The size of a set.
For finite sizes, the definition is simple, and the intuitive name "size" matches well.
But for infinity, things are messier, e.g. the size of the real numbers is strictly larger than the size of the integers as shown by Cantor's diagonal argument, which is kind of what justifies a fancier word "cardinality" to distinguish it from the more normal word "size".
The key idea is to compare set sizes with bijections.
10 TINY Micro Robots and Nano Drones by JUST AMAZING (2020)
Source. - cyborg beetle from Hirotaka Sato
- RoboBee
- paywall: www.science.org/doi/10.1126/scirobotics.abq8184 A gyroscope-free visual-inertial flight control and wind sensing system for 10-mg robots by Fuller, Yu and Talwekar from the University of Washington, more precisely the Autonomous Insect Robotics Lab. TODO vs RoboFly also from Washington?
If Ciro Santilli ever becomes rich, he's going to solve this with: website front-end for a mathematical formal proof system, promise.
They come up a lot in many contexts, e.g.:
One of the first 1 million USD (zero artistic value) porn movie. And also a piece of shit! Hotter porn has been shot in kitchens around the world using iPhones.
IMDb entry: www.imdb.com/title/tt0477457/.
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The approach many courses take to physics, specially "modern Physics" is really bad, this is how it should be taught:
- start by describing experiments that the previous best theory did not explain, see also: Section "Physics education needs more focus on understanding experiments and their history"
- then, give the final formula for the next best theory
- then, give all the important final implications of that formula, and how it amazingly describes the experiments. In particular this means: doing physics means calculating a number
- then, give some mathematical intuition on the formulas, and how the main equation could have been derived
- finally, then and only then, start deriving the outcomes of the main formula in detail
This is likely because at some point, experiments get more and more complicated, and so people are tempted to say "this is the truth" instead of "this is why we think this is the truth", which is much harder.
But we can't be lazy, there is no replacement to the why.
Related:
- settheory.net/learnphysics and www.youtube.com/watch?v=5MKjPYuD60I&list=PLJcTRymdlUQPwx8qU4ln83huPx-6Y3XxH from settheory.net
- math.ucr.edu/home/baez/books.html by John Baez. Mentions:
This webpage doesn't have lots of links to websites. Websites just don't have the sort of in-depth material you need to learn technical subjects like advanced math and physics — at least, not yet. To learn this stuff, you need to read lots of booksCiro Santilli is trying to change that: OurBigBook.com.
- web.archive.org/web/20210324182549/http://jakobschwichtenberg.com/one-thing/ by Jakob Schwichtenberg
Condensed matter physics is one of the best examples of emergence. We start with a bunch of small elements which we understand fully at the required level (atoms, electrons, quantum mechanics) but then there are complex properties that show up when we put a bunch of them together.
Includes fun things like:
As of 2020, this is the other "fundamental branch of physics" besides to particle physics/nuclear physics.
Condensed matter is basically chemistry but without reactions: you study a fixed state of matter, not a reaction in which compositions change with time.
Just like in chemistry, you end up getting some very well defined substance properties due to the incredibly large number of atoms.
Just like chemistry, the ultimate goal is to do de-novo computational chemistry to predict those properties.
And just like chemistry, what we can actually is actually very limited in part due to the exponential nature of quantum mechanics.
Also since chemistry involves reactions, chemistry puts a huge focus on liquids and solutions, which is the simplest state of matter to do reactions in.
Condensed matter however can put a lot more emphasis on solids than chemistry, notably because solids are what we generally want in end products, no one likes stuff leaking right?
But it also studies liquids, e.g. notably superfluidity.
One thing condensed matter is particularly obsessed with is the fascinating phenomena of phase transition.
What Is Condensed matter physics? by Erica Calman
. Source. Cute. Overview of the main fields of physics research. Quick mention of his field, quantum wells, but not enough details.
The best personal webpages of all time by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01These are basically technically minded people that Ciro Santilli feels have similar interests/psychology to him, and who write too much for their own good:
- cat-v.org
- gwern.net. Dude's a bit overly obsessed with the popup preview though! "new Wikipedia popups (this 7th implementation enables recursive WP popups)" XD
- settheory.net by Sylvain Poirier
- HyperPhysics
- Orange Papers
Maybe one day these will also be legendary, who knows:
Another category Ciro admires are the "computational physics visualization" people, these people will go to Heaven:
Related:
Institution led:
- www.biology.arizona.edu/ The Biology Project
Other mentions:
- arngren.net/ lots of images of toys and gear with descriptions in Norwegian
The markup language of OurBigBook.com.
The one markup language to rule them all?
Documentation at: docs.ourbigbook.com.
There are unlisted articles, also show them or only show them.