Motifs in Science

Programmers have long made it their job to deal explicitly with managing complexity. I think the same type of introspection goes on in science, but just isn’t introduced to students as soon.
In programming, such introspection often takes on the aura of religion, since it is complex human behaviour that is being studied. Human behaviour is difficult to study objectively due to its non-uniformity both across different individuals and for the same individual at different times. This is compounded by the fact that good approaches to handling complexity are often most valuable when few people know them, providing a strong drive to misinteprete the statistics of small numbers.

It is essential then, for me to avoid giving the impression that I am presenting the One-True-Way of looking at science during this course. I merely aim to make a difference by inspiring you to find your own understanding.

The specific topics I have in mind are

  • Bayes Theorem
    • Why should predictions precede observation?
    • With finite time and resources, what types of compromises between generality and specificity are possible?
  • Inductive Tools
    • Black Boxes,
      • Using
      • Building
        • Testing using
          • Symmetries like
            • Invertibility
          • Limits
    • Representations
  • Deductive Tools
    • Approximations
      • Expansions, some
        • Convergent
        • Asymtoptic
    • Transforms
    • Axiomatic Logic
      • Combinatorial Spaces
        • Computation

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