Turing Machine

Its said that the Turing machine is capable of the most powerful capacity to calculate over any computing mechanism known to man. But I cant figure out how that could be as it appears to me to be the simplest computing machine and nothing more. I has the absolute minimum of all thats required to be a computer:
- A single line (or tape) of one character symbols in its "program code"
- One character capacity of RAM (in the reading head)
-It can only read one symbol or write on symbol at a time
The only thing I can see that makes it complex is the internal instrction set that the reading head uses to react to the symbols it reads. So whats so special about the Turing Machine over any other computing machine?

If you could make the most powerful computing mechanism known to man out of a couple of dice, a pencil, and a roll of toilet paper, NASA wouldn't spend billions of dollars on Crays and the like.

A simple Turing machine is certainly NOT the most powerful computing mechanism, so wherever you got that information from may very well be implying something else. The principles behind simple Turing machines are the same basic principles used in making all computers, so perhaps they were saying that a simple Turing machine was not all that different from the most powerful computing mechanisms.

Well if you check the page on Wikipedia for Turing Machines:
http://en.wikipedia.org/wiki/Turing_machine
youll see this in the second section:

Quote:

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A Turing machine is a pushdown automaton made more powerful by relaxing the last-in-first-out requirement of its stack. (Interestingly, this seemingly minor relaxation enables the Turing machine to perform such a wide variety of computations that it can serve as a model for the computational capabilities of all modern computer software.)

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And after reading that I still dont see what makes it such a universal model for computing other than its simplity.