#
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.

Continue reading

52 Comments | tags: 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!

Continue reading

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!

Continue reading

40 Comments | tags: AI, bowling ball, brain mind problem, Church-Turing thesis, computer model, computer program, computers, 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…

Continue reading

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.

Continue reading

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