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If fundamental physics were making big progress, I'd be all over it - that's what I wanted to do ever since I was a kid. But it's stagnant: the action is elsewhere, like using category theory to design radical new kinds of software. So these days I get some of my physics fix by studying the *history* of physics.
After studying the hell out of particle physics and general relativity, I went back and dug into the history of electromagnetism, which is really just as fascinating. Now I'm going back to medieval physics - because the idea that everyone was an idiot until Galileo is just plain wrong.
"Natural philosophers" in the 1200s and 1300s developed key concepts, utterly necessary for modern physics, but almost invisible now because we're so used to them - except for students, who find physics really hard because we don't bother to CLEARLY EXPLAIN those concepts: we act like children are born knowing them.
I'm talking about concepts like "the speed of an object at a moment of time". What the hell does that even mean? How can you figure out how fast something is going in one instant of time, when doesn't have time to go anywhere?
Well, that was clarified by calculus, and we credit it to Newton and Leibniz. But they had to have the idea already, in order to clarify it! And the idea of "instantaneous velocity" was developed around 1340 by the Oxford Calculators, a school of thinkers like Heytesbury and Swineshead - geniuses we never hear about.
Now I'm going back further. Did you know that back in 420 AD Martianus Capella had a theory where Mercury and Venus revolved around the Sun? And this was known to thinkers in Charlemagne's day... and also Copernicus! Wow!
Anaxagoras (c. 500 BC) told the Moon was cold and reflecting the light of the Sun, which was a globe of incandescent metal.
@GustavinoBevilacqua - I want to learn more details of how Greek physics was lost in western Europe but later reintroduced via Arabs, Persians, Byzantium, etc. I don't think Charlemagne's scholars knew about Anaxagoras.
@johncarlosbaez @GustavinoBevilacqua Roy casagranda has loads of really enjoyable lectures on YouTube about that, and other things. Probably not as scholarly as you'd like, but will certainly send you in the direction of some important Arab philosophers and mathematicians. His lectures hit some kind of blissy asmr mark for me too!
In Italy we have Alessandro Barbero, a university history professor who is very skilled to explain things in an easy way, but I don't remember if he has lectures about physics in ancient Greece.
@GustavinoBevilacqua @johncarlosbaez tell him make one. It's perfect for some weekend morning after an overindulgence.
@johncarlosbaez @GustavinoBevilacqua A book I liked recently on Anaxagoras's astronomy and related: https://global.oup.com/academic/product/science-before-socrates-9780199959785
Re transmission of some texts back to the west, another recent read: https://www.penguinrandomhouse.com/books/546484/the-map-of-knowledge-by-violet-moller/ but I thought it less interesting
@abecedarius - thanks! I had guessed you were talking about my friend Carlo Rovelli's book on Anaxagoras, but I see this is something more scholarly. Interesting! I'm really interested in the transmission of classical texts, too. Once I saw a great "family tree" of versions of Euclid's Elements, but I can't find it anymore. 
@johncarlosbaez @GustavinoBevilacqua He seemed skeptical of Rovelli's take on Anaximander -- maybe in a bit of discussion of what would make someone "the first scientist", I don't remember. Anyway I enjoyed Rovelli's book! It takes imagination to make sense of the scraps that came down to us.
@johncarlosbaez At least we have observations we can't explain. Back when I studied physics (mid 1990s) we didn't even have that, since people didn't yet believe the observations that now make us talk about "dark matter" and "dark energy". And I hope we'll one day make progress on this!
@bert_hubert - yes, if I were doing observational astrophysics and cosmology I'd be quite happy nowadays! I try to keep up with that work in a general way. But being a more mathematical sort, I'm mainly *frustrated* by the dark matter puzzle. (Dark energy might just a cosmological constant, though observations might eventually rule that out.)
@johncarlosbaez @bert_hubert regarding dark matter: besides mond, I remember hearing of works on an entirely different alternative explanation of its effects, refusing the Newtonian approximation of Einstein equations. Any thoughts on that? From an outsider, this sounds somewhat elegant
@D3Reo - this class of theories is called MOND or Modified Newtonian Dynamics.
The idea sounds elegant until you see how complicated the equations need to be to come close to 1) agreeing with the many confirmed predictions of general relativity while 2) still giving effects that look like dark matter. There have been many attempts to do this; they're all quite complicated, and I don't think any of them captures *all* the complicated things that we see dark matter do. E.g. there are some small galaxies that seem to have no dark matter, which might make sense if dark matter is a kind of stuff, but seems harder to explain if you're just changing the law of gravity: why would *some* galaxies not follow this modified law?
I'm not saying MOND is a dead duck, just that there are many versions of it, and none of them is a silver bullet.
Here's a great pop article by @startswithabang making the case *against* MOND. Then you should read some in favor of it.
@johncarlosbaez @D3Reo @startswithabang still, we live in GLORIOUS times that we have numerous laws of physics that give correct results to 9 decimal places yet when we look at the sky the universe is misbehaving in a specific way. The answer to this all must be awesome.
@bert_hubert - It's glorious, I agree! But if you have a job trying to figure out the fundamental laws of nature, you'll notice that we haven't figured out a new fundamental law since roughly 1980.
@johncarlosbaez @bert_hubert @startswithabang i had in mind something like square-torsion gravity, of which I have far from a good understanding, but which I thought was different from MOND. Is that not the case? My understanding was that mond works after the Newtonian approximation, whereas theories such as square-torsion gravity are "instead of" the approximation, or with a different approximation altogether. But again, I'm out of my depth here, so any clarification is very much appreciated!
Solid state physics had lots of such, ttbomk basically at any time. (I'm not sure whether y'all would call it fundamental physics though; it's in large part about creating models for situations where we already think we have good, albeit intractable, models.)
@johncarlosbaez I wonder what is Orbis Elementorum. And the fact that the orbit of Venus touches both the orbit of the Moon and Mars is also surprising.
@mfranc @johncarlosbaez That's the sphere of the (four) elements, which lies inside the celestial sphere, where the heavenly bodies move.
@johncarlosbaez Also don't forget the Islamic Golden Age where some studied the optics and astronomy, which helped advance the knowledge and set up the later works in the dawn of modern science!
@thebluewizard - yes, I've been studying a bit of Arabic and Persian work - but not nearly enough, because Europe was really just the benighted boondocks for a long period of time.
@johncarlosbaez True. We need to "uncover" more history in various areas (in math and science, of course; just too many other stuff to worry about). Like what India people did with math in early times (I learned about those on Wikipedia...after I graduated from college and was not aware of those). Hmm...what, if any, India people did with science/physics? I am surprised I am drawing blank on that!
P.S. I use "India people" to prevent the confusion with "Indians" (which ones??? Another fine mess of English language...)
@thebluewizard - for a good Indian mathematician, check out Brahmagupta (598 – 668 AD). For example, he discovered a recursive algorithm for finding integer solutions x,y of the equation
Nx² + 1 = y²
and a formula for writing the product of two sums of squares as a sum of squares.
@simsa03 - I love Oresme! Before Oresme, Heytesbury gave a *verbal* proof of the Mean Speed Theorem, which I could never understand until someone explained it to me yesterday:
https://johncarlosbaez.wordpress.com/2024/11/07/the-mean-speed-theorem/#comment-186034
@johncarlosbaez @simsa03 Yes, #Oresme was quite interesting. I know him for two other achievements:
1. Relativity of motion: He had already the famous “ship argument” that #Galileo used to show that physics in a moving object must be the same as in a standing one — the only difference is that Oresme, living in Paris, used a ship on a river and not at sea. (https://todayinsci.com/O/Oresme_Nicole/OresmeNicole-Forerunner.htm)
2. He proved the divergence of the harmonic series. (https://en.wikipedia.org/wiki/Nicole_Oresme#Mathematics)
@simsa03 @johncarlosbaez
The earliest notion of a "instantaneous motion" known to me would be in Bhāskara the 2ⁿᵈs works on planetary motion, around ~1200 https://en.wikipedia.org/wiki/Bh%C4%81skara_II#Calculus
@johncarlosbaez I'd be very interested to hear your opinion on why fundamental physics has stagnated. There are theories like "the low hanging fruit is gone" to "string theorists colonized the funding bodies and only funded string theory". I'm curious how it looks from your perspective.
@robinadams - I've given a talk arguing that so-called fundamental physics has stagnated, and giving advice to students about what to do instead:
https://m.youtube.com/watch?v=oZLDZTwl8Hw
But I think it's much harder to say *why* it's stagnated. I should try to say a bit about that sometime.
@johncarlosbaez What sort of materials are there that give us a record back so far?
Manuscripts copied from previous manuscripts copied from previous manuscripts, which survive in one copy, often containing not the original text, but a mention/critique of the text by another author.
@rmathematicus's website is a marvelous resource:
@christinkallama @johncarlosbaez @rmathematicus That's amazing. Thank you! And this blog just pulled me in.
@JosephTLapp wrote: "What sort of materials are there that give us a record back so far?"
If you're really curious, try this book:
https://libgen.li/ads.php?md5=064910775786106B47442B3DC57ADC31
It's all about astronomy in the age of Charlemagne. The author of this book studied manuscripts which were actually written in the reign of Charlemagne in the late 800s. For example, there are about 50 copies of Martianus Capella's "De nuptiis Philologiae et Mercurii" dating back to the 800s, still available in various monasteries and libraries. Martianus Capella himself wrote this book in 420 AD, and it contains the cool theory I mentioned, but these later manuscripts prove it was known to Europeans during the reign of Charlemagne's grandsons - when other, better astronomical texts from ancient Greece were only available in the Muslim world!
@johncarlosbaez hey have you tried looking into optical physics? there's some really cool recent work in femtosecond laser pulses that might touch on what you're interested in here
Is instantenous speed a central example here? I'm asking because I'm surprised to find it's not an intuitive notion: I don't remember fellow classmates struggling with it (and I do remember struggles with abstractions such as a function that happens to be linear. I will probably ask my 6~8yr old "nephews" in the coming days; suggestions on concrete questions that show the difficulty are very welcome.)
= 
log
) @robryk @johncarlosbaez
From a certain point of view, it can seem that, instantaneously, nothing moves, therefore, how could there be speed? Zeno's paradoxes.
I don't think children are likely to start with that worldview based on anecdotal evidence: I don't know anyone who initially considered Zeno's (Xeno's?) paradox to be intuitive (@timorl , did you?). When I first learned of it (sometime in primary school) it seemed contrived to me.
Oof, I wrote a long-ish response and only then remembered that this is not about that Zeno’s paradox – we are talking about the one with the arrow not moving at a specific point in time, right? The other ones always seemed to me more like jokes (i.e. subverting intuitive expectations), but this one did make some sense. Although I think rather than pointing to the difficulty in accepting instantenous speed, it points to the counterintuitive concept of considering a situation at a specific point in time altogether. I think the intuitive approach to understanding everyday mechanics is much more dynamic, and introducing any moment-by-moment abstraction requires some work, including the fact that speed is still associated with objects (even if the fact by itself is not particularly hard to accept).
But these are guesses, our current culture is soaked in this understanding of dynamics to an extent that almost surely influences children even before they get formally introduced to physics, so it’s hard to tell which things are a priori intuitive – for that you really gotta study history like @johncarlosbaez does. 
@johncarlosbaez Mercury and Venus orbiting the Sun makes so much sense! It would explain why they are always in the same part of the sky. If they orbited the Earth instead you would have to explain why they are never visible at midnight the way Jupiter and the Moon are.
I wonder how the earth-is-the-center-of-everything people explained this fact, which has been obvious since prehistoric times.
I notice that the diagram you showed has Mercury closer to the Sun than Venus, which is another inference one can straightforwardly make from direct observations: Venus gets visibly farther from the Sun than Mercury ever does.
Not exactly related, but possibly interesting in the same way: In 1580, how do you explain why it is hotter at lower latitudes than at higher ones? https://blog.plover.com/math/dotproduct1580.html
@johncarlosbaez If you want to eventually branch out, I recommend Science and Civilization in China. https://en.m.wikipedia.org/wiki/Science_and_Civilisation_in_China
@johncarlosbaez One guy whom I found out about recently is John Philoponus ("Lover of hard work"), a fifth-century Alexandrian thinker, who among other things wrote a commentary on Aristotle where he explicitly denied A's theory of motion. He anticipated the idea of inertia, suggesting that air actually impeded the motion of projectiles and that vacuua could in principle actually exist.
@johncarlosbaez Okay, checking his dates via wiki, I find he was more a sixth-century person (c 490-c570) than fifth.
@korydg - cool! I will check out his work.
@johncarlosbaez One thing I've learned in the modest efforts I've made into learning the history of mathematics is, that mathematicians are spectacularly bad at history, and what little history we do talk about tends to be very far from the truth.
The history of Calculus is yes, particularly notable in that it's commonly believed that Newton and Leibniz invented calculus more or less out of thin air, when in fact they were building on a lot of less-than-obvious ideas that already existed.
@johncarlosbaez This is rather interesting. I often feel that history is written retrospectively after major events, ignoring the generative events leading to them.
... as, if by magic, certain people had major insights and did everything by themselves.
@johncarlosbaez Another example is Darwin. Of course he made major contributions, including doing field work, clearly articulating the ideas in writing, and forcefully presenting them verbally at official scientific meetings. But at least two people had similar ideas before him on record.
@MartinEscardo - it's as if we cheer the fireworks but ignore the people who made the fireworks.
@johncarlosbaez wait why only Mercury and Venus? That's super interesting
@timhenke @johncarlosbaez Maybe because unlike the other planets, Venus and Mercury were never observed in opposition to the sun. So their paths around the earth must be somehow coupled to the sun.
@juergensoergel @timhenke - yes, Mercury and Venus have long been called "inferior planets" for this reason: they were recognized to be different from the rest. So it makes sense to have a "semi-heliocentric" cosmology where they revolve around the Sun, but not the rest. But I'd never thought of it, much less knew that Copernicus was aware of it!
@johncarlosbaez @juergensoergel I seem to recall there was a Greek mathematician who already speculated about a heliocentric system, right? Aristarchus of Samos? (I googled, didn't know that one by heart)
Wikipedia says Copernicus knew about his "moving earth" theory, though we're not sure he knew it was heliocentric
@timhenke @juergensoergel - People tend to say Aristarchus had a heliocentric cosmology but I don't think we have many writings from him - maybe only remarks in Aristotle? Now I'm interested in the early Middle Ages and the earlier "Carolingian Renaissance" started by Charlemagne, and at this time even Aristotle and Ptolemy were lost to the benighted west... but not Martianus Capella, a guy from north Africa, with his "semi-heliocentric" theory! Somehow his writings were very well-known! This would seem to grease the wheels for full-fledged heliocentrism.
@johncarlosbaez @juergensoergel Makes sense! Very cool ^^
@timhenke - it looks like Aristarchu's original heliocentric text was lost and we know of it only through a book of Archimedes. Wikipedia says:
The original text has been lost, but a reference in a book by Archimedes, entitled The Sand Reckoner describes a work in which Aristarchus advanced the heliocentric model as an alternative hypothesis to geocentrism:
"You are now aware ['you' being King Gelon] that the "universe" is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the "universe" just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface."
This is a very cool text, but I'm not sure I get the proportion at the end. It's something like A is to B as C is to D.
@johncarlosbaez To me it sounds like he's saying "The distance of the stars is so great that the size of the Earth's orbit may be assumed to be 0 in comparison"
Which is a funny thing to say considering parallax, but perhaps that's too subtle for the Greeks to resolve with the naked eye?
@timhenke - yeah, that's how it seems to read to me too, but it's hard to believe Archimedes would say something so mathematically "sloppy". Maybe it's not sloppy. By the way, this is in his famous book The Sand-Reckoner, in which he introduces names for really large numbers - numbers up to
10^(8 ⋅ 10^16)
So the theme of infinity, or at least really large numbers, may be percolating beneath the surface here.
I'm sure Archimedes was good enough to understand parallax if he cared! After all his pal Eratosthenes had accurately measured the radius of the Earth by comparing shadows at noon at two latitudes.
@johncarlosbaez I assume you know @rmathematicus and his blog (in particular the series "From τὰ φυσικά to physics": https://thonyc.wordpress.com/from-%cf%84%e1%bd%b0-%cf%86%cf%85%cf%83%ce%b9%ce%ba%ce%ac-ta-physika-to-physics/ )
@j_bertolotti @rmathematicus - yes, this is a delightful blog and I should read every article... and then read them all again!
@johncarlosbaez "instantaneous velocity" is an incredibly difficult concept for students... and (as I know you likely know) goes back to Zeno's paradoxes. And questions about those still relate to arguments between physicists about fundamental physics e.g. continuity vs discreteness of spacetime and the concept of time.