The wave equation can be seen as infinitely many infinitesimal coupled oscillators by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01TODO confirm, see also: coupled oscillators. And then this idea can be used to define/motivate quantum field theory in terms of quantum harmonic oscillators with second quantization.
- youtu.be/SMmFgIEGYtw?t=324 Quantum Field Theory 2a - Field Quantization I by ViaScience (2018)
The World Of Enrico Fermi by Harvard Project Physics (1970) by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Ciro Santilli approves of this one, related: Section "Free gifted education".
The downside of the Thiel Fellowship is that it is realistically impossible for its fellows to do anything in deep tech, only information science startups would be possible, as they would not have the labs, or lab skills required for any deep tech if they drop out before a PhD. Related: Section "The only reason for universities to exist should be the laboratories".
The only solution is the harder process of actually remodelling our very broken educational system.
To some extent, the ultimate achievement of a TAS is to achieve arbitrary code execution (ACE) on a game, although this has been becoming rarer and rarer in newer consoles. The Nintendo 64 is the current interesting ACE discovery frontier as of 2020.
Post ACE, you then get into more subtle categories which tend to be more geometric clipping through wall glitches, but those can still be fun.
The most beautiful TAS content ever made are:
- Super Mario 64
- Super Mario 64 A press challenge
- 1-key any percent run:
- 2016 emulator run: www.youtube.com/watch?v=TkOkJvLKxUY
- AGDQ 2018 commented TASBOT console verification: www.youtube.com/watch?v=xvWOLT9G6tM
- Why we need one key: gaming.stackexchange.com/questions/249969/in-mario-64-speedruns-why-are-the-keys-necessary/351595#351595
- related: Super Mario 64 reverse engineering project
- Super Mario World for the SNES arbitrary code execution
- www.youtube.com/watch?v=OPcV9uIY5i4 with in-game programmed Pong and Snake, 2014
- www.youtube.com/watch?v=HxFh1CJOrTU Seth Bling does the credit warp manually in about 3 minutes, 2015. Later reduced to less than 1 minute: www.youtube.com/watch?v=Jf9i7MjViCE
- www.youtube.com/watch?v=voL3e0iqugo ACE was initially not forbidden in 11 exit rules, so Seth made an in-game manual ACE that programs an in-game accessible "exit stage now" functionality!!! This was later forbidden of course, but it was fun while it lasted.
- then he injected a Flappy Bird clone manually!!! www.youtube.com/watch?v=hB6eY73sLV0, 2016
- Ocarina of Time
- 2020 ACE via use after free including a non-TAS credit warp faster than the 2016 wrong glitch: www.polygon.com/2020/1/24/21080568/zelda-ocarina-of-time-arwing-spawn-video-speedrun-credits-ace-cheat-code ACE later reproduced in Majora's Mask, which has a similar game engine.
- 2016 Zelda Ocarina of Time wrong warp glitch:
- www.youtube.com/watch?v=Gso4MuNSuV8 EZScape explains the glitch, 2016
- Zelda Majora's Mask debug menu
It is also amusing to see console verification of emulations, e.g.: Video 1. "Super Mario 64 '120 Stars' in 1:20:41.52 Console Verified by Soul Umbreon (2012)".
Topological Quantum Computer by Professor John Preskill
. Source. Topological Quantum Computation by Jason Alicea (2021)
Source. Topological Quantum Course of the University of Oxford by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-012010- professor: Steven H. Simon
Lecture notes/book: www-thphys.physics.ox.ac.uk/people/SteveSimon/topological2021/TopoBook-Sep28-2021.pdf
Course page index: www-thphys.physics.ox.ac.uk/people/SteveSimon/
Ciro Santilli really likes this genre.
This is the first thing you have to know about supervised learning:Both of those already have hardware acceleration available as of the 2010s.
- training is when you learn model parameters from input. This literally means learning the best value we can for a bunch of number input numbers of the model. This can easily be on the hundreds of thousands.
- inference is when we take a trained model (i.e. with the parameters determined), and apply it to new inputs
Training, validation, and test data sets by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01There's a billion simple looking expressions which are not known to be transcendental numbers or not. It's cute simple to state but hard to prove at its best.
Open as of 2020:
Bibliography:
- www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/ How Math Achieved Transcendence by David S. Richeson (2023).
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact