Imagining the Universe

I've always wondered what would happen aliens suddenly came to Earth, and then, as an ultimatum, declared that humanity would be spared if and only if one human was taken and put in some kind of stasis field for eternity -- literally forever. What that one person would see would be an endless white expanse, so he/she would have nothing to but to sit and think. Forever. And I always imagined what would happen if that person was me.

That's kind of a disturbing thought, to be trapped like that, with nothing to do. It's sort of a childish flight of fancy (but quite intriguing to think about, I have to admit), but these days I've been sort of using this as the foundation for a thought experiment.

Recently, I've come across several articles aluding to the possibility that mathematics, the traditional abstract, ideal, removed-from-the-universe branch of science, was actually just another observational science, like astronomy or biology. Now that's preposterous, you say. Mathematics is one of those lofty pillars of human thought that transcend observation and experimentation -- a truth of mathematics is immortal and can be derived independently of any physical observation, right?

This brings up the question of "What is derivation?" Plato believed that mathematical objects already "exist" (in that realm of universals), and we are merely observing "instances" of these ideal objects. So are we truly discovering mathematical truths when we prove something? Or are we simply observing what is already there in the universe?

Mathematicians like to believe that there is some special, unique faculty of humans that allows for that jump of insight, that flash of intuition that leads them to epiphanies about the mathematical universe. Most junior-high students taking plane geometry will tell you it's damn hard to figure out proofs. Indeed, to come up with a logical pathway to some truth in question seems like the act of creativity, which we believe to be a quality unique to humans. It's that feeling that humans are being creative that leads to the conclusion that, indeed, humans are creating mathematics. Proving a conjecture is as much a process of creation as painting.

My thought experiment: would this man, stuck in eternity with nothing but his logical faculties intact, be able to derive -- no, create -- all of mathematics? And from there would he be able to formulate the laws of physics exactly as they are in our universe? He would become a God, in a sense, creating the universe in his mind.

The idealist in me says "yes." I (wish to) believe this because I like the idea of the universe's existence being contingent only on the rules of physics, those being contigent on the rules of mathematics, and those being contingent on the irrevocable laws of logic. In other words, the universe is ideally perfect.

But it is hard to believe that this is so. Much of our mathematics comes from physical observations. We hear of Greek mathematicians (such as Pythagoras) verifying the now-irrefutable laws of triangles and geometry by scratching very precise diagrams in sand. Newton invented a branch of mathematics dealing with infinitesimal sums and limits to explain the cosmos. It seems that for most of history, mathematics has been tailored to the beck and call of physics.

(Slight digression: I wrote Newton "invented" calculus. The subtle question here is: did he really? Or did he merely "observe" the process of calculus taking place in the universe, and put it together in a conceptual framework that humans can understand?)

It is only a recent development of mathematics (past 2-3 centuries), it seems, to deal with the incredibly abstract that have no direct connection to physical reality, such as number theory. Number theory is a sort of a "meta-mathematics" - a formalized logic system to verify the validity of mathematics itself. Can you really call it mathematics? Perhaps we should really divide mathematics into two camps: mathematics used to describe and model physical reality, and the mathematics used to describe the first. It seems that one is yet another framework attempting to model the previous one.

So here we have sort of a hierarchy (top-down):

1. Physical reality (as is), which leads to:
2. Physics, man's capacity to model physical reality using:
3. (Physical) Mathematics, which is described by:
4. (Logical) Mathematics, which is based on the pillars of:
5. Logic, which is __________

Thus far in history, the cause-and-effect of the development of the branches of science and mathematics has been top-down: observing the cosmos led to physics which led to development of physical mathematics which inspired mathematicians to create logical mathematics which is inspiring computer scientists and mathematicians alike to-day to ponder the foundations of logic.

My question is: in the universe, is the hierarchy reversed? In other words, does simply having the foundations of logic give growth to everything else?

More to come in Imagining the Universe, Part 2

LHC: Why does it matter to us?

The entire physics community is pretty excited these days, but it just seems that this excitement is only prevalent in that community. I suppose that's to be expected -- after all, why does it matter to non-physicists?

What is this excitement all about, anyways? I speak of the near-completed Large Hadron Collider (LHC) near Geneva, Switzerland. It is a monumental addition to the existing CERN particle collider that has served as the forefront of particle physics research for a good half century now. Places like CERN have produced an amazing amount of good experimental research that have propelled the frontier of physics ever forward. Experimental verification of quantum theory, the electroweak theory, and most impressively the Standard Model have all come out of particle colliders.




I suppose the question could be extended to all this: why do huge, multibillion dollar projects that do nothing but smash infinitesimally small particles matter to anybody? It seems like a very, very large and expensive toy for a physicist, doesn't it?

The core reason is because we have generally reached the upper limit with our current particle accelerators -- they can only accelerate particles to a certain energy level and the results we get cannot answer the burning questions of physics anymore. It seems like a paradox, that it takes higher and higher energy levels to probe deeper and deeper into the world of the small -- so small, in fact, that quantum mechanics is an inadequate description of this world.

The most intriguing area of physics, in my opinion (some physicists will disagree), is string theory. It is also the most tenuous area of physics -- because it is so theoretical (and in the words of my friend, Benedikt Riedel: so full of bullshit) and mathematical we do not know if any of it is "true" (in the sense of experimental evidence). The fact is, there is not a single piece of evidence supporting string theory -- and physicists have been working on modern string theory for the past twenty years. But what has been keeping them going is its sheer mathematical elegance. Can something be so elegant that it has to be true? Certainly, many physicists think so.

But the LHC is the reason why many physicists are starting to place bets now -- because they're hoping with the awesome level of energy that is attainable with this machine, it can start to shed some light on the most fundamental questions of physics today. For example, physicists are eagerly awaiting the experiment to test the existence of the fabled Higgs Boson. Of all the particles predicted by the Standard Model, the Higgs Boson is the only one that remains unidentified by experiments. The Standard Model has proved its success and versatility with everything else so far. The Higgs Boson is, simply, the particle hypothesized to give everything a property of mass (for everything that has mass, of course). That's pretty big stuff. Can you imagine that without this particle, nothing would have mass?

Hopefully, too, some aspects of string theory can be tested. That would re-instill a much needed sense of purpose, direction, and excitement in the field of high energy physics. And some deep, fundamental questions about the fabric of reality and its constituency could be answered.