Over the last three posts I’ve been exploring the idea of system states and how they might connect with computational theories of mind. I’ve used a full-adder logic circuit as a simple stand-in for the brain — the analog flow and logical gating characteristics of the two are very similar.
In particular I’ve explored the idea that the output state of the system doesn’t reflect its inner working, especially with regard to intermediate states of the system as it generates the desired output (and that output can fluctuate until it “settles” to a valid correct value).
Here I plan to wrap up and summarize the system states exploration.
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!
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…