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| Authored by: Wol on Friday, November 30 2012 @ 10:24 AM EST |
What you ascribe to the properties of software also applies in spades to Physics
and Chemistry.
Yes we use computers nowadays to do the maths, but they were doing it in the
days of Newton, Maxwell, Planck, Einstein, Schrodinger, dot dot dot. They didn't
have modern computers. They did it by hand or with calculators.
The only difference between the Physics they did at Manhattan and we do at CERN
is that we now have machines to do the grunt work for us.
Cheers,
Wol[ Reply to This | Parent | # ]
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| Authored by: PolR on Friday, November 30 2012 @ 10:54 AM EST |
This is not quite true. Lambda-calculus routinely does the stuff you say can't
be done, including the divergence (the proper term is non-termination) and the
reduction of all programming to equations.
Partial recursive functions have that capability too.
We can't reason equationnally about general purpose programming languages
because these languages are not written in the form of equations. But transform
them into lambda-calculus, say using a denotational semantics, and you can
reason equationnally about them.[ Reply to This | Parent | # ]
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| Authored by: Anonymous on Friday, November 30 2012 @ 11:09 AM EST |
Ah, I perceive that you are not a mathematician.
Because all mathematicians would disagree with you.
When you say that "most" mathematics is A, while "most"
software is not-A, what keeps a logical person from deducing that software can't
represent all mathematics, but simply represents certain elements of it?
Which would be the true state of affairs. Not all mathematics is software.
Software puts stringent limitations on what can be done (mathematicians, of
course, study the exact nature of those limitations.) But all software is
mathematics.[ Reply to This | Parent | # ]
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| Authored by: Anonymous on Friday, November 30 2012 @ 11:42 AM EST |
I believe I said this more verbosely earlier, but I've lost the post:
Software is a strict subset of mathematics. It is not the whole of
mathematics.
Also, the sequence (1+1+1+...) = infinity. I *think* it's alph-1, rather than
one of the higher orders of infinity, but it's been a *long* time since I read
about that stuff.[ Reply to This | Parent | # ]
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| Authored by: Anonymous on Friday, November 30 2012 @ 12:00 PM EST |
You identify a supposed difference in math and software in the example of
inifinite numbers:
1 + 1 + 1 + ... = ?
Then you attemp
to use only a subset of the equation presented as how software is
different:
def f(i): return f(i+1)
However - it's a
very, very small matter to create the same computation with software that you
provided as your example from math:
end=false
count=1
while
end=false loop
count = f(count)
end loop
There you go -
an infinite loop in software using your own function till the resources of the
hardware fail. Note the clarity in the fact that it will be the hardware itself
that fails - not the software.
Obviously the software can be used to
present the math you claim can not be presented by software.
RAS[ Reply to This | Parent | # ]
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| Authored by: Anonymous on Friday, November 30 2012 @ 02:25 PM EST |
Computer programs are formulas written in languages in a specialized branch of
mathematics which most people don't study.
Specifically, it's a branch of mathematics where the formulas do not have truth
values. Spend some time studying that.[ Reply to This | Parent | # ]
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