De novo Updated 2025-07-16
Paywall Updated 2025-07-16
Symmetric bilinear map Updated 2025-07-16
Subcase of symmetric multilinear map:
Requires the two inputs and to be in the same vector space of course.
The most important example is the dot product, which is also a positive definite symmetric bilinear form.
As of 2020s and much earlier, Ciro Santilli believes that undergrad studies were fundamentally broken (considering the Information Age which completely changed what would be possible) because university had only two goals, with the exception of a few enlightened professors:
  • rank students from worse to best so they can get into PhD programs.
    For regular jobs grades didn't even matter as much compared the prestige of your university (and therefore, university entry exam grades) and your ability to stand the stress of exams to get minimal passing grade.
    In particular, being able to rank requires setting the difficulty level at a point where you can see a normal distribution in grades, and not have everyone at either 0 nor 100%.
    Also, this split could be caused by either shitty learning materials/conditions, or by mere volume. It doesn't matter.
  • get money from the students. Of course, in countries where university is "free", this means reporting how many students you had to some government office so they can give you a corresponding budget. But you still have an incentive to enroll as many as possible.
As a result, most students, who would not go on to do a PhD essentially do a simple trade: all their time, and possibly some money, in exchange for imbuing themselves with the incredible name of a respected institution so they can get better jobs later on.
Beauty, deep understanding, and learning awesome things comes basically as a second thought.
It is interesting to see how your own ideas shift with time, and Ciro Santilli doesn't think the following are very important anymore, so he was lazy to migrate them.
When he did the original website Ciro was in a "I must show off my skills to get a job mindset", but then after he landed a few jobs he moved to a "CV websites are useless, just do amazing projects and showcase them on your website to help them succeed" mindset.
Computer Updated 2025-07-16
The artistic instrument that enables the ultimate art: coding, See also: Section "The art of programming".
Much more useful than instruments used in inferior arts, such as pianos or paintbrushes.
Unlike other humans, computers are mindless slaves that do exactly what they are told to, except for occasional cosmic ray bit flips. Until they take over the world that is.
Video 1.
A computer is the equivalent of a bicycle for our minds by Steve Jobs (1980)
Source. Likely an excerpt from an interview done for a documentary in 1980. TODO exact source.
Video 2.
Steve Jobs talking about the Internet (1995)
Source.
The web is incredibly exciting, because it is the fulfillment of a lot of our dreams, that the computer would ultimately primarily not be a device for computation, but [sic] metamorphisize into a device for communication.
also:
Secondly it exciting because Microsoft doesn't own it, and therefore there is a tremendous amount of innovation happening.
then he talks about the impending role for online sales. Amazon incoming.
Computers basically have two applications:
Generally, the smaller a computer, the more it gets used for communication rather than computing.
The early computers were large and expensive, and basically only used for computing. E.g. ENIAC was used for calculating ballistic tables.
Communication only came later, and it was not obvious to people at first how incredibly important that role would be.
This is also well illustrated in the documentary Glory of the Geeks. Full interview at: www.youtube.com/watch?v=TRZAJY23xio. It is apparently known as the "Lost Interview" and it was by Cringely himself: www.youtube.com/watch?v=bfgwCFrU7dI for his Triumph of the Nerds documentary.
Updates Updated 2025-07-16
This section contains the a list of cool things Ciro Santilli has been up to in chronological order, including small quick ones. Many/most of those are also posted on Ciro Santilli's accounts such as:
For a more theme-oriented version of the best results see: Section "The best articles by Ciro Santilli".
DNA methylation Updated 2025-07-16
The first found and most important known epigenetic marker.
Happens only on adenine and cytosine. Adenine methylation is much less common in mammal than cytosine methylation, when people say "methylation" they often mean just cytosine methylation.
It often happens on promoters, where it inhibits transcription.

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