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I was a judge for my daughter’s science fair tonight. I have been asked many, many times to judge science fairs, and I’ve successfully dodged all but (now) two requests. This time I was captured by a desperate letter begging for more judges, and my own daughter’s plaintive cries that she really wanted me to do it. I finally said I would.

I don’t like judging science fairs. Now I know why.

First let me say that many of the kids worked really hard, lots of parents were involved with their kids’ activities, the teachers put in a lot of time and effort that frankly won’t help them get those test scores up, and so on. I’m in favor of all those things. So I don’t want to be too negative. Any time you spend supporting a kid (your kid, someone else’s kid, what have you) is valuable time. I applaud everyone for the effort.

Now that I’ve got that out of the way.

I always knew I didn’t like science fairs. Why? I was vague. There were a lot of possible reasons:

– the “scientific method” mantra and the fact that real science doesn’t work that way

– the competition aspect

– the arbitrariness of the judging

But now I know what I want to say about science fairs. I don’t like science fairs because they limit the wonder, and wonder must not be limited.

I used to think my biggest complaint was the fact that science fairs teach the scientific method – hypothesis, experiment, conclusion – and that real science rarely works that way. But that’s not really my complaint. My complaint is that I don’t think science education should be about teaching kids how to do science at all. It’s not the point, or at least it shouldn’t be. Most people will not become scientists. But everyone, everyone, can make science a part of their lives. How? By experiencing the wonder, the beauty, the joy of it.

In the same way, most arts students won’t become artists, but everyone can experience the wonder of putting color on paper, playing a musical instrument, or performing in a play. Why do we encourage students to do these things? Not as vocational education, surely, but because of the experience itself.

We do science in science class, quite frankly, because it’s fun, it’s wondrous, it’s exciting, it’s a little bit dangerous. It engages your senses, it makes you think, it makes you wonder.

If, as it must be seen whether this is the intention or not, the science fair is meant to serve as the pinnacle of the science experience, just as the spring musical is the pinnacle of the theater experience, the recital the pinnacle of the orchestra experience, and the senior show the pinnacle of the art experience, then the science fair falls far, far short. Why? Because it limits the wonder.

The wonder of science is in so many things. It is in the doing, but not the hypothesis-experiment-conclusion style of doing championed by the science fair. It is in using an amazing piece of equipment, creating some fascinating reaction, touching, seeing, feeling something you’ve never touched, seen, or felt before. It is the fun and the wonder of the act, not the funneling of that act into a result.

It is also in learning what is already known, uncovering the wonders of our world, and learning how clever people uncovered those wonders through the use of their unlimited imaginations and unparallelled ingenuity. It is finally, I believe most deeply, in the connections between these two things. How can the things I do with my own hands link me to amazing discoveries and wondrous events?

Instead of hypothesis-experiment-conclusion science fairs, I propose a science festival, in which students are encouraged to study those things they find most interesting. Perhaps a report on the life of Charles Darwin is coupled with the extraction of DNA. Perhaps a demonstration of a powerful and thrilling chemical reaction could be coupled with research into the atomic theory of matter, and the scientists who first journeyed into that fantastic realm.

Some students might be most interested in applying the laws of science to invent something new. Others might prefer to study how scientific ideas have changed over time. Still others might practice the quiet science of observation – backyard wildlife, the sky at night, the colors of the sunset.

Perhaps all these things make science fairs impossible to judge. To that I say, they’re impossible to judge now!  Putting a subjective judgment on a 1 to 5 scale does not make it objective! But I also say, so what if the judging becomes impossible? Better than judging, always, is mentoring, talking, discussing with a student what she’s learned, what she still doesnt know, what she’s gained and what she wants to know next. These discussions are where the real gold lies, not in the trophy or the medal awarded at the end.

Make the science fair a science festival. Let all scientific interests be reflected. Open the doors for wonder. That I will judge, and without the begging.

I love my life. I love watching my children grow, walking hand-in-hand with my wife, listening to the sound of the waves against a sandy beach, feeling the warmth of the sun and smelling the freshly-opened flowers on a perfect spring day.

I love reading about the world around us and the ways that men and women, using their ingenuity and imaginations, have discovered how it works. I love watching the beauty of a well-played baseball game. And of course I love teaching.

On this eve of Darwin Day, I find myself reflecting on how much of the wonder of life springs directly from 1) understanding the lessons that Darwin has taught us and 2) utterly ignoring them.

This is so often misunderstood by Darwin haters. Darwin’s view of the world, they feel, is bleak, without purpose or deeper meaning. In some ways they’re exactly right. But what they miss is that it isn’t what Darwin discovered that matters, but that he, as a representative of the human species, was able to discover it at all.

In a Darwinian world view, the currency is offspring. The more offspring you have, and the more resources you can give them, the more successful you are. And that’s it. Really. But most of us don’t live this way. Most of us have discovered that the path to a good life inevitably involves fooling our genes. Something strange happened to human beings during our evolution, something that (as far as we know) has not really revealed itself in any other living species. We humans have discovered a way to trick evolution. Consider this list:

birth control

artificial sweeteners

organized sports




public education



art museums

salt substitute

the library

I could keep the list going for a very long time. The point is, most of our everyday actions are not aimed at propogating our genes, which is the only currency in Darwinism that makes any sense. We’ve awakened in this universe, a place we’ve entered (so far as we can tell) totally by accident, and we’ve found it to be full of wonder. We’ve found ourselves with these marvelous brains, and we’ve found that – if we do it just right – we can sometimes spread the ideas our brains concoct even more efficiently than we can spread our own genes.

We write books. We paint. We sculpt. We perform plays. All this with the goal of showing something of ourselves, having others find value in that piece of us, take it up and incorporate it into what makes them. We’ve circumvented the genetic need to reproduce and, in many ways, replaced it with an intellectual need to spread our thoughts.

But it’s more than that. We’ve also discovered joy. The joy of a sunset or a shooting star. The pleasure of playing a sport or singing a song. The wonder of watching atoms explode and molecules dance. The mystery of listening to a story while staring into a campfire. These things are internal. They make no difference to our ability or inability to reproduce our genes. Instead, they feed something inside us, a craving that sprang up, as far as we can tell, as an unintended consequence of those marvelous brains that so define our species.

Unlike Darwin’s co-discoverer of Natural Selection, Alfred Russell Wallace, I do not claim that the brain is so wonderful it cannot have been shaped by natural selection. I think it is certainly true that our brains (the one piece of our anatomy that truly distinguishes us) have helped humans successfully reproduce. I think the brain is primarily a sexual organ, and I think it is certainly true that art, literature, even (despite the stereotype) science can be and has been used to aid the  performer in obtaining a mate. But I think the brain is so complex, is such a case of runaway evolution, that unintended consequences were inevitable. And, I argue, it is precisely those unintended consequences, the ability to both create and appreciate a beautiful sonata, a beautiful painting, and a beautiful scientific theory, that make life worth living.

Happy Darwin Day everyone, and enjoy your unintended consequences!

I have to be honest. Of all 13 episodes of Cosmos, this may be my least favorite. I loved the story of Milton Humason, but so much time on the cosmology of India seemed to me unnecessary, as if Sagan couldn’t think of anything else to say. But he recovers nicely in the final three episodes, so I guess it’s ok to let this one partial clunker slide.

One section of the episode, besides the Humason biography, that I very much enjoyed was the description of how the Doppler shift is used in cosmology. To me this is Sagan at his best, using his narrative as an excuse to teach an exciting science idea. The Doppler shift is not only an interesting effect that shows the deep analogies to be made between sound waves and light waves, but it is also an example of human ingenuity. The tiny clue to be found in the shifting of dark spectral lines, like the tiny clues provided by the spectral lines themselves in discovering the makeup of the stars, reveals so much when human beings put that clue to work.

I think the thing that makes science teaching unique, special, and worthwhile is the way it can link to our everyday lives. We are all of us surrounded by the mystery of the cosmos every day. For instance, everyone has had the experience of flipping on and off a light switch. You flip the switch up, the light comes on. You flip the switch down, the light goes off. But therein lies a deep mystery.

If you look inside any switch, you find wire connected to metal. When the two separate pieces of metal join, electric current flows and the light comes on. When the two pieces are pulled apart, the electric current stops and the light goes off. But the connection between the pieces of metal is a problem.

Most metal, such as the copper of many electrical connections, is covered with a layer of oxidation. This layer is not good at conducting electricity. And yet electric current can flow through this layer. Why? Because of a bizarre effect known as quantum tunnelling. On a macroscopic scale, we’d be very surprised if, while pounding a hammer against a wall, our hammer suddenly disappeared and rematerialized on the other side. It is possible, but highly unlikely. On an atomic scale, however, such things happen quite often, and it is exactly this sort of tunnelling that allows a switch to turn on. Electrons tunnelling through the non-conducting oxidizing layer and appearing on the other side are precisely the electrons that cause the switch to turn on and off.

Why can electrons do this? Because, unlike hammers, electrons are so tiny and so relatively energetic that their wavelengths are much larger than their particulate sizes. A hammer’s wavelength at ordinary speeds is so tiny that for all practical purposes the hammer is the size of, well  a hammer. But an electron, with a wavelength much larger than its own pinpoint size, is like a cloud of probability. And every once in a while, quite by accident, the electron finds itself in a part of the cloud that allows it to jump over an apparently impassible gap, such as the gap between two pieces of metal in an ordinary light switch.

The Doppler effect is at work every time we look into the night sky. Quantum tunnelling is responsible for every flip of a switch. The wonder and mystery of science is around us every day. We are all of us on the edge of forever.

Our local newspaper, The Columbus Dispatch, today has an article about local clergy who support evolutionary theory, seeing it as evidence of God at work in the world. (I would link to the article, but the Dispatch has become a pay site, so unless you subscribe you can’t read it.)

I cringe whenever I read this type of article.

It’s a great moral dilemma for me. We must teach gently. We must approach our learners with humility. We must never rise above. But we must also teach truth. And sometimes truth is hard.

When a male gorilla takes over a band from an aging silverback, the first thing the new alpha does is grab all the gorilla babies from their mothers and bash the infants’ heads against the nearest tree until they are dead. Lions also kill the babies when they take over a pride. This behavior is not unusual in the animal world. From the vantage point of Darwin, this action makes horrible good sense. The male gorilla must get his DNA into the next generation, and infanticide is the quickest and surest way. Those silverbacks who did not perform in this way didn’t pass their DNA on. The genes that cause (or at least encourage) this behavior have a selective advantage.

If one sees God in the beauty of a flower, in the elegance of a spiderweb, in the complexity of a rain forest, then surely one must also see God in the selective advantage provided by infanticide. Yet if a human being did such a thing, we would all condemn the murderer and demand justice, or at least protection. If you believe that evolution is “how God did it,” then if I am truly a corageous teacher I must ask you, gently, what do the cruelest aspects of evolution say about the nature of God?

It is a difficult puzzle for me, one I do not know how to solve. How do we teach gently, yet not shy away from unpleasant, jarring, important truths?

OK, OK, I know. There are lots and lots of proofs of the Pythagorean Theorem. (My favorite appears at the bottom of this entry, in case you want to skip to it.) I’m not trying to overthrow thousands of years of math here. I’m just wondering about something, and I’ve been unable to find any treatment of this particular problem. 

Suppose you’re walking along and come to an empty lot. You have to get from the northwest corner of the lot to the southeast corner of the lot. You could just walk all the way down the west side (side A), then walk all the way along the south side (side D). You’d find the total distance equals the length of side A plus the length of side D.empty-lot

We all know that to shorten your distance, you simply cut across the lot. H (the hypotenuse) does not equal A + D, but is always less than A + D.

But let’s suppose for just a minute that we don’t really know what it means to cut across. We don’t, in other words, understand diagonal.  Suppose you’ve got some strange condition where you can only move north-south and east-west, but nothing in between. Now you try to take a shortcut across the lot, but you get this:

shortcut-1Now if you add up your distance, you’ll find that it’s (more or less) 1/2 A + 1/2 D + 1/2 A + 1/2 D = A + D ! You didn’t do any better by cutting across the lot in this way.

OK, maybe if we do a little better. What about this zigzag path?

shortcut-2This path looks a lot more like the hypotenuse. In fact, you can make the zigzags arbitrarily small, maybe a million turns, or a billion, or any other ridiculous number you want. Your total distance traveled is still exactly A + D ! You haven’t done any better by taking the shortcut!

And yet, if you make even a small diagonal movement, you instantly see the benefit. Consider this path, in which you travel most of A, cut across the corner, then travel most of D. Your total distance will be less than A + D. betterSo what’s going on here? Clearly the hypotenuse is the best path, but I can’t approximate that hypotenuse, even a little, by using only north-south and east-west movements. What is this “diagonal” and why is it so powerful? Any thoughts?

OK, here’s the elegant proof of Pythagoras that I like, the one that Albert Einstein found on his own when as a boy he fell in love with what he called “holy geometry.”


The first thing to notice is that there are three three similar triangles in this picture. Why? Because:

1) similar triangles all have the same internal angles.

2) all triangles have the same internal angle measure (we know it’s 180 degrees, but that doesn’t matter – what matters is that all triangles have the same measure, whatever it is).

3) by 1 and 2, if two right triangles share an angle, then they have to be similar.

The three similar triangles are:

ABC, ACX, and CBX (notice that the order of the letters is crucial here, matching the appropriate angles).

In similar triangles, the ratios of the sides are equal. So the triangle CBX compared to the triangle ABC gives

a/x = c/a

Cross-multiplying gives a^2 = cx

The triangle ABC compared to the triangle ACX gives

c/b = b/(c – x)

Cross-multiply again and you get

b^2 = c^2 – cx

But we already know cx = a^2 from before, so now we have

b^2 = c^2 – a^2

Rearranging, we get the familiar

a^2 + b^2 = c^2

The Pythagorean Theorem! THAT is a beautiful bit of math.

It occurs to me that the proof depends on the very existence of triangles, and triangles only exist in a two-dimensional world. Somehow, the Pythagorean theorem emerges from the existence of two dimensions as opposed to one. I still don’t see how, but it’s interesting.

Here’s something else. If you made it through my light clock blog entry, you know that Special Relativity comes right out of the Pythagorean Theorem. The light clock is a two-dimensional argument, so it seems that even if we reduced our universe from three spacial dimensions to only two, Special Relativity would still work. Flatlander twins would still experience the paradox if one rocketed off in a two-dimensional spacecraft, then returned to find her twin aged and wrinkled (would flat creatures wrinkle?) But what isn’t clear to me is whether or not Special Relativity would apply in a one-dimensional universe, one in which everything existed on a line, since in such a universe, there are no shortcuts.

Anyway, if anyone has any thoughts on why the Pythagorean Theorem works, or if you’ve ever seen an analysis of this sort of north-south, east-west approach and why it fails, I’d love to hear about it.

If you’re hoping to read about Britney and Nicole, or Burt and Loni, or That Woman Who’s Famous But No One’s Sure Why, turn back now!

OK, if you’re still here, this is about Cosmos Episode Nine. This episode has to have my very favorite first line ever. “If you wish to make an apple pie from scratch, you must first create the universe.” Sagan then shows how the universe has evolved to its present state through the lives and deaths of the stars.

Science is all about making connections, finding simplifications. The periodic table, featured in this episode, is an elegant example of this idea. The fundamentals of the periodic table were understood before the structure was explained. There was obviously an elegant pattern hidden there, but what was the source of the pattern? The answer came when JJ Thomson, Ernest Rutherford, and James Chadwick, each a student of the one before, discovered, in turn, the electron, the proton, and the neutron. Those three particles, put together in various logical combinations, explained everything. “Chemistry,” Sagan says, “is just numbers.” A beautiful thought.

I love how Sagan links the evolution of the stars to our own existence here on Earth, and I turned to this topic many times in  my own book (shameless plug alert).

Sometimes, though, science teachers try to make connections that hide, rather than bring out, connections. I remember arguing with a college education professor that the evolution of stars (the main topic of this episode of Cosmos) is fundamentally different from the evolution of life. My argument, poorly formulated at the time, was that there was some fundamental difference between the chemical and physical changes happening in a star and the complex interactions of striving and struggling living things. I remember her saying, “Well, then, you don’t understand evolution,” and of course that got my ire up. I didn’t have the words then to explain what I meant, but I think I do now.

The fundamental difference is this: in the evolution of stars (like the evolution of planets, the evolution of the elements, etc.) why questions have exactly one answer. In the evolution of life, why questions have two answers.

For instance, if we ask why Betelgeuse is a red giant, the answer is that Betelgeuse has used up nearly all the hydrogen in its core. When the hydrogen ran low, the star started to collapse. This increased the temperature in the outer shell, causing hydrogen there to fuse into helium. This fusing hydrogen pushed the outer layers of the star out, bloating it hugely larger than before, and cooling off the now faraway surface so that the color of the star shifted toward the red. That’s the whole answer. It might be a complex answer, but it is the entire answer.

If we ask why an apple is red, on the other hand, we have two answers. One might be useful and important for one purpose, while the other is useful and important for another. An apple is red because it absorbs all colors but red – or it reflects a set of colors that when added together give red. If we wanted, we could isolate the pigments in the apple, discover the chemistry of those pigments, even reproduce them.


But if that’s the only answer we go after, we’re missing a big part of the story, perhaps the more interesting part (depending on just what we want to know.) Apples are red because trees evolved in a world in which animals can distinguish color. It is better for trees if animals eat their apples and take the seeds away to be “deposited” later somewhere else. Red apples tell us a lot about trees. Trees compete with nearby trees for light and water. Trees that can spread their seeds over large areas survive better than trees that deposit their seeds right near their trunks. Trees devote energy to apples, not to be nice to apple-hungry animals, but to spread their seeds, and so they want to advertise these juicy morsels using a color very different from the greens and browns that come from mere utility.

Red apples also tell us a lot about animals. If we were alien visitors to the Earth, and the first thing we saw was an apple tree, we could immediately deduce that there must be color-detecting, mobile organisms here that digest food and dispose of the leftover bits. We could know that not all living things on this planet harvest sunlight to make their food, but instead there is some level of parasitism on this planet. We could know that at least some plants have evolved to make use of those plant parasites (what we call animals) to help in their own reproduction. That’s a lot to know from just seeing a red apple hanging from a tree.

And that’s what I wish I’d said to my education professor. Yes, analogies are powerful, but sometimes differences are even more important and informative than similarities.

My first book, called The Turtle and the Universe, was published by Prometheus Books in July 2008. You can read about it by clicking on the link above.
My second book, Atoms and Eve, is available as an e-book at Barnes and Noble. Click the link above. You can download the free nook e-reader by clicking the link below.
February 2009
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A blog by Stephen Whitt

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