Survey by Ciro Santilli: math.stackexchange.com/questions/1985/software-for-drawing-geometry-diagrams/3938216#3938216
Many plotting software can be used to create mathematics illustrations. They just tend to have more data-oriented rather than explanatory-oriented output.
Power, Sex, Suicide by Nick Lane (2006) part 5 "Murder or suicide" mentions that apoptosis has two main functions:
- prevent cancer
- but it is also an important part of body development, e.g. fingers are separated because cells between them kill themselves. Otherwise we would have webbed feet like ducks. There is also a lot of apoptosis during the development of the brain. This has been observed notably in C. elegans see also: Section "C. elegans cell lineage".
dumps.wikimedia.org/enwiki/latest/enwiki-latest-all-titles-in-ns0.gz Characterization:
- contains redirects, e.g. en.wikipedia.org/wiki/"Ampere_North" redirects to en.wikipedia.org/wiki/Ampere_North,_New_Jersey and both are present. Noted in this comment: stackoverflow.com/questions/24474288/how-to-obtain-a-list-of-titles-of-all-wikipedia-articles#comment136016773_24474476
In 2019, a paper proved that MTG is Turing complete with a legacy legal deck. Live demo with some hand waving: Video "I Built a COMPUTER in Magic: The Gathering by Because Science (2019)". As Ciro Santilli comments at: github.com/cirosantilli/cirosantilli.github.io/issues/42 this was an interest addition to the previous "indefinite infinite loop" e.g. as found in a Four Horsemen combo deck
This is closely linked to the Pauli exclusion principle.
What does a particle even mean, right? Especially in quantum field theory, where two electrons are just vibrations of a single electron field.
Another issue is that if we consider magnetism, things only make sense if we add special relativity, since Maxwell's equations require special relativity, so a non approximate solution for this will necessarily require full quantum electrodynamics.
As mentioned at lecture 1 youtube.com/watch?video=H3AFzbrqH68&t=555, relativistic quantum mechanical theories like the Dirac equation and Klein-Gordon equation make no sense for a "single particle": they must imply that particles can pop in out of existence.
Bibliography:
- www.youtube.com/watch?v=Og13-bSF9kA&list=PLDfPUNusx1Eo60qx3Od2KLUL4b7VDPo9F "Advanced quantum theory" by Tobias J. Osborne says that the course will essentially cover multi-particle quantum mechanics!
- physics.stackexchange.com/questions/54854/equivalence-between-qft-and-many-particle-qm "Equivalence between QFT and many-particle QM"
- Course: Quantum Many-Body Physics in Condensed Matter by Luis Gregorio Dias (2020) from course: Quantum Many-Body Physics in Condensed Matter by Luis Gregorio Dias (2020) give a good introduction to non-interacting particles
In this tutorial, we will use the Jena SPARQL hello world as a starting point. Tested on Apache Jena 4.10.0.
Basic query on rdf/vcard.ttl RDF Turtle data to find the person with full name "John Smith":Output:
sparql --data=rdf/vcard.ttl --query=<( printf '%s\n' 'SELECT ?x WHERE { ?x <http://www.w3.org/2001/vcard-rdf/3.0#FN> "John Smith" }')---------------------------------
| x |
=================================
| <http://somewhere/JohnSmith/> |
---------------------------------To avoid writing Output:
http://www.w3.org/2001/vcard-rdf/3.0# a billion times as queries grow larger, we can use the PREFIX syntax:sparql --data=rdf/vcard.ttl --query=<( printf '%s\n' '
PREFIX vc: <http://www.w3.org/2001/vcard-rdf/3.0#>
SELECT ?x
WHERE { ?x vc:FN "John Smith" }
')---------------------------------
| x |
=================================
| <http://somewhere/JohnSmith/> |
---------------------------------Bibliography:
- UniProt contains some amazing examples runnable on their servers: sparql.uniprot.org/.well-known/sparql-examples/
- owns the entire stack and creates high quality highly optimized systems
- creates closed lock-in systems without inter-operability and actively fights users from owning their devices
- do they give back enough to open source, or do they leech mostly?
The Mapple Store and Steve Mobs from The Simpsons
. Source. edisciplinas.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter7-boltzman.pdf mentions
- sedimentation
- reaction rate as it calculates how likely it is for particles to overcome the activation energy
Whenever Ciro's wife starts with "the Asian fetish talk", Ciro reminds her of her own claimed "tall person fetish", and they call it quits.
Asian fetish is much more than sex. It is about the culture, the history, the language. It is the same fetish that makes great mathematicians an Artists do what they do.
When Ciro Santilli was at École Polytechnique, he had to do a presentation for his stupid English courses that all students were forced to take, no matter how good their English was.
The topic was likely something like "pick a country", and Ciro was delighted when he managed to pick "China", after it had gone around a table with many many people before him.
The PowerPoint presentation Ciro made over the weekend was so amazing (and making it was actually fun to make, Ciro actually remembers it a bit!), drawing partly from stuff his wife then girlfriend showed him, that at the end the one of the other students asked him if he had lived in China.
It is a shame Ciro couldn't find the presentation when he wrote this line many many years later. Anything that is not in a BLOB-free monorepo, will disappear, heed my words. But he's certain about two things which it contained:
en.wikipedia.org/wiki/Asian_fetish#History_of_originssubservient, passive, mysterious are understandable. But Hyper-sexual and villainous? OMG have these people never seen real Asians?
en.wikipedia.org/wiki/Asian_fetish#Pornography:
In the United States, women of East and Southeast Asian descent are sometimes stereotyped as subservient, passive, mysterious, villainous in nature, and hyper-sexual.
en.wikipedia.org/wiki/Asian_fetish#Pornography:
The matrix ring of degree n is the set of all n-by-n square matrices together with the usual vector space and matrix multiplication operations.
Open source ones:
- www.quora.com/Are-there-good-open-source-standard-cell-libraries-to-learn-IC-synthesis-with-EDA-tools/answer/Ciro-Santilli Are there good open source standard cell libraries to learn IC synthesis with EDA tools?
Explains how it is possible that everyone observes the same speed of light, even if they are moving towards or opposite to the light!!!
This was first best observed by the Michelson-Morley experiment, which uses the movement of the Earth at different times of the year to try and detect differences in the speed of light.
This leads leads to the following conclusions:
- to length contraction and time dilation
- the speed of light is the maximum speed anything can reach
The "special" in the name refers to the fact that it is a superset of general relativity, which also explains gravity in a single framework.
Since time and space get all messed up together, you have to be very careful to understand what it means to say "I observed this to happen over there at that time", otherwise you will go crazy. A good way to think about is this:
- use Einstein synchronization to setup a bunch of clocks for every position in your frame of reference
- on every point of space, you put a little detector which records events and the time of the event
- each detector can only detect events locally, i.e. events that happen very close to the detector
- then, after the event, the detectors can send a signal to you, who is sitting at the origin, telling you what they detected
The following things come to mind when you look into research in this area, especially the search for BB(5) which was hard but doable:
- it is largely recreational mathematics, i.e. done by non-professionals, a bit like the aperiodic tiling. Humbly, they tend to call their results lemmas
- complex structure emerges from simple rules, leading to a complex classification with a few edge cases, much like the classification of finite simple groups
Bibliography:
A single line in the emission spectrum.
So precise, so discrete, which makes no sense in classical mechanics!
Has been the leading motivation of the development of quantum mechanics, all the way from the:
- Schrödinger equation: major lines predicted, including Zeeman effect, but not finer line splits like fine structure
- Dirac equation: explains fine structure 2p spin split due to electron spin/orbit interactions, but not Lamb shift
- quantum electrodynamics: explains Lamb shift
- hyperfine structure: due to electron/nucleus spin interactions, offers a window into nuclear spin
- math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors/3503875#3503875
- math.stackexchange.com/questions/1520832/real-life-examples-for-eigenvalues-eigenvectors
- matheducators.stackexchange.com/questions/520/what-is-a-good-motivation-showcase-for-a-student-for-the-study-of-eigenvalues
There are unlisted articles, also show them or only show them.