The key thing in a good system of units is to define units in a way that depends only on physical properties of nature.
Ideally (or basically necessarily?) the starting point generally has to be discrete phenomena, e.g.
- number of times some light oscillates per second
- number of steps in a quantum Hall effect or Josephson junction
What we don't want is to have macroscopic measurement artifacts, (or even worse, the size of body parts! Inset dick joke) as you can always make a bar slightly more or less wide. And even metals evaporate over time! Though the mad people of the Avogadro project still attempted otherwise well into the 2010s!
Standards of measure that don't depend on artifacts are known as intrinsic standards.
Computational physics is a good way to get valuable intuition about the key equations of physics, and train your numerical analysis skills:
- classical mechanics
- "Real-time heat equation OpenGL visualization with interactive mouse cursor using relaxation method" under the best articles by Ciro Santillis
- phet.colorado.edu PhET simulations from University of Colorado Boulder
Other child sections:
Paraprasing a friend of Ciro Santilli:
Magic: The Gathering is like cocaine in card form.
Luckily, early teens Ciro Santilli was partly protected from this by Ciro Santilli's cheapness.
But Ciro distinctly remembers one day in his early teens that he couldn't sleep very well, and he got up, and the was decided that he would become the greatest Magic: The Gathering player who ever lived. Can you imagine the incredible loss that this would have been to humankind? And talk about the incredible lack of development opportunity present in poor countries, related:
Supervised and unsupervised learning by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Feud between Sabine Hossenfelder and Luboš Motl by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
The key is to define only the minimum number of measures: if you define more definitions become over constrained and could be inconsistent.
Learning the modern SI is also a great way to learn some interesting Physics.
Lie Groups, Physics, and Geometry by Robert Gilmore (2008) by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
The author seems to have uploaded the entire book by chapters at: www.physics.drexel.edu/~bob/LieGroups.html
And the author is the cutest: www.physics.drexel.edu/~bob/Personal.html.
Overview:
- Chapter 3: gives a bunch of examples of important matrix Lie groups. These are done by imposing certain types of constraints on the general linear group, to obtain subgroups of the general linear group. Feels like the start of a classification
- Chapter 4: defines Lie algebra. Does some basic examples with them, but not much of deep interest, that is mostl left for Chapter 7
- Chapter 5: calculates the Lie algebra for all examples from chapter 3
- Chapter 6: don't know
- Chapter 7: describes how the exponential map links Lie algebras to Lie groups
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