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.
O brave new quantum world!
It seems to me that both this: “… so ploddingly deterministic, with no blemeshes” and “A world in which noise is not possible, everything is digital, and a robust computation” could describe the same universe. Indeed, they could describe our universe.
What one person describes as “noise” could be the very same thing that another person calls “information”. It just depends on what one is trying to compute or measure.
As for being “ploddingly deterministic”; even in a completely deterministic universe, interesting things are possible. In the completely deterministic universe, a sufficiently insightful outsider may be able to predict the exact state of the universe at any point in time, and so it may seem boring to that outsider. But in general, those living inside of the universe will not be able to see the big picture. They won’t even be able to tell whether or not the universe is deterministic. Maybe I’ve missed the point of what you trying to say; but in my eyes, there is nothing boring about determinism. It sure beats pure randomness.
> Our generous universe comes equiped with the ability to compute.
Dave,
if you divide the possible universes into the ones which allow computation and others which do not, then another good question would be if there are universes which allow some computations but not others.
E.g. in our universe ‘hyper-tasks’ seem impossible (infinite number of operations in finite time) but perhaps they are possible in other universes?
Perhaps some universes allow for classical computation but have strong limits on quantum-cimputers (our unverse?). etc.
A hierarchy of universes based on computational capability…
Now here comes the anthropic cosmologist and wonders which type of universe are we most likely to inhabit. It has to allow some computation for life to exist, but perhaps not too much (e.g. universes which allow ‘hyper-tasks’ might be very rare and improbable).
Damn, I wish you’d been in Waterloo a week earlier, and that you’d been in the audience for my talk at the Operational Quantum blah blah blah workshop. Some of your post’s ideas sound very familiar. I’d have loved to hear your comments… though, on further reflection, some of the ideas I expressed about quantum Darwinism and its relevance, I may have cribbed from this very blog (e.g., “if a closed quantum system existed, then it wouldn’t exist”).
Quick question: isn’t the tradeoff between robustness and relevance quantum-only? Is there any contradiction in imagining a classical universe full of robust, information-sharing computers? (other than the usual problems with black-body radiation, inward-spiraling electrons, etc…)
Isn’t there a book called “A madman dreams of Turing machines”? If so, it would seem to call into question your sanity.
Have you read Vernor Vinge’s “A Fire upon the Deep/Deepness in the Sky,” series, which contains at least three computationally different “universes.” I’m looking forward to the next one, which may be set in a universe like your computationally rich one.
“So I don’t see how this noisy and information are a matter of perspective the same thing.” – D. Bacon
This sentence is noisy and contains information.
zevans: The kind of determinism in the universe which you cannot compute is different than the determinism of a computing universe. In the universe in which you cannot compute, you could only do things, like say, perform xors of two bits, rendering yourself computationally not universal. So no the non-computing universe is not bleak because of determinism (or indeterminism) but bleak because of the computational impotency. In other words it is bleak not because of predicatbility, but because of its computational impotency.
Also noise to me is a process, information is a property of a system. Noise which completely and totally randomizing, from all perspectives, destroys information. So I don’t see how this noisy and information are a matter of perspective the same thing.
I have read “A Fire Upon the Deep” but not “Deepness in the Sky.” Actually I remember having interesting ideas while I was reading “A Fire..” but can’t recall what they were! Have to pick up “Deepness in the Sky,” I’m a sucker for a prequel (I mean I actually went to the first three Star Wars 🙂 )
Dave,
This might seem a like a strange thing to say, but how do we know that universal computation within our universe is actually universal.
In the XOR universe you mention, I’m not sure they could be aware of computation beyond XORs, and to a certain extent this might carry over to our own universe.
If we can simulate a type of computation, even inefficiently (i.e. QC) then that type of computation most certainly exists. If however there is some type of computation beyond what is simulable with NANDs, then I don’t see how we could ever represent it, and so ever become aware of it’s existence.
In the XOR universe, there is no way of ever performing an AND, no matter how inefficiently, and so I’m thinking that maybe this is something that may carry over to us to.
That said, it does sound like quite a crackpot idea.
What do you mean the universe can’t be computed.
Let me put the numbers to you…
zero=infinity=God
God=infinity=0
Same ole same ole..
Hippocrates squares the circle but “rounds” out the equation.
Eric:
Infinity= One divided by Zero
and I’m not sure what numerical value to asign God
I like rounding equations because I’m a physicist.