Time, Reality, and Turing Machines

I often find thinking about various metaphysical problems in terms of Turing machines is an extremely powerful tool, particularly the problem of consciousness. I was inspired a few moments ago by this xkcd comic (one of my favourites):

http://imgs.xkcd.com/comics/a_bunch_of_rocks.png

My thought was this: how does the rate of passage of time in the simulation correspond to the actual rate of passage of time of the 'real' Turing machine? Surely the rate at which reality progresses has absolutely no influence on the rate at which time passes for the inhabitants of the simulation? The simulator could go extremely fast or extremely slowly. He could even vary his speed or stop altogether for a while. But exactly the same algorithm would be enacted, and exactly the same brain activity of the simulatees would be emulated, so surely they sould experience the same rate of time passing?

But then, what determines their rate of time? Where does it come from?

As an aside, a thought I've had once before is this: it's my belief that anything simulated by a Turing machine is objectively real; an aspect of corporeality. But then, the Turing machine itself must be objectively real (and so on).

Just a couple of thoughts there. What are yours?

This is way too deep to be thinking about in a sleep-deprived state but I'll give it a go.

I would say for a simulated person, the flow of time appears to remain constant, even if the simulation is sped up, slowed, halted, or even reversed, as long as everything related to the simulation was scaled by the same factor.

The mechanism by which time is perceived is modified by the same factor as the simulation, so the reference point appears unchanging. For example, if you double the speed, a simulated watch runs twice as fast, and the person's neuronal activity proceeds twice as fast, and events proceed twice as fast, so there's no noticeable difference.

Now if we sped up the person's simulated brain whilst leaving other aspects of the simulation unchanged, time would appear to proceed more slowly, since more thought occurs between events, and analysis can be performed at a higher resolution of time.

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how does the rate of passage of time in the simulation correspond to the actual rate of passage of time of the 'real' Turing machine?

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The rate at which time proceeds in the simulation and the "real" timeframe are unconnected. The simulated timeline can flow both ways at any speed within the limits of computation. Reality is fixed in one direction at a single speed.

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But then, what determines their rate of time? Where does it come from?

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By reference to the flow of simulated events, and the rate at which the mechanism for the perception of time works at.

If it takes 1000 years to caculate 1 year, then their rate of time will be exactly, 1000 times slower.. 1 second for us will be 1 millisecond for them.

Anyway, cool strip.. maybe the guy in the desert was God? One day humanity will also create a simulation of the universe, who says a previous civilization hasn't done it before us? If time is infinite, then the amount of time already past must also be infinite, making the possibility of this already having happened.. 100%. If you have infinte time to roll a dice, the probabilit y of rolling a 6 is 100%

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Originally Posted by Xei

Just a couple of thoughts there. What are yours?

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I thought about this when I first heard that human beings could someday enhance their intelligence with bio or nanotech. Using either method we could speed up our rates of thoughts, but then I wondered if we would perceive them as faster, or if they would seem the same to us, but faster relative to the external world. I think my original thought was, would we feel like we are reacting faster, or would it just feel like time slowed down? And then I wondered how this innovation would change our relationships with each other. Add virtual reality and then it would become more efficient to operate in the virtual world than reality, because of physical limitations that wouldn't exist in the virtual world. Of course being the lazy person I am I thought about how you could have extended vacations, one day lasting a month, etc.