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Why Mathematics Is Natural

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There is nothing obvious about the mathematics we know. It is basically neurology we learn, that is, that we learn to construct (with a lot of difficulty). Neurology is all about connecting facts, things, ideas, emotions together. We cannot possibly imagine another universe where mathematics is not as given to us, because our neurology is an integral part of the universe we belong to.

Let’s consider the physics and mathematics which evolved around the gravitational law. How did the law arise? It was a cultural, thus neurological, process. More striking, it was a historical process. It took many centuries. On the way, century after century a colossal amount of mathematics was invented, from graph theory, to forces (vectors), trajectories, equations, “Cartesian” geometry, long before Galileo, Descartes, and their successors, were born.

Buridan, around 1330 CE, to justify the diurnal rotation of Earth, said we stayed on the ground, because of gravity. Buridan also wrote that “gravity continually accelerates a heavy body to the end” [In his “Questions on Aristotle”]. Buridan asserted a number of propositions, including some which are equivalent to Newton’s first two laws.

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