The continuum, Zeno's paradox and the price we pay for coordinates 117 | Math Foundations

In this video we venture into a range of topics, from the nature of the continuum, to the paradoxes of Zeno, to an understanding of some of the consequences for mathematics in the shift from geometry to arithmetic that flowed from the Cartesian revolution.

As we let go of the real numbers, we must prepare ourselves to appreciate that the arithmetical view of geometry does not always exactly fit with our physical intuition. Our biology constrains us in important ways, and so guides our thinking down certain paths, for better or worse.

If we demand that mathematics adheres to our biological orientation and physical intuitions, then we can be led astray. Such is the reason why modern pure mathematics has lost its way logically, with its unreasonable insistence that there is a theory of real numbers.

Video Contents:
00:00 Giving up the dream of "real numbers"
3:45 How to model the continuum
6:51 Another version of Zeno's paradox
8:52 Nature of the physical continuum
12:10 Mathematical continuum
14:46 Physical/practical intuitions
20:10 Identifying straight lines and circles
23:31 Identifying order relations
25:12 The price we pay for co-ordinates
28:21 Geometry created from Cartesian approach

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