My daughter and I just went to see Particle Fever. What a lovely, well-done movie; emotional, exciting, filled with well-spoken scientists talking about their passion. By far my favorite part was near the end, when images of European cave paintings are superimposed with images of equations on a chalkboard.


Bear with me, because the metaphor is beautiful and deep. Our ancestors wanted to understand the world. They painted gorgeous, intricate, carefully considered images of the natural world as they saw it – horses, rhinos, lions. They were expressing a deep need to connect with this world into which we find ourselves thrown. They were the dragon hunters, the myth makers, the dreamers of dreams.


Today physicists scribble chalk on a chalkboard, or ink on paper, or electrons on a screen. But the goal is the same. They want to understand. They want to connect. They want to grasp something of what this world is. Not just for survival, but because they are driven by an urge, one they don’t understand and perhaps are not even aware of, to know. What’s under that rock? What’s in the next valley? What’s on the backside of the Moon? What is the world made of?

higgs decay

Some of the physicists in the movie expressed concern, even fear, that what they uncover might not be so beautiful, might lead in the end to disappointment. Nonsense. It isn’t the facts that matter. It’s that we, a stack of walking meat with senses that often mislead us and that at their best barely get us through the day, have nonetheless grasped something of how the universe works. We did that. People. The most significant phenomenon in the universe. We can understand.

Today’s particle physicists are the dragon hunters. They are the makers of myth. They go to that dark place Joseph Campbell talks about and pull the beast out into the light. I can’t wait to see what they discover next.

I’m often reminded of the importance of teaching gently – usually when I’m on the receiving end of less-than-gentle teaching myself. It makes me want to explain (gently, of course) why such teaching is so destructive, and to redouble my own efforts to teach gently myself.

I remember myself in far too much less-than-gentle teaching. Science teachers are trained from the crib to hate and detest that most evil of memes, the misconception. I’ve been just as evangelical as anyone else at times. But I see the world differently now. Misconceptions are models of the world, and all our models are imperfect. We are always at the beginning of infinity.

Think about what that means! It means that every time we teach, of necessity we teach misconceptions. They are unavoidable, because all our knowledge is filled with them. Every time we teach, we are helping our learners to create castles of the mind, structures that never before existed, structures that are as unique and individual as each of our learners. This act of creation, imperfect and messy, is to be celebrated.

And sure, much of learning involves un-learning our misconceptions (and replacing them with better misconceptions). This is as true for the Kindergartner as it is for the practicing physicist.

Science teaching (and maybe all teaching, I’ll have to give that one some more thought) is all about metaphor. We link the unknown to the known, we build on existing (imperfect) knowledge. Too often, I think, the fear of misconception prevents the exploration of metaphor. Too often, metaphors are loaded down with caveats and equivocations. If all teachers would embrace the fact that no matter what they teach they are teaching misconceptions, and if we imbued our learners with this knowledge, and a deep skepticism as well, think of how far we might go.

Embrace misconception! It is the path to even better misconception.

If you read my last post about light, you know that light of all kinds (visible and invisible) is produced when things with an electric charge (like electrons) are jiggled.

Today the science blogs and even the ordinary news websites are abuzz with the announcement that researchers with an experiment called BICEP2 (what a great name!) have detected gravitational waves in the microwave radiation left over from the Big Bang. Deep, exciting, but still somewhat preliminary, this is a discovery worth watching. It could settle once and for all whether cosmic inflation really happened and may even give us insight into whether or not we live in a multiverse. So what in the world are gravitational waves, and what, if anything, do they have to do with light?

Jiggling electric charge produces electromagnetic waves (radio light, visible light, x-ray light, and so on). Is there such a thing as “gravitational charge”? Yes there is. We call it mass. But since all matter particles have mass, they all possess this “charge.”

We notice gravity every day when we stand up, jump, or try to keep our meatballs from rolling off our plate. Mmm, meatballs. This is because we live on Earth, and Earth has a lot of mass. But everything, not just things with a lot of mass, produces a gravitational pull. It’s just that, for most things, the pull of gravity is incredibly small.

Yet even this small pull has been measured. In 1797-98, English scientist Henry Cavendish measured the gravitational force between two heavy balls. His experiment was so sensitive that Cavendish had to observe it from far away, ensuring that his own movements wouldn’t disturb the delicate equipment. A telescope focused on the apparatus led out of Cavendish’s basement laboratory and to the enraptured scientist stationed far away. He watched as the two balls oh so delicately pulled toward one another. Cavendish had just measured the strength of gravity.

A modern version of Cavendish's experiment, using a light source and a mirror to measure the gravitational pull.

A modern version of Cavendish’s experiment, using a light source and a mirror to measure the gravitational pull between the larger balls, M, and the smaller, m.

Cavendish’s experiment helped us know the value of the gravitational constant, G, that appears in Newton’s equation for gravity. G plays the same role in Newton’s gravity equation that εand µplay in the equations for electric and magnetic fields.

\ F_C = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}


F = G \frac{m_1 m_2}{r^2}\

Just as Maxwell’s manipulations showed that electromagnetic waves (i.e. light, both invisible and visible) moved through space with a particular speed c, Albert Einstein’s work with gravity showed that it, too, moved through space with a particular speed. What is that speed? Amazingly, it is that same value c, the speed of light (and, as it turns out, gravitational waves). Einstein’s work showed that, just as jiggling an electron up and down produced electromagnetic waves, jiggling any massive object up and down produces gravitational waves. The catch is that gravitational waves are so incredibly weak that they are extremely difficult to detect.

While the BICEP2 data is not what most scientists would call a direct detection of gravitational waves, it is (if it holds up) excellent evidence for their existence. However, despite what some web stories are claiming, this is not the first indirect gravitational wave detection in history. In 1974, Joseph Taylor and Russell Hulse, using data collected from the Arecibo radio telescope in Puerto Rico, found two neutron stars traveling about one another in tight, fast orbits. These neutron stars are so massive, and are orbiting so quickly, that they produce copious gravitational waves.

The diagram shows how the two neutron stars in the Taylor-Hulse system lose energy to gravitational radiation as they orbit one another.

The diagram shows how the two neutron stars in the Taylor-Hulse system lose energy to gravitational radiation as they orbit one another.

Just like light waves, gravitational waves carry away energy. That energy has to come from somewhere; Einstein’s theory showed that the energy for gravitational waves produced by two such orbiting bodies must come from their orbital energy, causing the bodies to move toward one another and spin even faster (a bit like water getting faster as it spins down a drain). Taylor and Hulse were able to measure this changing rotation rate, and it matched Einstein’s prediction beautifully. While they hadn’t detected gravitational waves directly, Taylor and Hulse had shown that the orbiting neutron stars behaved exactly as if gravitational waves were real.

The lovely and impressive Arecibo radio telescope, where Hulse and Taylor made their observations.

The lovely and impressive Arecibo radio telescope, where Hulse and Taylor made their observations.

There’s a beautiful symmetry between the behavior of electromagnetic waves and gravitational waves. Both are, in an important way, properties of the fabric of spacetime – both are something the universe does. Both move at a particular speed, c. Both come in “colors” determined by their frequency. And, crucially, both give us a window to understand the universe.

When new kinds of electromagnetic waves beyond visible light were discovered, they revolutionized our understanding. Radio light, infrared light, ultraviolet light, x-ray light, and gamma ray light all gave us new insights when they were collected from the sky, including discoveries of pulsars (neutron stars), quasars, black holes, gamma ray bursts, and the cosmic microwave radiation itself. If and when we’re able to not just infer but in fact detect and study gravitational waves, we’ll have an entirely new way of “seeing” the universe. Who knows what discoveries await?

Light is something the universe does.


I wanted to use that statement in an article I wrote a long time ago, but the editor didn’t allow it. What ever could I have meant by such an odd statement? Just this.

Light is ubiquitous. We know what happens when we enter a dark room and flip on a light switch. Suddenly (and it does seem to be sudden) objects in the room become visible. A flashlight can do something similar, and we can even direct the beam of the flashlight at particular objects and not at others.

I remember being puzzled by the car’s rearview mirror. I’d ask an adult what the mirror was for and learn that it gave a view behind and outside the car. Not from my vantage point, though. Apparently the light entering another’s eyes could be different than the light entering my own.

I also remember standing outside on a warm summer day, feeling the heat of the Sun on my face, my hands, my back. Light bulbs that had been on were hot to the touch, and a crayon positioned under a lamp would melt into a waxy puddle. Light could do things.

But what was it?

Another early memory is of my dad building for me an electromagnet from a battery and some wire. Pressing on the wire over the battery brought the wire into contact with the button at the top, completing the circuit and allowing the whole thing to pick up paper clips, screws, and so on. How was it that completing a circuit could turn wire and a battery into a magnet?

What I didn’t know was that every time I completed that circuit, I was sending electrons streaming along the wire, and those electrons were sniffing out the space all around. The way that electrons sniff involves spreading electric (if the electrons are still) or both electric and magnetic (if the electrons are moving) fields, and the ability to sniff in a particular medium (air, say, or water, or rubber, or anything else in the space) is called the permittivity (for electric fields) or permeability (for magnetic fields) of the medium.

What if there is no medium? What if the circuit is just surrounded by pure vacuum? Even here there is a permittivity, as well as a permeability. In fact, these are constants of nature, known as ε(read as epsilon zero, the permittivity constant) and µ(read as mu zero, the permeability constant). These values show up in the most interesting places; for instance εappears in the formula stating how strongly two electrically-charged objects feel each other when separated by some distance r:

\ F_C = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}

Meanwhile an analogous formula for magnetic field strength includes µ0


(Note that magnetic fields are about electric current I, while electric fields are about electric charge q, indicating that it’s moving electrons that cause magnetic effects).

What does all this have to do with light? Just this. Around 1861 Scottish physicist James Clerk (pronounced “Clark”) Maxwell was fiddling around with the equations for electric and magnetic fields. What happened next changed our understanding of the universe forever. Maxwell found that his equations predicted that electric and magnetic fields could propagate through empty space, one producing the other on and on. That propagation would take the form of a varying electric and magnetic field moving in a particular direction. The speed of that propagation came out as a constant number, dependent only on the electric and magnetic constants εand µ0.


Even more amazing, though, was the number Maxwell got when he plugged those numbers into the equation. The value of c came out suspiciously close to the measured value for the speed of light! Put the equations of electricity and magnetism together, and the speed of light comes flying out of your math, unbidden and unexpected, but undeniably there.

We now know that any time electrons jiggle, whether it’s in the radio transmitter of your cell phone, in the awesome accelerated motion of an x-ray machine, or even in the hot filament of a flashlight, the result is light. Some of that light you can see, like a small portion of the light from a hot light bulb filament. Much of it you can’t see, like the radio light flying away from your cell phone or the x-ray light bouncing off your dental fillings, or the infrared light that does much of the work in heating your face in the Sun or your crayons under a lamp. Yet every bit of it is light, an electrical and magnetic vibration in the very fabric of the universe.

Light is something the universe does.

A recent discussion about young Earth creationism has got me thinking about my view of the world.

Young Earth creationism (YEC) is such an easy target that is is tempting to be misled, and I realize that I have often fallen into the trap I’ll shortly describe.

YEC proponents claim that the Earth and in fact all the universe is something like six to ten thousand years old, that humans and animals appeared in pretty much their modern form at the beginning of time, that most extinctions occurred and geological formations like the Grand Canyon appeared due to a single worldwide flood, and so on, and that God was responsible for it all. The first part of this argument is so bad that it’s easy to get stuck there, and never get to the second part of the argument, which is in fact infinitely worse. This is the trap.

We can demonstrate that the universe is much older than a few thousand years. We can show that humans and animals have evolved. We can present evidence for the slow formation of landforms. But these demonstrations have no effect on YECs. Why? Because that’s not what YEC is truly all about. Instead, and this is the key point we miss, YEC is actually all about the second statement “God did it.” That’s a statement we can’t refute – which ironically is precisely what makes it such a spectacularly bad explanation.

Old-Earth creationists, intelligent designers, and so on, are far more clever than YECs, and we can see in their arguments the crux (no pun intended) of the issue. They might say, “Fine, we accept all that science and history and geography demonstrate. The universe is 13 some billion years old and began with a Big Bang. But God still did it.” Even though this argument matches (by definition) all the findings of science, it is still a bad explanation.

Let’s set up an imaginary scenario in which YEC or some other similar claim is not such fish-in-a-barrel easy pickings in order to explore why. Suppose an upcoming mission to the Moon discovers, inscribed in the original Hebrew, a replica of the Ten Commandments.


You can imagine the mixture of celebration, consternation, “I-told-you-so” finger wagging, and so on that would ensue. Would this discovery prove the existence of the supernatural entity called God?

Many would be convinced. If I’m honest to my convictions, I have to say that such a discovery would not, in fact could not, convince me. For even with evidence like this, the idea that “God did it” is still a spectacularly bad explanation. If I accept the idea that life (not just science) is all about finding good explanations, then even with the inscribed tablets from the Moon I would have to reject the “God did it” argument as a bad explanation.

What would I say instead? First eliminate the obvious. Is it a hoax? Is this a modern Shroud of Turin, created by Earthlings with an agenda? If we can eliminate that by, perhaps, obtaining an accurate date, demonstrating that this material originated on the Moon itself, showing that the letters were carved in a way inconsistent with a hoax, and so on, then we move on.

Could it be that the tablets arose via natural processes? This is an exceedingly bad explanation. However, it is still better than the idea that a supernatural entity acted in our universe, for the simple reason that the tablets themselves must contain far less unexplained order than the entity that supposedly carved them. Even so, I’d be quite unsatisfied with such an explanation.

No, my conclusion, I believe, would be something like this: the stories of the Old Testament have more truth than I’d supposed. Perhaps there were original tablets, maybe even a person named Moses who received them, and perhaps he even thought he’d received them from God. But such a God, acting in our universe, must be part of our universe, must be, perhaps, a creature like the “Q” of Star Trek, an immensely powerful, knowledgeable, yet still evolved being of our universe, a being that still obeyed and obeys the laws of physics.While we have no evidence for such a race (other than these imaginary tablets, of course), this is still a far better explanation than the supernatural notion that “God did it.” Faced with magic, we must try to discover how the magic works.

What was the point of this imaginary exercise? Just this: the fact that YEC is demonstrably wrong is beside the point. Even if, through some utterly unlikely chain of events, modern science were to discover that the YECs were right all along, that the Earth really is only a few thousand years old and so on, such a discovery in no way validates the much worse claim that a supernatural entity known as God is responsible for our existence. Supernatural explanations are always bad explanations. This is why “debating” YECs (or old Earth creationists, or intelligent design advocates) is pointless.

This argument might feel uncomfortable. It seems like dogma, this out-of-hand denial of the supernatural. Isn’t this the equivalent of a religious claim, an unproved (and unprovable) belief that the universe makes sense? Consider the alternative (which is very much the “world” we live in, and by world I mean society). She claims “God did it”. He claims “The Flying Spaghetti Monster did it”. Another claims Allah, Vishnu, the Raven, the Great Turtle, and so on. Supernatural claims are infinitely variable because they are definitionally untestable. The only path forward we’ve ever found, the only way we’ve ever made any progress, is by assuming that the world makes sense.

Arthur Clarke famously said “Any sufficiently advanced technology is indistinguishable from magic.” Bull, I say! If you believe in reason, you will analyze the “magic”, find out how it works, and change your view of the world to accommodate the new information. But you won’t give up on reason. If we decide that “magic” is both real and unexplainable, we’ve lost.

As I’ve written before, I hate fiction.

Lord of the Flies is a book  by William Golding. I read it in high school, and found it both intriguing and terrifying. But now I’ve read Pinker, and I’ve read Deutsch, and that has changed everything.

I just finished Lord of the Flies again. It isn’t hard to sum up the message of the book. “What evil lies in the heart of men (er, um, boys)?” The first time I read the book the message resonated with me. I was deeply interested in the question of evil. Are we basically good, but trapped in a society that drives us to evil acts? Or are we basically evil, with the veneer of society (barely) keeping us from one another’s throats?

It was clear to me then. I was of the former persuasion; this book was of the latter. It was a challenge to me, and I remember convincing myself (rather unconvincingly) that the boys who turned to savagery had been trained by the society in which they were raised. After all, I said to myself, they are only on this island because they themselves were escaping war. War was pounded into their good little hearts from the beginning. How could they have become anything other than what they were? Society made them evil.

Golding, I believe, had just the opposite opinion, and would respond by saying that we had created that society, we had created that war. Even after all the years of bloodshed, we still hadn’t learned our lesson. Here we were, bombing and killing even now as we try to teach our children better.

What a pair of simple souls. Now I know better. The choice  is a false one. All evil results from a lack of knowledge. And there was plenty of missing knowledge on that island.

This is not a condemnation of the boys. They were faced with the task of creating a new society. That the society they finally formed was an immoral, irrational, awful mess is no surprise. Almost every society in the history of humankind has been an immoral, irrational, awful mess.

These boys, however, came from the West. They tried to emulate what they’d learned of the grownup world. Ralph found the conch, the symbol of civilization, lawful rule, and reasoned discussion. The boys tried to create knowledge. They used Piggy’s glasses to create fire. They made smoke to send a signal to the outside world. They tried to encourage creative thought and rational criticism. And they almost succeeded.

In the end, they failed. The beast became their god. The conch was destroyed, along with Piggy, the voice of reason on the island. Anti-rational memes are powerful things, and humans are imperfect, prone to error, bound to make mistakes. The biggest mistake of all, the one that proved literally fatal, was the suppression of criticism, the use of violence rather than discussion, the slavish devotion to ritual and superstition instead of creative thought and critical analysis.


But why the beast? Why the failure? What is it about humans that makes us so bad at government? This is what Golding was trying to get at, and where in the end I think he failed, falling back on the evil in men’s hearts business. I don’t know any better than Golding did, but I do know this. It’s easy to be wrong, and hard to be right. All our knowledge is fallible. The West, the Enlightenment, civilization, are far from perfect. But they’re our only hope.

My hope comes from a human trait that Golding little explored, but that I believe is deep and ingrained. When you have a sore in your mouth, you have to touch it with your tongue, even though you know it will hurt. When you hear a bump in the night, you have to go see what it is, even though you may be frightened. When God told Eve not to eat of the Tree of Knowledge, what did she do? Crunch!

The beast was only a dead parachutist. Golding made one enormous error in having only Simon ever try to find this out. We all wanted to know. That’s why Golding told us. The boys would have wanted to know, too. They would have gone. They would have investigated, despite their fear. They would have poked the beast with a stick, ran, slunk back, poked again. Finally, they would have learned the truth.

That same trait, of course, led to the “atom bomb” war that Golding was so convinced was our destiny. The keys to heaven and hell are identical. But we cannot ignore them.

If the beast is in us, as Simon tells learns via the terrifying pig’s head, then our only chance is to go face the beast, journey to the mountain, stare the creature down with the only tools we have, our rational selves.

Some work I’ve been doing recently plus an exciting report from the Kepler mission has got me thinking about the Drake equation and extraterrestrial civilizations.

I haven’t found a great Drake equation online, but here’s one that’s ok, and will serve my purposes. Go ahead and try it, then come back and we’ll compare numbers:

So what did you get? Are you optimistic about the number of civilizations in our galaxy?

As I think about the question, “Do you believe in extraterrestrial civilizations?” it occurs to me that there are in fact three possible responses. The first is no. The second is yes. The third is, “what a ridiculous question.” Let me explain.

Change the question to, “Do you believe in China?” At one point in Western history, such a question might have logically received a yes or no answer. Eventually, though, the existence of China became obvious. Today, no rational person could deny the existence of China. The proper answer is, “what a ridiculous question.”

We can easily imagine living in a world where the question, “Do you believe in extraterrestrial civilizations?” would equally be silly. If extraterrestrials had obviously altered their environment, if they were visiting our planet regularly, or if, in fact, we had been colonized by these beings, there would be no denying the existence of intelligence other than us.

We don’t live in such a world. That’s a data point. And that data point informs my thoughts about the Drake equation. If you believe (as I do) that a civilization can span an entire galaxy, you have to ask, “Where are they?”

Here are my numbers; let me know where we differ and why.

R (in this version of the Drake equation it’s the number of Sunlike stars in the galaxy – in others it’s a rate of star formation)

This should be the most certain number in the entire equation, but it turns out to be more difficult than you might suppose. The key is “Sunlike”. How wide or narrow a net does that cast? Could stars in double star systems still be Sunlike? What about stars that lack metals, because they didn’t form near enough to supernova remnants? What about stars too near a black hole or other radiating body? I’m going to use a number of 100 billion here, although I suspect this number may be a bit too high.

Fp and Ne (the fraction of stars with planets and the number of Earthlike planets per system)

This is where the new Kepler data comes into play. Kepler gives us a number of around 20% for Earth-sized planets in an Earthlike orbit – pretty large, considering all the ways things might go wrong in a Solar System. Here I’m assuming that to be Earthlike a planet merely has to be the right size and at the right distance. There might be all sorts of other factors I’m leaving out, like needing a big Moon and so on. But I’ll combine Fp and Ne into 20% (times 1), even though I think it might be too high.

Fl (the fraction of Earthlike worlds on which life begins)

I’d always been highly optimistic on this number, until I read an argument by Paul Davies in The Eerie Silence. My original feeling was that because life seems to have appeared on Earth as soon as it possibly could have, life’s origins must not be all that difficult, given a few million years and a planet’s-worth of the right ingredients. Davies’ argument made me question that assumption. Here it is: we’re here. It took almost 4 billion years for us to get here. At best the planet has another billion years left where our evolution would have been possible. Perhaps it is only on that (maybe small) subset of worlds where life started quickly that intelligent life had the time to develop. So of course we find ourselves on a world where life started almost right away.

Maybe. It’s an interesting argument. But if life was an incredibly lucky accident, why couldn’t complexity have happened a lot faster via its own set of lucky accidents? We’ve only just started this origin of life business, and there are already so many possible channels, it seems to me likely that life can get started quickly, and unlikely that there’s some fundamental barrier to every path.

This is one factor that could potentially get a lot more certain very soon. If we were to discover just one independent origin of life, either on Mars, in the biosphere signature of an extrasolar planet, or even here on Earth, then the likelihood of life beginning elsewhere would shoot up. I think this will happen – the stuff of life is just too common in the universe for life’s origin to be some rare one-time occurrence on this planet. I remain guardedly optimistic on the question of life and enter a figure of 90% for the number of Earth-like worlds on which at least simple life gains a toehold.

Fi (the fraction of living worlds that develop intelligence)

Now things get interesting. The same argument that makes me believe life is common also leads me to believe that complex life, animal life in particular, is perhaps exceedingly rare. The counter-arguments are that dolphins, crows, even octopuses have evolved intelligence essentially separately from humans. OK, sort of. But they’re all animals. Consider this chart:

tree of life

Once upon a time we looked at the natural world and saw just animals and plants. Animal, vegetable, mineral, remember? Then we made a concession to the oddballs and called them protists. Now we look out there and see a plethora of groups, with only a tiny few (the plants, the animals, and the fungi) showing a move toward complexity. We, it turns out, are the oddballs. And of these oddballs only animals have developed even a little intelligence. How much would change if that one, thin twig holding animals had been snipped early on? To put it another way, how much would you miss any of the other branches?

The late Lynn Marguils and her colleagues developed an alternate tree that emphasized symbiosis over branching – i.e. we’re not just animals. We’ve incorporated other beings into our ever cell. Mitochondria for animals, chloroplasts for green plants, even our own DNA-holding nuclei. All these were once free-living organisms, members of one of those other branches. That, I think, makes my point even stronger. How many events had to happen just so to make complex life even possible? What if even one had turned out differently? Complexity, history seems to be telling us, might be quite rare, and intelligence rarer still.

The calculator I’m using here only goes down to one in a million for Fi. I think that might still be too optimistic, but I’ll go with it for now.

Fc (the fraction of worlds with intelligence that develop civilization – which we’ll define as the ability to be noticed over cosmic distances, via radio or another medium)

We are so very, very new at this technology thing. There are people alive today that still remember the very first radio broadcasts. Even though we’re a young species, the amount of time we’ve had a technological civilization is a tiny fraction even of that number. It took us a long time to get here. Might we have not made it at all?

As a test case, I point to the Neanterthal. Here’s a species that arose, just as we did, from African ancestors. Neanderthals expanded into Europe and Asia, became adapted to cold weather, evolved huge brains (in many cases bigger than ours), learned to use fire, probably had spoken language, hunted the largest and most dangerous creatures in their ecosystem, and of course made and used tools. But here’s the rub. Neanderthals developed a stone tool kit and then did not change that kit for 100,000 years! It’s astounding to even think about that level of stasis. Life 200 years ago is practically unrecognizable today. Even pre-civilization, our ancestors were inventing bone fishhooks, musical instruments, art, jewelry, sewing needles, and on and on. But the Neanderthals stood stock still for a hundred thousand years.

Suppose we had never come on the scene? Could all of life’s pageant, nearly four billion years of evolution, have resulted in the Neanderthals and then have gone no further? Why not? The Neanderthals stood technologically still for 100,000 years. Would they ever have developed radio telescopes, if the world had been left to them? Why would they, when in 100,000 years they didn’t even learn how to fish?

What if, at any time before today, a giant asteroid had come our way? Not only could the Earth have not prevented an impact, but not one species on Earth would even have known it was coming, or even that such a thing might be remotely possible. No Neanderthal was ever going to deflect an asteroid.

Neanderthals are just one example of the move away from complexity. When one studies the evolutionary record, one sees again and again a move away from innovation and creativity and back toward the tried and true. Ancient apes evolved into innovative chimpanzees and of course our clever ancestors, but also into non-innovative gorillas and orangutans. Australopithecines gave rise to the first homo, but also to their own robust forms with giant jaws and sedentary lifestyles. And homo itself gave us the hobbits, H florensis, as well as the Neanderthals. An honest assessment says there are plenty of ways to not develop radio astronomy.

And then there’s the fact that even we H. sapiens could easily have never experienced the Enlightenment, could easily have disappeared without ever understanding what a star is, let alone what a radio wave is. Both pre-history and history suggest to me that arriving at one achievement (like a big brain) is absolutely no guarantee of moving up to the next one. Maybe I’m too pessimistic here, but again I’m going to pick the one in a million option.

L (the lifetime of a technological civilization)

Finally we come to the lifetime question, where hand-wringing and moralizing abound. We’re going to blow ourselves up. We’re going to create nanobots that will turn everything to grey goo. We’re going to unleash a genetically modified disease that will wipe us out. We’re going to use up all our resources and slowly choke on our own exhaust, buried in our own garbage.

Well, maybe. It’s all so moralistic. We’re too successful. We’re too powerful. Our knowledge is greater than our wisdom. Admittedly, humans are different from any species that has ever lived on this planet, so comparisons may no longer work. But keep in mind that too much of anything isn’t what brought on extinction for virtually every species that has ever evolved on this world. Rather, these species went extinct precisely because they were living within their means, and then something came along that did it better.

Similarly, human societies have not fallen due to overuse of resources. Rather, they have fallen due to lack of knowledge.

I take a different view. I learned from David Deutsch that the only infinite future is one that is unsustainable, one that depends upon the next innovation. I learned from Steven Pinker that we’re not getting worse, we’re getting better. We’re smarter, more moral, and less violent than at any time in our past. I believe this is (once an event like the Enlightenment happens) the most likely path for any intelligent species. Even if it’s not, I think we at least see how such a future is possible. And if it’s possible, then surely one (and it only takes one) civilization will make it. Not just to a long-lived civilization, but to a galaxy-transforming civilization.

Now we return to my original point. Where are they? If I’m right, if civilizations aren’t limited even by the life of their own star, why don’t we see evidence of the extraterrestrials in our neighborhood? Let’s run the numbers. I’m going to put 100% in for L, even though of course this wouldn’t apply to the home star of the civilization – since it certainly takes some time to evolve. It refers, instead, to the overall lifetime of the universe, and reaches into the tens of billions of years.

What’s my final number?


Wow. I’m saying that in this galaxy we are very likely alone. That’s why we don’t see them. They’re not there.

But wait. The universe is very large. Multiply that 0.036 by the number of suitable galaxies we can see, maybe another hundred billion. What do we get?

3 billion

My argument is that of all the galaxies we can see in the sky, roughly one out of a hundred is home to a technological civilization that is even now in the process of colonizing their galaxy. We’ll probably never talk to these beings, but we still might know they’re there. How? By their works.

If these beings are truly independent of their own star, then they must of necessity be “terraforming” their own galaxy to make it more suitable for themselves. Perhaps they’re building Dyson spheres around clusters of stars, so as to collect every bit of energy it gives out. Perhaps they are altering the rates of supernovas or gamma ray bursts, so as to protect themselves from catastrophe. Perhaps they are harnessing the power of black holes in a detectable way. Perhaps they are altering galaxies in ways we can’t even imagine.

When the signal comes, and I believe it will, it won’t come from our own galaxy. It won’t be a radio transmission welcoming us into the federation of planets. Instead, the signal will come from a galaxy far, far away, a galaxy that at first looks a little peculiar. As we examine its feeble light more closely, as we one by one eliminate natural explanations, we’ll slowly realize that something extraordinary is happening (or rather, did happen, as we’ll be looking into a long-ago past, delivered on light beams millions or even hundreds of millions of years old).

And what would such a discovery mean? Just this. Someone made it. Someone figured out how not to push the red button, how not to release the grey goo nanobots, how not to destroy what we’ve created but rather work together to make a society that might last not just a long time but forever.

We may never know much about these beings’ science, and even less about their art, their religion, their philosophy. But we will know that they found a way. And so might we.


The Hubble Deep Field, around 3000 galaxies in a tiny patch of sky. Of these, perhaps 50-100 are home to a billions-year-old civilization. Are any of these galaxies even now sending us light that will one day reveal an extraordinary truth?

Special relativity is famous for drawing shocking conclusions from relatively (ha) straightforward math. Yet the derivation of E = Mc2 is often left out of these simple derivations. Science writers need a good way of answering the question “Why does E = Mc2?” and so I’m writing this down, inspired by a discussion in The Universe in the Rearview Mirror by Dave Goldberg.

First comes a qualitative description, which becomes beautifully quantitative with just one additional step. It also mirrors Einstein’s actual derivation of the formula. Ready? Here we go . . .

Begin with two bedrock principles. One, the conservation of energy, which will play a small part in the following, and only toward the end. Two, the conservation of momentum, which will play a larger part right from the beginning.

OK, imagine if you will an atom sitting perfectly still. That atom emits a pair of photons of exactly equal frequency (f) in exactly opposite directions.

(“Ah, ha!” you say, “already you’re violating one of your bedrock principles, or else assuming what you’re setting out to prove, for where did the atom get the energy to emit two photons? Don’t worry about that for now. Just assume that the atom was “energized” somehow. We know that atoms emit photons like this often, so it’s no stretch to begin the thought experiment with an observed phenomenon.)

Since a photon’s momentum is determined by its frequency (see below), and the frequencies are equal, we know that these two photons have identical momentum. Since they also are emitted in exactly opposite directions, their momenta exactly cancel. As predicted by the conservation of momentum, the atom does not move. It is in the same position before and after the emission.

Now imagine that same situation, but think of the atom moving slowly across your field of view (maybe the atom is moving, maybe you are moving. According to the Principle of Relativity, it doesn’t matter.) We specify slow motion to show that this is not an effect of high speed, but rather an effect of any motion at all.

Photons always move at the speed of light (c), so the emitted photons (whether against the direction of the atom’s motion or with the direction of the atom’s motion) will just move at the speed of light, no faster and no slower. Instead of changing speed, they change frequency (f). The photon emitted in the direction of motion is “squashed” into a higher frequency f’, while the photon emitted opposite the direction of motion will be “stretched” into a lower frequency f’’. This is just the Doppler effect for light.

Photons have momentum. We know this because light shining on a surface actually pushes on that surface. However, the momentum of a photon can’t be given by mass times speed, because photons have no rest mass. Instead, we know that the photon’s momentum is given by p = hf/c, where p is the momentum, h is Planck’s constant, and c is the speed of light.

Now we notice something strange. In the non-moving frame, we see that momentum is conserved quite naturally: hf/c = – hf/c as the left and right photon momenta cancel. In the moving frame, though, the atom keeps moving at the same speed before and after the emission (this is necessary by the principle of relativity; we can’t tell if the atom is moving and we’re sitting still or if we’re moving and the atom is sitting still – or even if we’re both moving at the same rate when we think we’re both at rest). This means that in the moving frame the atom’s momentum plays no role if the atom is the same before and after the emission. This is crucial, so hold it in your mind.

In the moving frame the photons are either squashed or stretched. This changes their momentum. In particular, there is suddenly more momentum in the forward direction and less in the backward direction. Uh oh! We said that one of our bedrock principles is that momentum is conserved. How can that be? It appears that in this example momentum is created from nothing.

There’s only one way to save our momentum conservation bedrock. The atom itself has to change. In particular, some of the atom’s mass must have disappeared. Where did it go? The only sensible place is into the photons. But since photons have no mass, that mass must have become energy. Wow!

Now for a more quantitative approach.

In our naïve assumption that the atom doesn’t change in the emission of photons, we ended up with something that made no sense. Here it is

The no sense “equation”:

momentum before  =  momentum after

mv = hf’/c – hf’’/c  + mv

where m is the mass of the atom and v is the atom’s speed. This “equation” tells us that hf’/c – hf’’/c must equal zero. We know that can’t be true, because when the atom is in motion the photons are no longer identical – one is squashed and the other is stretched; this changes their frequencies and therefore their momenta.

We know by the Principle of Relativity that the v’s have to be the same on both sides of the equal sign. This means the two m’s in this equation are not the same.

Let’s call the m before the emission m0. Let’s call the mass after the emission m’.

OK, here’s the equation again; this time it really is an equation:

momentum before = momentum after

m0v = hf’/c – hf’’/c + m’v

now we rearrange a little

(h/c)(f’ – f’’) = (m0 – m’)v                             (1)

This equation (we’ll call it equation 1 because we’ll need to call on it later) tells us that the difference in momentum between the two photons must be equal to the difference in momentum (which comes down to the difference in mass) between the atom before emission and the atom after emission.

So what is the difference in momentum of the two photons? This is something we can know experimentally, or we can use the formula for the Doppler effect for light. We’ll do the latter here.

For the photon emitted in the direction of motion:

f’ = f(1 + v/c + (v/c)2 + (v/c)3 + . . . )    NOTE: frequency gets bigger for the squashed photon

For the photon emitted opposite the direction of motion:

f’’ = f(1 – v/c + (v/c)2 – (v/c)3 + . . . )    NOTE: frequency gets smaller for the stretched photon

Here’s the nice thing about using a very slow atom. v is much, much smaller than c, so for anything bigger than (v/c)2, the number becomes tiny, tiny, tiny. We can ignore such tiny numbers, hooray!

Now let’s go back to equation (1), putting in our new values for f’ and f’’.

Equation 1:

(h/c){ f(1 + v/c + (v/c)2 + (v/c)3 + . . . ) – f(1 – v/c + (v/c)2 – (v/c)3 + . . . ) } = (m0 – m’)v

and simplify:

(h/c){f(2v/c)}  = (m0 – m’)v    NOTE: all the other terms either cancel {f – f and (v/c)2 – (v/c)2} or else are so small that we can ignore them.

And simplify some more (the v terms cancel, the c terms are combined)

2hf/c2 = (m0 – m’)

We’re almost there!

We know that the energy of the two photons is just 2hf (again, the Principle of Relativity tells us that the energy in the rest frame and the energy in the moving frame has to be the same). We also know that the term m0 – m’ is just the change in mass. Let’s call that change in mass M

Then 2hf = E

(m0 – m’)  = M

E/c2 = M

And finally,

E = Mc2

Wow indeed. The energy that came out as two photons is just the mass lost by the atom, multiplied by the speed of light squared.

It’s official. Pinellas County, Florida has located a new-record number of loggerhead turtle nests for the 2013 season, with another month or so still to go. Here’s an article that discusses the record:

Unfortunately CMA has not published any data on the hatching of nests yet, but I’m proud to say that my nest #62 is one of those 209 plus nests that make up the new record.

Go turtles!sea turtles

Amid many life changes at the end of May, I totally missed a crazy story out of Arizona:

So here are our characters:

Juan Mendez, atheist legislator who offered some thoughts about what it is to be human, including a quote from Carl Sagan.

Steve Smith, religious lawmaker who took offense, saying what Mendez did was out of order because it wasn’t a prayer.

But, most importantly, another lawmaker named Andy Tobin who spoke in support of Mendez’ speech.

Tobin is the snake in the grass here . Let me explain.

Arizona House Speaker Tobin, along with Senate President Andy Biggs, had just finished voicing their support for the idea of beginning governmental functions with a prayer. Tobin, with a more far-reaching and global perspective than Smith, understood immediately that if he’s going to fight for opening prayers, he’d better let someone like Mendez have his say. Tolerance and all that. Sounds good on the face of it, especially when you read or watch what Mendez said.

But here’s the thing: Mendez didn’t have to say all those nice things.

Now don’t get me wrong. I believe my atheism makes me a better person. I make better moral choices because of my lack of faith. I can see that morality is more than the social relativists make it out to be. There are moral truths, having to do with the dignity of individuals, the rights of free expression, and lots of other good stuff. But a strict definition of atheism doesn’t include these beliefs. A strict definition just reflects lack of belief in a higher power. Such a person could hold any number of horrible, immoral ideas and still be an atheist.

What if Mendez was that kind of atheist? Would he still have the right to lead the prayer?

Yes, of course he would, and that’s why this whole idea of prayer to begin government functions is wrong-headed. Religion is a blanket that covers any set of crazy, immoral, and incorrect ideas. Suppose next you have a legislator use the prayer to support child abuse, slavery, and death to infidels (does that list ring any bells?) As long as it’s religion, such a speech is covered. But of course the backlash would be a gigantic mess, distracting everyone from the task at hand. Our government’s task should not be sorting out religion but rather operating the government.

This is at the heart of separation of church and state. It isn’t, “let’s all be tolerant of everyone’s religion in government affairs.” Rather, it’s “Let’s keep religion out of government affairs.” Why? Because government by nature needs to value logic and sound, evidence-based argument, not appeals to unquestioned – and unquestionable – faith.

This is why Tobin and his colleague Biggs are the real villains here. It’s great that Mendez is a nice guy, and that his atheism has led him to a good place in his philosophy. But people like Tobin and Biggs would make the argument that, “See? We can be tolerant of all faiths, even a lack of faith. So we should be able to keep our government-sponsored prayer.”

No! It’s easy to be open and tolerant when the ideas offered are actually palatable (except to someone like Smith, who either is deeply ignorant or – more likely – is pandering to his bigoted constituency). But openness and tolerance mean opening the door for a whole parcel of extremely bad ideas, bad ideas that can do nothing but act as a source of distraction from the task at hand.

The Smiths of the world are easy to spot, easy to mock, easy to dismiss. Watch out, instead, for the Tobins. They are the dangerous ones. Leave religion out of government!

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.
April 2014
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A blog by Stephen Whitt

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