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 want to write Structure and Interpretation of Geometric Optics. I have an outline already in my notes and I'm convinced that the computing-first approach would benefit the field immensely. I've been learning optics for a while and writing a python library [0]. With a background in software it's very obvious that there is strong SICP vibes in lenses, refraction, etc. I just need someone to trust me and write me a check for 1 or 2 years salary so I can go full bunker mode and write it =)
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.
Of course. To him that would be modern mechanics. Or just mathematical natural philosophy, or whatever.
> Maybe we should categorize sciences based on the spatial scale at which they operate.
That would not be very useful, because there is no boundary. Nothing in general relativity says "below this everything is Newtonian". As a matter of fact we need to consider relativistic effects in quantum chemistry calculations that involve some heavy elements, at length scales smaller than 0.1 nm. Similarly, they just gave a Nobel prize for work on "Quantum properties on a human scale".
> For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality.
That is not at all how these frameworks are built, and that is not the dominant epistemological approach. The mainstream view is that there is a theory of everything that exists but is unknown to us, and that our various theories are approximations of that theory under different assumptions. They look categorically different because we don’t understand the overarching framework, not because nature is fundamentally different depending on scale.
Also, I don’t see how the logic is fundamentally different between e.g. quantum mechanics and general relativity. Both rely heavily on things like Hamiltonian mechanics or symmetries. Some behaviours are different (like photons following geodesics and not straight lines, or superpositions of quantum states), but these are not a fundamental problem: a straight line is a limit case of a geodesic in a flat space, and a unique state is a limit case of superposition.
I am not saying that everything is fine and we know everything, just that there is no clear boundary between the situations in which different theories are required and we cannot neatly decompose the universe into different realms where different theories apply.
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.
I don't know which it was but Dr. Jorge Diaz has an excellent video on Lagrangian mechanics as part of a series on quantum mechanics (this video just pertains to the formalism applicable classically)
Ah, nice, I'll try that. SICM in particular relies on numerical routines and things for scientific computing that this perhaps doesn't cover. We'll see. Thanks!
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 want to write Structure and Interpretation of Geometric Optics. I have an outline already in my notes and I'm convinced that the computing-first approach would benefit the field immensely. I've been learning optics for a while and writing a python library [0]. With a background in software it's very obvious that there is strong SICP vibes in lenses, refraction, etc. I just need someone to trust me and write me a check for 1 or 2 years salary so I can go full bunker mode and write it =)
[0] https://victorpoughon.github.io/torchlensmaker/
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.
We call music from Newton's age "classical".
As the past recedes, "the golden age" advances in time. "Hollaback Girl" is now a classic oldie.
> Newton wouldn't have called it so.
Of course. To him that would be modern mechanics. Or just mathematical natural philosophy, or whatever.
> Maybe we should categorize sciences based on the spatial scale at which they operate.
That would not be very useful, because there is no boundary. Nothing in general relativity says "below this everything is Newtonian". As a matter of fact we need to consider relativistic effects in quantum chemistry calculations that involve some heavy elements, at length scales smaller than 0.1 nm. Similarly, they just gave a Nobel prize for work on "Quantum properties on a human scale".
> For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality.
That is not at all how these frameworks are built, and that is not the dominant epistemological approach. The mainstream view is that there is a theory of everything that exists but is unknown to us, and that our various theories are approximations of that theory under different assumptions. They look categorically different because we don’t understand the overarching framework, not because nature is fundamentally different depending on scale.
Also, I don’t see how the logic is fundamentally different between e.g. quantum mechanics and general relativity. Both rely heavily on things like Hamiltonian mechanics or symmetries. Some behaviours are different (like photons following geodesics and not straight lines, or superpositions of quantum states), but these are not a fundamental problem: a straight line is a limit case of a geodesic in a flat space, and a unique state is a limit case of superposition.
I am not saying that everything is fine and we know everything, just that there is no clear boundary between the situations in which different theories are required and we cannot neatly decompose the universe into different realms where different theories apply.
From my little knowledge, logic at Quantum scale appears quite different:
* Things don't have their own location or identity
* Spatial and temporal extents don't exist
* Something may be true and false at the same time, or concept of true and false may not be defined
* cause and effect goes for a toss, as behavior of time is different
* Existence and non-existence co-exist, or come into existence together
Similar effects at relatively-infinite scale (maybe purely mathematical)
* Comparisons (big/small/equal) breakdown
* Regular arithmetic and logic breaks down
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.
Do you remember which video that was?
I don't know which it was but Dr. Jorge Diaz has an excellent video on Lagrangian mechanics as part of a series on quantum mechanics (this video just pertains to the formalism applicable classically)
https://www.youtube.com/watch?v=QbnkIdw0HJQ
There’s also Functional Differential Geometry by the same Sussman and Wisdom:
https://mitp-content-server.mit.edu/books/content/sectbyfn/b...
Does anybody know of a way to run the code in this book? I've tried a couple of times but never quite succeeded.
https://groups.csail.mit.edu/mac/users/gjs/6946/installation...
https://stackoverflow.com/questions/62518079/scmutils-for-si...
Easter egg: if you dig deeper into the code you will find the "amazing bug" (footnote on page 5)
https://arxiv.org/abs/1211.4892
The bug being "perturbation confusion"?
The specific bug in sicm is discussed on pages 19-21
(Sorry, it's been a while, but iirc the code comments call it the amazing bug, with credit to Radul)
You can run it in Racket with the SICP language.
https://docs.racket-lang.org/sicp-manual/SICP_Language.html
Ah, nice, I'll try that. SICM in particular relies on numerical routines and things for scientific computing that this perhaps doesn't cover. We'll see. Thanks!
https://github.com/perceptual-ai/sicm-scheme-exercises
This is what I tried, unsuccessfully if I remember correctly. I'll give it another try, thanks!