On Monday, February 11, 2013 1:29:55 PM UTC-5, John Clark wrote:
> > all those concepts of geometry, like the trigonometric functions, can be
>>> derived from one dimensional numerical sequences with no pictures or
>>> diagrams involved and if told that a particle with N degrees of freedom
>>> changes in a certain way and then changed again in a different way but one
>>> that is still consistent with those functions a one dimensional geometer
>>> could still specify what the coordinates of that particle will now have in
>>> N space.
>> >> That's my point. There is never any need to have more than one
>> dimension. All there need be is numerical sequences.
> Then why can't a one dimensional Turing machine do geometry,
It can solve geometry problems, but it can't generate geometric forms. It
has nowhere to draw a triangle and nothing to draw it with, no eyes to see
it, and no mind to appreciate it as a form.
> after all the number of points in a one dimensional line is the same as
> the number of points in a square or in a 3D box (or 4D or 5D or 6D or...).
> Obviously if you insist he remain one dimensional the poor machine can't
> draw a 2 dimensional triangle, but ask a question about triangles and he
> will give you a good answer,
Absolutely. That's what I'm saying. It can tell you all kinds of things
about triangles, just like Mary can tell you all kinds of things about red,
but there is no experience which is triangular. A universe generated by
Turing-like arithmetic would not and could not have any use for
multi-dimensional presentations. Since we actually do live in a universe of
mega-multi demensional sensory presentations, that means that comp fails as
a cosmology to explain the universe that we actually experience. It could
explain a mathematical cosmos, but that would of course be invisible,
intangible, silent, and unconscious.
> or ask what a tesseract will look like when that 4 dimensional cube
> intersects with 3 dimensional space at a particular angle and it will
> figure out a accurate description.
Yes, yes, we can make a computer simulate our visual expectations, but we
can't find a reason why anything should have visual expectations if it can
simulate them in the first place.
> > We have access to multiple spatial dimensions of geometry through our
>> sensory-motor participation
> There is no reason a machine couldn't do the same, and we might only have
> direct sensory access to 2 spatial dimensions not 3. Recent theoretical
> arguments indicate that the maximum amount of information that can be
> contained inside a volume of space is proportional to the area of a sphere
> enclosing that space not of its volume as you might expect. So our 3D world
> could be a sort of holographic projection of a flat 2D surface.
Yes, I've heard about the 2D thing. Makes sense since our 3D vision only
arises by the comparison of two 2D images. Still though, the point is not
that a machine could not have a drawing tablet and a screen installed on
its motherboard, its that that obviously would be redundant. The computer
has no need whatsoever to visualize geometric forms. They are superfluous
> John K Clark
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