Structure and Interpretation of Classical Mechanics (2014)
tgvaughan.github.io65 points by the-mitr 10 hours ago
65 points by the-mitr 10 hours ago
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.
> 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
Most of these things are misunderstandings of quantum mechanics, as we know it today.
The main thing that is at the root of all of them is the word "things". In QM, the ground truth of the world is the wavefunction of the system. The wavefunction assigns some amplitude (potentially 0) to any possible state of the system that it describes. It then evolves purely deterministically from past to future, according to Schrodinger's equation (or Dirac's equation, if you want to discuss speeds close to that of light). The only kink is interaction with a measurement device (what constitutes a measurement device is one of the big mysteries that we don't yet have an answer for). After a measurement, the wavefunction collapses non-deterministically to one of the states that the measurement device was set up to detect, with a probability that is proportional to the amplitude of the wave function of that state.
Now, this is the "ground truth" of QM. Everything else, such as particles and space-time and so on are just stories we tell to make sense of the wavefunction and its behavior. Sometimes those descriptions break down, and they start assigning weird fanciful ideas, such as retrocausality etc - but these just prove that the stories are wrong, that they are misinterpreting the math of the wavefunction.
I'd also note that the main "time is weird" factoid you encounter related to QM experiments, the delayed-choice quantum eraser, is mostly a misunderstanding / sensationalization of the actual physics and the experiment. It again only proves that certain interpretations of what the wavefunction and its collapse represent are not temporally consistent, but the direct conclusion from this should be that the interpretations are wrong, not that "cause and effect goes for a toss, as behavior of time is different".
> > 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".
You are just saying "well ackshually". I dare you to build a cabinet using the Hamiltonian. I double-dog-dare you.
> > 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.
Again, 99.999% of all functional mechanics don't involve epistemology.
> 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.
Oh! You're so close to seeing the point... There are multiple levels of approximation (at least two), and the one we all experience is Newtonian. Perhaps more accurately, our senses mostly believe pre-Newtonion approximations, which is why it took until Newton to realize how inaccurate they were.
> Also, I don’t see how the logic is fundamentally different between e.g. quantum mechanics and general relativity.
You're pretty radically moving the goalposts here. GP was talking about Newtonian mechanics, not Hamiltonian.
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.
There’s also Functional Differential Geometry by the same Sussman and Wisdom:
https://mitp-content-server.mit.edu/books/content/sectbyfn/b...
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)
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)
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.
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!
This is what I tried, unsuccessfully if I remember correctly. I'll give it another try, thanks!