Author: dabacon

I dream of computation.
Our generous universe comes equiped with the ability to compute. That it didn’t have to be this way is, of course, a truism. An unspeakable truism–for that it is this way, is what allows us to even ask the question of why it is this way. But down this rabbit hole I sometimes drop. And a haunted world I find. For what could be worse than a universe in which computation is not possible? What a nightmare world, one which allows for, at most, the basic order of the universe to transform impotently. No computers is an insignificant consequence. No life, now that is larger. Even grander, nothing digital nor coarsely analog that is not uniform and changable in ways which aren’t transparently tractable. So totally random or so ploddingly deterministic, with no blemeshes. For me this world seems like an absolute hell. The perfect embodiment of the boring. A universe made up of a solved problem.
And yet, dispite the depressing thought of realities without computation, even our universe is not so generous as to make computation the norm. Certainly, even if life is prevaliant all throughout our galaxy, large chunks of our universe seem devoid of computing anything at all interesting. When I look up at the night sky and the light of photons traveling years in my reference frame strikes my eye, what useful computation has been performed? The universe as a computer is the other truism, this one equally dangerous. For computation is more than just dynamics. More than just that photon going its merry way across the universe, refracting, reflecting, dying as it passes beyond my eye lash. Computation, or at least the kind of computation worth caring about, is more than just trajectories through spacetime, it is instead a robust movement of something signficant. Just because the universe is doing a calculation, if we cannot be privy to it, then it does not count as computation, at least for mere mortals like us. The lesson of chaos, the lesson of statistical physics, the lesson of fault-tolerant computation, is that that generous gift called robust computation is a rare one in our universe.
Which leads us to yet another alternative reality, pressing further along the ladder of possibilities. This universe is the one which is the opposite of a world in which computation is not possible. A universe in which all that exists is perfect robust computation. A world in which noise is not possible, everything is digital, and a robust computation. In this world that photon which travelled across the universe did perform a computation. And this computation will be robust to any inhomogeneity it has experience in its life. Those reflections and refractions which could previously lead it to wobble, unstable, on the brink of a computation, have now all been eliminiated, or at least immunized against. Indeed in this overly computational universe, your own path in life would be so immunized against interaction with things outside of yourself that it is not clear that competing computational entities could even arise in this universe. Every competing entity, if it is to obey our law of perfect robustness, must be part of yourself or it will possibly violate your own robustness. Indeed, we may as well call this the universe of the Borg, that great monolithic enemy in Star Trek, but where, by definition and in contrast to in Star Trek, everything has been assimilated.
Three universes, ours, a world where nothing computes, and a world where everything robustly computes. And what I dream about at night is, of course and in total abhorance of the part of me which hates any-centric reasoning, how wonderous our Goldilock’s of a universe seems to be. But what keeps waking me up from this wonderful dreaming, in this world were robust computation seems the true jewel, is whether this idea, this form of a computational universe, shows up in the heart of the theory of our universe or the theory of our computers.
Questions. What role does error correction play in the fundamental physics of our universe? What role does statistical physics play in our understanding of complexity classes? For both these questions we have peripheral answers, indeed when I pose these questions in this forum, I am immediately given by commentors examples of both contributions. But these are, at best, small hints. Is there a deep and wonderous connection, one which in a hundred years we will find as obvious as the idea that mathematics can be used to describe how our universe operates? Of all the universes I imagine, when I try to turn the deity dial from a universe with no computation to one with perfect robust computation, do I find a continuum or islands of stability, with our universe being one of these islands? Is the universe the way it is because of the properties of how any universe could possible support or not support computation?
Through nightmares of boredom and perfection fairytales, to perturbations around our own universe, I dream of computation. And wonder where this dream’s computation about computation will finally lead.