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Atom by Ciro Santilli 37 Updated 2025-07-16
Theory that atoms exist, i.e. matter is not continuous.
Much before atoms were thought to be "experimentally real", chemists from the 19th century already used "conceptual atoms" as units for the proportions observed in macroscopic chemical reactions, e.g. . The thing is, there was still the possibility that those proportions were made up of something continuous that for some reason could only combine in the given proportions, so the atoms could only be strictly consider calculatory devices pending further evidence.
Subtle is the Lord by Abraham Pais (1982) chapter 5 "The reality of molecules" has some good mentions. Notably, physicists generally came to believe in atoms earlier than chemists, because the phenomena they were most interested in, e.g. pressure in the ideal gas law, and then Maxwell-Boltzmann statistics just scream atoms more loudly than chemical reactions, as they saw that these phenomena could be explained to some degree by traditional mechanics of little balls.
Confusion around the probabilistic nature of the second law of thermodynamics was also used as a physical counterargument by some. Pais mentions that Wilhelm Ostwald notably argued that the time reversibility of classical mechanics + the second law being a fundamental law of physics (and not just probabilistic, which is the correct hypothesis as we now understand) must imply that atoms are not classic billiard balls, otherwise the second law could be broken.
Pais also mentions that a big "chemical" breakthrough was isomers suggest that atoms exist.
Very direct evidence evidence:
Less direct evidence:
Subtle is the Lord by Abraham Pais (1982) page 40 mentions several methods that Einstein used to "prove" that atoms were real. Perhaps the greatest argument of all is that several unrelated methods give the same estimates of atom size/mass:
Isomorphism by Ciro Santilli 37 Updated 2025-07-16
Something analogous to a group isomorphism, but that preserves whatever properties the given algebraic object has. E.g. for a field, we also have to preserve multiplication in addition to addition.
Other common examples include isomorphisms of vector spaces and field. But since both of those two are much simpler than groups in classification, as they are both determined by number of elements/dimension alone, see:we tend to not talk about isomorphisms so much in those contexts.
This is a list of video games that are good to watch other people playing, even if you don't play yourself. And often they are better to watch than to play as you don't have to waste your time as much!
Cayley graph by Ciro Santilli 37 Updated 2025-07-16
You select a generating set of a group, and then you name every node with them, and you specify:
  • each node by a product of generators
  • each edge by what happens when you apply a generator to each element
Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the
Laplace transform by Ciro Santilli 37 Updated 2025-07-16
Video 1.
The Laplace Transform: A Generalized Fourier Transform by Steve Brunton (2020)
Source. Explains how the Laplace transform works for functions that do not go to zero on infinity, which is a requirement for the Fourier transform. No applications in that video yet unfortunately.
Planned obsolescence by Ciro Santilli 37 Updated 2025-07-16
The first time Ciro Santilli Googled this was when trying to repair his cell phone.
2019 cell phones are glued together with adhesive, which makes them impossible to repair them unless you have a heat gun, spend hours and hours learning and planning, and accept the risk of breaking the screen
If you take a phone less than 300 dollars to a repair shop in the first world, they will say: I've never repaired this crap, and likely for the price of the repair you should just buy a new one, and so to the trash goes the old one, polluting the planet, and in comes a new one, enriching the manufacturer further.
Mediocre Amateur by Ciro Santilli 37 Updated 2025-07-16
About 50k subscribers on 2021, which feels way too little for the video quality and quantity.
Ciro Santilli believes that this channel will go very far, certainly achieving 1M subscribers in they keep it for one or two more years. Update: it didn't, as of 2024, shame.
They are Utah-based, and they do many many amazing weekend trips. They mostly drive from home to some trailhead, and then climb up and down it the entire day.
No technical rock climbing, only bouldering, but they still manage to reach many amazing places, and there is a level of danger in many of their ascents.
They also often ski down the mountains when there is snow.
The cool thing about this channel is that as the name suggests, they are not professionals, and what they do can be done by anyone without working full time on it, as long as you have adequate preparation.

There are unlisted articles, also show them or only show them.