On 6/11/2016 3:44 PM, John Clark wrote:
On Sat, Jun 11, 2016 at 3:03 PM, Brent Meeker <[email protected]
<mailto:[email protected]>>wrote:
>
There are no "incorrect calculations".
2+2=5
If you programmed a Turing machine to start with "2" and "2" on it's
tape and print out "5" it just means it didn't compute the sum of 2 and
2. If you program your computer to print out "2+2=5" the computer will
still do a correct computation. It's just your interpretation of the
output as applying to something other than what the computer did that is
incorrect. The computer still executed your program correctly.
>
It's just a universal Turing machine that runs all one step
programs, all two step programs, etc. Some programs stop. Some
programs fall into infinite loops. Some just keep computing.
And some are consistent with the
Peano postulates
and some are not, those that aren't physicists have no use for
because they can attach no meaning to them.
Actually physicists often use continuum mathematics, which are not
consistent with Peano axioms, e.g. every number has a divisor.
Mathematicians could start with 2+2=5 as an axiom and build some form
of arithmetic from that, it would be a pretty silly thing to do but it
wouldn't surprise me if some mathematician had actually done it. And
that's the trouble with mathematicians, sometimes when they drift
higher and higher into the stratosphere they start to sound like
Minnie Mouse on helium. Physicist are bound by something,
observational facts, but mathematicians have no such bound so
sometimes they end up moving in all directions and going nowhere.
>
These are all abstract processes that "exist" in the mathematical
sense.
What sense is that?
For every integer x there *exists* a successor of x, S(x). There *exist*
infinitely man prime integers. In every continuous mapping of a compact
convex set into itself there *exists* a point that is mapped into itself.
>
There is no sense in which they can be correct or incorrect.
What about non-sense?
You mean what about something that is not a computation, not an
implementation of an algorithm?
Brent
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