On Sun, Feb 10, 2013 Craig Weinberg <[email protected]> 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
