Thursday, July 28, 2005

3 Questions - Part 1

Three deeply intertwined questions:

In order to give a possible explanation for A and B, let's first examine a simplified C: what is this reality thing anyways? Well, we are most immediately familiar with our own conscious experiences - indeed, they are the only things that each of us can be 100% positive exist! Our sensory input reveals to us a complex exterior world, which we can then form ideas about. One good meta-idea is to make our proposed ideas about this exterior reality testable: i.e. if an idea correctly models some phenomenon of the world, then it predictions for that phenomenon will be verified. Iterate this trial and error method many times over, building upon previous successes, and you can discover a set of theories that model the structure of the universe very well.

With the discoveries of Boltzmann, Einstein, Bohr, Schrodinger, Heisenberg, Pauli and Pauling and many others some 100 (± 20) years ago, it became clear that the laws of chemistry (and thus biology and neuroscience and the rest of reality) were many body approximations of fundamental physics, thus beginning the unification of all natural phenomenon into a coherent explanatory structure (say that three times fast!). And I think that it is very likely that physics, the substrate of reality, isn't just very well described by mathematical structures, but actually is a mathematical structure. Given the successes of General Relativity and Quantum Field Theory, it isn't too ambitious to attempt a complete description of the foundations of our universe - perhaps string theory will succeed in this endeavor.

One might object that just because a complete description was found, that doesn't mean the universe actually is that description - our universe is the rich unfolding of those laws acting on vast numbers of particles, resulting in the quirky history we find ourselves in (say you sitting in that chair, reading this right now, with those trees out the window swaying as those particular clouds blow by, etc...). I.e. there is a crucial distinction between implicit and explicit representations of information - between, say, the short program, and it's it long output. This view is tempered by the Many Worlds Interpretation of quantum mechanics. In short it states that there isn't just this reality we find ourselves experiencing - this particular permutation of atoms - but indeed all histories, all possible permutations of atoms, exist. When experiments are set up just right, and there are only a few interacting particles for which we can receive all information on their states, we can observe very nearby histories through interference (i.e. the double slit experiment, and the first quantum computing results). But usually vast numbers of particles are involved and we only receive partial information on their states, and the resulting decoherence leads to the apparent collapse of the wavefunction and our single history experiences (i.e. you don't receive any information from the photons that comprise the magnetic field in the Stern-Gerlach experiment, and thus you only see up or down for each electron). The view that the universe is actually the collection of all possible permutations of matter and energy (with specific weightings for different permutations...), 'feels' a great deal more mathematical. It is still on the explicit side of things - but explicit structures are no less mathematical than implicit ones: for instance, the generating algorithm for the Mandelbrot set and limiting behavior of all the points in the complex plane under that recursive algorithm are both mathematical structures. Thus, if one was to find a successful theory of everything, it would then be valid to declare that our universe is in fact a mathematical structure.

The thing is, I doubt we will ever find a absolute, final theory of everything! We still start from the natural assumption that our universe is a mathematical structure. But then it is just that - another type of mathematical structure, and it acquires no special status just because it happens to contain observers. This spurs the next natural assumption: that all mathematical structures exist - there can be no difference between possible and realized mathematical structures. Name this giant collection of mathematical structures the ensemble. But our universe is not just one member within the ensemble! Rather there will be a vast class of structures that have the same limiting behavior as we observe in our universe. A couple of the structures in this class will bottom out and not be much more complex than the laws we have confirmed to date, but these will be vastly outnumbered by those with far deeper structure. Thus, if this is correct and all mathematical structures exist, then one statistically predicts that we will never find a final TOE, but rather we will always be finding fundamentally new phenomenon (Dark matter? Dark Energy?...) that require expanding and generalizing the previous laws. Each structure in this class would be well defined and finitely complex, but the aggregate effect of all of them would cause the universe's laws to be bottomless.

Thus we have formed a possible explanation for question B (and A as well since A ⊂ B) - all possible structures exist, and this explanation makes the meta-prediction that we will always be discovering ever deeper mathematical laws for reality.

Next, question C...

I'm glad you are here to think about these kinds of things, Travis. I am too busy thinking about what to make for dinner. I'm looking forward to seeing you on the New England trip. I may have a little something from England with me...
I'll keep looking for Part 2 of this post.
Also, I expected a post about the new planet (or plants). Maybe you will comment once you've figured out the universe.
Hi Allison! Hmmm, maybe I'll post about the new planet... I've got lots of things to blog about - I'll try to get part 2 out soon, and do some other cool things as well. See you in a week!
Robert Laughlin (a nobel prize winner) on why there is no one (or main) Theory of Everything.
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