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.
E notation Updated 2025-07-16
What do you prefer, 1 \times 10^{10} or 1E10.
Singularity Updated 2025-07-16
Source code Updated 2025-07-16
Terminal emulator Updated 2025-07-16
Once upon a time young Ciro Santilli spent lots of time evaluating the features of different terimnals. The many windows of Terminator. The pop-uppiness of Guake/Yakuake.
But then one day he met tmux, and he was enlightened
Terminal choice doesn't matter. Just use tmux.
Quartz Updated 2025-07-16
Unitary matrix Updated 2025-07-16
Applications:
Autodidacticism Updated 2025-07-16
There are two types of people:
  • those who are autodidacts
  • those who didn't really learn
Some possible definitions:
  • learning without a gun pointed at your head
  • learning from an e-book or video rather than from a talking head 5 rows of chairs in front of you
    How that is different from a video, you tell me.
Physicists love to talk about that stuff, but no one ever has the guts to explain it into enough detail to show its beauty!!!
Perhaps the wisest thing is to just focus entirely on the part to start with, which is the quantum electrodynamics one, which is the simplest and most useful and historically first one to come around.
Perhaps the best explanation is that if you assume those internal symmetries, then you can systematically make "obvious" educated guesses at the interacting part of the Standard Model Lagrangian, which is the fundamental part of the Standard Model. See e.g.:
One bit underlying reason is: Noether's theorem.
Notably, axelmaas.blogspot.com/2010/08/global-and-local-symmetries.html gives a good overview:
A local symmetry transformation is much more complicated to visualize. Take a rectangular grid of the billiard balls from the last post, say ten times ten. Each ball is spherical symmetric, and thus invariant under a rotation. The system now has a global and a local symmetry. A global symmetry transformation would rotate each ball by the same amount in the same direction, leaving the system unchanged. A local symmetry transformation would rotate each ball about a different amount and around a different axis, still leaving the system to the eye unchanged. The system has also an additional global symmetry. Moving the whole grid to the left or to the right leaves the grid unchanged. However, no such local symmetry exists: Moving only one ball will destroy the grid's structure.
Such global and local symmetries play an important role in physics. The global symmetries are found to be associated with properties of particles, e. g., whether they are matter or antimatter, whether they carry electric charge, and so on. Local symmetries are found to be associated with forces. In fact, all the fundamental forces of nature are associated with very special local symmetries. For example, the weak force is actually associated in a very intricate way with local rotations of a four-dimensional sphere. The reason is that, invisible to the eye, everything charged under the weak force can be characterized by a arrow pointing from the center to the surface of such a four-dimensional sphere. This arrow can be rotated in a certain way and at every individual point, without changing anything which can be measured. It is thus a local symmetry. This will become more clearer over time, as at the moment of first encounter this appears to be very strange indeed.
so it seems that that's why they are so key: local symmetries map to the forces themselves!!!
axelmaas.blogspot.com/2010/09/symmetries-of-standard-model.html then goes over all symmetries of the Standard Model uber quickly, including the global ones.

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