On Sat, Feb 16, 2013 Craig Weinberg <whatsons...@gmail.com> wrote:
>> With complex numbers you can make a one to one relationship between the
>> way numbers add subtract multiply and divide and the way things move in a
>> two dimensional plane. What more could you want arithmetic to do in support
>> of geometry, where on earth is the incompatibility??
> > It doesn't matter whether arithmetic *supports* geometry or not.
> What matters is that if we cannot explain to how arithmetic *actually
> becomes geometry*, why it *must become geometric* under some arithmetic
Well, "under some arithmetical conditions" numbers behave exactly precisely
in the way that Euclid said geometric objects should behave. Numbers have
also told us something we could not have found out in any other way, that
Euclid's way is not the only way that geometric objects can behave that is
logically consistent. And then Einstein, also using numbers, showed that
not only is this non-euclidean way possible it is the only way to figure
out how things change in very powerful gravitational fields.
> we *certainly cannot* claim that a purely arithmetic universe could
> possibly contain any geometry at all.
Given the above what aspect of geometry have numbers failed to capture?
>AI programs wouldn't need to be written if computers could use cameras to
And people wouldn't need brains if eyes could see, but eyes can't see. Eyes
and TV cameras do the same thing, they both use a encoding protocol to turn
the information in a 2D image into a 1D signal that can be sent down a wire
(the wire can be made of copper or protoplasm) to a processing unit made of
neurons or transistors. If 2 cameras or 2 eyes are used the processing unit
can obtain additional information about the third dimension if the correct
sort of data processing is used.
>> But the only way to prove that to others is by successfully maneuvering
>> something through a 3D obstacle course, and existing AI programs can
>> already do this.
> > Why would I need to prove that to others?
For the same reason you demand that a AI prove it is conscious.
John K Clark
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