# Mathematical Consciousness

*This post is spurred by reading Permutation City, which is excellently thought-provoking. Greg Egan is now one of my favorite authors.*

## Thought Experiments

I hold no dualist notions, and do not find philosophical zombies very convincing either. As such, I am fully prepared to believe that if you were to create a sufficiently-detailed simulation of my brain, and run it inside a sufficiently-powerful computer, it would experience consciousness. There are certainly short- and medium-term practical obstacles to this, in terms of our poor understanding of what is necessary for a sufficiently-detailed brain simulation. But I see no reason this wouldn’t be possible eventually.

Let’s consider what this simulation really is: a program, which generates a series of (very long) numbers. Each number represents the state of the computer’s memory at that point in the simulation. Let’s take the sequence of numbers representing ten simulated minutes of brain time. As the machine’s memory evolves according to these numbers throughout ten minutes, we have a simulacrum of me experiencing consciousness.

What would happen if we evolved the computer’s memory a bit more slowly? Say, instead of holding these numbers in memory at their original rate, we took twice as long—twenty minutes. What does the simulacrum-me experience? Obviously, it still experiences ten minutes of consciousness; it has no frame of reference that tells it that “out there” twenty minutes have passed.

Let’s try something else. What if we got rid of the program simulating the brain, and simply replaced it with a dumb program that read the ten-minutes-of-numbers off disk and loaded them into memory, in sequence. This should be functionally identical; it doesn’t matter whether the memory was computed ahead of time or in real time. The system will still have a conscious experience. It can’t tell whether those numbers came from the CPU or the hard disk.

What if I, the physical human, wrote down all those numbers on pieces of paper in sequence? Does that written-on paper now experience consciousness? It seems like it should; there’s nothing magical about transistors. Remember, no dualism allowed.

Does it make a difference how good my handwriting is?

What if I only wrote down the first such number? Assuming a deterministic universe, there is a set of rules that will evolve that single number forward in time, to live a full life (even beyond the ten minutes we originally ran the computer program for). Maybe I’d need to write down some encoding of those deterministic rules, too—although I’m not sure why. Does that single written-down number experience consciousness?

What if we never involved computers, computer memory, or paper at all? The number still exists, even without me writing it down, as do the rules for evolving it. (Even without humans around to count, the number five still exists.) Does … something … still experience consciousness?

## Thought Conclusions

I imagine there are two reactions to this. Perhaps the more common will be to assume I’m performing a *reductio ad absurdum* on the idea of simulating conscious experience. I started from that premise, and came to the conclusion that my (simulated?) consciousness exists and experiences things independent of any physical substrate. Seems absurd, so something must have gone wrong, right?

I don’t think so. Not only is the chain of logic inescapable, but this line of thinking also points toward a sublime solution to some of the biggest questions around. Namely, why does anything exist at all? And, why is mathematics so spectacularly effective at describing the physical universe?

The answer is that the universe itself is simply a timeless mathematical construct. Of what type, we’re not exactly sure yet; it’s looking like it’ll be some kind of mashup of a 3+1-dimensional pseudo-Riemannian manifold with tensor fields obeying certain partial differential equations, plus operator-valued fields on ℝ^{4} with certain commutation relations acting on an abstract Hilbert space. But when we do have our theory of everything, plus the initial conditions of the universe, it’s clear to me that within its Platonic mathematical structure lies all of the manifest complexity and consciousness we observe around us.

There’s no need to run a simulation. The mathematical structure exists, independent of human discovery, or of computers to run it. And that’s why you and I exist.

## Further Reading

If you find this interesting and potentially compelling, I recommend the following resources:

- Permutation City places these ideas in a fictional context, to great effect
- Tegmark’s papers: Is “the theory of everything” merely the ultimate ensemble theory? (1997) and The mathematical universe (2007)
- Peter Woit’s critique of Tegmark, pointing out that this does not make any real testable predictions and thus is more philosophy than science (which is fine by me)
- Hans Moravec’s Simulation, Consciousness, Existence which contains a deeper investigation of these issues, including some talk of morality