Genes are Lumpy!

I love sobering thoughts. Here’s one. Around the year 1900, Charles Darwin’s (and AR Wallace’s) theory of variation and selection was virtually forgotten. What is today hailed (rightly) as the greatest intellectual achievement of 19th century science was all but discarded by the beginning of the 20th century.

Why? Because given the world as it was known then, it couldn’t have worked.

I often encounter natural selection described as a beautiful, simple idea. “How could I have been so stupid not to think of it myself,” is the sentiment described. The fact that no one, not Newton, not Descartes, not Aristotle nor Galileo nor Hypatia nor Euclid, thought of it first indicates that it’s not so simple. The fact that the beautiful, simple idea was later discarded is even better evidence.

These days there’s an evangelical named Ray Comfort who is criticizing evolution with what he thinks is a simple, beautiful argument. He’s right; it is simple and beautiful, but also wrong. It is wrong because the facts of the real world take us somewhere else. It is wrong in the same way the rejection of natural selection by 1900 was wrong. It is wrong because it is ignorant of another simple, beautiful idea. Genes are lumpy.

Comfort’s argument goes like this. “Evolutionists” say that elephants evolved from non-elephant ancestors. But the first elephant (for Comfort the first is always a male) had to find a wife. Isn’t it an odd coincidence that just when the male elephant came along, a female elephant evolved, too? But if not, with what creature did the elephant mate?

If you don’t know anything about genetics, this might be a convincing answer. And in fact it was (in different form) the argument that in part caused the rejection of natural selection the first time around.

To choose another example, suppose a white moth were to appear in a population of black moths. That white moth would have to mate with a black moth. If (as was believed at the time) inheritence is blended, their offspring would be grey. These grey moths in turn would overwhelmingly mate with black moths, resulting in even darker offspring, and so on. In this way, any unique traits would disappear almost as soon as they arose.

Ah, but genes don’t blend in this way. Instead, here’s what might happen. A white moth mates with a black moth. Their offspring are ALL BLACK! White has disappeared, not over several generations, but instantly. But isn’t this a backwards step? Patience, grasshopper.

Now the all-black moths mate. Occasionally, two black moths  that each have a white parentwill mate. In this cross, one out of four of their offspring will be white! The white trait, hidden in the first generation of offspring, reappears in the second.

If you’ve taken a biology class, you probably recognize this. It’s a common piece of pedagogery, and reveals the pea plant experiments of Gregor Mendel, a contemporary of Darwin whose work was forgotten in his lifetime. Big deal, right?

The big deal (so often missed in introductory material on this subject) is that this discovery, that genes are discrete (I prefer the word “lumpy”), gave natural selection the tool it needed to work! The result is the world you see around you. Because unique traits could survive as discrete lumps of genetic material, even hiding in generations, all manner of variability could eventually appear, spread, and fluorish.

So what does all this have to do with Comfort and his elephants? The point is that Comfort would be right – if inheritance blended. But it doesn’t. Genes are lumpy. An elephant ancestor needn’t be an elephant to carry elephant traits. It can carry genes for elephant-like traits, and those genes can hide within the genome. When those genes come together in the right individual, the traits (completely accidentally) can make that individual more likely to survive, and so the traits are passed on. Eventually, the traits become common in the population, and you have elephants.

The point is not so much that Comfort and the 1900-era biologists were wrong. Being wrong is part of learning. The point is that scientists, by working out sometimes simple, beautiful relationships, such as Gregor Mendel and his peas, can reveal not just a deep truth, but can show us just how and why it is true. This knowledge, gained through long, hard, arduous work, is now available to everybody. You can know things that Aristotle never could have imagined, not because you’re smarter, but because you are alive, here and now, in a world positively brimming with simple, beautiful, and true ideas.

Now that’s a sobering thought.

Science Doesn’t Matter – Ain’t It Grand!

As I often do, I am listening to a science book on CD as I drive to and from work. Yes, I’m falling behind on all the important politics and news of Britney Britney and Menudo, but for me those few minutes of audio immersion in science are some of the best of my day.

It struck me today as I listened, though, how none of it really mattered, and that it was great. The speaker was talking about the invention of things like the steam engine, the airplane, and the automobile, and how little role science or scientists played in those inventions. Later on, of course, that changed, as inventions like nuclear reactors, the transistor, and the laser were driven almost entirely by science. It would be ridiculous to look around at the modern world and deny the role of science.

Yet most people have no idea how a nuclear reactor, a transistor, or a laser works. Some, like doctors, may need to know what a laser does, but knowing the science behind it is virtually irrelevant to actually using the thing. And here’s my point: for most people, the science behind the thing doesn’t matter.

There are things that do matter. I’m in the process of selling my house. I have to know things, like what an interest rate is, how to negotiate a selling price, how to read and sign my name. I’m working on various grants at work. I have to know how to spell, how to talk to people without making them dislike me, how to answer e-mail. I’m trying to sell a new book. I have to know how to write a cover letter, how to look for an agent, and how to accept rejection. But for none of these things does science matter. Yes, if I were a working scientist, science would really matter. But if I were a working auto mechanic, then auto mechanic-y stuff would really matter. If I were a baker, then . . . etc. etc.

Educators make a huge mistake when they try to convince their learners that science is Important, that it Matters. No it doesn’t. It’s wonderful and exciting, but it doesn’t matter in the same way that knowing how to read, count, or talk to people matters. If you’re trying to find the right combination of ingredients to make a room temperature superconductor, then science matters. But for most of us, science doesn’t matter, not really, and that is wonderful. It frees us up to just have fun, to know science for what it is – a grand exploration of the world, for no better reason than the world exists and is begging to be explored.

Let’s see what we can discover next!

Neutrinos

Something I heard shook me. There are 60 billion neutrinos from the Sun passing right through your thumbnail every second.

Neutrinos are one of my favorite topics. They say something about science and what we know. Here’s the story.

Alpha decay and beta decay are both types of radioactivity. Other than that, they’re about as different as two processes can be. Alpha decay involves the ejection of an alpha particle, really a helium nucleus. Alpha particles are two protons and two neutrons, and throwing them around is the equivalent of tossing bowling balls around in the subatomic world.

Beta decay involves the ejection of an electron (or a positron in special circumstances). Compared to an alpha particle, a beta particle – an electr0n – is just a bit of fluff. Though they usually penetrate deeper than alpha particles, they don’t carry nearly the oomph.

That’s the obvious difference between the two. But there’s a more subtle difference, beautiful and deep. Alpha decay is, for any particular decay of an isotope, always exactly the same. If you get an alpha from U-238, the energy of that alpha is always the same. There are some isotopes that can decay in different modes; yet even so, the emission spectrum is always discrete, like the light from a laser, rather than continuous, like a light bulb. If you know where an alpha particle came from, you know its energy.

Beta decay isn’t like that. The spectrum of electron energies from beta decay is more like the spectrum from an incandescent bulb. There’s an upper limit, but between that limit and zero, the electrons take on all sorts of values.

This bothered scientists when they discovered it. Why should beta decay have this strange property? Where did the extra energy go (or, alternatively, where did it come from)? Given this evidence, some scientists were prepared to give up the conservation of energy.

A desperate alternative was tried instead. Perhaps, it was suggested, an invisible, electrically neutral, non-reactive particle came flying out of beta decay along with the electron. This invisible particle could carry that extra energy. Voila! The conservation of energy was saved!

Enrico Fermi named the particle “neutrino”, Italian for “little neutral one.” Cute.

It seemed like a trick, fixing the books. We can’t find the extra energy? Fine, we’ll just make up a story. Here it is, in a place we can never find it. Quite convenient, and also not very scientific.

So things stood for decades. Physicists had a neat solution, but also a big problem. Where was the evidence for the neutrino? There was none. The calculated properties of the neutrino meant that a single particle would, on average, travel through several light years of solid material before interacting. Hence the 60 billion through your thumb every second. Even if you’re exceptionally odd, your thumb is nowhere near as thick as a light year, so you have little chance of stopping any particular neutrino.

Ah, but the power of large numbers means that with lots and lots of neutrinos, occasionally a few will do something unusual. Just as the average U-238 atom will last 4.5 billion years, but some are always defying the odds and decaying anyway, a few neutrinos will also defy the odds and get absorbed, even in relatively small amounts of matter.

But how do you know that you’ve caught a neutrino?

In 1955, two scientists named Fred Reines and Clyde Cowan decided to try it. They filled a tank with cadmium chloride and surrounded the tank with detectors. They were looking for two gamma rays flying away in opposite directions. This would indicate that an electron and positron had been annihilated. And that would mean that a proton had just absorbed a neutrino, in the process shooting off a positron and turning itself into a neutron.

The details aren’t that important, though they are fascinating and maybe I’ll write about them later. The important point is that Reines and Cowan found the neutrino. It was really there!

This is astonishing. First, scientists noticed something that they didn’t expect – the continuous spectrum of beta decay. The observation violated one of the physicists’ most cherished ideas, the conservation of energy. To fix it, they created out of wholecloth this invisible particle with virtually no properties. But then, their patch turned out to be a real thing! This, to me, shows that physics has in some sense found out something true about the universe.

Science isn’t just observation and classification. As this example shows, science can actually touch on something we might call truth. The neutrinos point the way. The truth is out there. Think about that next time you gnaw on your thumbnail.

Non-Overlapping Magisteria

This has been gnawing on me ever since the Templeton Lecture at COSI. Today I was reminded of it again by a brilliant piece on YouTube by Feynman.

http://www.youtube.com/watch?v=zeCHiUe1et0

And then I read again the essay by Gould on Non-Overlapping Magisteria.

 I adore Stephen Jay Gould. He and I share many things (besides a first name) – a passion for baseball and It’s a Wonderful Life, a love of quirky history, and a commitment to the idea that evolution isn’t just true, but marvelously pointless, that the real message of evolution isn’t survival of the fittest, but rather unrepeatable contingency. Gould taught me evolutionary biology, afternoons in the school library reading his marvelous essays. Certainly he taught me far more than my creationist 10th grade biology teacher ever did. When Gould died, it affected me, just as Carl Sagan’s early death affected me. (I remember the day Feynman died, because my quantum mechanics professor talked about it in class, talked about how Feynman had touched his life and career, but I didn’t really know of Feynman at the time. Now I look back and realize that death was the greatest loss of these three great losses.)

Gould’s NOMA essay, and the longer work Rock of Ages on the same topic, both hurt me. When I read them, I felt like Gould was not being honest, either with himself or with the world at large, and I didn’t understand why. It was like discovering that a long-trusted friend was actually stealing money, or was a Baltimore Ravens fan.

The idea of NOMA sounds so PC, so reasonably middle ground on its face. But when you dig into it, as you might a pretty, fluffy dessert, you discover there’s nothing there. NOMA suggests that both science and religion respect one another’s boundaries, that they deal with separate realms and that therefore one has nothing to say about the other.

Balderdash.

Science cannot be bound. Science must be free to investigate all things. Perhaps there are some things that science can never know. But we won’t know that until we investigate! Starting out with a blanket prohibition is out of bounds. And for NOMA to have any meaning, it must create these prohibitions.

For instance, in the essay Gould quotes the pope as saying that science can’t speak to the ensoulment of humans. Why? What does “ensoulment” mean? If it means any change, any change at all, then it becomes the object of scientific exploration. Is there any evidence for humans having a soul? Some would point to a moral sense. Fine. A moral sense is a physical manifestation. We can investigate it. We can determine if any rudimentary moral sense exists in animals. We can find out if a moral sense, via reciprocal altruism, might have had survival value to early humans and pre-humans. We can investigate what’s going on in the brain when we think about morality.

The point isn’t that science will find the answers; the point is that science can, will, and must look for these answers. Prohibiting such a search violates NOMA right off the bat. But any such prohibition is out of bounds, not just this one. The beginning of life, the “cause” of the Big Bang, and the eventual fate of the universe are all examples of fields that religion might be tempted to claim. Religion can’t have them. Science must be free to roam.

What we’re left with, then, is a religion with nothing left to do. If by definition it can’t affect the natural world, then what’s left? Of what possible consequence could it be to the actual world?

Suppose someone says they’ve received a message from God. That message must have been received by something in the body, a single neuron, perhaps. Science can investigate that neuron, find out what exactly happened at the moment the message was received. Was it electromagnetic? A gravity wave? A neutrino pulse? What? If it was nothing, then it couldn’t have affected the neuron, because the neuron is a physical object in the universe, and the thoughts it engenders are real, physical things. If it was something, then scientists could (in theory, at least) investigate the source of the signal. Perhaps they’d trace it to an ancient planet circling a faraway star in Pisces. Or maybe not. The point is, they could investigate the claim, and that makes it a scientific question.

The only way NOMA works is if religion completely folds, surrenders all territory with absolutely no resistance, admits to no affect whatever on the natural world.

And if that happens, we have to be courageous and ask the next question. What good is it?

 

Negative Entropy – a great blog!

I’ve been reading an interesting blog by three local skeptics. They posted a fantastic review of the evolution discussion (better than mine), and they’ve got lots of other fun and thought-provoking things to read there, too. Enjoy.

http://negativentropy.blogspot.com/

Uncertainty

Back in my sophomore year at college, I saw one of the most beautiful things I’d ever seen.

It was an equation on the blackboard in my quantum mechanics class.

Yes, you’re right. I was popular with the ladies.

My professor, Dr. Bill Reay, showed the class that day exactly where the uncertainty principle comes from. It wasn’t how Heisenberg derived it, but it was a beautiful derivation based on two things: one, classical wave mechanics; and two, the crazy idea that electrons can behave as waves.

As soon as that idea is unleashed on the world, uncertainty comes along automatically. It is amazing in its beauty and simplicity. I wrote about it once before, but I want to try again.

First imagine an electron as a wave. What in the world does that mean? Well, an electron as a particle would occupy one discreet place in space. It is there absolutely, and is absolutely nowhere else.

If you give an electron wave properties, it still has to behave like an electron. Electrons are generally one place and not another. Sort of. Think of an electron as a “wave pulse.” Here’s a picture.

The key thing to realize is that the electron is mostly still in one general place. The line (which could represent space as easily as time) stretches off to infinity in both directions pretty much on zero. So there’s (pretty much) no electron back there <– or up there –>, only in the middle is there a good chance of finding the electron.

Now that the electron is a wave, though, some strange things start to happen. We make the wave pulse by adding up lots of waves together. This is called superposition. The superimposed waves essentially cancel everywhere except in the general area where the electron is. But each of these superimposed waves has a slightly different wavelength. It’s the difference in wavelength that causes the canceling, and that wavelength difference gives us a range of uncertainty about the electron.

Suppose we make that wavelength difference smaller. What happens to our wave pulse? It spreads out! We’re less certain of the location of the electron if we know its wavelength better. Suppose we make the wavelength difference greater? Now we can locate the electron better, but we know much less about its wavelength. These two variables, position and wavelength (and for an electron, wavelength matches up with momentum), are like silly putty. If you squash it one way, it comes squirting out somewhere else. There’s an inherent uncertainty in an electron (and any other particle-wave) that you just can’t get rid of. That’s the uncertainty principle!

This is to me the beauty and wonder of quantum mechanics. It is exactly classical mechanics, with this one, historical, bizarre idea. Particles have a wavelength! Once you get that, all the weirdness of quantum mechanics, living/dead cats, quantum entanglement, the double slit experiment, all of it, comes along for free. From just one weird thought. Now THAT is beautiful.

A Good Answer

At a recent discussion of faith and evolution, I was all prepared to ask my favorite question. Then something I never expected happened. One of the panelists, Dr. Francisco Ayala, answered the question I was about to ask, and it was a good answer.

Here’s the question. Gorillas (Dr. Ayala used baboons, but I prefer gorillas because they have something of a reputation these days of being gentle giants) are infanticidal. When a male gorilla takes over a troop, the first thing he does is go around to all the nursing mothers, rip the babies from their mothers’ arms, and kill them. This is a sensible thing for the male to do from a natural selection standpoint. It sends the mothers into estrus so that he may mate with them and produce his own offspring, and of course it eliminates potential competitors who are not carrying his genes. So if you decide that “evolution is how God did it,” aren’t you giving God some pretty nasty attributes?

The reason I ask this question is perhaps a devious one.

Eugenie Scott, also on the panel, has an opposite view from mine. She stated that many times in her classes, when students learned what evolution was, they were pleasantly surprised. They’d always been told, Scott reported, that evolution meant you couldn’t believe in God. They were relieved that all evolution meant was that animals change over time.

I hold a different view. I’ve encountered many people who have no problem reconciling faith and evolution. That seems to be the popular, consensus-building, politically correct thing to do. Before last night I would have said it is misguided. I still think it is unnecessary, but Dr. Ayala’s statement made me see that, with careful (VERY careful) thought, it is possible to do so, if you really feel the need. But you have to do it just so.

Most people aren’t nearly as careful as Dr. Ayala. For most I’ve encountered, the reconciliation of faith and evolution comes from a misunderstanding of evolution. And so I feel it is important to point out just how cruel, arbitrary, and wasteful evolution is. Is the creator of this mess really the diety you want to worship? Look the natural world straight in the eye, realize that it not only has no need for a creator, but in fact shows absolutely no sign, not the slightest whiff of evidence of such a creator.  Instead, it looks at every step exactly like a universe without a plan.

The alternative, I think, is dangerous. It leads to magical thinking. It leads to the idea that Mother Earth will provide. It leads to the thought that the universe would never be designed so poorly that we could be wiped out by an asteroid, or a giant volcano. It leads to the crazy idea that parents should be allowed to deny their children medical care because of religious belief. It leads to the idea that there’s some plan. But what if the only plan is the one we make ourselves?

OK, so what was Dr. Ayala’s answer. He brought up the example of babboons committing infanticide. He asked, “How could God condone such behavior?” His answer was that babboons and all other animals are not moral agents. Humans are moral agents. God gave us that, and made us different from all other animals.

It’s an interesting argument, but I don’t buy it. In some societies it is considered just fine to kill baby girls. Many cultures have practiced genocide against their neighbors. We humans have done some thoroughly nasty things.

Once again, religion has an answer. The Fall from Grace, the need for salvation. Just as with Dr. Ayala, yes, you can make the argument, but why? Why go to all the trouble and effort, to in the end get to a place where all you can say is that you believe in something for which there is (and can be) absolutely no evidence?

Science can’t disprove the existence of God. I’ll say it again. Science can’t disprove the existence of God. God could very well exist, and science could never touch her. If she can take any form you want, have any set of attributes you choose, then there’s nothing science can do to show she isn’t there. But what good is that?

The fact that I have to ask, I guess, shows that I just don’t get it.

Here’s my problem. I don’t have many skills. I’m not particularly good at math, I’m certainly not athletic, and I’m hopeless trying to fix anything. The one thing I can do is remember. In particular, I remember exactly what it was like to be eight years old. (In fact, I rather suspect that I’m still eight and that this is all just a dream from which I’ll wake up any moment now. OK, not yet.)

When I was eight, I was saved. I grew up in a family of southern baptists. One day in church, I got up and went to the altar to get saved. It felt good. But even then, deep inside, I knew. There was part of me, that deep spark inside that is the same spark I still have now, that said, “Come on! You know better than this. You know this is isn’t the way the world works. You know there’s nothing there.”

I fought it off for a while. I tried to convince myself, but deep inside I still knew. I remember so vividly the feeling, knowing that I didn’t really believe. Finally I gave up, let myself be myself.

So here’s the thing. I could go through all the arguments, I suppose. I could convince myself that, despite all the evidence that the universe is an unplanned mess, there really is a well-hidden designer running the cogs. But I still wouldn’t really believe it. And isn’t that what belief means?

A Request

Chapter Two

Madame Eve Dalrymple stood before the most distinguished men of science, prepared to demonstrate absolute proof that atoms could be taken apart. Behind her, stretched out on a long, crowded experimental table, lay her apparatus, a gleaming monster of glass and gutta percha. She spoke.

“Gentlemen,” and a snigger escaped from the crowd. Eve paused, then went on. “Gentlemen, today I reveal to you a true wonder. We call it the electron.”

Eve stepped behind her table, pushed a lock of dark hair behind her ear, and electrified the vacuum pump. A hiss of sparks jumped from the metal clips, then the pump rattled and chugged to life. Eve connected the high-voltage transformer to the crystal-clear glass tube. Gradually, in the darkness, a blue-white glow, like some strange writhing snake, appeared within the glass.

“All the great thinkers in history,” Eve went on over the gasps and calls from the audience, “have considered the atom to be the indivisible particle, the primordial element from which all else is built. But within this simple glass tube fly particles thousands of times smaller than the atom itself. We—“ and with a hiss of air, the glow vanished. The vacuum pump continued for a moment, grew louder, then shut off with a metallic clank. Eve rushed behind the table to assess the damage. Bad, but repairable, she decided quickly.

“There will be a delay, gentlemen . . .” she began. A short while later–or what she thought was a short while–Eve looked up. Her workshop was empty. The dozen or so town boys who had come to watch her latest demonstration had vanished, off to catch frogs or play a game of baseball before supper.

Eve stood alone in her empty workshop. Really it was only the back room of her father’s livery building. The shelves and cabinets she had scavenged or built for herself lay filled with the results of Eve’s constant tinkering. The smells of ozone and axle grease filled the air.

Eve knew the boys hadn’t come so much to learn as to stare at this strange creature, a girl who could fix things and “do magic” as they called it. Well, it was magic, at least to her. Eighteen years old that spring and leaving for University in just weeks, Eve Dalrymple had found her passion and joy in the study of modern science. She followed with breathless wonder the latest discoveries –Roentgen and his x-rays, Becquerel with his mysterious uranium, the great JJ Thomson’s electron –and she dreamed of being part of it. Someday, she thought. Someday soon.

Eve returned to her repairs. She knew the boys would be back.

*    *    *    *    *   

The blue-white snake Eve Dalrymple created in her laboratory is called plasma. It is sometimes called “the fourth state of matter,” but this is silly for a number of reasons. Most importantly, plasma was not only the first kind of matter formed in the universe, it remains today the universe’s most common form of ordinary (not dark*) matter.

*We still have no idea what dark matter is, but it almost certainly isn’t plasma.

Protons and electrons are different. No one knows why. But the fact of their difference is what makes the world possible. Protons are found in the nucleus, a spot so small that if the atom were the size of a baseball field, the nucleus would be a ladybug crawling in the grass just behind the pitcher’s mound. The nucleus is much, much smaller than the atom.

All around the bases of our baseball field atom are the electrons, tiny bits of fluff that have (compared to the nucleus) practically no mass, but the same electric charge as the proton. This equal charge but wildly unequal mass makes all the difference. Electrons are free spirits. They won’t stay in the nucleus even if you try to attach one of those police collars. They fly all over, hang out at the outskirts of the atom. And that’s what made Eve’s snake.

When Eve electrified the tiny bit of gas in her tube, electrons flew through, knocked loose other electrons with a powerful, energy-giving jolt, and thereby created a plasma. That plasma, a soup of free electrons and positively-charged atoms missing one or more electrons, started to glow as electrons fell back into their atoms, releasing their stored energy as visible (and also invisible) light. You do the same thing every time you flip on a fluorescent bulb. That’s right, you are a destroyer (and creator) of atoms!

The plasma inside a bulb is peanuts compared with the much more common plasma found in the Sun and other stars. Here not just a few electrons, but essentially all the electrons are stripped off, creating a wild party of free electrons and bare, positively charged nuclei. The nuclei fly about frantically, heated to ridiculous temperatures, repelled on all sides by similar bare nuclei with fierce and concentrated positive charge.

Occasionally two of these nuclei find themselves on a collision course. They do everything they can to avoid one another, pushing back with all their might with their two bare positive charges. But it’s no good. The heat is so great that the two nuclei collide and (maybe, if things are just right) stick. Three such collisions can fuse hydrogen into helium. The star has turned on. Thermonuclear fusion has released energy as for hydrogen nuclei stick to make one helium nucleus. Add up all the masses of what went in and what came out, and you find that a little mass is missing in your equation. Where did it go? You’re using that mass right now. Every time you blink, or move a finger, or even think a thought, you’re using energy that began deep inside the Sun, energy that came from the Sun burning up a little of its mass. Mass is just concentrated energy. Energy is mass set free.

PS This little piece on plasma was requested by a colleague and fellow blogger. There you go, Doug. Is that chicken soup enough?

By the way, the beginning of this entry is from a (so far unpublished) book I’ve written called “Atoms and Eve.” If there are any publishers out there, I’m still looking . . . Oh, and DON’T go to the Amazon page for my first book and look at the sales rank. ‘K?

Spinning Through Space-Time

Spinning Through Space-Time

What does an old-fashioned amusement park ride have to do with space and time? Plenty! Climb aboard the Rotor for a mind-blowing adventure with three of the world’s greatest scientists – Ike, Ernie, and Al – to find out for yourself.

The Rotor is a ride you either love, or would love to forget. Just last year you had an unfortunate incident involving this attraction and a plate of cheese fries. But this time will be different – you hope. Inside the Rotor, a round floor is edged by a roughly-padded wall. As you, Ike, Ernie, and Al press your backs against that wall, the whole contraption starts to spin. You feel yourself pinned against the padding and, faster than you can say “lose my cookies,” the floor falls out from under you. Instead of dropping along with it, though, you find yourself stuck, like a fly on paper, to the wall behind. Faster and faster the Rotor spins, pressing you deeper into the padding. Will the madness never end?

“I don’t get this,” you say above the whine of the motor, “Why aren’t we falling?”

“It is friction,” shouts out Al, a kind-looking man with wild hair and a woolen sweater.

“Yes,” agrees Ernie, his voice traveling through his rough beard, not surprisingly, at Mach one (the speed of sound), “You provide the outward force, the wall responds with an inward force, and the roughness of the wall provides an upward force to keep you in place.”

“But,” replies Ike, a disagreeable sort wearing, of all things, a powder-white wig, “the deeper question is this: why do we feel ourselves pressed to the wall at all?”

Al and Ernie both groan. Either they’ve heard this before, or they’re feeling their lunch of bratwurst and sauerkraut. As your own stomach churns, Ike expositates on the nature of rotation. “Objects in motion tend to stay in motion in a straight line,” he recites, “Only a force, such as that supplied by the wall of our spinning cylinder, can change straight-line motion into curved motion. To do this, the wall must push on us, otherwise we’d continue in straight line motion, traveling past the cylinder until we finally splatter on the midway beyond,” he declares with a slightly evil grin.

“But suppose,” Ike goes on, “that not just our cylinder, but the ground below, and in fact the entire Universe, were spinning along with us. I submit that we would still feel the force of the wall. We spin, not relative to any outside object, but relative to Absolute Space itself!”

“No,” Ernie breaks in, “this is not correct. We cannot measure absolute space, so we cannot claim it exists. The Rotor must spin in relation to real objects. If the ground below were to spin with the Rotor, then the Rotor’s motion could be compared to more distant objects, such as the distant stars.”

“Are you suggesting,” Ike replies with a sneer, “that in a totally empty Universe, a Universe containing only us and this infernal spinning cylinder, we would not be pressed against said wall, but rather would float alongside as if it were motionless?”

“Precisely,” says Ernie. “Consider: in an empty Universe, how could one judge that the Rotor is spinning? There are no outside landmarks: no coney stand, no Matterhorn, no Dunk the Clown and Win a Prize. Not even the distant stars could serve as markers, for in this scenario they no longer exist. In a totally empty Universe, there is no difference between a still Rotor and one that is spinning madly. In such a Universe, we would not be pressed to the wall, but instead float alongside it, exactly as if we and the Rotor were motionless.”

“That is ludicrous,” spits out Ike, “How could the faraway stars affect events here and now?”

“And I,” replies Ernie, “might ask how one can base a scientific theory on something, such as your Absolute Space, that by definition cannot be measured?”

“Ah,” says Al, speaking finally, as a young child at last finding his voice, “but you forget, Ernie, that the Rotor exists not just in space, but in time, as well. When we combine our ideas of time and space, we see that the Rotor is spinning with respect to something: it spins with respect to its own past self!” The kindly eyes blaze with passion as Al reaches a crescendo, and you are certain he must be right. He goes on.

“We move through time always, in a straight line from then to now. When we move through space, we affect this motion through time. However, as long as our space motion does not change, in either speed or direction, we feel no force, because our path, not in space, not in time, but in space-time, remains a straight line.

Now, if we speed up, slow down, or change direction in space, we feel a pressing against ourselves. This is because we have changed our path through space-time from a straight line to one that is curved.

Al continues. “Imagine, as Ernie suggests, that we and the Rotor are alone in the Universe. Suppose it moves, without spinning, in a straight line at a single speed through space. No experiment we can do will reveal this motion to us. Why? Because in space-time this motion is no different from not moving at all. Both trace straight line paths. But if the Rotor spins, its motion through space-time is distinguishable, even in an otherwise empty Universe. The path traced by the spinning Rotor, and by those riding within, is not a straight path, but a curve. It is for this reason that, even in an otherwise empty Universe, we still feel the pressing of the Rotor walls against us. We move, not relative to the imaginary entity called Absolute Space, but relative to our own normally straight-line paths through space-time!”

The motor’s whine diminishes, and the Rotor slows. You and the three scientists slide down the wall until your feet gently touch the floor. Your head spinning in more ways than one, you forget all about your churning stomach and race your three new friends to the bumper cars.

Unreciprocated giddiness

Math makes me giddy. It’s not an easy feeling to translate.

I was recently trying to help a student with what I thought was a fun and interesting math exercise. Here it is: What is the weight in tons of $1 billion in $100 bills?

Just because it’s fun, let’s go through the solution.

OK, I just lost almost everyone. If you’re still reading, $1 billion in $100 bills is 10 million bills. Around 6 bills would cover a sheet of copy paper, and 100 sheets weigh 1 pound. (And of course 2000 pounds is 1 ton.) We’ve now got all the information to turn bills into tons, just by lining everything up and canceling the units. I find it beautiful and amazing. It makes me giddy.

So we’ve got (10,000,000 bills/1) x (1 sheet/6 bills) x (1 pound /100 sheets) x (1 ton/2 x 1000 pounds).

Five of the zeroes cancel, so we’re left with 100/(6 x2) tons = 50/6 = 25/3 = 8 1/3 tons = wow that’s a lot of lifting. It makes the whole idea of stealing a billion dollars in $100 bills look pretty near impossible unless you’ve got a dump truck. And that’s pretty cool.

My learner didn’t think so. To her this was painful, boring, totally pointless. When teachers try to make an exercise like this fun, they almost always fail with almost all their learners. I did a similar activity with high school students once, convincing myself that they were actually getting this beautiful and incredibly useful idea of unit cancellation. Later I found out they were passing the answers around the class for all to copy.

Kids are smart. They know the game. They know it’s more important to you than it is to them, and they’ll use that against you. If you can’t catch them somehow, get them to feel giddy, too, they just won’t learn.

It’s kinda lonely, getting giddy about math.