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.
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
Memento mori Updated 2025-07-16
Memory semantics Updated 2025-07-16
These are the rules which specify what different concurrent read/write memory accesses from different threads/processes can or cannot see.
Notable such set of rules include:
- C++ memory model. These are also reflected on the semantics of memory of the corresponding instruction set architecture
- SQL transaction isolation level
History of DNA methylation research Updated 2025-07-16
Incredible that there hasn't been a Nobel Prize for it as of 2022, e.g. as mentioned at: theconversation.com/no-nobel-but-epigenetics-finally-gets-the-recognition-it-deserves-18970
Some old dudes getting another prize in 2016: www.cuimc.columbia.edu/news/pioneers-epigenetics-awarded-horwitz-prize
Meta breaking glitch Updated 2025-07-16
A meta breaking glitch of a video game is a glitch that when discovered significantly breaks the meta.
In non-video game-game, it does sometimes happen that a meta is broken as well, but these events tend to be rarer and less dramatic than meta-breaking due to computer program glitches.
In PvP games, those glitches are generally forbidden by existing rules, and quickly patched after discovered.
In speedrunning however, they are either incorporated in the existing strategy, or may lead to the creation of a new run category for particularly significant glitches.
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