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| Authored by: Wol on Saturday, May 11 2013 @ 04:43 PM EDT |
And he also didn't consider other factors. How would you sum all the numbers
from 1 to 1000?
If you've got a computer, the obvious way is a do-loop or for-next.
But if you're a mathematician, the answer is obvious. 500*1001 = 500500. So a
half-way decent mathematician should be able to do a lot of stuff that a
computer programmer with a computer would find hard.
That said there are plenty of things a mathematician with a computer would find
hard :-)
Cheers,
Wol[ Reply to This | Parent | # ]
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| Authored by: dio gratia on Saturday, May 11 2013 @ 05:20 PM EDT |
I commend to you the novel Souls in the Great
Machine by Sean McMullen. At least up until several years ago there were
various calculor societies in Great Britain, where people would get together and
emulate a human based computer and run programs, which from the novel would
include a defined architecture and operating system as well as error
checking.
The basic idea similar to that of the assembly line, that a
collection of people each doing part of a task can do something otherwise
impossible for one person in a reasonable length of time. Essentially adding
parallelism.
There's also the problem that programs tend to grow in
complexity (sometimes needlessly) to fill the capacity of the machines they run
on. Notice how terse descriptions of software implemented 'inventions' tend to
be in patents. A case of separating the wheat from the chaff.
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| Authored by: FreeChief on Sunday, May 12 2013 @ 02:44 PM EDT |
Turing just didn't consider those factors.
That's
because software does not consider those factors. I can easily write a correct
program to compute 10!!!!!, e.g.:
((rep factorial 5) 10)
That's a
correct Scheme program; it needs about ten more obvious lines to define rep and
factorial.
The fact that it won't run to completion on this old laptop has
nothing to do with the software.
You could probably get a patent if you
could build hardware powerful enough to run the program, but it would be a
patent on the hardware, not my software.
— Programmer in
Chief
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| Authored by: PolR on Sunday, May 12 2013 @ 09:41 PM EDT |
These things were considered. The decision is to expressly ignore them.
Suppose we define "computable" as "can be computable by pencil
and paper within a human life", then by this definition simple addition is
not computable. You can't add numbers with trillions of decimals in this manner.
We have to ignore human limitations when defining what is a mathematical
computation.
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| Authored by: Anonymous on Monday, May 13 2013 @ 05:08 PM EDT |
Math is math - period, end of line, full stop.
The human mind can't
complete the calculation of PI.
But then neither can a computer given PI
is infinite.
Just because the human couldn't complete a particular
computation in one human's lifetime doesn't alter the reality that the
computation is abstract.
Should the computer - which can complete some
computations which one generation of human mind could not - be patentable
subject matter? Absolutely!
But not the software! The power is in the
physical computer - the software is just an abstract human
instruction/communication - nothing more.
RAS[ Reply to This | Parent | # ]
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