Re: Another clueless wikipedia article

It would take too much effort from me to explain it completely, but I
am going to remove those uninformed assumptions that the tape of a
turing machine is an actually infinitely long resource. In fact, at any
moment, the turing machine has a finite ID, and thus the infinity
talked of is potential infinity (much like the infinity of Z)
Furthermore, the TM is a mathematical model. Every TM denotes a
particular computation. The author probably doesn't recognize that. The
potential infinity there is an idealization. It does not mean that
physical machines cannot be TMs!

If you followed that naive logic, just because you can define finite
state machines that would not fit into this universe, desktop pcs would
not even be finite state machines.

Think about that for a while. What do I mean by "Every TM denotes a
particular computation"?

I am hoping it is clear now, and now this bit about desktop pcs not
being TMs is goodbye kansas. Why on earth do you think we are studying
turing machines then?

The standard reason for the potentially infinite tape of the TM is to
model the fact that an ongoing computation may extend the tape
(allocate more memory). This is usually thought to be a property of
desktop PCs as well. With some effort, it is possible to extend the PC
with as much memory as you want. There are no hard limits (except
physical limits which apply to EVERYTHING including FSMs). Did you ever
connect two PCs with a network? Fine. Then you know what this means.

For the record, all of this can be shown rigorously.
If you followed that naive logic, just because you can define finite
state machines that would not fit into this universe, desktop pcs would
not even be finite state machines.

Think about that for a while. What do I mean by "Every TM denotes a
particular computation"?

I am hoping it is clear now, and now this crap about desktop pcs not
being TMs is goodbye kansas. Why on earth do you think we are studying
turing machines then!!???

.

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