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Tag Archives: Church-Turing thesis

This continues my discussion of **A Computational Foundation for the Study of Cognition**, a 1993 paper by philosopher and cognitive scientist **David Chalmers** (republished in 2012). The reader is assumed to have read the paper and the previous post.

I left off talking about the differences between the causality of the (human) brain versus having that *“causal topology”* abstractly encoded in an algorithm implementing a Mind CSA (Combinatorial-State Automata). The contention is that executing this abstract causal topology has the same result as the physical system’s causal topology.

As always, it boils down to whether process matters.

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52 Comments | tags: algorithm, brain, brain mind problem, Church-Turing thesis, computation, computationalism, computer model, computer program, David Chalmers, human brain, human mind, mind, positronic brain, theory of mind | posted in Computers

No, sorry, I don’t mean the Bletchey Bombe machine that cracked the Enigma cipher. I mean his *theoretical* machine; the one I’ve been referring to repeatedly the past few weeks. (It wasn’t mentioned at the time, but it’s the secret star of the *Halt! (or not)* post.)

The Turing Machine (TM) is one of our fundamental definitions of calculation. The Church-Turing thesis says that *all* algorithms have a TM that implements them. On this view, any two *actual* programs implementing the same algorithm do the same thing.

Essentially, a Turing Machine *is* an algorithm!

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8 Comments | tags: Alan Turing, algorithm, Church-Turing thesis, flowchart, state diagram, Turing Halting Problem, Turing Machine, Universal Turing Machine | posted in Computers

*“Ouch!”*

Over the past few weeks we’ve explored background topics regarding calculation, code, and computers. That led to an exploration of software models — in particular a software model of the human brain.

The underlying question all along is whether a *software* model of a brain — in contrast to a *physical* model — can be conscious. A related, but separate, question is whether some algorithm (aka Turing Machine) *functionally* reproduces human consciousness without regard to the brain’s physical structure.

Now we focus on why a software model isn’t what it models!

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40 Comments | tags: AI, algorithm, bowling ball, brain mind problem, Church-Turing thesis, computationalism, computer model, computer program, consciousness, hot resistor, human brain, human consciousness, human mind, laser light, magnetron, microwaves, mind, software model, Theory of Consciousness | posted in Computers

Is that you, HAL?

Last time, in *Calculated Math*, I described how information — *data* — can have special characteristics that allow it to be interpreted as *code*, as instructions in some special language known to some “engine” that executes — *runs* — the code.

In some cases the code language has characteristics that make it Turing Complete (TC). One cornerstone of computer science is the Church-Turing thesis, which says that all TC languages are equivalent. What one can do, so can all the others.

That is where we pick up this time…

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1 Comment | tags: Alan Turing, algorithm, Church-Turing thesis, code, data, flowchart, lambda calculus, state diagram, stored program computer, Turing Machine, Universal Turing Machine, Von Neumann architecture | posted in Math

The previous post, *Halt! (or not)*, described the Turing Halting Problem, a fundamental limit on what computers can do, on what can be *calculated* by a program. Kurt Gödel showed that a very similar limit exists for any (sufficiently powerful) mathematical system.

This raises some obvious questions: What is *calculation*, exactly? What do we mean when we talk about a *program* or *algorithm*? (And how does all of this connect with the world of mathematics?)

Today we’re going to start exploring that.

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7 Comments | tags: Alan Turing, algorithm, binary digits, calculation, Church-Turing thesis, code, computer program, data, information theory, lambda calculus, mathematical expression, Turing Machine, Universal Turing Machine | posted in Math, Opinion