18个量子比特纠缠是什么?量子计算机为何如此强大?量子的纠缠态与叠加态

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Joseph Fourier is Still Transforming Science

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

Symmetry, Algebra and the “Monster”

Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher.

https://www.quantamagazine.org/symmetry-algebra-and-the-monster-20170817/

Summary:

  • Symmetry of a Square
  • Isometry (*) or Rigid Motion (刚体运动) = no change in shape and size after a transformation
  • What is a Group (群 “CAN I” ) ? = Closure Associative Neutral Inverse
  • Monster Group = God ?
  • String Theory: Higgs boson (玻色子) aka “God Particles”

Note (*): “保距映射” (Isometry),是指在度量空间 (metric space) 之中保持距离不变的”同构“关系 (Isomorphism) 。几何学中的对应概念是 “全等变换”