Insights · Michaël PerreaultThe Bridge of Thought

Insights

Immanent and Transcendent: Spacetime and Frequency Domains

Michaël Perreault · 2025

  • Space­time domain: Local, ex­ten­sion, di­men­sion, ex­pe­ri­ence—man­i­fest­ed per­cepts.
  • Fre­quen­cy domain: Non-local, ex­ten­sion­less, di­men­sion­less, pure thought—un­der­ly­ing con­cepts.

The Fouri­er trans­form is the math­e­mat­i­cal Bifröst, en­abling both ascent (from space­time to fre­quen­cy, per­cept to con­cept) and de­scent (from fre­quen­cy to space­time, con­cept to per­cept):

F(ν)=∫−∞∞f(t)e−2πiνtdtF(\nu) = \int_{-\infty}^\infty f(t)\, e^{-2\pi i \nu t}\, dt
  • f(t)f(t): local per­cept (func­tion of time or space).
  • F(ν)F(\nu): tran­scen­dent con­cept (fre­quen­cy/math­e­mat­i­cal source).
  • ν\nu: fre­quen­cy.
  • ii: imag­i­nary unit.
  • ee: Euler’s number.

Re­versible by:

f(t)=∫−∞∞F(ν)e2πiνtdνf(t) = \int_{-\infty}^\infty F(\nu)\, e^{2\pi i \nu t}\, d\nu

Phys­i­cal re­al­i­ty is gran­u­lar, each “pixel” of size ℓP\ell_P (Planck length):

ℓP=ℏGc3\ell_P = \sqrt{\frac{\hbar G}{c^3}}
  • ℓP\ell_P: small­est unit of space (im­ma­nent point).
  • ℏ\hbar: re­duced Planck con­stant.
  • GG: grav­i­ta­tion­al con­stant.
  • cc: speed of light.

Each pixel is a local ex­pres­sion of a global zero-sum of con­cepts, a node in the uni­ver­sal wave.

Sum­ma­ry Table: On­to­log­i­cal Cor­re­spon­dence

DomainNatureMath­e­mat­i­cal Rep­re­sen­ta­tionRole
Space­time DomainIm­ma­nent (Per­cept = pro­ject­ed con­cept)f(t)f(t), tt, ℓP\ell_PLocal, ex­ten­sion, di­men­sion, ex­pe­ri­ence
Fre­quen­cy DomainTran­scen­dent (Con­cept, zero sum)F(ν)F(\nu), ν\nu, eixe^{ix}, ei(x+π)e^{i(x+\pi)}Non-local, ex­ten­sion­less, di­men­sion­less, think­ing. Every form is bal­anced by its anti-form (π\pi ra­di­ans away).