I think it’s worth noting that, like with a lot of things, calculus of variations requires defining a set of boundary conditions on which to derive the Euler Lagrange equations. Donald E Kirk’s Optimal Control theory has the best exploration of the consequences of this for various derived optimization problems. But the Newtonian style formulation is a differential equation, where the boundary conditions are NOT inherent in the expression of the equations of motion, they are ad hoc and specific to the particular problem.
What I’m trying to say is that the teleological approach of Lagrangian mechanics already assumes a fixed beginning and end, where the Newtonian formulation does not. Lots of physical laws do this, Maxwell’s equations have an integral and a differential form, where the integral equations (a global, teleological form) have the boundary conditions embedded in them, and the differential ones (a local, more obviously causal form) do not. So it is circular reasoning to look at the Lagrangian, global formulation and discover that this implies a fixed endpoint, this is in fact an assumption of the method, not a consequence.
*which kinda stinks, I don't have enough income to support all the substacks I read, and I hate subscribing 'cause it means more stuff in my email inbox. Idea for substack, charge me ~$100 a year and I get to 'support' ~10 substacks, and also not get any emails, maybe one summary email/ week
I must admit that I do not understand what "Langragian" means here. Are you saying the universe acts like as if it would be trying to find optimal functions? But doesn't that follow from something like entropy or the conservation of energy, that suboptimal functions get outcompeted by optimal functions by some kind of an energy loss?
1) Philosophers always borrow from science. Aristotle borrowed from biology, organic nature, hence final causes. Moderns borrow from Newtonian physics, inorganic nature, hence no final causes. Darwin explicitly had put final causes back into biology, into organic nature, but few philosophers noticed. Those few are excellent, look up Ruth Garrett Millikan's idea of "proper functions".
2) "given some information about the force of the throw and the weight of the rock, told you exactly where it would land. But if those data were sufficient to tell you exactly where it would land, what need was there for anything else in the explanatory account? Suddenly those final causes look totally vestigial."
"control over nature"
Newton liked to talk about cannons, not rocks, because it sent the not too subtle message to VIPs that this geekery can be used to win wars. (Descartes was already an arty officer.) So control over nature more often than not was about winning wars, hence control over people.
This developed a certain poverty of modern understanding. Because a state geared towards war is i in the "get things done, nothing else matters" mindset. Practicality, pragmatism, is not primarily about the market, profits or capitalism. It is about war. Capitalism comes second, as generally the logistics arm of the warfare state, war had more to do with the development of early industrial revolution capitalism than markets did.
The premoderns like Aristotle were not so pragmatic. They were after some kind of a wisdom, not just predictions. This becomes a little more clear if you look at some presocratics, such as Pythagoreans, Pythagoreanism was a kind of a quasi-religion. Anyhow to understand these people they were a bit like hippie-era gurus like Maharishi, who combined spiritual stuff with rather pseudo science for a purpose of wisdom, not prediction.
3) I just don't understand now how you are a Christian, John. Every proof for the existence of God is syllogisms without empirical reality checking. Aquinas, Feser etc. in fact it is precisely because of the overly-pragmatic get-things-done, prediction-centric poverty of the modern mindset, into which I buy into way too much, is why I find it really hard to "get" religion. I cannot simply accept logical arguments without empirical proof.
Those journalists you criticize actually have it right. The universe does try all paths for the particles. Are you familiar with Feynman's reformulation of Quantum physics? The extreme classical paths (variational minimums or maximuns) appear from interference from *all possible paths.
Perhaps you have seen the QFT explanation for why there is no teleology, and you mention it in the footnote, but I didn't see a response. Is your point that there are situations where the optimization is not explained by cancellation?
Every possible path has an amplitude(a unit complex number). But the amplitude rotates fast as a function of the path, so that there is cancellation except at the critical path where the derivative of the action is 0, so nearby paths reinforce rather than cancel the amplitude. Since probability of the path is proportional to |amplitude|^2, the paths around the critical paths are most likely to be traversed.
I didn't expect to like this review so much! Thanks a lot for the link to Ted Chiang's story. I was already a fan of "Arrival", but didn't know it was based on a short story. While it's a pity that Villeneuve (probably had to) left out the Lagrangian part, I do think the movie has gained immensely in poignancy and power compared to the story, and that is a rare achievement.
One of my persistent annoyances is that universities teach two kinds of physics courses - the Newtonian kind, that they teach to engineering students and other non-majors, and the Lagrangian kind, that they teach to physics students.
I think it’s worth noting that, like with a lot of things, calculus of variations requires defining a set of boundary conditions on which to derive the Euler Lagrange equations. Donald E Kirk’s Optimal Control theory has the best exploration of the consequences of this for various derived optimization problems. But the Newtonian style formulation is a differential equation, where the boundary conditions are NOT inherent in the expression of the equations of motion, they are ad hoc and specific to the particular problem.
What I’m trying to say is that the teleological approach of Lagrangian mechanics already assumes a fixed beginning and end, where the Newtonian formulation does not. Lots of physical laws do this, Maxwell’s equations have an integral and a differential form, where the integral equations (a global, teleological form) have the boundary conditions embedded in them, and the differential ones (a local, more obviously causal form) do not. So it is circular reasoning to look at the Lagrangian, global formulation and discover that this implies a fixed endpoint, this is in fact an assumption of the method, not a consequence.
OMG Conan and physics. I'm now an unpaid subscriber*, so a shout out to the least action principle in the Feynman lectures. https://www.feynmanlectures.caltech.edu/II_19.html
*which kinda stinks, I don't have enough income to support all the substacks I read, and I hate subscribing 'cause it means more stuff in my email inbox. Idea for substack, charge me ~$100 a year and I get to 'support' ~10 substacks, and also not get any emails, maybe one summary email/ week
I must admit that I do not understand what "Langragian" means here. Are you saying the universe acts like as if it would be trying to find optimal functions? But doesn't that follow from something like entropy or the conservation of energy, that suboptimal functions get outcompeted by optimal functions by some kind of an energy loss?
Excellent, John! Some remarks:
1) Philosophers always borrow from science. Aristotle borrowed from biology, organic nature, hence final causes. Moderns borrow from Newtonian physics, inorganic nature, hence no final causes. Darwin explicitly had put final causes back into biology, into organic nature, but few philosophers noticed. Those few are excellent, look up Ruth Garrett Millikan's idea of "proper functions".
2) "given some information about the force of the throw and the weight of the rock, told you exactly where it would land. But if those data were sufficient to tell you exactly where it would land, what need was there for anything else in the explanatory account? Suddenly those final causes look totally vestigial."
"control over nature"
Newton liked to talk about cannons, not rocks, because it sent the not too subtle message to VIPs that this geekery can be used to win wars. (Descartes was already an arty officer.) So control over nature more often than not was about winning wars, hence control over people.
This developed a certain poverty of modern understanding. Because a state geared towards war is i in the "get things done, nothing else matters" mindset. Practicality, pragmatism, is not primarily about the market, profits or capitalism. It is about war. Capitalism comes second, as generally the logistics arm of the warfare state, war had more to do with the development of early industrial revolution capitalism than markets did.
The premoderns like Aristotle were not so pragmatic. They were after some kind of a wisdom, not just predictions. This becomes a little more clear if you look at some presocratics, such as Pythagoreans, Pythagoreanism was a kind of a quasi-religion. Anyhow to understand these people they were a bit like hippie-era gurus like Maharishi, who combined spiritual stuff with rather pseudo science for a purpose of wisdom, not prediction.
3) I just don't understand now how you are a Christian, John. Every proof for the existence of God is syllogisms without empirical reality checking. Aquinas, Feser etc. in fact it is precisely because of the overly-pragmatic get-things-done, prediction-centric poverty of the modern mindset, into which I buy into way too much, is why I find it really hard to "get" religion. I cannot simply accept logical arguments without empirical proof.
The Lagrangians are not arbitrary and follow from required invariances under symmetry.
Look up Noether's Theorems.
No need to invoke "Tachyonic Instability".
And, there is an even deeper version of all this called Hamiltonian Mechanics, which is covered in
the Goldstein Book and key for Quantum Mechanics.
It also is deeply connected to Noether's Theorems.
Those journalists you criticize actually have it right. The universe does try all paths for the particles. Are you familiar with Feynman's reformulation of Quantum physics? The extreme classical paths (variational minimums or maximuns) appear from interference from *all possible paths.
Perhaps you have seen the QFT explanation for why there is no teleology, and you mention it in the footnote, but I didn't see a response. Is your point that there are situations where the optimization is not explained by cancellation?
Every possible path has an amplitude(a unit complex number). But the amplitude rotates fast as a function of the path, so that there is cancellation except at the critical path where the derivative of the action is 0, so nearby paths reinforce rather than cancel the amplitude. Since probability of the path is proportional to |amplitude|^2, the paths around the critical paths are most likely to be traversed.
I didn't expect to like this review so much! Thanks a lot for the link to Ted Chiang's story. I was already a fan of "Arrival", but didn't know it was based on a short story. While it's a pity that Villeneuve (probably had to) left out the Lagrangian part, I do think the movie has gained immensely in poignancy and power compared to the story, and that is a rare achievement.
One of my persistent annoyances is that universities teach two kinds of physics courses - the Newtonian kind, that they teach to engineering students and other non-majors, and the Lagrangian kind, that they teach to physics students.
And they're not at all alike!