BM Category Theory II 1.1: Declarative vs Imperative Approach

Math Online Tom Circle

Excellent lecture using Physics and IT to illustrate the 2 totally different approaches in Programming:

  1. Imperative (or Procedural) – micro-steps or Local 微观世界
  2. Declarative (or Functional) – Macro-view or Global 大千世界

In Math:

  1. Analysis (Calculus)
  2. Algebra (Structures, Category)

In Physics:

  1. Newton (Law of Motions), Maxwell (equations)
  2. Fermat (*) (Light travels in least time), Feynman (Quantum Physics).

In IT: Neural Network (AI) uses both 1 & 2.

More examples…

In Medicine:

  1. Western Medicine: germs/ viruses, anatomy, surgery
  2. Traditional Chinese Medicine (中医): Accupunture, Qi, Yin-Yang.

Note (*): Fermat : My alma mater university in Toulouse (France) named after this 17CE amateur mathematician, who worked in day time as a Chief Judge, after works spending time in Math and Physcis. He co-invented Analytic Geometry (with Descartes), Probability (with Pascal), also was the “Father of Number Theory” (The Fermat’s ‘Little’ TheoremandThe Fermat’s ‘Last’ Theorem). He…

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