OT: One-color Lava Lamp

[narf poit chez BOOM]

What's a Turing Machine?

I've heard of the Turing Test, but never a Turing Machine.

[Will]

Turing Machine is a theoretical computer. As far as I know, an actual Turing Machine does not exist, only machines that are equivalent to it (in the mathematical sense). I guess it would be possible to build one, but it would be highly inefficient. It's called a Turing Machine after Alan Turing, who thought it up while doing cryptography work for Britain in WWII.

The following should be sprinkled liberally with "IIRC"... it's been a while since I've looked at the specifics of Turing machines:
Basically, you have a set of "states", denoted by Q, and an "alphabet", denoted by a capital gamma. The alphabet has at least two "symbols", of which one is the "empty symbol", usually "0". The states are initialized to one of the symbols in the alphabet. A state "s" existing in Q is called the "start state", and a set of states F exists in Q denoting "final states". Finally, there is a function denoted by lowercase delta that maps actions to be taken with this Turing Machine. You start in s (the start state), and keep going until you get "stuck" in a state; if this state is a "final state", that's your answer, otherwise the answer is undefined. So, for example, you start in s, which holds the symbol "a". Delta maps s and "a" to 'change current state symbol to "b", move to state s3'. And you would keep going until you reach a point where you loop in a single state forever, or reach some condition, etc. It all depends on the specific definition you use.

The point of the whole thing is that anything your computer can do, or any computer, a Turing Machine can do. A corollary is that what any one computer can do (compute), any other computer can as well. So, the first electronic computer, ENIAC, could have done exactly the same calculations as the world's fastest supercomputer now. The only difference is it would be a bit harder to tell ENIAC to do the same thing as the supercomputer, and ENIAC would be a lot slower. But the idea is, it is theoretically possible for that to happen.

So, Turing-equivalence basically means that you can translate any program into pure mathematics, and vice versa, and thus any way of programming can accomplish exactly the same thing as any other way of programming. However, hardly anyone is insane enough to do the translation that way. It's like doing mathematics entirely within the space of Russel's conversion of arithmetic to logic, where proving that 2 + 2 = 4 takes 21969 steps, including all the subtheorems, etc. used to get there.

[narf poit chez BOOM]

Don't know what Russel's conversion is, but I get your point.

I can prove that 2 + 2 = 4 with 4 peas.

2 peas here.
2 peas here.
Put them together and get 4 peas. A pre-schooler can understand that, if their parents have been teaching them.

However, as I understand your point, to unravel all the impulses from start to finish would take a long time. (Read somewhere that it takes millions of calculations just to move your little finger - Don't know how true that is).

[Instar]

C++ is easy, believe me... wait till you try doing assembly (or even just the raw machine bytes...), or COBOL.
C++ is easy, because you can do easy C stuff. After some basic procedural stuff, moving on to simple objects is easy enough.
Pointers are easy enough, but for some reason people get them wrong...
Anyhow, starting C++ is easy. Understanding the high level ideas is harder.

[Strategia_In_Ultima]

Will said:
Turing Machine is a theoretical computer. As far as I know, an actual Turing Machine does not exist, only machines that are equivalent to it (in the mathematical sense). I guess it would be possible to build one, but it would be highly inefficient. It's called a Turing Machine after Alan Turing, who thought it up while doing cryptography work for Britain in WWII.

Neal Stephenson's "Cryptonomicon" points this out as well. I'm not saying that what it says is entirely true (though I believe the basics behind the Turing machine as explained in Cryptonomicon are), but it is still a good - no, make that excellent read.

but as for your 1-color lavalamp NA, that's really relaxing.