**Euclidean vs Fractal
approaches in the history of math and physics**

450 B.C.E.: Euclid’s axioms vs Zeno’s paradoxes of infinite regress – Euclid wins. Infinity is banished.

1200
AD: Fibonacci shows recursive sequence useful in modeling nature.

1615
Kepler brings back concept of “infinitesimal” for convergence to a limit as
infinity is approached, but “infinity itself” is still banished.

1831 Gauss: “I must protest
most vehemently against your use of the infinite as something consummated, as
this is never permitted in mathematics. The infinite is but a façon
de parler, meaning a limit to which certain ratios may approach as closely as
desired when others are permitted to increase indefinitely.

1877:
Cantor creates first fractal, inventing transfinite set theory. Later Lebesgue,
Hausdorf and others invent new measurements.

1900:
David Hilbert: Cantor’s transfinite mathematics is both crisis and opportunity.
Hilbert invents his own fractal, but also declares search for axiomatic proof
of the completeness of all mathematics. “No one can expel us from the paradise
created by Cantor.”

1920:
Wiener proves that Brownian motion is a fractal. Later harmonic theory uses
scaling structure in waveform decomposition.

1925
Hiesenberg shows that abstract algebraic description of quantum physics is
possible.

1927
von Neumann proves that quantum physics can be reduced to a purely axiomatic
system.

**The foundation: chaos or
logic????**