses per second, and delivers them to the lamp. The lamp's flicker is almost undetectable because it is so fast and the limited energy in each pulse prevents the discharge from consuming too much power. It's a much better system. Compact fluorescent lamps use it exclusively.

So where might high voltage fit into this story? Well, there are some fluorescent lamps that don't heat their electrodes with filaments. They rely on the discharge itself to drive electrons out of the electrodes and into the gas to sustain the discharge. But that begs the question: "how does such a lamp start its discharge?" It uses high voltage. Because of cosmic rays and natural radioactivity, gases always have some electric charges in them: ions and electrons. When the voltage difference between the two ends of the lamp becomes very large, the electric field in the lamp propels those naturally occurring ions and electrons into the constituents of the lamp violently enough to start the lamp's discharge. The voltages needed to start these "cold cathode" lamps are typically in the low thousands of volts. For example, the cold cathode fluorescent lamps used in laptop computer displays start at about 2000 volts and then operate at much lower voltages.

But appearances can be deceiving. Since energy is a conserved quantity, the energy that you invest in the firewood can't disappear. It simply becomes difficult to find because it is dispersed in the burned gases that were once the wood.

To find that energy, imagine compressing the burned gases into a small container to make their weight more noticeable and reduces buoyant effects due to the atmosphere. You could then carry those burned gases, which include all of the firewood's atoms, back down the hill. As you descended, the container of burned gases would transfer its gravitational potential energy to you.

I've swept a number of details under the rug, such as the fact that many of the oxygen atoms in your container were originally part of the atmosphere rather than the log. But even when all those details are taken into account, the answer is the same: the firewood's gravitational energy doesn't disappear, it just gets more difficult to find.

Since eye safety requires limiting the amount of laser power that can enter a person's eye, you can make a laser more eye-safe by enlarging its beam. Even a powerful laser can be eye-safe if only a small fraction of the laser light can enter a person's iris and focus on their retina.

Although it's natural to think of a laser beam as a narrow pencil of light that stays narrow forever, that's not really the case. The diameter of a laser beam changes with distance from its source. The beams from typical lasers, including laser pointers, start relatively narrow and widen as gradually as the physics of light propagation will allow. But with the help lenses, you can change that widening process dramatically. For example, if you send a typical laser beam through a converging lens that has a focal length of 1 foot, the laser beam will converge to a very narrow "beam waist" 1 foot beyond the lens and will then spread relatively quickly with distance. It will return to its original diameter 1 foot beyond its waist and to 10 times its original diameter 10 feet beyond its waist. With its light spread out by a factor of 10 in both height and width, it will have only 1/100th the intensity (power per unit area) of the original beam. Because of its large size, only a fraction of the beam and its light power will now enter a person's iris and focus on their retina.

Using this scheme, you can have a beam that is extremely intense for the first 2 feet, including a super-intense waist at the 1-foot mark. But beyond that point, the beam spreads quickly and soon becomes so wide that it is no longer a eye hazard.

If the temperature of overly moist air is 32 F or below, planes preparing for takeoff can accumulate heavy burdens of ice. When water vapor condenses as ice directly onto the wings themselves, that condensation process is called deposition and is familiar to you as frost. Deposition is a relatively slow process, so most of the trouble for planes occurs when it is actually snowing or sleeting. Removing the ice then requires either heat or chemicals.

When the plane is flying at high altitudes, however, the air is extremely dry. Even though the air temperature is far below the freezing temperature of water, the fraction of water molecules in the air is nearly zero and the relative humidity is much less than 100%. That means that an ice cube suspended in that dry air would actually evaporate away to nothing. Technically, that "evaporation" of ice directly into water vapor is call sublimation and you've seen it before. Think of all the foods that have experienced freezer burn in your frost-free (i.e., extremely dry air) refrigerator or the snow that has mysteriously disappeared from the ground during a dry spell even though the temperature has never risen above freezing. Both are cases of sublimation — where water molecules left the ice to become moisture in the air.

The first approach, shifting the frequencies/wavelengths, is seriously difficult. There are optical techniques for adding and subtracting optical waves from one another and thereby shifting their frequencies/wavelengths, but those techniques work best with the intense waves available with lasers. For example, the green light produced by some laser pointers actually originated as invisible infrared light and was doubled in frequency via a non-linear optical process in a special crystal. The intensity and pure frequency of the original infrared laser beam makes this doubling process relatively efficient. Trying to double infrared light coming naturally from the objects around you would be extraordinarily inefficient. In general, trying to shift the frequencies/wavelengths of the various electromagnetic waves in your environment so that you can see them is pretty unlikely to ever work as a way of seeing the invisible portions of the electromagnetic spectrum.

The second approach, imaging invisible portions of the electromagnetic spectrum and then presenting a false-color reproduction to the viewer, is relatively straightforward. If it's possible to image the radiation and detect it, it's possible to present it as a false-color reproduction. I'm talking about a camera that images and detects invisible electromagnetic radiation and a computer that presents a false-color picture on a monitor. Imaging and detecting ultraviolet and x-ray radiation is quite possible, though materials issues sometimes makes the imaging tricky. Imaging and detecting infrared light is easy in some parts of the infrared spectrum, but detection becomes problematic at long wavelengths, where the detectors typically need to be cooled to extremely low temperatures. Also, the resolution becomes poor at long wavelengths.

Camera systems that image ultraviolet, x-ray, and infrared radiation exist and you can buy them from existing companies. They're typically expensive and bulky. There are exceptions such as near-infrared cameras — silicon imaging chips are quite sensitive to near infrared and ordinary digital cameras filter it out to avoid presenting odd-looking images. In other words, the camera would naturally see farther into the infrared than our eyes do and would thus present us with images that don't look normal.

In summary, techniques for visualizing many of the invisible portions of the electromagnetic spectrum exist, but making them small enough to wear as glasses... that's a challenge. That said, it's probably possible to make eyeglasses that image and detect infrared or ultraviolet light and present false-color views to you on miniature computer monitors. Such glasses may already exist, although they'd be expensive. As for making them small enough to wear as contact lenses... that's probably beyond what's possible, at least for the foreseeable future.

Part of the reason why it takes so long for the dissolved gases to come out of solution is that the gas can only leave through the exposed surface of the liquid. In an open bottle of carbonated beverage that may be only a few square inches or a few dozen square centimeters. The dissolved gas has to find its way to that exposed surface and break free of the liquid. That's a slow process. The same thing is happening in your wine: the dissolve carbon dioxide and oxygen gases must normally find their way to the top of the tank and then break free to enter the gaseous region at the top of the tank — another slow processes. To speed the escape of dissolved gases, you can enlarge the exposed surface of the liquid by bubbling an inert gas through the liquid. Here, inert gas is any gas that doesn't dissolve significantly in the liquid and that doesn't affect the liquid if it does dissolve. Nitrogen is great for wine because it doesn't interact chemically with the wine. As you let bubbles of nitrogen float upward through the wine, you provide exposed surface within the body of the liquid wine and allow carbon dioxide and oxygen to break free of the liquid and enter those bubbles.

The spherical interface between the gas bubble and the surrounding liquid is a busy, active place — gas molecules are moving between the gas and liquid in both directions. Because carbon dioxide is over-concentrated in the liquid, it is statistically more likely for a carbon dioxide molecule to leave the liquid and enter the bubble's gas than the other way around. It takes a little energy to break those carbon dioxide molecules free of the liquid and that need for energy affects the balance between dissolved carbon dioxide and gaseous carbon dioxide at equilibrium. The harder it is for the carbon dioxide molecules to obtain the energy they need to escape from the liquid, the greater the equilibrium concentration of dissolved carbon dioxide — the saturated concentration. But your wine is supersaturated, containing more than the equilibrium concentration of dissolved carbon dioxide, so carbon dioxide molecules go from liquid to gas more often than the other way around.

When the degree of supersaturation (excess gas concentration) is high, the transfer of gas molecules from liquid to gas bubble can be fast enough to make the bubbles grow in size significantly as they float up through the wine. You can see this type of rapid bubble growth in a glass of freshly poured soda, beer, or champagne. In beer, champagne, and your wine, however, the liquid surface of the bubble contains various natural chemicals that alter the interface with the gas and affect bubble growth. The "tiny bubbles" of good champagne reflect that influence.

Another way to provide the extra exposed surface in the wine and thereby allow the supersaturated dissolved gases to come out of solution would be to agitate the wine so violently that empty cavities open up within the wine. Although that approach would provide lots of extra surface, it would probably not be good for the wine. Bubbling gas through the wine is a much more gentle.

The exact choice of gas barely matters as long as it is chemically inert in the wine. Argon or helium would be just as effective, but they're more expensive (and in the case of helium, precious). The temperature of the gas doesn't matter significantly, but the temperature of the wine does. The cooler the wine, the higher the concentration of dissolved carbon dioxide and oxygen it will contain at equilibrium so you'll remove more of those gases if you do your bubbling while the wine is relatively warm.

Metals are good conductors of electricity and effectively "short out" any electric fields that are parallel to their surfaces. Microwaves reflect from the metal walls because those walls force the electric fields of the microwaves to cancel parallel to their surfaces and that necessitates a reflected wave to cancel the incident wave. Because of that cancellation at the conducting surfaces, the intensity of the microwaves at the walls is zero or very close to zero.

The ant survived by staying within a tiny fraction of the microwave wavelength (about 12.4 cm) of the metal surfaces, where there is almost zero microwave intensity. Had the ant ventured out onto your cup, it would have walked into real trouble. Once exposed to the full intensity of the microwaves, it would not have fared so well.

If you let the flames go on long enough and enough carbon develops, you'll probably start getting plasma balls in the oven (lots of fun, but not great for the oven... you can scorch its top surface because those plasma balls rise and skittle around the ceiling of the oven). Anyway, you can probably find the carbon areas if you look closely enough, but they're no worse than a little burnt toast.

By shrinking the volume of gas over the soda, your boyfriend reduces the number of CO₂ molecules that must enter the gas phase in order to reestablish that equilibrium. BUT, when dense gas develops in the squeezed bottle, the high pressure of that gas will reinflate the bottle to its original size. The benefits of shrinking the gas volume will thus be lost.

To succeed in keeping more of the CO₂ molecules in solution, you have to make sure that the squeezed bottle stays squeeze. That's hard to do. You're probably better off pouring the soda gently into a smaller bottle, one that just barely holds all of the liquid. That smaller bottle won't expand as a dense gas of CO₂ forms above the liquid soda and the soda will reestablish its equilibrium without losing too many of its dissolved CO₂ molecules.

When you watch a distant object move, you don't see it change angles quickly so you perceive it as moving relatively slowly. Take the moon for example: it is moving thousands of miles an hour yet you can't see it move at all. It's just so far away that you see no angular change. And when you look down from a high-flying jet, the distant ground is changing angles slowly and therefore looks like it's not moving fast.

In practice, however, most of the radiation involved in baking these desserts and letting them cool on a kitchen counter is in the infrared and it's hard to tell just what color a brownie or cake is in the infrared. It's likely that both are pretty dark when viewed in infrared light. Basically, even things that look white to your eye are often gray or black in the infrared. Thus I suspect that both the brownie and cake absorb most of the thermal radiation they receive while being baked and emit thermal radiation efficienty while they're cooling on the counter.

The fact that light waves can travel in vacuum, and don't need any material to carry them, was disturbing to the physicists who first studied light in detail. They expected to find a fluid-like aether, a substance that was the carrier of electromagnetic waves. Instead, they found that those waves travel through truly empty space. One thing led to another, and soon Einstein proposed that the speed of light was profoundly special and that space and time were interrelated by way of that speed of light.

That said, however, let me make two comments. First, the question quickly turns to computer interface issues, as though the chemical analysis part is trivial in comparison to computer presentation part. Physical science and computer science are truly different fields and not everything in the scientific domain can be reduced to a software package. Physics and chemistry haven't disappeared with the advent of computers and there will never be a firmware upgrade for your microwave oven that will turn it into a nutritional analysis laboratory. As a society, we've gone a bit too far in replacing science education with technology education, particularly computer software.

Second, while remote chemical analysis isn't easy, it can be done in certain cases with the clever use of physics and chemistry. One of my friends here at Virginia, Gaby Laufer, has developed an instrument that studies the infrared light transmitted by the air and can determine whether that air contains any of a broad variety of toxic or dangerous gases in a matter of seconds. Air's relative transparency makes it easier to analyze than an opaque casserole, but even when you can see through something it's not trivial to see what it contains. Gaby's instrument does a phenomenal job of fingerprinting the gas's absorption features and identifying trouble.

Note added: a reader informed me that there are now microwave ovens that can read bar codes and adjust their cooking to match the associated food. A scale in the base of the oven can determine the food's weight and cook it properly. Another reader suggested that a microwave oven might be able to measure the food's microwave absorption and weight in order to adjust cooking power and time. While that's also a good possibility, ovens that sense food temperature or the humidity inside the oven can achieve roughly the same result by turning themselves off at the appropriate time.

To clarify the term "net force," note that when an object is experiencing several separate forces, it doesn't accelerate in response to each one individually. Instead, it accelerates in response to the sum of all the forces acting on it: the net force. Remember that forces have directions associated with them (forces are vector quantities), so when you sum them you must consider their directions carefully. The proper force to consider in Newton's second law is actually the net force on the object. If you know both the net force on the object and the object's mass, you can predict the object's acceleration. And if the net force is zero, then the object doesn't accelerate at all — it coasts.

Despite the scary title "microwave radiation," a microwave oven is basically just another household electronic device. It is an extremely close relative of a convention cathode-ray-tube television set. If you're OK with putting CRT televisions and computer monitors in the landfill, you should have no problems with putting microwave ovens there, too. Even when the microwave oven is on, all it has inside it is microwave radiation and that's just not a big deal. The instant you turn it off, it doesn't even have those microwaves in it. It's just boring inert electronic parts and they'll sit in the landfill for generations, rusting and decaying like every other abandoned electronic gadget. I'd rather see it go to a recycling center and have its precious materials returned to the resource bin, but as landfill junk goes, it's not all that bad. Given that toxic chemicals are the primary concern with landfills, microwave ovens are probably rather innocuous. They have no radioactive contents and although the high-voltage capacitor might have oil in it, that oil can no longer be the toxic PCBs that were common a few decades ago. Even when that oil leaks into the environment, it's probably not going to do much.

So there you have it, microwave ovens go to their graves no more loudly or dangerously than old televisions or computers or cell phones.

In fact, I might start calling cell phones "microwave phones" because that's exactly what they are. They communicate with the base unit by way of microwave radiation. Given the number of people who have cell phones semi-permanently installed in their ears, concerns about microwave radiation should probably be redirect from microwave ovens to "microwave phones." Think about it next time your six-year-old talks for an hour with her best friend on that "microwave phone."

So far, so good. But if you make that straw longer, you'll need to suck harder. That's because as the column of water gets taller, it gets heavier. It needs a more severe pressure imbalance to push it upward and support it. By the time the straw and water column get to be about 40 feet tall, you'll need to suck every bit of air out from inside the straw because the pressure imbalance needed to support a 40-foot column of water is approximately one atmosphere of pressure. If the straw is taller than 40 feet, you're simply out of luck. Even if you remove all the air from within the straw, the atmospheric pressure of the water below the straw won't be able to push the water up the straw higher than about 40 feet.

To get the water to rise higher in the straw, you'll need to install a pump at the bottom. The pump increases the water pressure there to more than 1 atmosphere, so that there is a bigger pressure imbalance available and therefore the possibility of supporting a taller column of water.

OK, so returning to your question: once a well is more than about 40 feet deep, getting the water to the surface requires a pump at the bottom. That pump can boost the water pressure well above atmospheric and thereby push the water to the surface despite the great height and weight of the water column. Suction surface pumps are really only practical for water that's a few feet below the surface; after that, deep pressure pumps are a much better idea.

OK, so there is actually a multi-way tie for first place in the speed rankings. Your daughter's question is what comes next? The actual answer is that it's a many-way tie between everything else. With enough energy, you can get anything moving at just under the speed of light, at least in principle. For example, subatomic particles such as electrons, protons, and even atomic nuclei are routinely accelerated to just under the speed of light in sophisticated machines around the world. The universe itself has natural accelerators that whip subatomic particles up until they are traveling so close to the speed of light that it's hard to tell that they aren't quite at the speed of light. Nonetheless, I assure you that they're not. The speed of light is so special that nothing that has any mass at all can possibly travel at the speed of light. Only the ephemeral non-massive particles such as light particles (photons), gravity particles (gravitons), and strong force particles (gluons) can actually travel at the speed of light. In fact, once photons, gravitons, and gluons begin to interact with matter, they don't travel at the speed of light either. It's sort of a guilt-by-association: as soon as these massless particles leave the essential emptiness of the vacuum and begin to interact with matter, even they can't travel at the speed of light anymore.

That said, I can still offer the likely second place finisher on the speed list. I'm going to skip over light, gravity, and the strong force traveling in extremely dilute matter because that's sort of cheating — if you take something that naturally travels at the speed of light and slow it down the very, very slightest bit, of course it will come ridiculously close to the speed of light. In real second place are almost certainly cosmic ray particles. These cosmic rays are actually subatomic particles that are accelerated to fantastic energies by natural processes in the cosmos. How such accelerators work is still largely a mystery but some of the cosmic ray particles that reach our atmosphere have truly astonishing energies — once in a while a single cosmic ray particle that is smaller than an atom will carry enough energy with it that it is capable of moving small ordinary objects around. Even if it carries the energy of a fly, that's a stupendous amount of energy for an atomic fragment. Those cosmic ray particles are traveling so close to the speed of light that it would be a photo-finish with light itself.

Coming up with good ideas is hard work and if I had them, I'd have gotten hold of such a magnet myself. Although science is often taught as formulas and factoids, it's really about thinking and observing, and good ideas are nearly always more important than good equipment. Good ideas don't linger unstudied for long when commercial equipment is all it takes to pursue them.

The optical elements in your eye that are responsible for this image formation are the cornea and the lens. The cornea does most of the work of converging the light so that it focuses, while the lens provides the fine adjustment that allows that focus to occur on your retina.

If you're farsighted, the two optical elements aren't strong enough to form an image of nearby objects on your retina so you have trouble getting a clear view while reading. Your eye needs help, so you wear converging eyeglasses. Those eyeglasses boost the converging power of your eye itself and allow your eye to form sharp images of nearby objects on your retina.

If you're nearsighted, the two optical elements are too strong and need to be weakened in order to form sharp images of distant objects on your retina. That's why you wear diverging eyeglasses.

People are surprised when I tell them that they're nearsighted or farsighted. They wonder how I know. My trick is simple: I look through their eyeglasses at distant objects. If those objects appear enlarged, the eyeglasses are converging (like magnifying glasses) and the wearer must be farsighted. If those objects appear shrunken, the eyeglasses are diverging (like the security peepholes in doors) and the wearer is nearsighted. Try it, you'll find that it's easy to figure out how other people see by looking through their glasses as they wear them.

Because your finger and your body conduct electricity, the pad's electric charge is actually interacting with the electric charge on your entire body. In contrast, a straw is insulating, so the pad can only interact with charge at its tip, and while your car keys are conducting, they are too small to have the effect that your body has on that pad.

There are at least two ways for a pad and its electronics to sense your body and its electric charges. The first way is for the electronics to apply a rapidly alternating electric charge to the pad and to watch for the pad's charge to interact with charge outside the pad (i.e., on your body). When the pad is by itself, the electronics can easily reverse the pad's electric charge because that charge doesn't interact with anything. But when your hand is near the pad or touching it, it's much harder for the electronics to reverse the pad's electric charge. If you're touch the pad, the electronics has to reverse your charge, too, so the electronics sense a new sluggishness in the pad's response to charge changes. Even when you're not quite touching the pad, the electronics has some add difficulty reversing the pad's charge. That's because the pad's charge causes your finger and body to become electrically polarized: charges opposite to those on the pad are attracted onto your finger from your body so that your finger becomes electrically charged opposite to the charge of the pad. When the electronics then tries to withdraw the charge from the pad in order to reverse the pad's charge, your finger's charge acts to make that withdrawal difficult. The electronics finds that it must struggle to reverse the pad's charge even though you're not in direct contact with the pad. Overall, your finger complicates the charge reversals whenever it's near or touching the pad.

The second way for the pad's electronics to sense your presence is to let your body act as an antenna for electromagnetic influences in the environment. We are awash in electric and magnetic fields of all sorts and the electric charge on your body is in ceaseless motion as a result. You've probably noticed that touching certain input wires of a stereo amplifier produces lots of noise in the speakers; that's partly a result of the electromagnetic noise in our environment showing up as moving charge on your body. The little pad on the soda dispenser picks up a little of this electromagnetic noise all by itself. When you approach or touch the pad, however, you dramatically increase the amount of electromagnetic noise in the pad. The pad's electronics easily detect that new noise.

In short, soda dispenser pads are really detecting large electrically conducting objects. Their ability to sense your finger even before it makes contact is important because they need to work when people are wearing gloves. I first encountered electrical touch sensors in elevators when I was a child and I loved to experiment with them. Conveniently, they'd light up when they detected something and there was no need to clean up spilled soda. We'd try triggering them with elbows and noses, and a whole variety of inanimate objects. They were already pretty good, but modern electronics has made touch pads even better. The touch switches used by some lamps and other appliances function in essentially the same way.

The explanation is both simple and interesting: the rate at which water molecules leave the cloths doesn't depend on whether the window is open or closed, but the rate at which water molecules return to the cloths certainly does. That return rate depends on the air's moisture content and can range from zero in dry air to extremely fast in damp air. Air's moisture content is usually characterized by its relative humidity, with 100% relative humidity meaning that air's water molecules land on surfaces exactly as fast as water molecules in liquid water leave its surface. When you expose a glass of water to air at 100% relative humidity, the glass will neither lose nor gain water molecules because the rates at which water molecules leave the water and land on the water are equal. Below 100% relative humidity, the glass will gradually empty due to evaporation because leaving will outpace landing. Above 100% relative humidity, the glass will gradually fill due to condensation because landing will outpace leaving.

The same story holds true for wet clothes. The higher the air's relative humidity, the harder it becomes for water to evaporate from the cloths. Landing is just too frequent in the humid air. At 100% relative humidity the clothes won't dry at all, and above 100% relative humidity they'll actually become damper with time.

When you dry clothes in a room with the window open and the relative humidity of the outdoor air is less than 100%, water molecules will leave the clothes more often than they'll return, so the clothes will dry. But when the window is closed, the leaving water molecules will remain trapped in the room and will gradually increase the room air's relative humidity. The drying process will slow down as the water-molecule return rate increases. When the room air's relative humidity reaches 100%, drying will cease altogether.

When you ground an appliance, you're are making it possible for electric charge to equilibrate between that appliance and the earth. The earth is approximately neutral, so a grounded appliance can't retain large amounts of either positive or negative charge. That's a nice safety feature because it means that you won't get a shock when you touch the appliance, even if one of its power wires comes loose and touches the case. Any charge that the power wire tries to deposit on the case will quickly flow to the earth as the appliance and earth equilibrate.

But charge can't escape from the appliance through the grounding wire instantly. Light takes about 1 nanosecond to travel 1 foot and electricity takes a little longer than that. For charge to leave your appliance for the earth might well require 50 nanoseconds or more. That's not a problem for ordinary power distribution, so grounding is generally a great idea. Each cycle of the 60-Hz AC power in the U.S. takes 18 milliseconds to complete, so the appliance and earth have plenty of time to equilibrate with one another. But a cycle of the microwave power in the oven takes less about 0.4 nanoseconds to complete and there's just no time for the appliance and earth to equilibrate. At microwave frequencies, the electric current flowing through a long wire is wavelike, meaning that at one instant in time the wire has both positive and negative patches, spaced half a wavelength apart along its length. It's carrying an electromagnetic ripple.

The metal screen on the oven's door has to reflect the microwaves all by itself. It does this without a problem because the holes are so much smaller than 12.4 centimeters that currents easily flow around them during a cycle of the microwaves. Those currents are able to compensate for the holes in the screens and cause the microwaves to reflect perfectly.

The story wouldn't be the same if the bird made the mistake of spanning the gap from one wire to another. In that case, current could flow through the bird from one wire to the other and the bird would run the serious risk of becoming a flashbulb. Squirrels occasionally do this trick when they accidentally bridge a pair of wires. Some of the unexpected power flickers that occur in places where the power lines run overhead are caused by squirrels and occasionally birds vaporizing when they let current flow between power lines.

Most likely, one of you has been in contact with a insulating surface that has exchanged charge with you. For example, if you walked across wool carpeting in rubber-soled shoes, that carpeting has probably transferred some of its electrons to your shoes and your shoes have then spread those electrons out onto you. Rubber binds electrons more tightly than wool and so your shoes tend to steal a few of electrons from wool whenever it gets a chance. If you walk around a bit or scuff your feet, you'll typically end up with quite a large number of stolen electrons on your body. When you then go and kiss Uncle Al, about half of those electrons spread suddenly onto him and that current flow is shocking!

Anyone who claims to be able to extract useful energy through a process that starts with water and ends with water is a charlatan. Either they aren't producing any useful energy or it's coming from some other source. In these sorts of frauds, there is usually some electrical component that is supposedly needed to keep a minor part of the apparatus functioning. That component isn't insignificant at all; it's what actually keeps the entire apparatus functioning!

Hydrogen has such a mythical aura to it, but in the context of energy, it's just another fuel. Actually, it's more of any energy storage medium than a basic fuel. That's because hydrogen doesn't occur naturally on earth and can only be produced by consuming another form of energy. There is so much talk about "the hydrogen economy"� and the notion that hydrogen will rescue us from our dependence on petroleum. Sadly, politicians who promote hydrogen as the energy panacea neither understand science nor respect those who do. Since it takes just as much energy to produce hydrogen from water as is released when that hydrogen burns back into water, hydrogen alone won't save us.

As we grow progressively more desperate for useable energy, the amount of fraud and misinformation will only increase. There are only a few true sources for useable energy: solar energy (which includes wind power, hydropower, and biomass), fossil fuels (which include petroleum and coal), geothermal energy, and nuclear fuels. Hydrogen is not among them; it can be produced only at the expense of one of the others. Even ethanol, which is touted as an environmentally sound replacement for petroleum, has its problems; producing a gallon of ethanol can all too easily consume a gallon of petroleum.

Where energy is concerned, watch out for fraud, hype, PR, and politics. If we survive the coming energy and climate crises, it will be because we've learned to conserve energy and to obtain it primarily from solar and perhaps nuclear sources. It will also be because we've learned to set politics and self-interest aside long enough to make accurate analyses and sound decisions.

I'll begin to looking at how dust settles in calm air near the ground. That dust experiences its weight due to gravity, so it tends to descend. Each particle would fall like a rock except that it's so tiny that it experiences overwhelming air resistance. Instead of falling, it descends at an incredibly slow terminal velocity, typically only millimeters per second. It eventually lands on whatever is beneath it, so a room's floor gradually accumulates dust. But dust also accumulates on vertical walls and even on ceilings. That dust is held in place not by its weight but by electrostatic or chemical forces. When you go into an abandoned attic, most of the dust is on the floor, but there's a little on the walls and on the ceiling.

OK, now to the space shuttle. The shuttle is orbiting the earth, which means that although it has weight and is falling freely, it never actually reaches the earth because it's heading sideways so fast. Without gravity, its inertia would carry it horizontally out into space along a straight line path. Gravity, however, bends that straight line path into an elliptical arc that loops around the earth as an orbit.

So far no real surprises: dust near ground level settles in calm air and the shuttle orbits the earth. The surprise is that particles of space dust particles also orbit the earth! The shuttle orbits above the atmosphere, where there is virtual no air. Without air to produce air resistance, the dust particles also fall freely. Those with little horizontal speed simply drop into the atmosphere and are lost. But many dust particles have tremendous horizontal speeds and orbit the earth like tiny space shuttles or satellites.

Whether they are dropping toward atmosphere or orbiting the earth, these space dust particles are typically traveling at velocities that are quite different in speed or direction from the velocity of the space shuttle. The relative speed between a dust particle and the shuttle can easily exceed 10,000 mph. When such a fast-moving dust particle hits the space shuttle, it doesn't "settle."� Rather, it collides violently with the shuttle's surface. These dust-shuttle collisions erode the surfaces of the shuttle and necessitate occasional repairs or replacements of damaged windows and sensors. Astronauts on spacewalks also experience these fast collisions with space dust and rely on their suits to handle all the impacts.

Without any air to slow the relative speeds and cushion the impacts, its rare that a particle of space dust lands gracefully on the shuttle's surface. In any case, gravity won't hold a dust particle in place on the shuttle because both the shuttle and dust are falling freely and gravity doesn't press one against the other. But electrostatic and chemical attractions can hold some dust particles in place once they do land. So the shuttle probably does accumulate a very small amount of accumulated space dust during its travels.

The first scantron systems, however, were far less capable. They read the pencil marks by shining light through the paper and into Lucite light guides that conveyed the transmitted light to phototubes. Whenever something blocked the light, the scantron system recorded a mark. The marks therefore had to be opaque in the range of light wavelengths that the phototubes sensed, which is mostly blue. Pencil marks were the obvious choice because the graphite in pencil lead is highly opaque across the visible light spectrum. Graphite molecules are tiny carbon sheets that are electrically conducting along the sheets. When you write on paper with a pencil, you deposit these tiny conducting sheets in layers onto the paper and the paper develops a black sheen. It's shiny because the conducting graphite reflects some of the light waves from its surface and it's black because it absorbs whatever light waves do manage to enter it.

A thick layer of graphite on paper is not only shiny black to reflected light, it's also opaque to transmitted light. That's just what the early scantron systems needed. Blue inks don't absorb blue light (that's why they appear blue!), so those early scantron systems couldn't sense the presence of marks made with blue ink. Even black inks weren't necessarily opaque enough in the visible for the scantron system to be confident that it "saw" a mark.

In contrast, modern scantron systems used reflected light to "see" marks, a change that allows scantron forms to be double-sided. They generally do recognize marks made with black ink or black toner from copiers and laser printers. I've pre-printed scantron forms with a laser printer and it works beautifully. But modern scantron systems ignore marks made in the color of the scantron form itself so as not to confuse imperfections in the form with marks by the user. For example, a blue scantron form marked with blue ink probably won't be read properly by a scantron system.

As for why only #2 pencils, that's a mechanical issue. Harder pencil leads generally don't produce opaque marks unless you press very hard. Since the early scantron machines needed opacity, they missed too many marks made with #3 or #4 pencils. And softer pencils tend to smudge. A scantron sheet filled out using a #1 pencil on a hot, humid day under stressful circumstances will be covered with spurious blotches and the early scantron machines confused those extra blotches with real marks.

Modern scantron machines can easily recognize the faint marks made by #3 or #4 pencils and they can usually tell a deliberate mark from a #1 pencil smudge or even an imperfectly erased mark. They can also detect black ink and, when appropriate, blue ink. So the days of "be sure to use a #2 pencil" are pretty much over. The instruction lingers on nonetheless.

One final note: I had long suspected that the first scanning systems were electrical rather than optical, but I couldn't locate references. To my delight, Martin Brown informed me that there were scanning systems that identified pencil marks by looking for their electrical conductivity. Electrical feelers at each end of the markable area made contact with that area and could detect pencil via its ability to conduct electric current. To ensure enough conductivity, those forms had to be filled out with special pencils having high conductivity leads. Mr. Brown has such an IBM Electrographic pencil in his collection. This electrographic and mark sense technology was apparently developed in the 1930s and was in wide use through the 1960s.

At the risk of telling you more than you ever want to know, I'll point out that the filament behaves approximately according to Ohm's law: the current that flows through it is proportional to the voltage difference between its two ends. The larger that voltage difference, the bigger the forces and the more current that flows. This ohmic behavior allows incandescent lightbulbs to survive decreases in voltage unscathed. They don't, however, do well with increases in voltage, since they'll then carry too much current and receive so much power that they'll overheat and break. Voltage surges, not voltage decreases, are what kill lightbulbs.

The other appliances you mention are not ohmic devices and the currents that flow through them are not simply proportional to the voltage supplied to your home. Motors are a particularly interesting case; the average current a motor carries is related in a complicated way to how fast and how easily it's spinning. A motor that's turning effortlessly carries little average current and receives little electric power. But a motor that is struggling to turn, either because it has a heavy burden or because it can't obtain enough electric power to overcome starting effects, will carry a great deal of average current. An overburdened or non-starting motor can become very hot because it's wiring deals inefficiently with the large average current, and it can burn out. While I've never heard of a refrigerator motor dying during a brownout, it wouldn't surprise me. I suspect that most appliance motors are protected by thermal sensors that turn them off temporarily whenever they overheat.

Modern electronic devices are also interesting with respect to voltage supply issues. Electronic devices operate on specific internal voltage differences, all of which are DC — direct current. Your home is supplied with AC — alternating current. The power adapters that transfer electric power from the home's AC power to the device's DC circuitry have evolved over the years. During a brownout, the older types of power adapters simply provide less voltage to the electronic devices, which misbehave in various ways, most of which are benign. You just want to turn them off because they're not working properly. It's just as if their batteries are worn out.

But the most modern and sophisticated adapters are nearly oblivious to the supply voltage. Many of them can tolerate brownouts without a hitch and they'll keep the electronics working anyway. The power units for laptops are a case in point: they can take a whole range of input AC voltages because they prepare their DC output voltages using switching circuitry that adjusts for input voltage. They make few assumptions about what they'll be plugged into and do their best to produce the DC power required by the laptop.

In short, the motors in your home won't like the brownout, but they're probably protected against the potential overheating problem. The electronic appliances will either misbehave benignly or ride out the brownout unperturbed. Once in a while, something will fail during a brownout. But I think that most of the damage is down during the return to normal after the brownout. The voltages bounce around wildly for a second or so as power is restored and those fluctuations can be pretty hard some devices. It's probably worth turning off sensitive electronics once the brownout is underway because you don't know what will happen on the way back to normal.

The evanescent wave problem is more likely. When any electromagnetic wave reflects from a conducting surface that has small holes in it, there is what is known as an evanescent wave extending into and somewhat beyond each hole. It's as though the wave is trying to figure out whether or not it can pass through the opening and so it tries. Even when it discovers that the hole is far too small for it pass through (i.e., much smaller than its wavelength), it still offers electromagnetic intensity in the region just beyond the hole. The extent of the evanescent wave increases with the size of the hole. The microwave oven's screen has very small holes and it is located inside the glass window. The evanescent waves associated with those holes cut off so quickly that you can hold your hand against the glass and not expose your skin to significant microwaves. But once you've torn a larger hole in the screen, the evanescent waves can extend farther through that screen and perhaps out beyond the surface of the glass window. If you press your hand against the window just in front of the tear while the microwave oven is on, you may burn your hand.

Finally, there is the issue of arcing. To reflect the microwaves, the conducting screen must carry electric currents. The microwaves' electric fields push electric charge back and forth in the conducting screen and it is that moving charge (i.e., electric current) that ultimately redirects the microwaves back into the cooking chamber as a reflection. Those electric currents in the screen are real and they're not going to take kindly to that tear. It's a weak spot in the conducting surface through which they flow. Weak electrical paths can heat up like lightbulb filaments when they carry currents. Moreover, charge that should flow across the torn region can accumulate on sharp edges and leap through the air as an arc. If either of these processes happens, it may scorch the window and the screen, and cause increasing trouble.

You could be lucky: the leakage could be zero, the evanescent waves could remain far enough inside the window to never cause injury, and the tear could never heat up or arc. But the risk of operating this damaged microwave oven is not insignificant. Since it's an installed unit, I'd suggest replacing the screen or the door. There are a number of websites that sell replacement parts for microwave ovens and I have used them to replace the door on our microwave oven.

Since the earth is so much more massive than the moon, their combined center of mass is 81 times closer to the middle of the earth than it is to the middle of the moon. In fact, it's inside the earth, though not at the middle of the earth. As a result, the earth's orbital motion takes the form of a wobble rather than a more obvious looping path. Nonetheless, the earth is orbiting.

I hope that you can see that there is no reason why the earth should be fixed in space while the moon orbits about it. You've been sold a bill of goods. The mistaken notion that the moon orbits a fixed earth is a wonderful example of the "factoid science" that often passes for real science in our society.

Because thinking and understanding involve hard work, people are more comfortable when the thought and understanding have been distilled out of scientific issues and they've been turned into memorizable sound bites. Those sound bites are easy to teach and easy to test, but they're mostly mental junk food. A good teacher, like a good scientist, will urge you to question such factoids until you understand the science behind them and why they might or might not be true.

When my children were young, I often visited their schools to help teach science. In third grade, the required curriculum had them categorizing things into solutions or mixtures. Naturally, I showed them a variety of things that are neither solutions nor mixtures. It was a blast. Science is so much more interesting than a collection of 15-second sound bites.

Lenses are often characterized by their f-numbers, where f-number is the ratio of effective focal length to effective lens diameter. Focal length is the distance between the lens and the real image it forms of a distant object. For example, if a particular converging lens projects a real image of the moon onto a piece of paper placed 200 millimeters (200 mm) from the lens, then that lens has a focal length of 200 mm. And if the lens is 50 mm in diameter, it has an f-number of 4 because 200 mm divided by 50 mm is 4.

Based on purely geometrical arguments, it's easy to show that lenses with equal f-numbers project images of equal brightness onto their image sensors and the smaller the f-number, the brighter the image. Whether a lens is a wide-angle or telephoto, if it has an f-number of 4, then its effective focal length is four times the effective diameter of its light gathering lens. Since telephoto lenses have long focal lengths, they need large effective diameters to obtain small f-numbers.

But notice that I referred always to "effective diameter" and "effective focal length" when defining f-number. That's because there are many modern lenses that are so complicated internally that simply dividing the lens diameter by the distance between the lens and image sensor won't tell you much. Many of these lenses have zoom features that allow them to vary their effective focal lengths over wide ranges and these lenses often discard light in order to improve image quality and avoid dramatic changes in image brightness while zooming.

You might wonder why a lens would ever choose to discard light. There are at least two reasons for doing so. First, there is the issue of image quality. The smaller the f-number of a lens, the more precise its optics must be in order to form a sharp image. Low f-number lenses are bringing together light rays from a wide range of angles and getting all of those rays to overlap perfectly on the image sensor is no small feat. Making a high-performance lens with an f-number less than 2 is a challenge and making one with an f-number of less than 1.2 is extremely difficult. There are specialized lenses with f-numbers below 1 and Canon sold a remarkable f0.95 lens in the early 1960's. The lowest f-number camera lens I have ever owned is an f1.4.

Secondly, there is the issue of depth-of-focus. The smaller the f-number, the smaller the depth of focus. Again, this is a geometry issue: a low-f-number lens is bringing together light rays from a wide range of angles and those rays only meet at one point before separating again. Since objects at different distances in front of the lens form images at different distances behind the lens, it's impossible to capture sharp images of both objects at once on a single image sensor. With a high-f-number lens, this fact isn't a problem because the light rays from a particular object are rather close together even when the object's image forms before or after the image sensor. But with a low-f-number lens, the light rays from a particular object come together acceptably only at one particular distance from the lens. If the image sensor isn't at that distance, then the object will appear all blurry. If a zoom lens didn't work to keep its f-number relatively constant while zooming from telephoto to wide angle, its f-number would decrease during that zoom and its depth-of-focus would shrink. To avoid that phenomenon, the lens strategically discards light so as to keep its f-number essentially constant during zooming.

In summary, larger diameter lenses tend to be better at producing photographic and video images, but that assumes that they are high-quality and that they can shrink their effective diameters in ways that allow them to imitate high-quality lenses of smaller diameters when necessary. But flexible characteristics always come at some cost of image quality and the very best lenses are specialized to their tasks. Zoom lenses can't be quite as good as fixed focal length lenses and a large-diameter lens imitating a small-diameter lens by throwing away some light can't be quite as good as a true small-diameter lens.

As for my sources, one of the most satisfying aspects of physics is that you don't always need sources. Most of the imaging issues I've just discussed are associated with simple geometric optics, a subject that is part of the basic toolbox of an optical physicist (which I am). You can, however, look this stuff up in any book on geometrical optics.

If a plate is "microwave safe," it will barely absorb the microwaves and heat extremely slowly. In effect, the microwave oven will be operating empty and the electromagnetic fields inside it will build up to extremely high levels. Since the walls of the oven are mirrorlike and the plate is almost perfectly transparent to microwaves, the electromagnetic waves streaming out of the oven's magnetron tube bounce around endlessly inside the oven's cooking chamber. The resulting intense fields can produce various types of electric breakdown along the walls of the cooking chamber and thereby damage the surface with burns or arcs. Furthermore, the intense microwaves in the cooking chamber will reflect back into the magnetron and can upset its internal oscillations so that it doesn't function properly. Although magnetrons are astonishingly robust and long-lived, they don't appreciate having to reabsorb their own emitted microwaves. In short, your plates will heat up slowly and you'll be aging your microwave oven in the process. You could wet the plates before putting them in the microwave oven to speed the heating and decrease the wear-and-tear on the magnetron, but then you'd have to dry the plates before use.

If a plate isn't "microwave safe," then it will absorb microwaves and heat relatively quickly. If it absorbs the microwaves uniformly and well, then you can probably warm it to the desired temperature without any problems as long as you know exactly how many seconds it takes and adjust for the total number of plates you're warming. If you heat a plate too long, bad things will happen. It may only amount to burning your fingers, but some plates can't take high temperatures without melting, cracking, or popping. Unglazed ceramics that have soaked up lots of water will heat rapidly because water absorbs microwaves strongly. Water trapped in pores in such ceramics can transform into high-pressure steam, a result that doesn't seem safe to me. And if a plate absorbs microwaves nonuniformly, then you'll get hotspots or burned spots on the plate. Metalized decorations on a plate will simply burn up and blacken the plate. Cracks that contain water will overheat and the resulting thermal stresses will extend the cracks further. So this type of heating can be stressful to the plates.

The water pressure increases quickly with depth because each layer of water must support the weight of all the water layers above it. Since water is dense, heavy stuff, the weight piles on quickly and it takes only 10 meters (34 feet) of descent to increase the water pressure from atmospheric to twice atmospheric. In contrast, the air in the hose is light, fluffy stuff, so its pressure increases rather slowly with depth. Even though each layer of air has to support the weight of all the layers of air above it, the rise in pressure is extremely gradual. It takes miles of atmosphere above the earth for the air pressure to build up to atmospheric pressure near the ground. The air pressure in your hose is therefore approximately unchanged by your descent into the water.

With the water pressure outside rising quickly as you go deeper and the air pressure in your mouth rising incredibly slowly as you go deeper, you quickly find it hard to breathe. Your muscles can push your chest outward against a modest pressure imbalance between outside and inside. But by the time you're a few feet below the surface, you just can't draw air into your lungs through that hose anymore. You need pressurized air, such as that provided by a scuba outfit or a deep-sea diver's compressor system.

Since the freezer has a nearly airtight seal, the air it contains remains inside it for a long time. That means that the odor molecules that occasionally break free of a pungent casserole at one end of the freezer have every opportunity to land on and stick to an ice cube at the other end. With time, the ice cube acquires the scent of the casserole and becomes unappealing.

To stop this migration of molecules, you should seal each item in the freezer in its own container. That way, any molecules that leave the food's surface will eventually return to it. Since ice cubes are normally exposed to the air in the freezer, keeping the odor molecules trapped in their own sealed containers keeps the freezer air fresh and the ice cubes odor-free.

Microwaves themselves have no well-defined shape but they do have firm rules governing their overall structures. Books usually draw microwaves (and all other electromagnetic waves) as wavy lines, as though something was truly going up and down in space. From that misleading representation, it's easy for people to suppose that electromagnetic waves can't get through certain openings.

In reality, electromagnetic waves consist of electric and magnetic fields (influences that push on electric charge and magnetic pole, respectively) that point up and down in a rippling fashion, but nothing actually travels up and down per say. The spatial structures of these fields are governed by Maxwell's equations, a set of four famous relationships that bind electricity and magnetism into a single, unified classical theory. Maxwell's equations dictate the structures of electromagnetic waves and predict that electromagnetic waves on one side of a conducting surface can't propagate through to the other side of that surface. Even if there are small holes in the conducting surface, holes that are much smaller that the wavelength of the waves, those waves can't propagate through the surface. More specifically, the fields die off exponentially as they try to penetrate through the holes and the waves don't propagate on the far side.

The choice of round holes in the oven mesh is simply a practical one. You can pack round holes pretty tightly in a surface while leaving their conducting boundaries relatively robust. And round holes treat all electromagnetic waves equally because they have no wide or narrow directions.

Even though pure cellulose can't be reshaped by melting, it can be softened with water and/or heat. Like ordinary sugar, cellulose is attracted to water and water molecules easily enter its chains. This water lubricates the chains so that the cellulose becomes somewhat pliable and heat increases that pliability. When you iron a damped cotton or linen shirt, both of which consist of cellulose fibers, you're taking advantage of that enhanced pliability to reshape the fabric.

But even when dry, fibrous materials such as paper, cotton, or linen have some pliability because thin fibers of even brittle materials can bend significantly without breaking. If you bend paper gently, its fibers will bend elastically and when you let the paper relax, it will return to its original shape.

However, if you bend the paper and keep it bent for a long time, the cellulose chains within the fibers will begin to move relative to one another and the fibers themselves will begin to move relative to other fibers. Although both of these motions can be facilitated by moisture and heat, time along can get the job done at room temperature. Over months or years in a tightly rolled shape, a sheet of paper will rearrange its cellulose fibers until it adopts the rolled shape as its own. When you then remove the paper from its constraints, it won't spontaneously flatten out. You'll have to reshape it again with time, moisture, and/or heat. If you press it in a heavy book for another long period, it'll adopt a flat shape again.

The stresses frozen into the tempered glass affect its polarizability and give it strange characteristics when exposed to the electromagnetic fields in light. This stressed glass tends to rotate polarizations of the light passing through it. As a result, you see odd reflections of the sky (skylight is polarized to some extent). Those polarization effects become immediately apparent when you wear polarizing sunglasses.

The force pushing mercury back down the column as it cools is tiny in comparison. Mercury certainly does contract when cooled, so that the manufacturer is telling you nonsense. But just because the mercury contracts as it cools doesn't mean that it will all flow back down the column. The mercury needs a push to propel it through its narrow channel.

Mercury is attracted only weakly to glass, so it doesn't really adhere to the walls of its channel. However, like all liquids, mercury has a viscosity, a syrupiness, and this viscosity slows its motion through any pipe. The narrower the pipe, the harder one has to push on a liquid to keep it flowing through that pipe. In fact, flow through a pipe typically scales as the 4th power of that pipe's radius, which is why even modest narrowing of arteries can dramatically impair blood flow in people. The capillaries used in fever thermometers are so narrow that mercury has tremendous trouble flowing through them. It takes big forces to push the mercury quickly through such a capillary.

During expansion, there is easily enough force to push the mercury up through the capillary. However, during contraction, the forces pushing the mercury back down through the capillary are too weak to keep the column together. That's because the only thing above the column of liquid mercury is a thin vapor of mercury gas and that vapor pushes on the liquid much too feebly to have a significant effect. And while gravity may also push down on the liquid if the thermometer is oriented properly, it doesn't push hard enough to help much.

The contracting column of mercury takes hours to drift downward, if it drifts downward at all. It often breaks up into sections, each of which drifts downward at its own rate. And, as two readers (Michael Hugh Knowles and Miodrag Darko Matovic) have both pointed out to me in recent days, there is a narrow constriction in the capillary near its base and the mercury column always breaks at that constriction during contraction. Since the top portion of the mercury column is left almost undisturbed when the column breaks at the constriction, it's easy to read the highest temperature reached by the thermometer.

Shaking the thermometer hard is what gets the mercury down and ultimately drives it through the constriction so that it rejoins into a single column. In effect, you are making the glass accelerate so fast that it leaves the mercury behind. The mercury isn't being pushed down to the bottom of the thermometer; instead, the glass is leaping upward and the mercury is lagging behind. The mercury drifts to the bottom of the thermometer because of its own inertia.

You're right that the glass tube acts as a magnifier for that thin column of mercury. Like a tall glass of water, it acts as a cylindrical lens that magnifies the narrow sliver of metal into a wide image.

Let's start with the differences in types of radiation. Basically, anything that moves is radiation, from visible light, to ultraviolet, to X-rays, to microwaves, to alpha particles, to neutrons, and even to flying pigeons. These different radiations do different things when they hit you, particularly the pigeons. While "ionizing radiations" such as X-rays, ultraviolet, alpha particles, and neutrons usually have enough localized energy to do chemical damage to the molecules they hit, "non-ionizing radiation" such as microwaves and pigeons do not damage molecules. When you and your organic friend worry about toxic changes in food or precancerous changes in your tissue, what really worry you are molecular changes. Microwaves and pigeons don't cause those sorts of changes. Microwaves effectively heat food or tissue thermally, while pigeons bruise food or tissue on impact.

Wearing a lead apron while working around ionizing radiation makes sense, although a simple layer of fabric or sunscreen is enough to protect you from most ultraviolet. To protect yourself against pigeons, wear a helmet. And to protect yourself against microwaves, use metal. The cooking chamber of the microwave oven is a metal box (including the screened front window). So little microwave "radiation" escapes from this metal box that it's usually hard to detect, let alone cause a safety problem. There just isn't much microwave intensity coming from the oven and intensity matters. A little microwaves do nothing at all to you; in fact you emit them yourself!

If you want to detect some serious microwaves, put that microwave detector near your cellphone! The cellphone's job is to emit microwaves, right next to your ear! Before you give up on microwave ovens, you should probably give up on cellphones. That said, I think the worst danger about cellphones is driving into a pedestrian or a tree while you're under the influence of the conversation. Basically, non-ionizing radiation such as microwaves is only dangerous if it cooks you. At the intensities emitted by a cellphone next to your ear, it's possible that some minor cooking is taking place. However, the cancer risk is almost certainly nil.

Despite all this physics reality, salespeople and con artists are still more than happy to sell you protection against the dangers of modern life. I chuckle at the shields people sell to install on your cellphones to reduce their emissions of harmful radiation. The whole point of the cellphone is to emit microwave signals to the receiving tower, so if you shield it you spoil its operation! It would be like wrapping an X-ray machine in a lead box to protect the patient. Sure, the patient would be safe but the X-ray machine would barely work any more.

Returning to the microwave cooking issue, once the food comes out of the microwave oven, there are no lingering effects of its having been cooked with microwaves. There is no convincing evidence of any chemical changes in the food and certain no residual cooking microwaves around in the food. If you're worried about toxic changes to your food, avoid broiling or grilling. Those high-surface-temperature cooking techniques definitely do chemical damage to the food, making it both tasty and potentially a tiny bit toxic. One of the reasons why food cooked in the microwave oven is so bland is because those chemical changes don't happen. As a result, microwave ovens are better for reheating than for cooking.

Momentum is a conserved physical quantity, meaning that it cannot be created or destroyed. It can only be passed from one object to the other. When you let go of the packaged egg and it begins to fall, the downward momentum that gravity transfers into the egg begins to accumulate in the egg. Before you let go, your hand was removing the egg's downward momentum as fast as gravity was adding it, but now the egg is on its own!

Because momentum is equal to an object's mass times its velocity, the accumulating downward momentum in the egg is reflected in its increasing downward speed. With each passing second, the egg receives another dose of downward momentum from the earth. By the time the egg reaches the pavement, it's moving downward fast and has a substantial amount of downward momentum to get rid of. Incidentally, the earth, which has given up this downward momentum, experiences an opposite response—it has acquired an equal amount of upward momentum. However, the earth has such a huge mass that there is no noticeable increase in its upward speed.

To stop, the egg must transfer all of its downward momentum into something else, such as the earth. It can transfer its momentum into the earth by exerting a force on the ground for a certain amount of time. A transfer of momentum, known as an impulse, is the product of a force times a time. To get rid of its momentum, the egg can exert a large force on the ground for a short time or a small force for a long time, or anything in between. If you let it hit the pavement unprotected, the egg will employ a large force for a short time and that will be bad for the egg. After all, the pavement will push back on the egg with an equally strong but oppositely directed force and punch a hole in the egg.

To make the transfer of momentum graceful enough to leave the egg intact, the protective package must prolong the momentum transfer. The longer it takes for the egg to get rid of its downward momentum, the smaller the forces between the egg and the slowing materials. That's why landing on a soft surface is a good start: it prolongs the momentum transfer and thereby reduces the peak force on the egg.

But there is also the issue of distributing the slowing forces uniformly on the egg. Even a small force can break the egg if it's exerted only on one tiny spot of the egg. So spreading out the force is important. Probably the best way of distributing the slowing force would be to float the egg in the middle of a fluid that has the same average density as the egg. But various foamy or springy materials will distribute the forces nearly as well.

In summary, (1) you want to bring the egg to a stop over as long as period of time as possible so as to prolong the transfer of momentum and reduce the slowing forces and (2) you want to involve the whole bottom surface of the egg in this transfer of momentum so that the slowing forces are exerted uniformly on the egg's bottom surface. As for the actual impact force on the egg, you can determine this by dividing the egg's momentum just before impact (its downward speed times its mass) by the time over which the egg gets rid of its momentum.

The walls of your home are simply hard to look through. They block visible, infrared, and ultraviolet light nearly perfectly and that doesn't leave snoopers many good options. A person sitting outside your home with a thermal camera—a device that "sees" the infrared light associated with body-temperature objects—or a digital camera is going to have a nice view of your wall, not you inside. There are materials that, while opaque to visible light, are relatively transparent to infrared light, such as some plastics and fabrics. However, typical wall materials are too thick and too opaque for infrared light to penetrate. Sure, someone can put a camera inside your home and access it via an optical fiber or radio waves, but at that point, they might as well just peer through your window.

The only electromagnetic waves that penetrate walls well are radio waves, microwaves, and X rays. If someone builds an X ray machine around your home, they'll be able to see you, or at least your bones. Don't forget to wave. And, in principle, they could use the radar technique to look for you with microwaves, but you'd be a fuzzy blob at best and lost in the jumble of reflections from everything else in your home.

As for using a laser to monitor your conversations from afar, that's a real possibility. Surfaces vibrate in the presence of sound and it is possible to observe those vibrations via reflected light. But the technical work involved is substantial and it's probably easier to just put a bug inside the house or on its surface.

Since I first posted this answer, several people have pointed out to me that terahertz radiation also penetrates through some solid surfaces and could be used to see through the walls of homes. In fact, the whole low-frequency end of the electromagnetic spectrum (radio, microwaves, terahertz waves) can penetrate through electrically insulating materials in order to "observe" conducting materials inside a home and the whole high-frequency end of that spectrum (X-rays and gamma rays) can penetrate through simple atoms (low atomic number) in order to "observe" complex atoms inside a home. Still, these approaches to seeing through walls require the viewers to send electromagnetic waves through the house and those waves can be detected by the people inside. They're also not trivial to implement. I suppose that people could use ambient electromagnetic waves to see what's happening in a house, but that's not easy, either. Where there's a will, there's a way: stealth aircraft have been detected by way of the dark spot they produce in the ambient radio spectrum and the insides of the pyramids have been studied by looking at cosmic rays passing through them. Nonetheless, I don't think that many of us need worry about being studied through the walls of our homes.

The laws of both energy conservation and thermodynamics are essentially mathematical laws—they depend relatively little on the specific details of our universe. Just about the only specific detail that's important is time-translation symmetry: as far as we can tell, physics doesn't change with time—physics today is the same as it was yesterday and as it will be tomorrow. That observation leads, amazingly enough, to energy conservation: energy cannot be created or destroy; it can only change forms or be transferred between objects. Together with statistical principals, we can derive thermodynamics without any further reference to the universe itself. And having developed energy conservation and the laws of thermodynamics, the game is over for free-energy motors and generators. They just can't work. It's not a matter of looking for one special arrangement that works among millions that don't. There are exactly zero arrangements that work.

It's not a matter of my bias, unless you consider my belief that 2 plus 2 equals 4 to be some sort of bias. You can look all you like for a 2 that when added to another 2 gives you a 5, but I don't expect you to succeed.

About once every month or two, someone contacts me with a new motor that turns for free or a generator that creates power out of nowhere. The pattern always repeats: I send them the sad news that their invention will not work and they respond angrily that I am not listening, that I am biased, and that I am part of the conspiracy. Oh well. There isn't much else I can do. I suppose I could examine each proposal individually at length to find the flaw, but I just don't have the time. I'm a volunteer here and this is time away from my family.

Instead, I suggest that any inventor who believes he or she has a free-energy device build that device and demonstrate it openly for the physics community. Take it to an American Physical Society conference and present it there. Let everyone in the audience examine it closely. Since anyone can join the APS and any APS member can talk at any major APS conference, there is plenty of opportunity. If someone succeeds in convincing the physics community that they have a true free-energy machine, more power to them (no pun intended). But given the absence of any observed failure of time-translation symmetry, and therefore the steadfast endurance of energy conservation laws, I don't expect any successful devices.

Friction's role with respect to temperature is in raising that temperature. Friction is a great disorderer. If a person running down the track falls and skids along the ground, friction will turn that person's ordered kinetic energy into disordered kinetic energy and the person will get slightly hotter. No energy was created or destroyed in the fall and skid, but lots of formerly orderly kinetic energy became disordered kinetic energy—what I often call "thermal kinetic energy."

The overall story is naturally a bit more complicated, but the basic idea here is correct. Once energy is in the form of thermal kinetic energy, it's stuck... like a glass vase that has been dropped and shattered into countless pieces, thermal kinetic energy can't be entirely reconstituted into orderly kinetic energy. Once energy has been distributed to all the individual molecules and atoms, getting them all to return their chunks of thermal kinetic energy is hopeless. Friction, even at the molecular level, isn't important at this point because the energy has already been fragmented and the most that any type of friction can do is pass that fragmented energy about between particles. So friction creates thermal kinetic energy (out of ordered energies of various types)... in effect, it makes things hot. It doesn't keep them hot; they do that all by themselves.

In actually, some of the water molecules have almost certainly left via a form of solid-to-gas evaporation known technically as "sublimation." You have seen this conversion of ice into gas when you have noticed that old ice cubes in your freezer are smaller than they used to be or when you see that the snow outside during a cold spell seems to vanish gradually without ever melting. Sublimation is also the cause of "freezer burn" for frozen foods left without proper wrapping.

Like so many "scientific" conmen, the purveyors of this particular scam claim to be victims of a hostile scientific establishment, which refuses to accept their brilliant discoveries. They typically attack the deepest and most central tenets of science and claim that a conspiracy is perpetuating belief on those tenets. Their refusal to submit their work to scientific peer review is supposedly based on a fear that such review will be biased and subjective, controlled by the conspiracy.

The sad reality is that the "scientific establishment" is more than willing to examine the claims, but those claims won't survive the process of inspection. In some cases, the authors of the claims are truly self-deluded and are guilty only of pride and ignorance. But in other cases, the authors are real conmen who are out to make a buck at public expense. They should be run out of town on a rail. >

Click here for more information about the "free electricity" hoax, sent in by readers of this site.

For the one-open-window problem, the solution is simple: open another window. That shifts the resonant frequency of the car's air and also helps to dampen the vibrations. Alternatively, you can close the opened window. In your case, the resonance appears to involve a less visible opening into the car, perhaps near the rear bumper. If you can close that leak, you may be able to stop the airflow from driving the air in the car into resonance. If you are unable to find the leak, your best bet is to do exactly what you've done: open another window.

However, the true meaning of the "40 foot-pound" specification is that the safety helmet is capable of absorbing 40 foot-pounds of energy during an impact on its crown. This energy is transferred to the helmet by doing work on it: by pushing its crown downward as the crown dents downward. The product of the downward force on the crown times the distance the crown moves downward gives the total work done on the helmet and this product must not exceed 40 foot-pounds or the helmet may fail to protect the wearer. Since the denting force typically changes as the helmet dents, this varying force must be accounted for in calculating the total work done on the helmet. While I'm not particularly familiar with safety helmets, I know that bicycle helmets don't promise to be useable after absorbing their rated energies. Bicycle helmets contain energy-absorbing foam that crushes permanently during severe impacts so that they can't be used again. Some safety helmets may behave similarly.

Finally, an object dropped from a certain height acquires an energy of motion (kinetic energy) equal to its weight times the height from which it was dropped. As long as that dropped object isn't too heavy and the helmet it hits dents without moving overall, the object's entire kinetic energy will be transferred to the helmet. That means that a 20-pound object dropped from 2 feet on the helmet will deposit 40 found-pounds of energy in the helmet. But if the wearer lets the helmet move downward overall, some of the falling object's energy will go into the wearer rather than the helmet and the helmet will tolerate the impact easily. On the other hand, if the dropped object is too heavy, the extra gravitational potential energy released as it dents the helmet downward will increase the energy transferred to the helmet. Thus a 4000-pound object dropped just 1/100th of a foot will transfer much more than 40 foot-pounds of energy to the helmet.

Like any black object, the stealth aircraft will heat up when exposed to intense electromagnetic waves. But trying to cook a stealth aircraft with microwaves isn't worth the trouble. If someone can figure out where it is enough to focus intense microwaves on it, they can surely find something better with which to damage it.

As for detecting the stealth aircraft with the help of cell phones, that brings up the issue of what is invisibility. Like a black bat against the night sky, it's hard to see a stealth aircraft simply by shining microwaves at it. Those microwaves don't come back to you so you see no difference between the dark sky and the dark plane. But if you put the stealth aircraft against the equivalent of a white background, it will become painfully easy to see. Cell phones provide the microwave equivalent of a white background. If you look for microwave emission near the ground from high in the sky, you'll see microwaves coming at you from every cell phone and telephone tower. If you now fly a microwave absorbing aircraft across that microwave-rich background, you'll see the dark image as it blocks out all these microwave sources. Whether or not this effect was used in the Balkans, I can't say. But it does point out that invisibility is never perfect and that excellent camouflage in one situation may be terrible in another.

But at sunrise and sunset, sunlight enters our atmosphere at a shallow angle and travels a long distance before reaching our eyes. During this long passage, most of the blue light is deflected away and virtually all that we see coming to us from the sun is its red and orange wavelengths. The missing blue light illuminates the skies far to our east during sunrise and to our west during sunset. When the loss of blue light is extreme enough, as it is after a volcanic eruption, so little blue light may reach your location at times that even the sky itself appears deep red. The particles in air aren't good at deflecting red wavelengths, but if that's all the light there is they will give the sky a dim, red glow.

At rest, the bicycle is unstable because it has no base of support. A base of support is the polygon formed by an object's contact points with the ground. For example, a table has a square or rectangular base of support defined by its four legs as they touch the floor. As long as an object's center of gravity (the effective location of its weight) is above this base of support, the object is statically stable. That stability has to do with the object's increasing potential (stored) energy as it tips-tipping a statically stable object raises its center of gravity and gravitational potential energy, so that it naturally accelerates back toward its upright position. Since a bicycle has only two contact points with the ground, the base of support is a line segment and the bicycle can't have static stability.

But when the bicycle is heading forward, it automatically steers its wheels underneath its center of gravity. Just as you can balance a broom on you hand if you keep moving your hand under the broom's center of gravity, a bicycle can balance if it keeps moving its wheels under its center of gravity. This automatic steering has to do with two effects: gyroscopic precession and bending of the bicycle about its steering axis.

In the gyroscopic precession steering, the spinning wheel behaves as a gyroscope. It has angular momentum, a conserved quantity of motion associated with spinning, and this angular momentum points toward the left (a convention that you can understand by pointing the curved fingers of your right hand around in the direction of the tire's motion; your thumb will then point to the left). When the bicycle begins to lean to one side, for example to the left, the ground begins to twist the front wheel. Since the ground pushes upward on the bottom of that wheel, it tends to twist the wheel counter-clockwise according to the rider. This twist or torque points toward the rear of the bicycle (again, when the fingers of your right hand arc around counterclockwise, your thumb will point toward the rear). When a rearward torque is exerted on an object with a leftward angular momentum, that angular momentum drifts toward the left-rear. In this case, the bicycle wheel steers toward the left. While I know that this argument is difficult to follow, since angular effects like precession challenge even first-year physics graduate students, but the basic result is simple: the forward moving bicycle steers in the direction that it leans and naturally drives under its own center of gravity. You can see this effect by rolling a coin forward on a hard surface: it will automatically balance itself by driving under its center of gravity.

In the bending effect, the leaning bicycle flexes about its steering axis. If you tip a stationary bicycle to the left, you see this effect: the bicycle will steer toward the left. That steering is the result of the bicycle's natural tendency to lower its gravitational potential energy by any means possible. Bending is one such means. Again, the bicycle steers so as to drive under its own center of gravity.

These two automatic steering effects work together to make a forward moving bicycle surprisingly stable. Children's bicycles are designed to be especially stable in motion (for obvious reasons) and one consequence is that children quickly discover that they can ride without hands. Adult bicycles are made less stable because excessive stability makes it hard to steer the bicycle.

The ant lives on the surface of the balloon, a two-dimensional world. The ant is unaware of the third dimension that you and I can see when we look at the balloon. The only directions that the ant can move in are along the balloon's surface. The ant can't point toward the center of the balloon because that's not along the surface that the ant perceives. To the ant, the balloon has no center. It lives in a continuous, homogeneous world, which has the weird property that if you walk far enough in any direction, you return to where you started.

Similarly, we see our universe as a three-dimensional world. If there are spatial dimensions beyond three, we are unaware of them. The only directions that we can move in are along the three dimensions of the universe that we perceive. The overall structure of the universe is still not fully understood, but let's suppose that the universe is a simple closed structure like the surface of a higher-dimensional balloon. In that case, we wouldn't be able to point to a center either because that center would exist in a dimension that we don't perceive. To us, the universe would be a continuous, homogeneous structure with that same weird property: if you traveled far enough in one direction, you'd return to where you started.

There is no true outward force acting on an object that's revolving around a center. Instead, that object's own inertia is trying to make it travel in a straight-line path that would cause it to drift farther and farther away from the center. The one true force acting on the revolving object is an inward one-a centripetal force. The object is trying to go straight and the centripetal force is pulling it inward and bending the object's path into a circle.

To get a feel for the experiences associated with this sort of motion, let's first imagine that you are the revolving object and that you're swinging around in a circle at the end of a rope. In that case, your inertia is trying to send you in a straight-line path and the rope is pulling you inward and deflecting your motion so that you go in a circle. If you are holding the rope with your hands, you'll feel the tension in the rope as the rope pulls on you. (Note that, in accordance with Newton's third law of motion, you pull back on the rope just as hard as it pulls on you.) The rope's force makes you accelerate inward and you feel all the mass in your body resisting this inward acceleration. As the rope's force is conveyed throughout your body via your muscles and bones, you feel your body resisting this inward acceleration. There's no actual outward force on you; it's just your inertia fighting the inward acceleration. You'd feel the same experience if you were being yanked forward by a rope-there would be no real backward force acting on you yet you'd feel your inertia fighting the forward acceleration.

Now let's imagine that you are exerting the inward force on an object and that that object is a heavy bucket of water that's swinging around in a circle. The water's inertia is trying to make it travel in a straight line and you're pulling inward on it to bend its path into a circle. The force you exert on the bucket is quite real and it causes the bucket to accelerate inward, rather than traveling straight ahead. Since you're exerting an inward force on the bucket, the bucket must exert an inward force on you (Newton's third law again). It pulls outward on your arm. But there isn't anything pulling outward on the bucket, no mysterious "centrifugal force." Instead, the bucket accelerates in response to an unbalance force on it: you pull it inward and nothing pulls it outward, so it accelerates inward. In the process, the bucket exerts only one force on its surroundings: an outward force on your arm.

As for the operation of a centrifuge, it works by swinging its contents around in a circle and using their inertias to make them separate. The various items in the centrifuge have different densities and other characteristics that affect their paths as they revolve around the center of the centrifuge. Inertia tends to make each item go straight while the centrifuge makes them bend inward. The forces causing this inward bending have to be conveyed from the centrifuge through its contents and there's a tendency for the denser items in the centrifuge to travel straighter than the less dense items. As a result, the denser items are found near the outside of the circular path while the less dense ones are found near the center of that path.

But you are wondering what controls the currents flowing in the two coils. The circuit it is connected to determines the current in the secondary coil. If that circuit is open, then no current will flow. If it is connected to a light bulb, then the light bulb will determine the current. What is remarkable about a transformer is that once the load on the secondary coil establishes the secondary current, the primary current is also determined.

Remember that the current flowing in the secondary coil is itself magnetic and because it is an alternating current, it is accompanied by its own electric field. The more current that is allowed to flow through the secondary coil, the stronger its electric field becomes. The secondary coil's electric field opposes the primary coil's electric field, in accordance with a famous rule of electromagnetism known as Lenz's law. The primary coil's electric field was pushing backward on current passing through the primary coil, so the secondary coil's electric field must be pushing forward on that current. Since the backward push is being partially negated, more current flows through the primary coil.

The current in the primary coil increases until the two electric fields, one from the primary current and one from the secondary current, work together so that they extract all of the primary current's electrostatic energy during its trip through the coil. This natural feedback process ensures that when more current is allowed to flow through the transformer's secondary coil, more current will flow through the primary coil to match.

Despite the fact that cellulose isn't as tasty as sugar, it does have one important thing in common with sugar: both chemicals cling tightly to water molecules. The presence of many hydroxyl groups (-OH) on the sugar and cellulose molecules allow them to form relatively strong bonds with water molecules (HOH). This clinginess makes normal sugar very soluble in water and makes water very soluble in cellulose fibers. When you dip your paper towel in water, the water molecules rush into the towel to bind to the cellulose fibers and the towel absorbs water.

Incidentally, this wonderful solubility of water in cellulose is also what causes shrinkage and wrinkling in cotton clothing when you launder it. The cotton draws in water so effectively that the cotton fibers swell considerably when wet and this swelling reshapes the garment. Hot drying chases the water out of the fibers quickly and the forces between water and cellulose molecules tend to compress the fibers as they dry. The clothes shrink and wrinkle in the process.

Ultraviolet light is high-energy light, meaning that whenever it is emitted or absorbed, the amount of energy involved in the process is relatively large. Although light travels through space as waves, it is emitted and absorbed as particles known as photons. The energy in a photon of ultraviolet light is larger than in a photon of visible light and that leads to interesting effects.

First, some molecules can't tolerate the energy in an ultraviolet photon. When these molecules absorb such an energetic photon, their electrons rearrange so dramatically that the entire molecule changes its structure forever. Among the organic molecules that are most vulnerable to these ultraviolet-light-induced chemical rearrangements are the molecules that are responsible for colors. The same electronic structural characteristics that make these organic molecules colorful also make them fragile and susceptible to ultraviolet damage. As a result, they tend to bleach white in the sun.

Second, some molecules can tolerate high-energy photons by reemitting part of the photon's energy as new light. Such molecules absorb ultraviolet or other high-energy photons and use that energy to emit blue, green, or even red photons. The leftover energy is converted into thermal energy. These fluorescent molecules are the basis for the "neon" colors that are so popular on swimwear, in colored markers, and on poster boards. When you expose something dyed with fluorescent molecules to sunlight, the dye molecules absorbs the invisible ultraviolet light and then emit brilliant visible light.

Note added: A reader pointed out that I never actually answered the question. He's right! So here is the answer: they use accelerometers. An accelerometer is essentially a test mass on a force sensor. When there is no acceleration, the test mass only needs to be supported against the pull of gravity (i.e., the test mass's weight), so the force sensor reports that it is pushing up on the test mass with a force equal to the test mass's weight. But once the accelerometer begins to accelerate, the test mass needs an additional force in order to accelerate with the accelerometer. The force sensor detects this additional force and reports it. If you carry an accelerometer with you on a roller coaster, it will report the force it exerts on the test mass at each moment during the trip. A recording device can thus follow the "g-forces" throughout the ride.

As far as how accelerometers work, modern ones are generally based on tiny mechanical systems known as MEMS (Micro-Electro-Mechanical Systems). Their test masses are associated with microscopic spring systems and the complete accelerometer sensor resides on a single chip.

Imagine standing in front of a 10-kilowatt light bulb (which emits about 1 kilowatt of visible light and the rest is other forms of heat) and then imagine that you can't see light at all and can only feel it when it is causing potential damage. Would you feel safe? Your video camera won't enjoy the microwave exposure, either.

If you want to videotape your experiments without having to view them through the metal mesh on the door, you can consider drilling a small hole in the side of the cooking chamber. If you keep the hole's diameter to a few millimeters, the microwaves will not leak out. Then put one of the tiny inexpensive video cameras that widely available a centimeter or so away from that hole. You should get a nice unobstructed view of the cooking process without risking life and limb.

However, if the fans are directing the cold air in a way that makes you more comfortable without having to cool all the room air or if the fans are creating fast moving air that cools you via evaporation more effectively, then you may be experiencing a real savings of electricity.

To figure out which is the case, you'd have to log the time the air conditioner cycles on during a certain period while the fans were off and the thermostat set to 75 °F and then repeat that measurement during a similar period with the fans on and the thermostat set to 78 °F. If the fans significantly reduce the units runtime while leaving you just as comfortable, then you're saving power.

In contrast, there should be very little voltage difference between the other wire (known as "neutral") and the earth. In a properly wired lamp, the large spade on the electric plug (the neutral wire) should connect to the outside of the bulb socket. That way, when you accidentally touch the bulb's base as you screw it in or out, you'll only be connecting your hand to the neutral wire and won't receive a shock. If you miswire the lamp and have the hot wire connected to the outside of the socket, you can get a shock if you accidentally touch the bulb base at any time.

This sort of accident happens fairly often and we rarely think much about it as we sponge up the spilled liquid inside the microwave oven. But had your friend been unlucky enough to stop heating the coffee a second or two before that POP, she might have been injured while taking the coffee out of the oven. The moral of this story is to avoid overcooking any liquid in the microwave oven. If you must drink your coffee boiling hot, pay attention to it as it heats up so that it doesn't cook too long and then let it sit for a minute after the oven turns off. If you don't like your coffee boiling hot, then don't heat it to boiling at all.

Glass containers are clearly the most likely to superheat water because their surfaces are essentially perfect. Glasses have the characteristics of frozen liquids and a glass surface is as smooth as... well, glass. When you overheat water in a clean glass measuring cup, your chances of superheating it at least mildly are surprisingly high. The spontaneous bubbling that occurs when you add sugar, coffee powder, or a teabag to microwave-heated water is the result of such mild superheating. Fortunately, severe superheating is much less common because defects, dirt, or other impurities usually help the water boil before it becomes truly dangerous. That's why most of us avoid serious injuries.

However, even non-transparent microwaveable containers often have glass surfaces. Ceramics are "glazed," which means that they are coated with glass for both sealing and decoration. Many heavy mixing bowls are glass or glass-ceramics. As you can see, it's hard to get away from trouble. I simply don't know how plastic microwaveable containers behave when heating water; they may be safe or they may be dangerous.

If you're looking for a way out of this hazard, here are my suggestions. First, learn to know how long a given amount of liquid must be heated in your microwave in order to reach boiling and don't cook it that long. If you really need to boil water, be very careful with it after microwaving or boil it on a stovetop instead. My microwave oven has a "beverage" setting that senses how hot the water is getting. If the water isn't hot enough when that setting finishes, I add another 30 seconds and then test again. I never cook the water longer than I need to. Cooking water too long on a stovetop means that some of it boils away, but doing the same in a microwave oven may mean that it becomes dangerously superheated. Your children can still "cook" soup in the microwave if they use the right amount of time. Children don't like boiling hot soup anyway, so if you figure out how long it takes to heat their soup to eating temperature and have them cook their soup only that long, they'll never encounter superheating. As for dad's coffee water, same advice. If dad wants his coffee boiling hot, then he should probably make it himself. Boiling water is a hazard for children even without superheating.

Second, handle liquids that have been heated in a microwave oven with respect. Don't remove a liquid the instant the oven stops and then hover over it with your face exposed. If the water was bubbling spasmodically or not at all despite heavy heating, it may be superheated and deserves particular respect. But even if you see no indications of superheating, it takes no real effort to be careful. If you cooked the water long enough for it to reach boiling temperature, let it rest for a minute per cup before removing it from the microwave. Never put your face or body over the container and keep the container at a safe distance when you add things to it for the first time: powdered coffee, sugar, a teabag, or a spoon.

Finally, it would be great if some entrepreneurs came up with ways to avoid superheating altogether. The makers of glass containers don't seem to recognize the dangers of superheating in microwave ovens, despite the mounting evidence for the problem. Absent any efforts on their parts to make the containers intrinsically safer, it would be nice to have some items to help the water boil: reusable or disposable inserts that you could leave in the water as it cooked or an edible powder that you could add to the water before cooking. Chemists have used boiling chips to prevent superheating for decades and making sanitary, nontoxic boiling sticks for microwaves shouldn't be difficult. Similarly, it should be easy to find edible particles that would help the water boil. Activated carbon is one possibility.

Last night's report wasn't meant to scare you away from using your microwave oven or keep you from heating water in it. It was intended to show you that there is a potential hazard that you can avoid if you're informed about it. Microwave ovens are wonderful devices and they prepare food safely and efficiently as long as you use them properly. "Using them properly" means not heating liquids too long in smooth-walled containers.

Nucleation usually occurs at hot spots during stovetop cooking or at defects in the surfaces of cooking vessels. Glass containers have few or no such defects. When you cook water in a smooth glass container, using a microwave oven, it is quite possible that there will be no nucleation on the walls of the container and the water will superheat. This situation becomes even worse if the top surface of the water is "sealed" by a thin layer of oil or fat so that evaporation can't occur, either. Superheated water is extremely dangerous and people have been severely injured by such water. All it takes is some trigger to create the first bubble-a fork or spoon opening up the inner surface of the water or striking the bottom of the container-and an explosion follows. I recently filmed such explosions in my own microwave (low-quality movie (749KB), medium-quality movie (5.5MB)), or high-quality movie (16.2MB)). As you'll hear in my flustered remarks after "Experiment 13," I was a bit shaken up by the ferocity of the explosion I had triggered, despite every expectation that it would occur. After that surprise, you'll notice that I became much more concerned about yanking my hand out of the oven before the fork reached the water. I recommend against trying this dangerous experiment, but if you must, be extremely careful and don't superheat more than a few ounces of water. You can easily get burned or worse. For a reader's story about a burn he received from superheated water in a microwave, touch here.

Here is a sequence of images from the movie of my experiment, taken 1/30th of a second apart:

As far as the food is concerned, the presence of the spoon redirected the microwaves somewhat, but probably without causing any noticeable changes in how the food cooked. There is certainly no residual radiation of any sort and the food is no more likely to cause cancer after being cooked with metal around than had there been no spoon with it. In general, leaving a spoon in a cup of coffee or bowl of oatmeal isn't going to cause any trouble at all. I do it all the time. In fact, having a metal spoon in the liquid may reduce the likelihood of superheating the liquid, a dangerous phenomenon that occurs frequently in microwave cooking. Superheated liquids boil violently when you disturb them and can cause serious injuries as a result.

By giving the sealed bottle a shake, your mother-in-law is simply speeding up the approach to equilibrium. She is helping the CO₂ molecules leave the beverage and enter the gas phase. The bottle then pressurizes faster, but at the expense of dissolved molecules in the beverage itself. If there is any chance that you'll drink more before equilibrium has been reached, you do best not to shake the bottle. That way, the equilibration process will be delayed as much as possible and you may still be able to drink a few more of those CO₂ molecules rather than breathing them.

Incidentally, shaking a new bottle of soda just before you open it also speeds up the equilibration process. For an open bottle, equilibrium is reached when essentially all the CO₂ molecules have left and are in the gas phase (since the gas phase extends over the whole atmosphere). That's not what you want at all. Instead, you try not to shake the beverage so that it stays away from equilibrium (and flatness) as long as possible. For most opened beverages, equilibrium is not a tasty situation.

About the lens: in principle, all you need is one convex lens. A giant magnifying glass will do. But it has a couple of constraints. Because your television screen is pretty large, the lens diameter must also be pretty large. If it is significantly smaller than the TV screen, it won't project enough light onto your wall. And to control the size of the image it projects on the wall, you'll need to pick just the right focal length (curvature) of the lens. You'll be projecting a real image on the wall, a pattern of light that exactly matches the pattern of light appearing on the TV screen. The size and location of that real image depends on the lens's focal length and on its distance from the TV screen. You'll have to get these right or you'll see only a blur. Unfortunately, single lenses tend to have color problems and edge distortions. Projection lenses need to be multi-element carefully designed systems. Getting a good quality, large lens with the right focal length is going to cost you.

The other big problem is more humorous. Real images are flipped horizontally and vertically relative to the light source from which they originate. Unless you turn your TV set upside-down, your wall image will be inverted. And, without a mirror, you can't solve the left-right reversal problem. All the writing will appear backward. Projection television systems flip their screen image to start with so that the projected image has the right orientation. Unless you want to rewire your TV set, that's not going to happen for you. Good luck.

But when you carry the sack horizontally at a steady pace, the upward force you exert on the sack and the horizontal distance it travels are at right angles to one another. You don't do any work on the sack in that case. The evidence here is that the sack doesn't become any more dangerous; its speed doesn't increase and neither does its altitude. It just shifts from one place to an equivalent one to its side.

However, the ball doesn't bounce all by itself when you drop it on a flexible surface. In that case, the surface also dents and is responsible for part of the ball's rebound. If that surface handles energy inefficiently, it may weaken the ball's bounce. For example, if you drop the ball on carpeting, the carpeting will do much of the denting, will receive much of the ball's original energy, and will waste its share as heat. The ball won't rebound well. My guess is that you dropped the ball on a reasonably hard surface, but one that began to dent significantly when the ball's pressure reached 12psi. At that point, the ball was extremely bouncy, but it was also so hard that it dented the surface and let the surface participate strongly in the bouncing. The surface probably wasn't as bouncy as the ball, so it threw the ball relatively weakly into the air.

I'd suggest repeating your experiment on the hardest, most massive surface you can find. A smooth cement or thick metal surface would be best. The ball will then do virtually all of the denting and will be responsible for virtually all of the rebounding. In that case, I'll bet that the 12psi ball will bounce highest.

About the humidity caveat: if you can blow dry air across your windshield, that will defrost it faster than just about anything else, even if that air is cold. The water molecules on your windshield are constantly shifting back and forth between the solid phase (ice) and the gaseous phase (steam or water vapor). Heating the ice will help more water molecules leave the ice for the water vapor, but dropping the density of the water vapor will reduce the number of water molecules leaving the water vapor for the ice. Either way, the ice decreases and the water vapor increases. Since you car's air condition begins drying the air much soon after you start the car than its heater begins warming the air, many modern cars concentrate first on drying the air rather than on heating it.

If you send a current backward through a battery, the battery extracts energy from the current and lowers its voltage. As it takes energy from the current, the battery adds to its store of chemical potential energy so that it recharges. Battery charges do exactly that: they push current backward through the batteries to recharge them. This recharging only works well on batteries that are designed to be recharged since many common batteries undergo structural damage as their energy is consumed and this damage can't be undone during recharging.

When you use a chain of batteries to power an electric device, you must arrange them so that each one pumps charge the same direction. Otherwise, one will pump and add energy to the current while the other extracts energy from the current. If all the batteries are aligned positive terminal to negative terminal, then they all pump the same direction and the current experiences a 1.5 volt (typically) voltage rise in passing through each battery. After passing through 2 batteries, its voltage is up by 3 volts, after passing through 3 batteries, its voltage is up by 4.5 volts, and so on.

The color filters that the camera employs to obtain color information misbehave when they're dealing with infrared light and so the camera is fooled into thinking that it's viewing white light. That's why your camera shows a white spot where the remote's infrared source is located.

I just tried taking some pictures through infrared filters, glass plates that block visible light completely, and my digital camera worked just fine. The images were as sharp and clear as usual, although the colors were odd. I had to use incandescent illumination because fluorescent light doesn't contain enough infrared. It would be easy to take pictures in complete darkness if you just illuminated a scene with bright infrared sources. No doubt there are "spy" cameras that do exactly that.

In all likelihood, the manufacturer of this unit has shielded all the light so that none of it reaches your eyes. If that's not the case, you should wear laser safety glasses that block 1064 nm light. But it's also possible that the irritation you're experiencing is coming from the burned material that you are machining. Better ventilation should help. High voltage power supplies, which may be present in the laser, could also produce ozone. Ozone has a spicy fresh smell, like the smell after a lightning storm, and it is quite irritating to eyes and nose.

The flattened poles are the result of rotation—as the planet spins, the need for centripetal (centrally directed) acceleration at its equator causes its equatorial surface to shift outward slightly, away from the planet's axis of rotation. The planet is therefore wider at its equator than it is at its poles.

Water can always evaporate into dry air, but it normally only does so at its surface. When water molecules leave the surface faster than they return, the quantity of liquid water gradually diminishes. That's ordinary evaporation. However, when water is heated to its boiling temperature, it can begin to evaporate not only from its surface, but also from within. If a steam bubble forms inside the hot water, water molecules can evaporate into that steam bubble and make it grow larger and larger. The high temperature is necessary because the pressure inside the bubble depends on the temperature. At low temperature, the bubble pressure is too low and the surrounding atmospheric pressure smashes it. That's why boiling only occurs at or above water's boiling temperature. Since pressure is involved, boiling temperature depends on air pressure. At high altitude, boiling occurs at lower temperature than at sea level.

But pay attention to the phrase "If a steam bubble forms" in the previous paragraph. That's easier said than done. Forming the initial steam bubble into which water molecules can evaporate is a process known as "nucleation." It requires a good number of water molecules to spontaneously and simultaneously break apart from one another to form a gas. That's an extraordinarily rare event. Even in a cup of water many degrees above the boiling temperature, it might never happen. In reality, nucleation usually occurs at a defect in the cup or an impurity in the water—anything that can help those first few water molecules form the seed bubble. When you heat water on the stove, the hot spots at the bottom of the pot or defects in the pot bottom usually assist nucleation so that boiling occurs soon after the boiling temperature is reached. But when you heat pure water in a smooth cup using a microwave oven, there may be nothing present to help nucleation occur. The water can heat right past its boiling temperature without boiling. The water then superheats—its temperature rising above its boiling temperature. When you shake the cup or sprinkle something like sugar or salt into it, you initiate nucleation and the water then boils violently.

Fortunately, serious microwave superheating accidents are fairly unusual. However, they occur regularly and some of the worst victims require hospital treatment. I have heard of extreme cases in which people received serious eye injuries and third degree burns that required skin grafts and plastic surgery.

You can minimize the chance of this sort of problem by not overcooking water or any other liquid in the microwave oven, by waiting about 1 minute per cup for that liquid to cool before removing it from the microwave if there is any possibility that you have superheated it, and by being cautious when you first introduce utensils, powders, teabags, or otherwise disturb very hot liquid that has been cooked in a microwave oven. Keep the water away from your face and body until you're sure it's safe and don't ever hover over the top of the container. Finally, it's better to have the liquid boil violently while it's inside the microwave oven than when it's outside on your counter and can splatter all over you. Once you're pretty certain that the water is no longer superheated, you can ensure that it's safe by deliberately nucleating boiling before removing the cup from the microwave. Inserting a metal spoon or almost any food into the water should trigger boiling in superheated water. A pinch of sugar will do the trick, something I've often noticed when I heat tea in the microwave. However, don't mess around with large quantities of superheated water. If you have more than 1 cup of potentially superheated water, don't try to nucleate boiling until you've waited quite a while for it to cool down. I've been scalded by the stuff several times even when I was prepared for an explosion. It's really dangerous.

For a reader's story about a burn he received from superheated water in a microwave, touch here.

The leaving rate (the rate at which molecules break free from the liquid water) depends on the temperature. The hotter the water is, the more frequently water molecules will be able to break away from their buddies and float off into the gas. The landing rate (the rate at which molecules land on the water's surface and stick) depends on the density of molecules in the gas. The more dense the water vapor, the more frequently water molecules will bump into the liquid's surface and land.

As you raise the temperature of the water in your glass, the leaving rate increases and the equilibrium shifts toward higher vapor density and less liquid water. By the time you reach 100° Celsius, the equilibrium vapor pressure is atmospheric pressure, which is why water tends to boil at this temperature (it can form and sustain steam bubbles). Above this temperature the equilibrium vapor pressure exceeds atmospheric pressure. The liquid water and the gas above it can reach equilibrium, but only if you allow the pressure in your enclosed system to exceed atmospheric pressure. However, if you open up your enclosed system, the water vapor will spread out into the atmosphere as a whole and there will be a never-ending stream of gaseous water molecules leaving the glass. Above 100° C, liquid water can't exist in equilibrium with atmospheric pressure gas, even if that gas is pure water vapor.

So how can you superheat water? Don't wait for equilibrium! The road to equilibrium may be slow; it may take minutes or hours for the liquid water to evaporate away to nothing. In the meantime, the system will be out of equilibrium, but that's ok. It happens all the time: a snowman can't exist in equilibrium on a hot summer day, but that doesn't mean that you can't have a snowman at the beach... for a while. Superheated water isn't in equilibrium and, if you're patient, something will change. But in the short run, you can have strange arrangements like this without any problem.

A cubic foot of air weighs about 0.078 pounds so the upward buoyant force on a cubic foot of helium is about 0.078 pounds. A cubic foot of helium weighs only about 0.011 pounds. The difference between the upward buoyant force on the cubic foot of helium and the weight of the helium is the amount of extra weight that the helium can lift; about 0.067 pounds. Since you weigh 85 pounds, it would take about 1300 cubic feet of helium to lift you and a thin balloon up into the air. That's a balloon about 13.5 feet in diameter.

Ordinary incandescent bulbs produce a thermal spectrum of light with a "color temperature" of about 2800° C. A thermal light spectrum is a broad, featureless mixture of colors that peaks at a particular wavelength that's determined only by the temperature of the object emitting it. Since the bulb's color temperature is much cooler than that of the sun's (5800° C), the bulb appears much redder than the sun and emits relatively little blue light. A fluorescent lamp, however, synthesizes its light spectrum from the emissions of various fluorescent phosphors. Its light spectrum is broad but structured and depends on the lamp's phosphor mixture. The four most important phosphor mixtures are cool white, deluxe cool white, warm white, and deluxe warm white. These mixtures all produce more blue than an incandescent bulb, but the warm white and particularly the deluxe warm white tone down the blue emission to give a richer, warmer glow at the expense of a little energy efficiency. Cool white fluorescents are closer to natural sunlight than either warm white fluorescents or incandescent bulbs.

To answer your question about shaves: without blue light in the illumination, it's not that easy to distinguish beard from skin. Since incandescent illumination is lacking in blue light, a shave looks good even when it isn't. But in bright fluorescent lighting, beard and skin appear sharply different and it's easy to see spots shaving has missed. As for makeup illumination, it's important to apply makeup in the light in which it will be worn. Blue-poor incandescent lighting downplays blue colors so it's easy to overapply them. When the lighting then shifts to blue-rich fluorescents, the blue makeup will look heavy handed. Some makeup mirrors provide both kinds of illumination so that these kinds of mistakes can be avoided.

The terminal velocity of an object depends on the object's size, shape, and density. A fluffy object (a feather, a parachute, or a sheet of paper) has a small terminal velocity while a compact, large, heavy object (a cannonball, a rock, or a bowling ball) has a large terminal velocity. An aerodynamic object such as an arrow also has a very large terminal velocity. A person has a terminal velocity of about 200 mph when balled up and about 125 mph with arms and feet fully extended to catch the wind.

The secondary circuit consists of little more than a huge coil of wire and some electrodes. This coil of wire is located around the same region of space occupied by the inductor of the primary circuit. As the magnetic field inside that inductor fluctuates up and down in strength, it induces current in the secondary coil. That's because a changing magnetic field produces an electric field and the electric field surrounding the inductor pushes charges around and around the secondary coil. By the time the charges in the secondary coil emerge from the coil, they have enormous amounts of energy; making them very high voltage charges. They accumulate in vast numbers on the electrodes of the secondary circuit and push one another off into the air as sparks.

While most circuits must form complete loops, the Tesla coil's secondary circuit doesn't. Its end electrodes just spit charges off into space and let those charges fend for themselves. Many of them eventually work their ways from one electrode to the other by flowing through the air or through objects. But even when they don't, there is little net build up of charge anywhere. That's because the direction of current flow through the secondary coil reverses frequently and the sign of the charge on each electrode reverses, too. The Tesla coil is a high-frequency device and its top electrode goes from positively charged to negatively charge to positively charged millions of times a second. This rapid reversal of charge, together with reversing electric and magnetic fields means that a Tesla coil radiates strong electromagnetic waves. It therefore interferes with nearby radio reception.

Finally, it has been pointed out to me by readers that a properly built Tesla coil is resonant—that the high-voltage coil has a natural resonance at the same frequency that it is being excited by the lower voltage circuit. The high-voltage coil's resonance is determined by its wire length, shape, and natural capacitance.

A diesel engine doesn't have spark ignition. Instead, it uses the high temperature caused by extreme compression to ignite its fuel. It compresses pure air to high temperature and pressure, and then injects fuel into this air. Timed to arrive at the proper instant, the fuel bursts into flames and burns quickly in the superheated compressed air. In contrast to gasoline, diesel fuel is formulated to ignite easily as soon as it enters hot air.

The magnet is part of the system that makes the surface move. Attached to the surface itself is a cylindrical coil of wire and this coil fits into a cylindrical channel cut into the speaker's permanent magnet. That magnet is carefully designed so that its magnetic field lines radiate outward from the inside of the channel to the outside of the channel and thus pass through the cylindrical coil the way bicycle spokes pass through the rim of the wheel.

When an electric current is present in the wire, the moving electric charges circulate around this cylinder and cut across the magnetic field lines. But whenever a charge moves across a magnetic field line, it experiences a force known as the Lorenz force. In this case, the charges are pushed either into or out of the channel slot, depending on which way they are circulating around the coil. The charges drag the coil and surface with them, so that as current flows back and forth through the coil, the coil and surface pop in and out of the magnet channel. This motion produces sound.

Instead of trying to interact through a natural resonance in water, a microwave oven just exposes the water molecules to the intense electromagnetic fields in strong, non-resonant microwaves. The frequency used in microwave ovens (2,450,000,000 cycles per second or 2.45 GHz) is a sensible but not unique choice. Waves of that frequency penetrate well into foods of reasonable size so that the heating is relatively uniform throughout the foods. Since leakage from these ovens makes the radio spectrum near 2.45 GHz unusable for communications, the frequency was chosen in part because it would not interfere with existing communication systems.

As for there being a laser in a microwave oven, there isn't. Lasers are not the answer to all problems and so the source for microwaves in a microwave oven is a magnetron. This high-powered vacuum tube emits a beam of coherent microwaves while a laser emits a beam of coherent light waves. While microwaves and light waves are both electromagnetic waves, they have quite different frequencies. A laser produces much higher frequency waves than the magnetron. And the techniques these devices use to create their electromagnetic waves are entirely different. Both are wonderful inventions, but they work in very different ways.

The fact that this misleading information appears in a science book, presumably used in schools, is a bit discouraging. It just goes to show you that you shouldn't believe everything read in books or on the web (even this web site, because I make mistakes, too).

Color sets create the impression of full color by mixing the three primary colors of light—blue, green, and red—right there on the inside surface of the picture tube. A set does the mixing by turning on and off three separate electron beams to control the relative brightnesses of the three primary colors at each location on the screen. The shadow mask is a metal grillwork that allows the three electrons beams to hit only specific phosphor dots on the inside of the tube's front surface. That way, electrons in the "blue" electron beam can only hit blue-glowing phosphors, while those in the "green" beam hit green-glowing phosphors and those in the "red" beam hit red-glowing phosphors. The three beams originate at slightly different locations in the back of the picture tube and reach the screen at slightly different angles. After passing through the holes in the shadow mask, these three beams can only hit the phosphors of their color.

Since the shadow mask's grillwork and the phosphor dots must stay perfectly aligned relative to one another, the shadow mask must be made of a metal that has the same thermal expansion characteristics as glass. The only reasonable choice for the shadow mask is Invar metal, an alloy that unfortunately is easily magnetized. Your son has magnetized the mask inside your set and because moving charged particles are deflected by magnetic fields, the electron beams in your television are being steered by the magnetized shadow mask so that they hit the wrong phosphors. That's why the colors are all washed out and rearranged.

To demagnetize the shadow mask, you should expose it to a rapidly fluctuating magnetic field that gradually decreases in strength until it vanishes altogether. The degaussing coils I mentioned above plug directly into the AC power line and act as large, alternating-field electromagnets. As you wave one of these coils around in front of the screen, you flip the magnetization of the Invar shadow mask back and forth rapidly. By slowly moving this coil farther and farther away from the screen, you gradually scramble the magnetizations of the mask's microscopic magnetic domains. The mask still has magnetic structures at the microscopic level (this is unavoidable and a basic characteristic of all ferromagnetic metals such as steel and Invar). But those domains will all point randomly and ultimately cancel each other out once you have demagnetized the mask. By the time you have the coil a couple of feet away from the television, the mask will have no significant magnetization left at the macroscopic scale and the colors of the set will be back to normal.

Incidentally, I did exactly this trick to my family's brand new color television set in 1965. I had enjoyed watching baseball games and deflecting the pitches wildly on our old black-and-white set. With only one electron beam, a black-and-white set needs no shadow mask and has nothing inside the screen to magnetize. My giant super alnico magnet left no lingering effect on it. But when the new set arrived, I promptly magnetized its shadow mask and when my parent watched the "African Queen" that night, the colors were not what you'd call "natural." The service person came out to degauss the picture tube the next day and I remember denying any knowledge of what might have caused such an intense magnetization. He and I agreed that someone must have started a vacuum cleaner very close to the set and thus magnetized its surface. I was only 8, so what did I know anyway.

Finally, as many readers have pointed out, many modern televisions and computer monitors have built-in degaussing coils. Each time you turn on one of these units, the degaussing circuitry exposes the shadow mask to a fluctuating magnetic field in order to demagnetize it. If your television set or monitor has such a system, then turning it on and off a couple of times should clear up most or all of the magnetization problems. However, you may have to wait about 15 minutes between power on/off cycles because the built-in degaussing units have thermal protection that makes sure they cool down properly between uses.

But when the fly is inside the van, the fly travels about in air that is moving with the van. If the van is moving at 70 mph, then so is the air inside it and so is the fly. In fact, everything inside the van moves more or less together and from the perspective of the van and its contents, the whole world outside is what is doing the moving—the van itself can be considered stationary and the van's contents are then also stationary.

As long as the fly and the air it is in are protected inside the van, the movement of the outside world doesn't matter. The fly buzzes around in its little protected world. But if the van's window is open and the fly ventures outside just as a signpost passes the car, the fly may get creamed by a collision with the "moving" sign. Everything is relative and if you consider the van as stationary, then it is undesirable for the van's contents to get hit by the moving items in the world outside (passing trees, bridge abutments, or oncoming vehicles.

However, quantum mechanics makes controlling the die truly impossible. The problem stems from the fact that position and velocity information are not fully defined at the same time in our quantum mechanical universe. In short, you can't know exactly where a die is and how fast it is moving at the same time. And that doesn't mean that you can't perform these measurements well. It means that the precise values don't exist together; they are limited by Heisenberg uncertainty. So quantum physics imposes a fundamental limit on how well you can know the initial conditions before your throw and it thus limits your ability to control the outcome of that throw. How much quantum physics affects your ability to throw a 6 depends on the complexity of the throw. If you just drop a die a few inches onto a table, you can probably get a 6 most of the time, despite quantum mechanics and without even knowing much classical information. But as you begin throwing the die farther, you'll begin to lose control of it because of quantum mechanics and uncertainty. In reality, you'll find classical physics so limiting that you'll probably never observe the quantum physics problem. Knowing everything about a system is already unrealistic, even in a classical universe. The problems arising from quantum mechanics are really just icing on the cake for this situation.

I watched the video on the "Counter Rotation Device" and found the discussion of "Newton's Fourth Law of Motion" quite amusing. The speaker claims that this fourth law was discovered about 30 years ago by a person now at their research lab. It is based on Newton's third law, which the speaker simplifies to "for every action there is an equal and opposite reaction." In a nutshell, his fourth law claims that you can take the reaction caused by a particular action and apply it to the action in the same direction—action causes reaction which causes more action which causes more reaction and so on. Pretty soon you have so much action and reaction that anything becomes possible. The video goes on to show devices that yield more power than they consume and that can easily become net sources of energy—by using part of the output energy from one of these energy multiplying devices to power that device, you can create endless energy from nothing at all.

Sadly enough, it's all just nonsense. Newton's third law is not as flexible as the speaker supposes and this endless feedback process in which reaction is used as action to produce more reaction is ridiculous. A more accurate version of Newton's third law is: "Whenever one object pushes on a second object, the second object pushes back on the first object equally hard but in the opposite direction". Thus when you push on the handle of a water pump, that handle pushes back on you with an equal but oppositely directed force. The speaker's claim is that there is a way to use the handle's push on you as part of your push on the handle so that, with your help, the handle essentially pushes itself through action and reaction. You can then pump water almost without effort. Sorry, this is just nonsense. It's mostly just playing with the words action and reaction in their common language form: if you scare me, I react by jumping. That action and reaction has nothing to do with physics.

The speaker uses at least three clever techniques to make his claims more compelling and palatable. First, he refers frequently to a power-company conspiracy that is out to destroy his company and its products. Conspiracy theories are so popular these days that having a conspiracy against you makes you more believable. Second, he describes the fellow who discovered the fourth law of motion as a basement inventor who has taken on the rigid scientific establishment. Ordinary people love to see pompous, highly educated academics brought low by other ordinary people; it's kind of a team spirit issue. And third, he makes casual use of technical looking equipment and jargon, as though he is completely at ease in the world of advanced technology. Movies have made it easier to trust characters like Doc Brown from "Back to the Future" than to trust real scientists.

In fact, there is no power-company conspiracy because there is no free electricity. The proof is in the pudding: if these guys really could make energy from nothing, they'd be doing it every day and making a fortune. They would be the power companies. If they were interested in public welfare rather than money, they'd have given their techniques away already. If they were interested in proving the scientific establishment wrong, they'd have accepted challenges by scientific organization and demonstrated their devices in controlled situations (where they can't cheat). The fact is, they're just frauds and of no more interest to the power companies than snake oil salespeople are to doctors. No decent people want to see others defrauded of money, property, or health, but the free electricity people present no real threat to the power companies.

The popular notion that an ordinary person is likely to upset established science is an unfortunate product of the anti-intellectual climate of our present world. Becoming a competent scientist is generally hard work and requires dedication, time, and an enormous amount of serious thinking. Physics is hard, even for most physicists. The laws governing the universe are slowly being exposed but it has taken very smart, very hardworking people almost half a millennium to get to the current state of understanding. Each new step requires enormous effort and a detailed understanding of a good part of the physics that is already known. Still, there is a common myth that some clever and lucky individual with essentially no training or knowledge of what has been discovered before will make some monumental breakthrough. The movies are filled with such events. Unfortunately, it won't happen. In new or immature fields or subfields, it is possible for an essentially untrained or self-trained genius to jump in and discover something important. Galileo and Newton probably fit this category in physics and Galois and Ramanujan probably fit it in mathematics. But most of physics is now so mature that broad new discoveries are rare, and accessible only to those with extremely good understandings of what is already known. A basement tinkerer hasn't got a prayer.

Finally, real scientists don't always walk around in white lab coats looking serious, ridiculing the less educated, and trying to figure out how to trick the government into funding yet another silly, fraudulent, or unethical research project. In fact, most scientists wear practical clothes, have considerable humor, enjoy speaking with ordinary folk about their science, and conduct that science because they love and believe in it rather than as a means to some diabolic end. These scientists use the words of science in their conversations because it is the appropriate language for their work and there is meaning in each word and each sentence. The gibberish spoken by "scientists" in movies is often offensive to scientists in the same way that immigrant groups find it offensive when people mock their native languages.

I don't know about any patent history for the free electricity organization but everyone should be aware that not all patented items actually do what they're supposed to. In principle, the U.S. Patent Office only awards a patent when it determines that a concept has not been patented previously, is not already known, is not obvious, and is useful. The utility requirement should eliminate items that don't actually work. One of my readers, a patent attorney, reports that he regularly invokes the utility regulation while escorting the "inventors" of impossible devices such as "free electricity" to the door. They consider him part of the conspiracy against them, but he is doing us all a service by keeping foolishness out of the patent system. However, proving that something doesn't work often takes time and money, so sometimes nonfunctional items get patented. Thus a patent isn't always a guarantee of efficacy. Patented nonsense is exactly that: nonsense.

Finally, how do I know that Free Electricity is really not possible? Couldn't I have missed something somewhere in the details? No. The impossibility of this scheme is rooted in the very groundwork of physics; at the deepest level where there is no possibility of mistake. For the counter rotation device to generate 15 kilowatts of electricity out of nothing, it would have to be a net source of energy—the device would be creating energy from nothing. That process would violate the conservation of energy, whereby energy cannot be created or destroyed but can only be transferred from one object to another or converted from one form to another. Recognizing that our universe is relativistic (it obeys the laws of special relativity), the actual conserved quantity is mass/energy, but the concept is the same: you can't make mass/energy from nothing.

The origin of this conservation law lies in a mathematical theorem noted first by C. G. J. Jacobi and fully developed by Emmy Noether, that each symmetry in the laws of physics gives rise to a conserved quantity. The fact that a translation in space—shifting yourself from one place to another—does not change the laws of physics gives rise to a conserved quantity: momentum. The fact that a rotation—changing the direction in which you are facing—does not change the laws of physics gives rise to another conserved quantity: angular momentum. And the fact that waiting a few minutes—changing the time at which you are—does not change the laws of physics gives rise to a third conserved quantity: energy. The conservation of energy is thus intimately connected with the fact that the laws of physics are the same today as they were yesterday and as they will be tomorrow.

Scientists have been looking for over a century for any changes in the laws of physics with translations and rotations in space and with movement through time, and have never found any evidence for such changes. Thus momentum, angular momentum, and energy are strictly conserved in our universe. For the counter rotation device to create energy from nothing, all of physics would have to be thrown in the trashcan. The upset would be almost as severe as discovering that 1+1 = 3. Furthermore, a universe in which physics was time-dependent and energy was not conserved would be a dangerous place. Free electricity devices would become the weapons of the future—bombs and missiles that released energy from nothing. Moreover, as the free electricity devices produced energy from nothing, the mass/energy of the earth would increase and thus its gravitational field would also increase. Eventually, the gravity would become strong enough to cause gravitational collapse and the earth would become a black hole. Fortunately, this is all just science fiction because free electricity isn't real.

For more information about the "free electricity" hoax, sent in by readers of this site, touch here.

A convenient arrangement for generating electricity endlessly is to mount a permanent magnet on a spindle and to place a coil of wire nearby. Then as the magnet spins, it will turn past the coil of wire and propel currents through that coil. With a little more engineering, you'll have a system that looks remarkably like the guts of a typical permanent magnet based motor. In fact, if you take a common DC motor out of a toy and connect its two electrical terminals to a 1.5 V light bulb or a light emitting diode (try both directions with an LED because it can only carry current in one direction), you'll probably be able to light that bulb or LED by spinning the motor's shaft rapidly. A DC motor has a special switching system that converts the AC produced in the motor's coils into DC for delivery to the motor's terminals, but it's still a generator. So the easiest answer to your question is: "find a nice DC motor and turn its shaft".

To magnetize a screwdriver permanently, you should expose it briefly to a very strong magnetic field. Touching the screwdriver's tip to one pole of a strong magnet will cause some permanent magnetization. Rubbing or tapping the screwdriver also helps to free up its domains so that they can align with this external field. But the better approach is to put the screwdriver in a coil of wire that carries a very large DC electric current.

The current only needs to flow for a fraction of a second—just long enough for the domains to align. A car battery is a possibility, but it has safety problems: it can deliver an incredible current (400 amperes or more) for a long time (minutes) and can overheat or even explode your coil of wire. Moreover, it may leak hydrogen gas, which can be ignited by the sparks that will inevitably occur while you are magnetizing your screwdriver.

A safer choice for the current source is a charged electrolytic capacitor—a device that stores large quantities of separated electric charge. A charged capacitor can deliver an even larger current than a battery can, but only for a fraction of a second—only until the capacitor's store of separated charge is exhausted. Looking at one of my hobbyist electronics catalogs, Marlin P. Jones, 800-652-6733, I'd pick a filter capacitor with a capacity of 10,000 microfarads and a maximum voltage of 35 volts (Item 12104-CR, cost: $1.50). Charging this device with three little 9V batteries clipped together in a series (27 volts overall) will leave it with about 0.25 coulombs of separated charge and just over 3.5 joules (3.5 watt-seconds or 3.5 newton-meters) of energy.

Make sure that you get the polarity right—electrolytic filter capacitors store separated electric charge nicely but you have to put the positive charges and negative charges on the proper sides. [To be safe, work with rubber gloves and, as a general rule, never touch anything electrical with more than one hand at a time. Remember that a shock across your heart is much more dangerous than a shock across you hand. And while 27 volts is not a lot and is unlikely to give you a shock under any reasonable circumstances, I can't accept responsibility for any injuries. If you're not willing to accept responsibility yourself, don't try any of this.]

If you wrap about 100 turns of reasonably thick insulated wire (at least 18 gauge, but 12 gauge solid-copper home wiring would be better) around the screwdriver and then connect one end of the coil to the positively charged side of the capacitor and the other end of the coil to the negatively charged side, you'll get a small spark (wear gloves and safety glasses) and a huge current will flow through the coil. The screwdriver should become magnetized. If the magnetization isn't enough, repeat the charging-discharging procedure a couple of times, always with the same connections so that the magnetization is in the same direction.

The fact that electricity itself travels at almost the speed of light just means that when you start the electrons moving at one end of a long wire, the electrons at the other end of the wire also begin moving almost immediately. But that doesn't mean that an electron from your end of the wire actually reaches the far end any time soon. Instead, the electrons behave somewhat like water in a long hose. When you start the water moving at one end, it pushes on water in front of it, which pushes on water in front of it, and so on so that water at the far end of the hose begins to leave the hose almost immediately. In the case of water, the motion proceeds forward at the speed of sound. In a wire, the motion proceeds forward at the speed of light in the wire (actually the speed at which electromagnetic waves propagate along the wire), which is only slightly less than the speed of light in vacuum.

Note for the experts: as one of my readers (KT) points out, the water-in-a-hose analogy for current-in-a-wire is far from perfect. Current in a wire flows throughout the wire, including at its surface, and the wire's resistance to steady current flow scales as the cross-sectional area of the wire. In contrast, water in a hose only flows through the open channel inside the hose and the hose's resistance to flow scales approximately as the fourth power of that channel's diameter.

When you put your eye in water, the eye's curved outer surface stops acting as a lens. That's because light travels at roughly the same speed in water as it does in your eye and that light no longer bends as it enters your eye. Everything looks blurry because the light doesn't focus on your retina anymore. But by inserting an air space between your eye and a flat plate of glass or plastic, you recover the bending at your eye's surface and everything appears sharp again.

The problem with this real image of the sun is simply that it's dazzlingly bright and that it delivers lots of thermal power in a small area. The real image is there in space, whether or not you put any object into that space. If you put paper or some other flammable substance in this focused region, it may catch on fire. Putting your skin in the focus would also be a bad idea. And if you put your eye there, you're in serious trouble.

So my suggestion with first graders is to stay in the shade when you're working with magnifying glasses. As soon as you go out in direct sunlight, that brilliant real image will begin hovering in space just beyond the magnifying glass, waiting for someone to put something into it. And many first graders just can't resist the opportunity to do just that.

These electromechanical watches are the modern descendants of the automatic mechanical watches. An automatic watch had a main spring that was wound by the motion of the wearer's hand. A small mass inside the watch swung back and forth on the end of a lever. Because of its inertia, this mass resisted changes in velocity and it moved relative to the watch body whenever the watch accelerated. If you like, you can picture the mass as a ball that rolls about inside a wagon as you roll the wagon around an obstacle course. When the lever turned back and forth relative to the watch body, the watch was able to extract energy from it. Gears attached to the lever allowed the watch to use the mass's energy to wind its mainspring. The energy extracted from the mass with each swing was very small, but it was enough to keep the mainspring fully wound. Ultimately, this energy came from your hand—you did work on the watch in shaking it about and some of this energy eventually wound up in the mainspring.

These same sorts of motions are what power the electromechanical watches of today. Instead of winding a spring, your wrist motions swing weights about inside the watches and these moving weights spin generators to produce electric power.

In principle, you could tap into a cloud and the ground beneath and extract the capacitor's charge directly with wires. But this would be a heroic engineering project and unlikely to be worth the trouble. And catching a lightning strike in order to charge a second capacitor is not likely to be very efficient: most of the energy released during the strike would have to dissipate in the air and relatively little of it could be allowed to enter the capacitor. That's because no realistic capacitor can handle the voltage in lightning.

Here's the detailed analysis. The power released during the strike is equal to the strike's voltage times its current: the voltage between clouds and ground and the current flowing between the two during the strike. Voltage is the measure of how much energy each unit of electric charge has and current is the measure of how many units of electric charge are flowing each second. Their product is energy per second, which is power. Added up over time, this power gives you the total energy in the strike. If you want to capture all this energy in your equipment, it must handle all the current and all the voltage. If it can only handle 1% of the voltage, it can only capture 1% of the strike's total energy.

While the current flowing in a lightning strike is pretty large, the voltage involved is astonishing: millions and millions of volts. Devices that can handle the currents associated with lightning are common in the electric power industry but there's nothing reasonable that can handle lightning's voltage. Your equipment would have to let the air handle most of that voltage. The air would extract power from the flowing current in the lightning bolt and turning it into light, heat, and sound. Your equipment would then extract only a token fraction of the stroke's total energy. Finally, your equipment would have to prepare the energy properly for delivery on the AC power grid—its voltage would have to be lowered dramatically and a switching system would have to convert the static charge on the capacitors to an alternating flow of current in the power lines.

To see why this arrangement is stable, consider what would happen if something tried to upset it. For example, what would happen if this mixture were to begin losing heat to its surroundings? Its temperature would begin to drop but then the water would begin to freeze and release thermal energy: when water molecules stick together, they release chemical potential energy as thermal energy. This thermal energy release would raise the temperature back to 32 F. The bath thus resists attempts at lowering its temperature.

Similarly, what would happen if the mixture were to begin gaining heat from its surroundings? Its temperature would begin to rise but then the ice would begin to melt and absorb thermal energy: separating water molecules increases their chemical potential energy and requires an input of thermal energy. This lost thermal energy would lower the temperature back to 32 F. The bath thus resists attempts at raising its temperature.

So an ice/water bath self-regulates its temperature at 32 F. The only other quantities affecting this temperature are the air pressure (the bath temperature could shift upward by about 0.003 degrees F during the low pressure of a hurricane) and dissolved chemicals (half an ounce of table salt per liter of bath water will shift the bath temperature downward by about 1 degree F).

More manageable pressures surround us everyday. Our bodies do their part in supporting the weight of the atmosphere overhead when we're on land or the weight of the atmosphere and a small part of the ocean when we're swimming at sea. The deeper you go in the ocean, the more weight there is overhead and the harder your body must push upward. Thus the pressure you exert on the water above you and the pressure that that water exerts back on you increases with depth. Even though gravity is decreasing as you go deeper and deeper, the pressure continues to increase. However, it increases a little less rapidly as a result of the decrease in local gravity.

As for the fact that even colored soaps create only white foam, that's related to the amount of dye in the soaps. It doesn't take much dye to give bulk soap its color. Since light often travels deep into a solid or liquid soap before reflecting back to our eyes, even a modest amount of dye will selectively absorb enough light to color the reflection. But the foam reflects light so effectively with so little soap that the light doesn't encounter much dye before leaving the lather. The reflection remains white. To produce a colored foam, you would have to add so much dye to the soap that you'd probably end up with colored hands as well.

Metals that bend permanently are experiencing plastic deformation. Their atoms change their relative orientations during the bend and they lose track of where they were. Once plastic deformation has occurred, the metal can't remember how to get back to its original shape and stays bent.

Metals that bend only temporarily and return to their original shape when freed from stress are experiencing elastic deformation. Their sheets of atoms aren't sliding about and they can easily spring back to normal when the stresses go away. Naturally, springs are made from materials that experience only elastic deformation in normal circumstances. Hardened metals such as spring steel are designed and heat-treated so that the atomic sliding processes, known technically as "slip," are inhibited. When you bend them and let go, they bounce back to their original shapes. But if you bend them too far, they either experience plastic deformation or they break.

Non-crystalline materials such as glass also make good springs. But since these amorphous materials have no orderly rows of atoms, they can't experience plastic deformation at all. They behave as wonderful springs right up until you bend them too far. Then, instead of experience plastic deformation and bending permanently, they simply crack in two.

One last detail: there are a few exotic materials that undergo complicated deformations that are neither temporary nor permanent. With changes in temperature, these shape memory materials can recover from plastic deformation and spring back to their original shapes.

But when something is moving at speeds approaching the speed of light, mass and kinetic energy no longer separate so easily. In fact, the relativistic equations of motion are more complicated than those describing slow objects and the way in which gravity affects fast objects is more complicated than simply giving them "weight."

Overall, you can view the bending of light by gravity in one of two ways. First, you can view it approximately as gravity affecting not on mass, but also energy so that light falls because its energy gives it something equivalent to a "weight." Second, you can view it more accurately as the bending of light as caused by a change in the shape of space and time around a gravitating object. Space is curved, so that light doesn't travel straight as it moves past gravitating objects—it follows the curves of space itself. The second or Einsteinian view, which correctly predicts twice as much bending of light as the first or Newtonian view, is a little disconcerting. That's why it took some time for the theory of general relativity to be widely accepted. (Thanks to DP for pointing out the factor of two.)

When the car starts forward, inertia tries to keep all of the objects in the car from moving forward. An object at rest tends to remain at rest. So the car must push you forward in order to accelerate you forward and keep you moving with the car. As the car seat pushes forward on you, you push back on the car seat (Newton's third law) and dent its surface. Your perception is that you are moving backward, but you're not really. You're actually moving forward; just not quite as quickly as the car itself.

The air in the car undergoes the same forward acceleration process. Its inertia tends to keep it in place, so the car must push forward on it to make it accelerate forward. Air near the front of the car has nothing to push it forward except the air near the back of the car, so the air in the front of the car tends to "dent" the air in the back of the car. In effect, the air shifts slightly toward the rear of the car. Again, you might think that this air is going backward, but it's not. It's actually moving forward; just not quite as quickly as the car itself.

Now we're ready for the helium balloon. Since helium is so light, the helium balloon is almost a hollow, weightless shell that displaces the surrounding air. As the car accelerates forward, the air in the car tends to pile up near the rear of the car because of its inertia. If the air can push something out of its way to get more room near the rear of the car, it will. The helium balloon is that something. As inertia causes the air to drift toward the rear of the accelerating car, the nearly massless and inertialess helium balloon is squirted toward the front of the car to make more room for the air. There is actually a horizontal pressure gradient in the car's air during forward acceleration, with a higher pressure at the rear of the car than at the front of the car. This pressure gradient is ultimately what accelerates the air forward with the car and it's also what propels the helium balloon to the front of the car.

Finally, when the car is up to speed and stops accelerating forward, the pressure gradient vanishes and the air returns to its normal distribution. The helium balloon is no longer squeezed toward the front of the car and it floats once again directly above the gear shift.

One last note: OGT from Lystrup, Denmark points out that when you accelerate a glass of beer, the rising bubbles behave in the same manner. They move toward the front of the glass as you accelerate it forward and toward the back of the glass as you bring it to rest.

The fact that we see mostly reflected light makes for some interesting experiments. A red object selectively reflects only red light; a blue object reflects only blue light; a green object reflects only green light. But what happens if you illuminate a red object with only blue light? The answer is that the object appears black! Since it is only able to reflect red light, the blue light that illuminates it is absorbed and nothing comes out for us to see. That's why lighting is so important to art. As you change the illumination in an art gallery, you change the variety of lighting colors that are available for reflection. Even the change from incandescent lighting to fluorescent lighting can dramatically change the look of a painting or a person's face. That's why some makeup mirrors have dual illumination: incandescent and fluorescent.

The one exception to this rule that objects only reflect the light that strikes them is fluorescent objects. These objects absorb the light that strikes them and then emit new light at new colors. For example, most fluorescent cards or pens will absorb blue light and then emit green, orange, or red light. Try exposing a mixture of artwork and fluorescent objects to blue light. The artwork will appear blue and black: blue wherever the art is blue and black wherever the art is either red, green, or black. But the fluorescent objects will display a richer variety of colors because those objects can synthesize their own light colors.

In answer to your question, my guess is that the larger bowl of water also exposes much more of that water to the air. Although the larger bowl had more water in it, it allowed that water to exchange heat faster with its environment. If the larger bowl contained twice as much water but let that water lose heat twice as fast, the two bowls would maintain equal temperatures. If you want to see the effect of thermal mass in slowing the loss of temperature, you'll need to control heat loss. Try letting equal amounts of hot water cool in two identical containers—one wrapped in insulation and covered with clear plastic wrap (to prevent evaporation) and one open to the air. You'll see a dramatic change in cooling rate. And if you want to compare unequal amounts of water, use two indentical containers that are only exposed to the cooler environment through a controlled amount of surface area. For example, try two identical insulated cups, one full of water and one only half full. If both lose heat only through their open tops, the full cup should cool more slowly than the half full cup.

You won't get any important quantitative results from this sort of experiment, but it'll be fun anyway. I wonder what fillings will make the ball bounce best or worst?

That is what happens when you carefully weave a needle into a latex balloon—the needle separates the polymer strands locally, but doesn't actually pull them apart or break them. Since breaking the latex molecules will probably cause the balloon to tear and burst, you have to be very patient and use a very sharp needle. I usually oil the needle before I do this and I don't try to insert the needle in the most highly stressed parts of the balloon. The regions near the tip of the balloon and near where it is filled are the least stressed and thus the easiest to pierce successfully with a needle. A reader has informed me that coating the needle with Vasoline is particularly helpful.

One final note: a reader pointed out that it is also possible to put a needle through a balloon with the help of a small piece of adhesive tape. If you put the tape on a pat