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Posts Tagged ‘turing machines’

The NKS summer school archive site is live.  I figured it would be best for me to wait until that was done before I attempted to post my project or write too much about other’s projects.

You can check out a summary of what I did personally on the Wolfram site.

Project Title 
Perturbing Turing Machines

Project
Perturbations to elementary cellular automata have been investigated thoroughly. Under a certain level of perturbation, there are slight changes to local patterns but the automata tend to recover globally. The more complicated rules show greater disturbance but still can tolerate perturbations. This study considers similar perturbations to Turing machines.

Do Turing machines exhibit similar behavior?

“And the reason this is important is that in any real experiment, there are inevitably perturbations on the system one is looking at” (NKS p. 324). We must account for the effects of perturbations to draw any connections between these simple constructs and their natural counterparts.

Every project done there was interesting.  I encourage readers to check them all out.  Some projects are more abstract than others and all were a good launch pad for further research or immediate practical use.

I do have to call out Ben Rapoport’s project on neuronal computations.  It was beautiful in many ways.

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Have you ever played Civilization, the computer game?

Determined and yet unpredicable

Determined and yet unpredicable

If you haven’t, it’s really fun.  However, that’s not the point of this post nor the title.

What makes Civ or Sim City or any of the other sim games so interesting is that they are a great example of what it means to be completely determined and yet totally unpredictable.

So what, you say?  It’s a computer game.

Ah, I contest this game is far more like the real world than one might suspect.  Yes, I can “freely” control what I do with my civilization – move my citizens around, build different things, arm, disarm, trade, war, research, pray, etc. etc.  However, I’m actually quite forced into almost every move once all the contingencies come home to roost.  Did the computer just attack me?  Do I have the money? Do I have the people? How much power do I have? All of those and more filter the space of all possible moves.  Perhaps there’s a few “free” choices left on each move that become probabilities but even those are held under control based on contingencies (like my preferences for how to move).

So why then are the games (life?) unpredictable?  For one, initial conditions.  The set up of the geography, placement on the map, type of people and so forth change every time you start the game, so the game (under the same predetermined moves) takes a completely different form.  I’m always careful in discussing initial conditions because you can’t really ever make a claim as to what a real “initial” condition is in the real world (or even the game), as something must determine the initial condition you are looking at (even if it is a “random number generator).

Amazingly, it’s not just interesting initial conditions.  Simple rules (even the most basic rules you can imagine) can operate in fully unpredictable ways.  examples: http://mathworld.wolfram.com/Rule110.html and http://www.johnkyrk.com/DNAtranscription.html and http://en.wikipedia.org/wiki/Prime_number.  These three examples all of very simple rules of operation (how you generate them, how they evolve, etc. etc), yet their outcome/their behavior/their product is not predictable.

I digress (and don’t you hate when people say “I digress”?).

Perhaps my silly use of computer games does nothing for my argument about there being things that completely determined and unpredictable.  I could, of course, turn your attention to cellular automata or turing machines or some other simple system -some of these types of systems are unpredictable and they all are completely determined.  Unfortunately, many folks will complain that these aren’t “real world.”  The real world is full of indeterminism and lots of messy things that aren’t like computer games or automata.

It’s true that the world is full of systems that aren’t computer games or automata!  However, it’s not obviously true that these systems are indeterminate! How can we figure that out?

One way, if I can show you determined systems that exhibit the same behavior as the supposed indeterminate systems, that’s some evidence for determinate systems.

If I can drill down on your indetermined system enough I will like find your “rules” that drive it.  That’s my conjecture.  Send me a system, and we can discuss.  (markets, DNA, whatever you want).

Human behavior exists in this world of determined and the unpredictable.  Reinforcers/consequences, conditioned stimuli, unconditioned stimuli, discriminant stimulus — (biology + genetics + nervous system + environment) — control the behavior.  Layers of rules applied to a complex biological system.  It’s all weirdly determined but completely unpredictable.

Falsify my claim.

Suppose this is true.  So what?  The implications are relative to you.  If indeterminism services your world view or scientific approach, perhaps the implications are grave.

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