Friday, March 11, 2005

Answers to "How Things Work" test.

1. Could someone invent an air-breathing engine that burns water?

(o) Yes.
(o) There's no way to know until it's tried.
(o) No, because water puts out fire.
(x) No, because water won't chemically react with oxygen.

"Burning" means the chemical combination of a substance with free oxygen (O_2). Water (H_2O) is what you get by burning hydrogen (H_2). You can't burn what's already burnt!


2. In the drawing below, a rock on a string is being whirled around counter-clockwise in a circle. If the string suddenly breaks, what path will the rock take?

(o) A
(x) B
(o) C
(o) None of the above.

The string is keeping the rock going in a circle. If the string breaks, the rock will just continue in the same direction it was going in just before the string broke. This is Newton's Second Law of Motion.

Interestingly, Aristotelian physics, i.e. the physics widely accepted in Europe from the time of the late Roman Empire until about the 1500s, would predict something like path C (a path that continues curving for a while). The reason is this: Aristotelian physics says objects have "natural" tendencies, which can be subverted by "impulses" (roughly what we mean by force multiplied by how long the forces is applied). When an impulse is applied to an object, it follows the forced motion, and when the impulse is exhausted, the object relaxes to its natural state.

So you could say the rock's natural motion is to fly away from the hand, but the impulse the string gives it keeps it in a circle. If the string breaks the rock continues in a circular way until the impulse is exhausted.

Studies have shown a substantial fraction of 21st century people still believe intuitively in Aristotelian physics. But they're not very good at softball or darts.


3. Can blood clot underwater?

(o) No, it can't dry out.
(x) Yes, the chemistry still works.

The clotting of blood is not just simply drying out, it's a complex cascade of biochemical reactions. That's why it doesn't do a haemophiliac any good to dry the blood off -- in his case, the chemistry is not working. The chemistry obviously works under water, because it works in a wet wound!


4. Why is the sound that bats emit to locate their prey in the dark at such a high frequency, so high it can't be heard?

(o) So the prey can't hear them coming!
(o) No reason. They could use any frequency, really.
(o) They need a really high repetition rate to track rapidly moving targets.
(x) They get more precise information about the prey's location with higher frequency sound.

When you "see" things by reflecting some kind of wave off them, you always get sharper "pictures" with shorter wavelength, or equivalently higher frequency, waves. The reason is, essentially, that only features in your target that are the same size or larger than the wavelength of your wave will perturb it. (Think of boats and waves: the boat will greatly perturb small ripples, or waves up to roughly their size, but a boat won't alter a giant wave at all.)


5. Not long ago the press reported that the Human Genome Project had finished determining "the" DNA sequence of human beings. But don't we each have our own unique set of genes?

(o) Yes, but our DNA sequence is all the same.
(x) Yes, but most of our DNA sequence is all the same.
(o) Yes, but the HGP didn't study the DNA in genes.
(o) No, but our interaction with the environment during growth and development makes us unique.

It's a bit of an error to say they sequenced "the" genome -- they sequenced "a" genome, literally. But the differences in DNA from one person to another are a very, very small fraction of the total DNA, so they do practically know the entire genome. Individual variations are "clean-up" work. Actually, we share most of our DNA with all higher animals. One of the reasons we can share so much DNA with animals
that are nothing like us is that most of our DNA is not used, it's just junk that we carry around.


6.How many bits per pixel are necessary to store an image with a
maximum of 255 colors?

(o) 7
(x) 8
(o) 32
(o) 255

A "pixel" = "PICTure ELement" is the smallest dot in a picture, and if there are 255 colors you need to be able to store 255 different numbers for each pixel, to label the color it might be. A "bit" = "BInary digIT" is a single digit in base 2. So we need as many bits as we need binary digits to store the numbers between 0 and 254.
11111110 in binary is 254, and it has 8 digits, so we need 8 bits.


7. When you throw a ball into the air, it falls back to the ground. So why don't the molecules that make up the Earth's atmosphere all fall to the ground? What keeps them up there?

(x) They do fall, but bounce back up, over and over, forever.
(o) They're so light they fall undetectably slowly.
(o) They're stacked up, higher molecules resting on those lower down.
(o) Wind keeps them stirred up, like bits of paper in a breeze.

Gravity certainly affects air molecules like it affects any other object thrown into the air. So air molecules will fall under the influence of gravity, just like a ball tossed up, and eventually hit the ground (although they may well ricochet off many other air molecules on the way). What's strange to our "common sense," however, is that they then always bounce up again. We might believe they could bounce a few times, but in that case we'd expect them to bounce lower and lower, eventually coming to rest on the Earth's surface.

So why don't they? The key difference between a ball that might bounce on the ground a few times, only to come to rest quickly, and the air molecules is that the ball has about a trillion trillion possible modes of internal vibration. These possible tiny wiggles and jiggles represent places to which the energy of the ball initially found in the bouncing motion can and does disappear. That is, the ball may start out with most of its energy in the bouncing motion, but very quickly this energy wanders off into the bazillions of internal jiggling and wiggling motions. Since there are so many of these internal vibrations, practically any amount of energy you initially give the ball (by throwing it higher and higher) will be quickly absorbed, much as water is absorbed by sand. Furthermore, the amount of energy that ends up in each wiggling motion is so very small (because it's divided among zillions of them) that the amplitude (size) of the wiggling will be imperceptibly small. In short, it will look as if the energy of the bouncing has vanished.

In the case of air molecules, there are at most 2 or 3 internal vibrations, so there really isn't anywhere for the bouncing energy to go. So it doesn't go anywhere, and the air molecules bounce up and down again, forever.


8. What determines the lowest frequency sound your stereo speakers can produce?

(o) The diameter of the speaker cone.
(o) The stiffness of the speaker cone material.
(o) The quality of the speaker cables.
(x) Nothing, there is no lower frequency limit.

A bit of trick question. Sound waves are longitudinal, meaning the air shakes back and forth. The size of the speaker has nothing to do with the wavelength it can produce, since it produces shorter or longer waves by moving frontwards and backwards faster or slower, and NOT by waving like a drumhead. So the lowest frequency it can produce is just the slowest it can move back and forth. Since, of course, it
can move back and forth infinitely slowly, there is no lower limit. The reason low-frequency speakers are larger than high frequency is because the human ear does not perceive long wavelengths well, so you need to make powerful waves when you make low frequency waves, i.e. move a lot of air back and forth.


9. If you drop a rifle bullet from your hand at the same instant, and from the same height, as you fire a rifle bullet horizontally from a rifle, which hits the ground first?

(o) the dropped bullet
(o) the fired bullet
(x) they both hit simultaneously

Classic Newtonian physics problem, just like the rock on a string. The truth is that the downward motion of the bullets is completely independent of the forward motion, so that the bullets, having both started with downward velocity of zero, and having the same distance to fall, will reach the ground at the same time. Of course, the fired bullet will reach the ground way far away, while the dropped bullet will reach the ground at your feet.

Folks who believe in Aristotelian physics get this wrong, too.


10. What's the most important reason HIV is hard to cure?

(x) The virus mutates frequently.
(o) HIV attacks the immune system.
(o) Very little is known about how HIV infects cells.
(o) You can't kill all HIV-infected cells without killing the patient.

To kill HIV you need to target some part of its genome that stays reasonably constant, and unfortunately it changes its genome very often. In fact, HIV would be an unimpressive virus, less dangerous that the cold, if it did not mutate so much. The immune system apparently has no trouble killing it initially, but it mutates so fast that before every bit is gone it has become something new, and the immune system must learn to recognize and kill the new version. Then it changes again. This arms race goes on for years if not decades, and AIDS only develops when (for reasons we don't yet know) the immune system exhausts its repertoire, and the virus finds a form that the immune system will no longer recognize and kill.


11. Why is there almost no hydrogen in Earth's atmosphere?

(o) It's a rare element, there's not much anywhere.
(o) There wasn't any in the part of the primordial cloud that condensed to form the Earth.
(x) Earth's gravity is too weak to hold it.
(o) It's so flammable it all burned up long ago to form water.

Most of the primordial cloud that formed the planets was hydrogen, and planets with a strong enough gravity like Jupiter and Saturn still have most of it. But it's a very light gas, and smaller planets like the Earth or Mars just don't have enough gravity to hold onto it.


12. In the device sketched below, water falls, turning a waterwheel, which then drives a bucket chain lifting the water back up. The wheel also supplies power. This device. . .

(o) is a Ptolemaic water wheel, used for irrigation
(x) is a perpetual motion machine of the first kind
(o) was used in ancient Egypt to irrigate fields

This device is impossible. A little thought should convince you that just as much energy is required to lift the water back up as is released by the water falling onto the water wheel. If the water wheel *also* supplies energy, then energy is being created out of nowhere. This violates the First Law of Thermodynamics, the principle
of Conservation of Energy ("energy is never created or destroyed"). It's called a perpetual motion machine of the first kind because, first, if it existed it would run forever (since it needs no energy to run), and, second, because it violates the First Law. Machines that violate the Second Law of Thermodynamics (the one about entropy) are called perpetual motion machines of the 2nd kind, and have more subtle flaws. You can find very respectable-looking companies offering to sell you shares in a perpetual motion machine of the 2nd kind all over the Web.


13. Why are fluorescent light bulbs more energy-efficient than regular light bulbs?

(o) They extract a higher percentage of the energy in electricity.
(x) They don't produce as much heat.
(o) They have a lower electrical resistance.
(o) They flicker, i.e. they're only really on about 50% of the time.

Regular light bulbs actually emit *most* of the electrical energy they consume as heat. (That's why they get so hot.) Fluorescent bulbs do a much better job of turning the electrical energy into visible light, not heat. (That's why they are cool to the touch.)


14. Mr. Wonka has hidden 5 golden tickets in a million candy bars. Charlie wants to find one. Charlie's Uncle Olaf buys 100 candy bars before Charlie gets to the store. Charlie's chance of finding a gold ticket has just. . .

(o) Increased, since there are fewer tickets left.
(o) Decreased, since Uncle Olaf might have found a ticket or two.
(x) Stayed the same. Uncle Olaf has had no effect.

Consider the first ticket Uncle Olaf buys. The probability of Charlie finding a ticket is now the probability Uncle Olaf *found* a ticket (5/1,000,000) times the probability that Charlie's ticket is one of the 4 remaining (4/999,999) plus the probability that Uncle Olaf did *not* find a ticket (1 - 5/1,000,000) times the probability that Charlie's ticket is a winner (5/999,999). Perhaps surprisingly, the result is 5/1,000,000, which is the same result as if Uncle Olaf had bought no tickets.

Another way to look at is this: whether the ticket is in Uncle Olaf's hands or still at the shop, or in someone else's hands, can have nothing to do with Charlie's chances of winning. It doesn't matter where the tickets that Charlie doesn't buy are!


15. The red color of blood has the same chemical source as the color of. . .

(o) poinsettia leaves
(x) rust
(o) red algae
(x) Mars

Both blood and Mars are red because it's the color of iron atoms when they are bound to oxygen. In essence, blood "rusts" in the lungs, to pick up oxygen, and then "unrusts" (gets reduced) in the capillaries to deliver oxygen to cells.


16. Why aren't birds electrocuted when they perch on power lines?

(x) They aren't also touching ground.
(o) The power lines are insulated.
(o) They're too light to make good contact with the electricity.
(o) They're smaller than the wavelength of the electricity.

Power lines are rarely insulated except by the air around them, because it would make the lines too heavy. But electricity cannot flow unless there's a place to flow to. Since the birds only touch the power lines, there's no place for the electricity to go.


17. Imagine a ball is dropped inside a box with perfect insulation. No energy can escape this box! How long will the ball bounce?

(o) Forever!
(o) Longer than when it's outside the box.
(x) Exactly the same time as when it's outside the box.
(o) Not at all.

One is tempted to think that, in general, the ball bounces lower and lower and then stops because its energy escapes. If so, then preventing the escape of the energy will prevent the ball from stopping, and the correct answer would be "Forever!" or at least "Longer than when it's outside the box."

But this understanding is false. What actually happens to make the ball stop bouncing is that the energy initially in the bouncing motion of the ball "gets lost" by spreading out into the zillions of tiny internal wiggling and vibrating motions of the ball, which are too small to see. You might say the bouncing turns into heat, in some sense. But in any sense, the energy does not really leave the ball so much as it's just that organized motion (bouncing) turns into unorganized motion (microscopic wiggling) that is too small to see. So insulating the ball will actually have no effect at all on its behaviour.


18. Suppose you accelerate in the passing lane on the Highway to Hell (which begins in Los Angeles but passes mostly through outer space) until your '56 Corvette is going 299,792,457 meters/second. (That's 1 m/s slower than the speed of light!) You open the window and throw an empty Bud can straight forward at 10 m/s. What do you observe?

(x) The can going 10 m/s faster than me. Duh!
(o) The can going 1 m/s faster than me. Can't go faster than light!
(o) The can going 0.14 m/s faster than me, roughly.
(o) The lights of a very angry cop in your mirror.

Most folks know that Einstein's Special Theory of Relativity predicts that nothing can go faster than the speed of light. But the more important prediction of his theory, relevant (ha ha) here, is that all physics experiments have to look the same no matter what "inertial" (not accelerating) reference frame you're in. That means anything you do while traveling steadily, even at an absurdly high speed, has to look exactly the same as it does when you are traveling at a safe and legal speed, or not traveling at all. Therefore, what you observe when you throw a beer can forward when you are not moving must be exactly what you observe when you throw a beer can forward when you are moving at nearly the speed of light.

But how does one reconcile the fact that, since you're traveling at 1 m/s less than the speed of light, the beer would now "seem" to be traveling 9 m/s faster than the speed of light? By realizing two things: first, and most important, this statement implies that we are talking about some "objective" beer can velocity that is "more real" than the velocity you report ("10 m/s faster than me"). For example, the velocity relative to some other observer. What does the cop at the side of the road see, in other words? Isn't the velocity he measures more "objective" than what you measure? Isn't that the "real" velocity? Well, no. Relativity says there are no privileged reference frame. The cop's measurement of velocity is no more "real" than yours (although you will not want to take this position in traffic court). The best the cop can say is "the can is traveling x m/s faster than me," where x is a number we would have to calculate.

Once you realize this, then we can set about calculating x, and it will turn out that, if we are to insist that (1) you see the can doing what it would do if you were stationary and (2) the policeman does not observe the can exceeding the speed of light, then we can't calculate the speed of the can from the point of view of the policeman by just adding 10 m/s to your speed. We have to do a more complicated calculation. It will also turn out that we need to allow you and the cop to disagree about the way time passes, too.

That's a lot to change about how we see things. Is it really required? Why can't you have a different experience throwing a can at nearly the speed of light than when stationary? Well, it simply turns out, that's the way the universe works. Experiments prove relativity is correct, and that's that.


19. Imagine one of those sleek glass-wall office buildings that looks in the daytime like a gigantic column of mirrors. You can't see in through the windows, but the people inside can see out. Why?

(o) The windows transmit more light inward than outward.
(o) The windows transmit more light outward than inward.
(o) The windows are polarized.
(x) It's usually darker inside than outside.

It's not possible for the windows, which are unpowered, to transmit more light in one direction than in the other. That would violate the Second Law of Thermodynamics (the one about entropy). One way to realize this is to realize that, if such a window could be devised, it could be used to construct a perpetual motion machine of the second kind, a way to recycle energy forever perfectly. (For example, you enclose whatever machinery you want to operate in a double-walled box made of these windows, set to pass energy only inwards. The waste heat from your machinery is trapped and concentrated by the box, and when the temperature inside your box rises higher than the temperature near your machinery, which it eventually must, you use the temperature difference to drive a steam engine that powers your machinery.)

The important fact here is just that it's normally darker inside the building than out. This has two effects: first, the light reflected from objects inside the building is much less than the light reflected from objects outside, simply because there's less light available. It is, of course, easier to see objects that are strongly illuminated than poorly illuminated. The windows magnify this effect, because they pass only a small fraction (say 5%) of the reflected light passing through them. However a brightly illuminated object (something outside) can easily afford to have 95% of the light reflected from it thrown away and still be visible, while a poorly illuminated object (something inside) might become completely undetectable if 95% of the light reflected from it is thrown away.

The other important effect is that your eyes, like a digital camera, adjust their sensitivity to the generally available light. In bright light, like outside, they become less sensitive, not sensitive enough to see the dim objects inside the windows. Inside the building, your eyes are more sensitive.

20. In Star Trek IV, Scotty tells a 20th century Earth firm the secret of transparent aluminum. What, theoretically, could produce a form of aluminum that conducted electricity but was perfectly transparent?

(x) Nothing. A perfectly transparent conductor is impossible.
(o) Treating aluminum at very high (currently impossible) pressures.
(o) Chemically combining aluminum with the right mix of other elements.
(o) Doping the aluminum with positive charge carriers.

Alas, Scotty discovery is not possible even in principle. To be transparent, a material must absorb no visible light. However, to conduct electricity a material must have free (mobile) electrons, and anything with mobile electrons can absorb light. A good way to understand this is to realize that light is a form of electromagnetic radiation, like radio waves. An antenna is something that can absorb electromagnetic radiation, and any conductor can be used to make an antenna.

The front of your LCD computer display is coated with conductor, however, and yet you can see through it. How is t his possible? The most important reason is that the layer is very thin, so that it need not be perfectly transparent.

21. If you are a normal healthy woman, you can be sure your body does
not contain. . .

(o) The genes that cause hemophilia.
(o) The genes for a penis.
(o) Both of the above.
(x) Neither of the above.

It's important to remember that genes need not be expressed (cause the
effects they are designed to cause).


22. When are you most likely to see a meteor?

(x) Just before dawn.
(o) Just after dusk.
(o) Midnight.
(o) During a lunar conjunction.

Just before dawn, you are facing forward in the Earth's orbit if you
look up in the sky. It's like looking out the windshield of a
speeding car -- you'll get a lot more bugs splatted on the windshield.
At dusk you're looking out the "back window", facing back along the
Earth's orbit, and meteors have to be able to catch the Earth (which
is moving at 18 miles/second) to hit it.


23. Which gear below will turn faster (more revolutions per minute)?

(o) The big one.
(x) The small one.
(o) They turn at the same rate.

This is why gears are useful, they can change the rate of rotation of
shafts without any loss of power.


24. Which is the main reason a hybrid car gets better gas mileage?

(x) The engine does not idle (run when the car is stopped).
(o) Regenerative braking. (The energy of the car is stored, not thrown away, when you brake.)
(o) During steady high speed driving the electric motor does most of the work.
(o) Because the engine is smaller the car is much lighter.

Typical stop-and-go driving wastes a tremendous amount of fuel idling
at stop lights and so forth. Remember, you get zero MPG under those
conditions, which really drags the average down. If you spend half
your travel time stopped at stop lights (not uncommon in a city) your
average MPG would be half what it is when you do not spend any time
stopped. A hybrid turns off the engine when the car is stopped, so
you never have to average in any zero MPG time.


25. Suppose you join an online bulletin board or website like OkCupid, and suppose they state in their advertising that anybody can join, and can post whatever they like. Suppose you make a few unpopular posts, and then the operators start deleting all your posts as soon as you write them. Have your First Amendment (free speech) rights been violated?

(o) Yes!
(o) Yes, as long as your posts were not hate speech.
(o) No, unless you paid to join the site.
(x) No.

OK, this is not about scientific principles at all, but it's still about important principles of everyday life.

Many folks have a vague impression that the First Amendment to the United States Constitution says that each of us has "the right to free speech," and that, therefore, anything anyone does that interferes with our saying what we please is an infringement of that right.

This is not correct. The text of the First Amendment reads in the relevant part: "Congress shall make no law...abridging the freedom of speech...." Hence, the shortest explanation for the answer to this question is that, since the operators of the bulletin board or website are not Congress, there is no Constitutional restriction whatsoever on their actions.

It is an important general principle of life in our Republic that the Bill of Rights restricts only the actions of the government, not those of our fellow citizens in their private capacity. For that reason, no property owner is required by the Constitution to allow any form of speech at all on his property. An oil refinery, for example, is under no obligation to allow peaceful protesters in their lobby, even if the lobby is commonly used by the public to transact business with the refinery.

And, to get back to this case, the private operator of a website is under no obligation to allow any speech on his website. He can accept or reject posts for any reason, including the vilest personal prejudice, or for no reason at all.

Armed with this understanding, you can make short work of First Amendment conundrums such as these:

  • Can a newspaper refuse to print letters to the editor that criticize the paper, or which take positions the editors don't like? You bet.
  • Does the FA mean a reporter must present all sides of a story? Or that a newspaper is forbidden from "slanting" the news it reports? Nope.
  • Can a billboard owner refuse to run an advertisement for Planned Parenthood on his bulletin board? Yes.
  • Do I have the right to yell "Fire!" in a crowded movie theater? No.
  • Do I have the right to yell "This movie sucks!" in a crowded movie theater? No!


26. Is the product of two prime numbers also prime?

(o) Always.
(x) Never.
(o) Sometimes.

A prime number is a number that has no factors (numbers that divide it
evently) other than itself and 1. Clearly a number N that's the
product of primes A and B has A and B as its factors! So N can't
ever be prime.


27.When you're prescribed antibiotics, why are you supposed to finish all of the prescription, even if that means you're taking pills long after you're cured?

(o) So the bacteria can't come right back.
(o) Because it's dangerous to leave the drugs lying around.
(o) So the drug companies make more money!
(x) So bacteria don't become resistant to the drug.

It's inevitable that some bacteria will be better able to resist the chemical attack of the drug. When you first start taking the drug, there will be very few of these. But of course, they are the only ones that will succeed in surviving long enough to reproduce. (Bacteria reproduce very fast, as often as every 15 minutes.) Hence soon enough most of the bacteria left alive in your body will be pretty resistant to the drug, since they will all be descendants of the very few who were initially resistant to the drug.

Now, if you continue the chemical artillery in an overwhelming amount and for an extended time, then even these tough guys will succumb and die, and all is well. But it is worth noting that some of them will survive long past the time when you have no more symptoms. (At that point, they are so few they no longer cause symptoms.)

What you don't want to do is quit the fight and let these last few very tought battle-hardened villains escape. Not for your own sake -- chances are you're immune to them now anyway -- but because you will loose them on the wide world. That means the next person who gets the disease, from descendants of your escaped POWs, will have to cope with bugs that are already pretty resistant to the antibiotic that helped you out.

When this process goes on for a decade or so (practically forever on the bacterial time scale) you can get major strains of bacteria which can't be killed by any known antibiotic. Which is trouble for all of us.


28. Why are there two prongs on an electrical plug?

(o) Because household electricity is AC (alternating current).
(x) Because electricity always needs a return path to the generator.
(o) Tradition.
(o) One for the positive charge, one for the negative.

Electricity is the flow of electrons, to have a flow you always need a
source and a sink, just like to have a flow of water you need a tap
and a drain. Hence all electrical circuits require two lines to the
power source: one that provides the electrons and one that takes them
back after they've flowed through the circuit.


29. If you're sitting in an airplane flying at 500 MPH in level
flight, and you throw something exactly straight up, where will it
fall back down?

(o) Slightly behind my hand (towards the back of the plane).
(o) Slightly ahead of my hand (towards the front of the plane).
(x) Exactly into my hand.
(o) Into my gin and tonic.

Very like the bullet question. You might think the motion of the
airplane affects the motion of the object. Nope. You might also
think the object, once free of contact with the airplane, starts to
slow down. Nope again. There's no force to slow it down. If the
object were outside the plane, i.e it were thrown out the window, then
of course it would slow down, because of the tremendous air
resistance. But inside the airplane, because the airplane carries all
the air with it, there's no air resistance, so the object does not
slow down.


30. It says right here that your brain begins to die after 6 minutes
without oxygen. But Tom Sietas of Germany, world record holder, has
held his breath for almost 9 minutes. What gives?

(o) Mr. Sietas is now brain-damaged, poor soul.
(o) Your brain can last longer without oxygen if you deep breathe first.
(x) You can get oxygen from the air trapped in your lungs, if your heart is still beating.
(o) 6 minutes is just an average, some folks can go longer.

Lungs don't take nearly all the oxygen out of the air. That's why CPR
works. It's really the failure to get that oxygen up to the brain
that is the problem.