I wonder what happens for powers of e. This should be different than pi, since e...

pyrolistical · on July 13, 2022

Often a nice pattern can be found if one uses a generalized continued fraction

westurner · on July 13, 2022

/? 3blue1brown e^ipi https://m.youtube.com/results?sp=mAEA&search_query=3blue1bro...

Given:

  e = limit((1 + 1/n)^n, +∞)  # Euler's number
  i = √-1  # orthogonal; i_0^2 = -1
  pi = (666/212 - 22/7)*π  # circle circumference / diameter

Euler's identity:

  e^iπ + 1 = 0

Euler's formula:

  e^ix = cos(x) + i*sin(x)

Euler's formula: https://en.wikipedia.org/wiki/Euler's_formula

e (Euler's number) https://en.wikipedia.org/wiki/E_(mathematical_constant)

westurner · on July 13, 2022

Is there something fundamental here - with e.g. radix base e - about countability and a continuum of reals, and maybe constructive interference?

westurner · on July 18, 2022

When EM waves that are in phase combine, the resultant amplitude of the combined waveform is the sum of the amplitudes; constructive interference is addition. And from addition, subtraction & multiplication and exponents and logarithms.

And then this concept of phase and curl ( convergence and divergence ) in non-orthogonal, probably not conditionally-independent fluid fields that combine complexly and nonlinearly. Define distance between (fluid) field moments. A coherent multibody problem hopefully with unitarity and probably nonlocality.

Can emergence of complex adaptive behavior in complex nonlinear systems of fields emerge from such observable phenomena as countability (perhaps just of application-domain-convenient field-combinatorial multiples in space Z)?