High flying bird vs gophers Updated 2025-07-16
Ciro once read that there are two types of mathematicians/scientists (he thinks it was comparing Einstein to some Jack of all trades polymath who didn't do any new discoveries):
- high flying birds, who know a bit of everything, feel the beauty of each field, but never dig deep in any of them
- gophers, who dig all the way down, on a single subject, until they either get the Nobel Prize, or work on the wrong problem and waste their lives
TODO long after Ciro forgot where he had read this from originally, someone later pointed him to: www.ams.org/notices/200902/rtx090200212p.pdf Birds and Frogs by Freeman Dyson (2009), which is analogous but about Birds and Frogs. So did Ciro's memory play a trick on him, or is there also a variant; of this metaphor with a gopher?
Ciro is without a doubt the bird type. Perhaps the ultimate scientist is the one who can combine both aspects in the right amount?
Ciro gets bored of things very quickly.
Once he understands the general principles, if the thing is not the next big thing, Ciro considers himself satisfied without all the nitty gritty detail, and moves on to the next attempt.
In the field of mathematics for example, Ciro is generally content with understanding cool theorem statements. More generally, one of Ciro's desires is for example to understand the significance of each physics Nobel Prize.
This is also very clear for example after Ciro achieved Linux Kernel Module Cheat: he now had the perfect setup to learn all the Linux kernel shady details but at the same time after all those years he finally felt that "he could do it, so that was enough", and soon moved to other projects.
If Ciro had become a scientist, he would write the best review papers ever, just like in the current reality he writes amazing programming tutorials on Stack Overflow.
Ciro has in his mind an overly large list of subjects that "he feels he should know the basics of", and whenever he finds something in one of those topics that he does not know enough about, he uncontrollably learns it, even if it is not the most urgent thing to be done. Or at least he puts a mention on his "list of sources" about the subject. Maybe everyone is like that. But Ciro feels that he feels this urge particularly strongly. Correspondingly, if a subject is not in that list, Ciro ignores it without thinking twice.
Ciro believes that high flying birds are the type of people better suited for venture capital investment management: you know a bit of what is hot on several fields to enough depth to decide where to place your bets and how to guide them. But you don't have the patience to actually go deeply into any one of them and deal with each individual shit that comes up.
Cosmos: A Personal Voyage (1980) episode 1 mentions as quoted by the Wikipedia page for Eratosthenes:That's Ciro.
According to an entry in the Suda (a 10th-century encyclopedia), his critics scorned him, calling him beta (the second letter of the Greek alphabet) because he always came in second in all his endeavors.
Matrix representation of a bilinear form Updated 2025-07-16
As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.
Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix which encodes the value for each possible pair of basis vectors.
Matrix ring Updated 2025-07-16
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.
Maxwell-Boltzmann distribution Updated 2025-07-16
Maxwell-Boltzmann distribution for three different temperatures
. Reference mark Updated 2025-07-16
Ciro Santilli had to see this in a few separate places, until he underestood: that little pictur emust be a thing! Examples:
- mojim watermarks: mojim.com/twy105509x7x2.htm
- some Japanese website: kotobank.jp/word/%E5%A4%A7%E7%96%91-556655
Maxwell's equations Updated 2025-07-16
Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.
The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:
- , , : directions of the electric field
- , , : directions of the magnetic field
Due to the conservation of charge however, those input functions have the following restriction:
Equation 1.
Charge conservation
. Also consider the following cases:
The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.
Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
Equation 2.
Gauss' law
. Equation 3.
Gauss's law for magnetism
. Equation 4.
Faraday's law
. Equation 5.
Ampere's circuital law
. You should also review the intuitive interpretation of divergence and curl.
Maxwell's equations in 2D Updated 2025-07-16
Reflections of the Moon on Erquan Updated 2025-07-16
Relationship between the quotient group and direct products Updated 2025-07-16
Although quotients look a bit real number division, there are some important differences with the "group analog of multiplication" of direct product of groups.
If a group is isomorphic to the direct product of groups, we can take a quotient of the product to retrieve one of the groups, which is somewhat analogous to division: math.stackexchange.com/questions/723707/how-is-the-quotient-group-related-to-the-direct-product-group
The "converse" is not always true however: a group does not need to be isomorphic to the product of one of its normal subgroups and the associated quotient group. The wiki page provides an example:
Given G and a normal subgroup N, then G is a group extension of G/N by N. One could ask whether this extension is trivial or split; in other words, one could ask whether G is a direct product or semidirect product of N and G/N. This is a special case of the extension problem. An example where the extension is not split is as follows: Let , and which is isomorphic to Z2. Then G/N is also isomorphic to Z2. But Z2 has only the trivial automorphism, so the only semi-direct product of N and G/N is the direct product. Since Z4 is different from Z2 × Z2, we conclude that G is not a semi-direct product of N and G/N.
This is also semi mentioned at: math.stackexchange.com/questions/1596500/when-is-a-group-isomorphic-to-the-product-of-normal-subgroup-and-quotient-group
I think this might be equivalent to why the group extension problem is hard. If this relation were true, then taking the direct product would be the only way to make larger groups from normal subgroups/quotients. But it's not.
Human vitamin Updated 2025-07-16
Maxwell's equations require special relativity Updated 2025-07-16
The following aspects of Maxwell's equations make no sense without special relativity:
- the Lorentz force would be different observers have different speeds, see e.g.: charged particle moving at the same speed of electrons thought experiment
- Maxwell's equations imply that the speed of light is the same for all inertial reference frames
When charged particle though experiment are seen from the point of view of special relativity, it becomes clear that magnetism is just a direct side effect of charges being viewed in special relativity. One is philosophically reminded of how spin is the consequence of quantum mechanics + special relativity.
Meal deal Updated 2025-07-16
x.com/Birdyword/status/1777591446612193667Singaporean taxi drivers are the cutest.
A while ago a Singaporean taxi driver asked me what a UK hawker centre lunch might cost. I explained that there aren't any. He asked what office workers ate, and I explained the concept of Meal deals. And he looked at me with such a powerful combination of pity and revulsion.
Measure theory Updated 2025-07-16
Main motivation: Lebesgue integral.
The Bright Side Of Mathematics 2019 playlist: www.youtube.com/watch?v=xZ69KEg7ccU&list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Mechanics problem Updated 2025-07-16
High temperature superconductor superconducting magnet Updated 2025-07-16
History Updated 2025-07-16
Mediocre Amateur Updated 2025-07-16
About 50k subscribers on 2021, which feels way too little for the video quality and quantity.
Ciro Santilli believes that this channel will go very far, certainly achieving 1M subscribers in they keep it for one or two more years. Update: it didn't, as of 2024, shame.
They are Utah-based, and they do many many amazing weekend trips. They mostly drive from home to some trailhead, and then climb up and down it the entire day.
No technical rock climbing, only bouldering, but they still manage to reach many amazing places, and there is a level of danger in many of their ascents.
Medium (website) Updated 2025-07-16
While this has some of the metrics features that Ciro Santilli wants to implement for OurBigBook.com, it limits the number of articles your readeres can read.
Melody of Longshuo Updated 2025-07-16
There are unlisted articles, also show them or only show them.