Tag Archives: Fourier

Joseph Fourier is Still Transforming Science

French, History, Physics, Science 1 Comment

Key Words: 250 years anniversary

  • Yesterdays: Fourier discovered Heat is a wave , Fourier Series, Fourier Transformation, Signal processing…
  • Today: IT imaging JPEG compression, Wavelets, 3G/4G Telecommunications, Gravitational waves …
  • Friends / bosses: Napoleon, Monge… Egypt Expedition with Napoleon Army.
  • Taught at the newly established Military Engineering University “Ecole Polytechnique”.
  • Scientific Research: Short period but intense.
  • Before Fourier died (he wrapped himself with thick blanket in hot summer), he was reviewing another young Math genius Evariste Galois’s paper on “Group Theory”.

https://news.cnrs.fr/articles/joseph-fourier-is-still-transforming-science

Moonshine Monster Group & Fourier

Modern Math Leave a comment

Moonshine 196,883
What object can exist in 196,883 dimension ?

Simon Norton: “I can explain to you what Moonshine (Monster Group) is in one sentence.
“It is the voice of God.”

While all the 5 mathematicians have been fully exhausted after 15 years of effort to categorize all Simple Groups in the Universe, only Simon Norton remains lonely in the search of the largest Monster Group (Moonshine).

Conway, who migrated from Cambridge to Princeton, does not want to touch anything on Group now, said, “Simon is the only person on earth who knows Moonshine”.

Monster Group M, order |M|=
2^{46}. 3^{20}. 5^{9}. 11^{2}. 13^{3}. 17.19.23.29.31.41.47.59.71

Moonshine Monster Group dimensions (dj) & relationship with Fourier expansion of coefficients (cj) in Modular Function:
x^{-1} + 744+196,884x + 21,493,760 x^{2} + 864,229,970x^{3} +\dots
c_n= c_1+c_2+...c_{n-1} + d_{n}
where
d_1 = 196,883
d_2 = 21,296,876
d_3 = 842,609,326
and
c_1 = 1+ d_1 = 196,884
c_2 = c_1+d_2 = 21,493,760
c_3 = c_1 + c_2 + d_3 = 864,229,970

What a coincidence! no wonder Conway said this discovery was the most exciting event in his life.