On 01 Feb 2013, at 22:09, Craig Weinberg wrote:

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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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