“If our universe is a computer simulation then Deterministic Finite Automata are to it what particles are to physics models.”
This very thought has me bugging lately a lot. I first tweeted it on June 4. I couldn’t help but think of this simile.
Until now, our pivotal model to explain and understand our world and the universe is the physics model. Since the advent of computers, though, with breakthroughs in software, logic and mathematics, some scientists argue that we have signs (but no conclusive proof yet) that our universe might be a computer simulation after all. And by extend, physics laws would be simple parameters that affect the simulation. In other words, “the rabbit hole goes deeper, Alice.” In fact, there might be infinite universes simulations, with infinite different ‘settings’ combinations and so forth and so on.
Key task for us is to prove this notion (its validity or inaccuracy) and understand how it actually works. I have not complete knowledge of this scientific domain but my gut tells me that, if in fact our universe is a simulation, then DFAs are to it what particles are to physics models. Mainly because such a universe would be completely deterministic (and as Donald Knuth said to me, “[…] and, as a result, we lose our free will“), hence these very small deterministic machines would be, I think, at its core.
The beauty of this idea is it initiates a debate around the intersection of its philosophical roots: logic, mathematics, physics, and philosophy itself. What do you think?
That’s very interesting topic and I keep thinking about it constantly.
Let me first give you a proof why particles are not the equivalent to DFAs. Your computer is the equivalent of a turing machine and it’s built by particles. So assuming particles are equivalent to DFAs, a model emerged from a DFA can’t be more powerful than a DFA. But, by definition Turing Machines are more powerful than DFAs, thus particles can’t be equivalent to DFAs.
What is more, a human beeing might be more like a turing machine. That comes from the fact that DNA/RNA itself seem to be a turing machine (http://stackoverflow.com/a/237121/439559), and models emerging from it can’t be more powerfull than a turing machine. Thus, a brain probably is equivalent to a turing machine, capable of running other turing machines as well.
So, here comes my point. Given that the brain is a turing machine, that means it can be simulated and for me that means that also the perception or the “soul” can be simulated as well. Free will is just a perception. For me and you, there will always be a machine that can simulate us. Laplace in a similar fashion introduced the thought experiment of a demon being able to predict the future given it has full knowledge of the current state (http://en.wikipedia.org/wiki/Laplace's_demon). Determinism comes from the fact that someone _knows_ the exact current state. Let me give you another example. For a computer there is no random thing. It can always know what’s the next number so for a computer there is only determinism. However, for the human perception, which might not have access to the current internal state of it, does this actually matter ? Will you feel less lucky if you win the lottery from numbers generated by a computer ?
I believe having full knowledge is impossible and thus determinism is well hidden under this constraint. In game theory that’s the equivalent of incomplete information. Thus, the free will is just ability of organisms to create strategies to cope with that incomplete information. Determinism doesn’t contradict free. It just emerges from our limited capacity of predicting the future.
BTW, please please please read “How Create A Mind” by Kursweill.
I think so, given Gödel’s Incompleteness Theorem.
— Other than that, wow, what a fucking epic comment. So awesome — so intriguing. I think I agree. Re: DFAs, my way of thinking was that theoretically one could (?) deconstruct all of the world’s actions and interactions in their simplest terms, thus a DFA would be able to describe them.
@Apostolos:
Regarding your response (“I think so, given Gödel’s Incompleteness Theorem”) to the belief that “having full knowledge is impossible”, one needs to remember the following thing relating to the Incompleteness Theorem (IT):
The IT talks (a) about consistent AXIOMATIC systems, containing theorems that can be numbered/listed by some kind of specific procedure, and (b) about TRUTH of the NATURAL NUMBERS and their relations. (i.e. not TRUTH IN GENERAL, but truths of relations of numbers in N)
From my understanding of the issue at stake, and its philosophical dimension/implications, Godel’s Incompleteness Theorem cannot be correlated with knowledge or truth in general, but under this specific linguistic/mathematical/axiomatic lens. There is a good chance that I am mistaken about it, so please feel free to correct me, or help me better understand the position of Godel’s IT in the discussion
Cheers.
Nice article – thanks for this. I enjoy reading and thinking about this topic. Kinda cool and it just came out – new book that talks about simulated universes running inside simulated universes and how the physical attributes of universes could evolve over time, through a process similar to natural selection. Simulated universes with certain physical traits would tend to survive longer and produce more habitable environments for more advanced civilizations to produce a higher number of simulated universes themselves with an increased amount of those physical traits, and so on. So, over time, there would be a tendency for simulated civilizations to reside in universes with the physics more suitable for life.
http://www.amazon.com/Computer-Simulated-Universes-Mark-Solomon/dp/0989832511/ref=sr_1_1?ie=UTF8&qid=1376689785&sr=8-1&keywords=computer+simulated+universes