On 01 Feb 2013, at 22:09, Craig Weinberg wrote:
I have mentioned this before, but it keeps haunting me.
If geometry did not exist.
Could you invent it with mathematics alone?
And if you could do that...
Why would you?
For instance: A triangle can be defined mathematically in different
ways, but without the inherently geometric presentations of lines
and angles, it seems that all you could generate is a description of
a set of values which have the same relation as the values which
would be present if a geometric shape were measured or sampled from
optical or tactile detections.
That is not to say that the list of mathematical definitions which
satisfy triangularity (a^2 + b^2 = c^2 for example), even an
exhaustive list, would suggest anything like the visible presence of
a shape. All of the mathematics can be done completely in the dark,
and no realism of points, plots, displays, manifolds, topologies,
etc, ever need to literally appear to anything.
We don't know that.
Bruno
So why do they?
Craig
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