Living in the Universe

Is Mathematics Universal?

Third Week of December and Last Blog Entry of 2007

This week I want to ask a very big question and catch up with a story from a few weeks ago. In earlier posts I’ve asked and answered the question of whether or not carbon is universal in the context of life. The answer is an emphatic yes. Carbon is everywhere, produced by stars, and spat out into interstellar space where it can be incorporated into planets and people or other life forms. The same question applies to water. Is water universal? It’s clearly an important part of our form of life. The answer once again is yes. Water is one of the most abundant molecules anywhere in the universe and will be found most places we can look. We expect there to be watery planets scattered throughout our galaxy and beyond.

Astrobiology of course is based on framing the question, is life universal? Again, we don’t know the answer yet, but astronomers are optimistic that many biological experiments will have taken place. We really have no idea whether technology and intelligence are universal, but with a smaller probability they’re likely to be found out in space as well.

Physicists and mathematicians are prone to ask another question. Is mathematics universal? Over the past few hundred years we have discovered laws of nature that are exquisitely described by elegant and sometimes very difficult mathematics. We naturally wonder: is this a universal phenomenon? Should we expect intelligent entities elsewhere in the universe to have stumbled upon the same mathematical rigor and beauty that we have? It’s a pretty profound question for science.

A recent op-ed piece in the New York Times by my colleague Paul Davies up the road at the Arizona State University caused a real storm. Paul Davies is a prolific cosmologist who’s written almost thirty books. He asserted in his op-ed piece that science, not unlike religion, rested on faith, not in God but in the idea of an orderly universe. “Without that presumption,” he said, “a scientist couldn’t function.” His argument of provoked a lot of mostly adverse reactions from other scientists, who objected to the claim that science depends on faith at all. Scientists generally reject that idea and consider science to be a logical, rigorous process that’s immune from any belief system.

But Davies did make an important point, which is the fact that the universe and its orderliness has been a predicate or a premise of science for two thousand years of observation and theorizing. That’s interesting, and it leads to a chicken-and-egg problem about the universe and the laws that describe it. Which came first: the laws or the universe? If the laws of physics are to have real explanatory power, they have to be good anywhere and everywhere including the big bang and every other galaxy in the universe. If the mathematics that describes them is potent then it will also prescribe everything in the universe.

Many thinkers going back to the Ancient Greeks have suspected that mathematics is at the heart of rational logic. Pythagoras famously said that the universe is based on number, that is was number. That must have been a very strange concept to an Ancient Greek for whom a rock was a rock and a tree was a tree and a fish was a fish. What on Earth did Pythagoras mean by saying that number was everything? But this rational idea of logic was built into science from the start. In addition to Pythagoras and his followers, Plato envisaged a higher realm of ideal geometric forms—perfect circles, chairs, perfect galaxies—in which the phenomena of the sensible world, the world we experience, were just flawed reflections of perfect mathematical forms. This transcendental idea of the essence of nature has been popular with scientists ever since.

Modern physicists are particularly attracted to this idea. Perhaps the most extreme example is Max Tegmark, who’s a cosmologist at MIT. In talks and recent papers he speculated that not only that mathematics describes the universe, but also that it is the universe. He maintains that we’re part of a mathematical structure, albeit one much more complicated than a circle, a multiplication table, or the symmetries of modern particle physics. Other mathematical structures, he predicts, exist as their own universes in some cosmic Pythagorean democracy, although not all of them will prove as rich as ours. In the New Scientist he said “Everything in our world is purely mathematical.”

That would explain why math works so well in describing the cosmos and also would answer a question posed by Stephen Hawking, noted English cosmologist, in his famous book A Brief History of Time. Hawking had asked “What is it that breathes fire into the equations and makes a universe for them to describe?” It’s mathematics that’s on fire, according to this idea, which has a long history. In the seventeenth century, Galileo said that the universe is a grand book written in the language of mathematics, and the famous physicist Eugene Wigner in the 1960’s said that the unreasonable effectiveness of mathematics demands an explanation.

If we know anything from modern physical theory it’s that mathematics underlies the heart of our explanations for the physical world, and if that realization means anything, then we must imagine that it applies elsewhere in the universe, and that mathematics will be universal, and that other intelligent creatures, should they exist, will have discovered and relished and used mathematics in similar ways to us. That’s an intriguing thought to bind everyone in this universe together as we close Living in the Universe for the year 2007. Join me again next year to explore what’s new in astrobiology.

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The Earliest Life in the Universe

Second Week of December 2007

A research report this week suggests that the first heavy elements in the universe could have been created half a billion years earlier than previously thought. New astrophysical simulations of conditions in the early universe suggest the earliest galaxies could have created heavy elements by the formation and then destruction of very massive stars, perhaps a hundred times more massive than the Sun. This moves forward in the timeline of the Universe by half a billion years the time at which carbon, nitrogen, oxygen, and other life giving elements could have been created.

This may seem to be of esoteric interest, but it shed light on an important issue in astrobiology, which is how long ago could life have possibly formed. The universe is known to be 13.7 billion years old. This recent research pushes back the time at which the first planets and carbon-based life forms could have been created to within a couple of hundred million years after the big bang. Let’s think about that for a minute. That means that the first planets and life could have formed thirteen billion years ago. Remember, the Earth is four and a half billion years old. That means that life elsewhere could have had a head start of eight or nine billion years on life on Earth.

Imagine an Earth clone that’s existing in space thirteen billion years ago, forming its microbial life, and that life becomes more advanced, eventually develops large animals, perhaps brains and technology as happened on the Earth. Where would that life have got to in those extra billions of years? It’s an extraordinary thought. Perhaps the best way to bring it into focus is to consider what I call futurology, the difficulty of predicting the future by mapping it backwards into the past. Think of our current situation: fifty years into the space race, thirty or twenty years into the age of computers, barely a decade into the age of the Internet. If we imagine our world just over ten years ago, there was no Internet. A hundred years ago, no mass transportation. A thousand years ago, no medicine. Ten thousand years ago, no civilizations or cities; Humans were hunter-gatherers. A hundred thousand years ago, no agriculture. We were very primitive at that point. And a million years ago we were barely becoming human.

If we project this timeline forward into the future, it’s very difficult to predict past the first two orders of magnitude of powers of ten. Ten years from now, we might safely predict technology, but a hundred years or a thousand or ten thousand? Not a chance. Our predictions almost always go badly wrong. Yet we are now faced with imagining what a civilization like ours might amount to, given billions of years of extra evolution because we’re saying that carbon-based life could have existed for billions of years before the Earth even formed. This possibility and this type of extrapolation is almost impossible for us to bend our minds around. However in astrobiology, where biological experiments could have been spawned billions of years before the Earth was even formed, we must consider the potential and the capabilities of extremely advanced life forms. They’d be as advanced to us as we are to bacteria on our planet. That provocation, spurred by this recent research, is the food for thought this week.

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Sending Motes into Space

First Week of December 2007

Picture this scene if you will. Just below a half-opened garage door, a tiny device is seen lurking at the feet of someone in the shadows. It looks like a blue dragonfly. Then its miniature wings begin to flap, and it slips under the door and darts along the street. After rising through the air, it hovers outside the window of a building several stories up. There’s an opening on the roof, and it slips inside flitting from room to room with its video camera eye transmitting pictures to a screen on a remote control unit strapped to the wrist of its clandestine operator.

This isn’t a scene from a Bond film, but an animated video produced by Onera, France’s national aerospace company, to explain REMANTA, a project to develop technologies needed for miniature robotic spacecraft and aircraft. These bug-like flying devices are being developed in other research labs. Some are small enough to be carried in a briefcase. Others are the size of a jet fighter and need a runway for takeoff. These devices are generically called UAVs, unmanned aerial vehicles. The smallest of them are about six inches across. The bug built by REMANTA has a wingspan that size, and it flies by flapping its wings, a bit like a real insect. This means it needs less power than helicopter type rotors and is better able to withstand winds and being blown off course. Harvard University researchers have developed a fly-like robot that weighs just two thousandths of an ounce and has a wingspan of three centimeters. It’s about the size of a real fly. It cannot, however, fly on its own yet, it needs a power tether.

What have these devices got to do with astrobiology and space travel? Well, the future may be in going small. If we think about the pioneer and landmark missions of the current day, they are huge spacecraft like Cassini at two tons, or the ton and a half of the Hubble Space Telescope. But if we go in the other direction and use miniaturization, there are some interesting possibilities in space travel. Back in the 1970s some MIT undergraduates managed to get an audience with a mid-level NASA bureaucrat and they tried to sell him on the idea of using a robotic ants connected by a neural net to explore Mars and look for life. Well they were a little ahead of the technology, and I guess they were laughed out of the room. But the time has now come to try small robotic space explorers.

Mason Peck, who’s an engineer at Cornell University, envisages thousands of miniature spacecraft drifting to different planets powered only by the Earth’s magnetic field. His novel magnetic propulsion method recently earned him a seventy-five thousand dollar grant from NASA’s Institute for Advanced Concepts. The biggest advantage of using small spacecraft is that it could shave hundreds of millions of dollars off a typical NASA satellite launch because it requires almost no rocket fuel once in orbit. What he’s designed is basically a set of chips that use the Lorentz force, a physics phenomenon that acts on electrically charged particles moving in a magnetic field. In this case, the force would help the chips escape Earth’s gravity and head for a distant planet. On arrival the chips would rain down on the planet, analyze atmospheric or surface samples, and then signal to Earth if they’d found anything interesting.

Peck and his team are testing Lorentz propulsion in the lab, and if all goes well they have plans, ambitious plans, to try this method to go to Europa, probably not for ten or fifteen years. Here’s how it works in a little more detail. Thousands of chips are packed into the nose of a rocket and launched into low orbit. Each chip’s solar panel sends electrons to a capacitor which pumps them through a long trailing wire to charge up the chip. Then, in orbit, the Lorentz force acts on the charged chip through the magnetic field that nudges the space chip to a higher altitude. After about a year the Lorentz force will have given enough energy to the chip to free the tiny device from the Earth’s magnetic gravitational field.

Timed properly, the swarm will fly freely on a trajectory for Jupiter’s large moon Europa. After a two to four year journey, tiny thrusters adjust the chip’s heading as they approach Europa. They are too small to burn up as they enter the atmosphere, and with several thousand en route, the mission will succeed even if some chips don’t make it. The chips then collect molecules from the air or the moon’s surface for analysis. Micro-particles will stick to liquid on the chip’s surface which will be sucked inside the chip. The chip could contain miniaturized versions of PCR, the polymerized chain reaction device that’s used to look for DNA. So this is one of the ways we could look for life on Europa using tiny robotic spacecraft.

More generally, scientists have always taken advantage of the gains implied by Moore’s law, the doubling of processor speed and computing capability every eighteen months. But the second aspect of Moore’s law is miniaturization. Small devices use less power and they are cheaper to launch and accelerate to very high speeds. If other intelligent civilizations are exploring the galaxy, they’re probably not doing it with starships, they’re probably doing it with smart motes.

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