I've often dreamed of a "Structure and interpretation" series of books.
Scheme is pretty close to a universal computation substrate that provides enough ergonomics to be human understandable and writing anything out in it provides genuine illumination to what's going on under the hood.
The "little" books are a tease of what that series could be.
I didn't get anywhere trying to read this book. Then I watched a youtube video about calculus of variations and suddenly Lagrangian dynamics made total sense to me. I should probably try reading the book again.
MIT Scheme (and ScmUtils) are unfortunately not getting enough maintainence, but they still work with a little effort. Probably better on Linux than any other environment. If you have a Mac you may try this:
Funny that we call it classical. Newton wouldn't have called it so. Maybe we should categorize sciences based on the spatial scale at which they operate.A specific scale might define a world that has it's logic system, purpose, reasoning etc. For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality.
The music of Newton’s age is Baroque music. Classical music either refers to the whole tradition of Western serious art music (starting approximately with Palestrina and continuing to the current day) or it refers to the period after Baroque.
So “ Baroque” is J.S. Bach, Handel, Charpentier, Purcell etc (1600-1750 ish), “classical” is mozart, J.C. Bach, Hayden etc up to Beethoven (1750ish-1800ish).
Classical mechanics as I was taught it is not to do with the time period,it means “mechanics when you don’t need to worry about relativity or quantum anything “.
That is very definitely classical mechanics, just that it emphasises the Lagrangian and Hamiltonian formulations rather than the Newtonian one (they explain their rationale for this in the beginning). These three formulations of classical mechanics are entirely equivalent though. When you learn mechanics at first you don’t learn the Hamiltonian at all and the Lagrangian isn’t mentioned by name but by formulating some problems in terms of kinetic and potential energy rather than equations of motion and showing that is equivalent. (Eg when I did mechanics we did that for simple harmonic motion).
I mean Newton wouldn’t recognize most of what we teach as Calculus because we use Leibnitz’ notation[1] or Lagrange’s notation almost exclusively, and only use Newton’s notation for derivatives with respect to time and don’t ever use Newton’s terminology (fluxions etc).
[1] So named because it was mostly invented by Euler.
Does anyone know a text which justifies why the Lagrangian approach works? This text and many others I have encountered just start with the Principle of Least Action taken as given and go from there but I'm left wondering why we define the Action as this object and why we should expect it to be minimised for the physical trajectory in the first place.
Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.
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[ 0.29 ms ] story [ 54.1 ms ] threadScheme is pretty close to a universal computation substrate that provides enough ergonomics to be human understandable and writing anything out in it provides genuine illumination to what's going on under the hood.
The "little" books are a tease of what that series could be.
https://github.com/kkylin/mit-scheme-intel-mac-patch?tab=rea...
Works well on Intel Macs and (with effort) mostly works on Apple Silicon.
I was able to make "CloJupyter" notebooks with the examples from the book. You can see some of my notes here (only goes till Chapter 2): https://www.thomasantony.com/projects/sicm-workbook/
As the past recedes, "the golden age" advances in time. "Hollaback Girl" is now a classic oldie.
So “ Baroque” is J.S. Bach, Handel, Charpentier, Purcell etc (1600-1750 ish), “classical” is mozart, J.C. Bach, Hayden etc up to Beethoven (1750ish-1800ish).
Classical mechanics as I was taught it is not to do with the time period,it means “mechanics when you don’t need to worry about relativity or quantum anything “.
I mean Newton wouldn’t recognize most of what we teach as Calculus because we use Leibnitz’ notation[1] or Lagrange’s notation almost exclusively, and only use Newton’s notation for derivatives with respect to time and don’t ever use Newton’s terminology (fluxions etc).
[1] So named because it was mostly invented by Euler.
https://mitp-content-server.mit.edu/books/content/sectbyfn/b...
Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.
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