On Sun, Feb 10, 2013  Craig Weinberg <whatsons...@gmail.com> 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, 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, 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.

> 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.

  John K Clark

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.


Reply via email to