You read the name and think: hmm, neural cords!
But then you see that his is one of its members:
Yup. That's your cousin. And it's a much closer cousin than something like arthropods, which at least have heads eyes and legs like you.
Convergent evolution is crazy!
The alternating groups of degree 5 or greater are simple by 
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-012020-so-far yes, Grover's algorithm would only effectively reduce key sizes by half:
but there isn't a mathematical proof either.
Programming languages without a decent dominating package system by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01Subgroup of the Poincaré group without translations. Therefore, in those, the spacetime origin is always fixed.
Or in other words, it is as if two observers had their space and time origins at the exact same place. However, their space axes may be rotated, and one may be at a relative speed to the other to create a Lorentz boost. Note however that if they are at relative speeds to one another, then their axes will immediately stop being at the same location in the next moment of time, so things are only valid infinitesimally in that case.
This group is made up of matrix multiplication alone, no need to add the offset vector: space rotations and Lorentz boost only spin around and bend things around the origin.
One definition: set of all 4x4 matrices that keep the Minkowski inner product, mentioned at Physics from Symmetry by Jakob Schwichtenberg (2015) page 63. This then implies:
The more familiar transitions we are familiar with like liquid water into solid water happen at constant temperature.
However, other types of phase transitions we are less familiar in our daily lives happen across a continuum of such "state variables", notably:
- superfluidity and its related manifestation, superconductivity
- ferromagnetism
A permutation group can then be described in terms of the generating set of a group of specific elements given in cycle notation.
E.g. en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Permutation_groups mentions that the Mathieu group is generated by three elements:which feels quite compact for a simple group with 95040 elements, doesn't it!
- (0123456789a)
- (0b)(1a)(25)(37)(48)(69)
- (26a7)(3945)
Physics Videos by Eugene Khutoryansky by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01These videos can give some geometric insight and do have their value.
But they are sometimes too slow, there are never any mention of experiments, just "the truth".
Most important application: produce X-rays for X-ray crystallography.
Note however that the big experiments at CERN, like the Large Hadron Collider, are also synchrotrons.
List of facilities: en.wikipedia.org/wiki/List_of_synchrotron_radiation_facilities
Education has become an expensive bureaucratic exercise, completely dissociated from reality and usefulness.
It completely rejects what the individual wants to achieve, and instead attempts to mass homogenize and test people through endless hours of boredom.
And the only goals it achieves are testing student's resilience to stress, and facilitating the finding of sexual partners. True learning is completely absent.
Teachers only teach because they have to do it to get paid, not for passion. Their only true incentive is co-authoring papers.
Education is meant to help us, the students, achieve our goals through passionate learning.
And, we, the students, are individuals, with different goals and capabilities.
The way we protest is to publish the knowledge from University for free, on the Internet, so that anyone can access it.
And we do this is a law-abiding way, without copyright infringement, so that no one can legally take it down.
We come to our courses just for the useless roll calls. But we already know all the subject better than the "teacher" on the very first day.
And we are already more famous than the "teacher" online, and through the Internet have already taught more way way more people than they ever will.
The effect of this is to demoralize the entire school system at all levels, until only one conclusion is possible: implosion.
And from the ashes of the old system, we will build a new one, which does only what matters with absolute efficiency: help the individual students achieve their goals.
A system in which the only reason why university exist will be to allow the most knowledgeable students to access million dollar laboratory equipment, and to pay the most prolific content creators so they can continue content creating.
No more useless courses. No more useless tests. Only passion, usefulness and focus.
OurBigBook.com PageRank-like ranking by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01It would be really cool to have a PageRank-link algorithm that answers the key questions:However, Ciro has decided to leave this for phase two action plan, because it is impossible to tune such an algorithm if you have no users or test data.
- what is the best content for subject X.For example, if you are reading
cirosantilli/riemann-integraland it is crap, you would be able to click the buttonwhich leads you to the URL: ourbigbook.com/subject/mathematics. This URL then contains a list of all pages people have written about the subjectVersions by other authors
mathematics, sorted by some algorithm, containing for example: - who knows the most about subject X. This can be found by visiting: ourbigbook.com/users/mathematics "Top Mathematics users", which would contain the list of users sorted by the algorithm:
Perhaps it is also worth looking into ExpertRank, they appear to do some kind of "expert in this area", but with clustering (unlike us, where the clustering would be more explicit).
Other dump of things worth looking into:
OurBigBook.com University lecture notes by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01Basically everything that applies to the blogs section also applies here, but university lecture notes are so important to us that they deserve a bit more talk.
It is arguable that this is currently the best way to learn any university subject, and that it can already be used to learn any subject.
We basically just want to make the process more efficient and enjoyable, by making it easier:
One major problem with lecture notes is that, as the name suggests, they are merely a complement to the lecture, and don't contain enough detail for you to really learn solely from them without watching the lecture.
The only texts that generally teach in enough depth are actual books, which are almost always commercial.
So in a sense, this project can be seen as a path to upgrade free lecture notes into full blown free books, from which you can learn from scratch without any external material.
And a major way in which we believe this can be done is through the reuse of sections of lecture notes by from other universities, which greatly reduces the useless effort of writing things from scratch.
The intended mental picture is clear: the topics feature docs.ourbigbook.com/#ourbigbook-web-topics will is intended to act as the missing horizontal topic integration across lecture notes of specific universities, e.g:
MIT calculus course UCLA calculus course
* Calculus <---> * Calculus
* Limit <---> * Limit
* Limit of a function
* Limit of a series <---> * Limit of a series
* Derivative <---> * Derivative
* L'Hôpital's rule
* Integral <---> * Integral
Example topics page of OurBigBook.com
. One important advantage of lecture notes is that since they are written by the teacher, they should match exactly what "students are supposed to learn to get good grades", which unfortunately is a major motivation for student's learning weather we want it or not.
One big open question for this project is to what extent notes written for lectures at one university will be relevant to the lectures at another university?
Is it possible to write notes in a way that they are naturally reusable?
It is our gut feeling that this is possible. But it almost certainly requires an small intentional effort on the part of authors.
The question then becomes whether the "become famous by getting your content viewed in other universities" factor is strong enough to attract users.
And we believe that it might, it just might be.
- HyperCard: we are kind of a "multiuser" version of HyperCard, trying to tie up cards made by different users. It is worth noting that HyperCard was one of the inspirations for WikiWikiWeb, which then inspired Wikipedia
- Semantic Web
- NLab
- physicstravelguide.com/ Nice manifesto: physicstravelguide.com/about by Jakob Schwichtenberg.
- OpenStax
- www.ft.com/content/5515ec3e-0040-4d90-85a9-df19d6e3ebd2 (archive) Twilio’s Jeff Lawson: an evangelist for software developersYou can never be first. But you can have the correct business model. That company's website must have gone into IP Purgatory, and could never be released as an open source website.As a student at the University of Michigan, he started a company that made lecture notes available free online, drawing a large audience of Midwestern college students and, soon enough, advertisers. At the height of the dotcom bubble, he dropped out of college, raised $10m from the venture firm Venrock and moved the company to Silicon Valley.His start-up drew interest from an acquirer that was planning to go public early in 2000. They closed the acquisition but missed their IPO window as the market plunged, and by August the company had filed for bankruptcy. Stock that Lawson and investors in his start-up received from the sale became worthless.He might actually be interested in donating to OurBigBook.com if it move forward now that he's a billionaire.
- Knol: basically the exact same thing by Google but 14 years earlier and declared a failure. Quite ominous:
- leanpub: similar goals, markdown-based, but the usual "you own your book copyright and you are trying to sell your book" approach
- nature Scitable
OK, just going random now:
There are unlisted articles, also show them or only show them.