But will you be helpful in rounding up other humans to toil in underground fluorescent plastic mines?

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That brings a whole new meaning to the term "train of thought".

Not to mention the term "system crash".

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and think of the havoc that could be wroght by a bug like a grasshopper or locust!

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As far as I remember the definition, a train system cannot represent a Turing machine, because a Turing machine has an infinite tape.

Also, there is no generic Turing machine. A Turing machine, afaik, is any finite automaton with an attached infinite tape.

The guys could probably build a finite-state machine out of railroad blocks, that's easy. But not a Turing machine!

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So just build the automaton-emulator automaton—the universal Turing machine. Though I gather that's not what they did... ?

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A finite TM can certainly "represent" an infinite TM - you just have to have a tape long enough to represent all the calculations of interest to you.

Calculating just how big this minimum tape length is then becomes an interesting problem, a bit like the "busy beaver" problem - how long can a FSM (finite state machine) run for, for a given number of states.

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That makes the term 'Turing machine' a pretty useless definition of a computing system than since it can never actually be applied to any real computing systems, only theoretical ones.

In order that the term be made more useful, I propose that it be accepted as a description of real systems with the obvious implied caveat that it's not actually a real turing machine by the most strict definition as it does not have infinite storage space.

That should satisfy all the pedants who object to such an implied definition without having it stated anymore, no matter how obvious it is.

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You seem to be of the mindset:

Anybody who wants to be my overlord is welcomed. They're welcome, even if they haven't actually stated they want to be my overlord but might possibly, in the far distant future, contemplate wanting the position. The more overlords, the better, because then they'll be too busy fighting to worry about me.

or something similar.

It's a fine mindset to have, but I just thought I'd note it in passing. :-)

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Do I understand you correctly that you suggest to redefine Turing machine to suit the purpose of the publication? Have you ever tried to apply this approach to solving other mathematical problems? E.g. prove that x^n + y^n = z^n does not have solutions for integer x, y, z and natural n > 2? Proof: let's redefine ^ operator to be multiplication. Voilá. Now you can go ahead and crack RSA.

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I wasn't proposing that anything be redefined. I was just noting jwz's desire to submit to it should it ever become an overlord.

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Sorry, I misunderstood you. :)

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Your posts are some of the most interesting on my friends list. Even the ones I don't understand.

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See also: a Turing Machine implemented in Conway's Game of Life.

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I have no idea what any of you are talking about but I like you anyway.

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*I* think you posted this for the matching colour scheme.

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