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Meta-Physics

Table of Contents

1. Not What you think

This isn't about "New Age" hippy nonsense. By "Metaphysics", I mean literally "about physics". As in, the conventions adopted to reason about physics. For example, in presenting "experimental facts" in the form of axioms, with the understanding their truth is provisional.

I present such things because I'm a mathematician writing a Zettelkasten, and I cannot afford the luxury of space: an experiment's results must be conveyed in a quarter of a slip of paper (roughly A6 in size). When citing my Zettelkasten I summarize it as a particular subclass of propositions.

1.1. Constructive Results

When introducing, e.g., temperature, it's a new undefined term. We measure it using a thermometer. Which just begs the question: what's a thermometer? I tend to think providing an idealized construction from what we have previously established works best.

1.2. Experimental Facts

Some examples of experimental facts taken for granted:

  • The universe is described using 3 spatial dimensions and 1 temporal dimension.
  • (Newton-Laplace Principle of Determinacy.) A physical system's evolution is uniquely determined by its initial position and velocity.

Other experimental facts are really just worked examples. Experiments (like the Cavendish experiment, for example) constitutes a particular mathematical register similar to what a mathematician would call an "example". (Indeed, almost of physics amounts to a litany of examples.)

2. Examples in Physics

Unlike mathematics, "examples" in physics are not an instructive detour but the constituents of the subject. Their importance is more akin to that of theorems in mathematics. Picking good examples requires choosing different physical situations, not different numeric values for the same situation.

2.1. Methods for Solving Physics

Briefly, I've read a number of different ways to solve physics problems. Back in the 1980s, there was a fascination with AI experts studying how human experts solve problems. It turns out that Freedman and Young's ISEE method is the basic approach that experts perform mostly subconsciously:

  1. Identify the relevant concepts. Also identify the target variable you're solving for. Write down the known and unknown quantities and their values. You should be able to answer the question, "What is being asked of me?"
  2. Setup. Write down the relevant equations from physical laws (like \(F=ma\)). Do not solve or substitute numeric values. Pick a coordinate system (if relevant). Draw diagrams (if relevant).
  3. Execute. "Do the math". As far as possible, do everything symbolically, only substitute in numeric values at the last step.
  4. Evaluate. How do we know our answer is correct? This could involve taking limits of the symbolic answer (e.g., when friction goes to zero, or when it goes to infinity). Can we recover previous results taking some appropriate limit? Perhaps we could do order-of-magnitude estimates. Also dimensional analysis is useful.

Sometimes the "Identify" and "Setup" steps are contracted into one "Identify and setup". When one gains expertise, the "identify" step becomes "automatic".

3. References

  • Atish Bagchi and Charles Wells, "Varieties of Mathematical Prose". Manuscript dated 1998, PDF.

Last Updated 2021-06-01 Tue 10:00.