Ciro Santilli @cirosantilli 37

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

The wiki comments: en.wikipedia.org/w/index.php?title=Ferromagnetism&oldid=965600553#Explanation

The Bohr-van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.

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Lorentz transform consequence: everyone sees the same speed of light by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.

Observers will measure the speed of light by calculating how long it takes the light going towards

+ x

cross a rod of length

L = x_{2} - x_{1}

laid in the x axis at position

X 1

TODO image.

Each observer will observe two events:

$(t_{1}, x_{1}, y_{1}, z_{1})$ : the light touches the left side of the rod
$(t_{2}, x_{2}, y_{2}, z_{2})$ : the light touches the right side of the rod

Supposing that the standing observer measures the speed of light as

c

and that light hits the left side of the rod at time

T 1

, then he observes the coordinates:

t_{1} x_{1} t_{2} x_{2} = T 1 = X 1 = \frac{L}{c} = X 1 + L

(1)

Now, if we transform for the moving observer:

t_{1}^{'} x_{1}^{'} t_{2}^{'} x_{2}^{'} = γ (t_{1} - \frac{v x _{1}}{c ^{2}}) = γ (x_{1} - v t_{1}) = γ (t_{2} - \frac{v x _{2}}{c ^{2}}) = γ (x_{2} - v t_{2})

(2)

and so the moving observer measures the speed of light as:

c^{'} = \frac{x _{2}^{'} - x _{1}^{'}}{t _{2}^{'} - t _{1}^{'}} = \frac{( x _{2} - v t _{2} ) - ( x _{1} - v t _{1} )}{( t _{2} - \frac{v x _{2}}{c ^{2}} ) - ( t _{1} - \frac{v x _{1}}{c ^{2}} )} = \frac{( x _{2} - x _{1} ) - v ( t _{2} - t _{1} )}{( t _{2} - t _{1} ) - \frac{v}{c ^{2}} ( x _{2} - x _{1} )} = \frac{\frac{x _{2} - x _{1}}{t _{2} - t _{1}} - v}{1 - \frac{v}{c ^{2}} \frac{x _{2} - x _{1}}{t _{2} - t _{1}}} = \frac{c - v}{1 - \frac{v}{c ^{2}} c} = \frac{c - v}{\frac{c - v}{c}} = c

(3)

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Lorentz boost by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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Two observers travel at fixed speed relative to each other. They synchronize origins at x=0 and t=0, and their spacial axes are perfectly aligned. This is a subset of the Lorentz group. TODO confirm it does not form a subgroup however.

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Perforce by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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Lysozyme by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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The second protein to have its structure determined, after myoglobin, by X-ray crystallography, in 1965.

Breaks up peptidoglycan present in the bacterial cell wall, which is thicker in Gram-positive bacteria, which is what this enzyme seems to target.

Part of the inate immune system.

It is present on basically everything that mammals and birds excrete, and it kills bacteria, both of which are reasons why it was discovered relatively early on.

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C# by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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JavaScript by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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The language all browsers converted to as of 2019, and therefore the easiest one to distribute and most widely implemented programming language.

Hopefully will be killed by WebAssembly one day.

Because JavaScript is a relatively crap/ad-hoc language, it ended up some decent tooling to make up for that, e.g. stuff like linting via ESLint and reformatting through Prettier is much more widespread than in other languages.

JavaScript data structure are also quite a bit anemic, which makes libraries such as lodash incredibly popular. But most of that stuff should be in the stdlib.

Our JavaScript examples can be found at:

Node.js example: examples that don't interact with any browser feature. We are just testing those on the CLI which is much more convenient.
JavaScript browser example: examples that interact with browser-specific features, notably the DOM

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Tcl by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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One of the first big interpreted programming languages to go a bit further than Bash' word replacement insanity.

To the modern viewer, it feels like a middle ground between Bash and Python.

It was completely insane however, and it just died: Python is much saner, and Bash, although totally insane still golfs better, especially on the file manipulation context.

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ARM architecture family by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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This ISA basically completely dominated the smartphone market of the 2010s and beyond, but it started appearing in other areas as the end of Moore's law made it more economical logical for large companies to start developing their own semiconductor, e.g. Google custom silicon, Amazon custom silicon.

It is exciting to see ARM entering the server, desktop and supercomputer market circa 2020, beyond its dominant mobile position and roots.

Ciro Santilli likes to see the underdogs rise, and bite off dominant ones.

The excitement also applies to RISC-V possibly over ARM mobile market one day conversely however.

Basically, as long as were a huge company seeking to develop a CPU and able to control your own ecosystem independently of Windows' desktop domination (held by the need for backward compatibility with a billion end user programs), ARM would be a possibility on your mind.

in 2020, the Fugaku supercomputer, which uses an ARM-based Fujitsu designed chip, because the number 1 fastest supercomputer in TOP500: www.top500.org/lists/top500/2021/11/
It was later beaten by another x86 supercomputer www.top500.org/lists/top500/2022/06/, but the message was clearly heard.
2012 hackaday.com/2012/07/09/pedal-powered-32-core-arm-linux-server/ pedal-powered 32-core Arm Linux server. A publicity stunt, but still, cool.
AWS Graviton

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Portable Network Graphics by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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Coinbase by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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Lie bracket of a matrix Lie group by

Ciro Santilli 37  Updated 2025-06-12  +Created 1970-01-01

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[X, Y] = X Y - Y X

(1)

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

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Gauge block by