Great doubt Updated 2025-07-16
The type of feeling of confusion and distrut for your sense that some Koans attempt to instill.
Some notable references:
The Klein-Gordon equation directly uses a more naive relativistic energy guess of squared.
But since this is quantum mechanics, we feel like making into the "momentum operator", just like in the Schrödinger equation.
But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...
So we just cheat and try to use the laplace operator instead because there's some squares on it:
But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.
So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.
Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:
taking the Hamiltonian twice leads to:
We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.
Two.js Updated 2025-07-16
Examples at: two-js/.
JavaScript library, works both on browser and headless with Node.js to SVG.
Feels good. Maybe not ultra featured, and could have more simple examples in docs, but still good.
One of the main features of Two.js appears to be the fact that it can natively render to either SVG and canvas, rather than creating SVG through DOM hacks as done by other projects.
Emscripten Updated 2025-07-16
Node.js Updated 2025-07-16
WellSync, if you are gonna useSync this wonky language thing inSync one place, you might as well useSync it everywhereSync and make it more decent. See also: how to convert async to sync in JavaScript.
TypeScript Updated 2025-07-16
TypeScript is good. It does find errors in your JavaScript. But it is a form of "turd polishing". But Ciro Santilli would rather have a polished turd than a non-polished one.
Part of the reason TypeScript became popular is due to the universality of asset bundlers. Once you are already using an asset bundler, changing the .js extension into .ts to get a less shitty experience is an easy choice.
The other big reason is that JavaScript is so lose with type conversions, notably undefined happily converting to strings without problems, and any missing properties of Object happily being undefined. We should actually use ES6 Map everywhere instead of using Objects as maps.
Since TypeScript is not the default form of the language however, it inevitably happens that you need to add external types for a gazillion projects that are using raw JavaScript, and sometimes fight a lot to get things to work. And so we have: github.com/DefinitelyTyped/DefinitelyTyped. Not sure if this is beautiful, or frightening.
But in the end, as with other type of static linters, TypeScript generally transforms a few hard to debug runtime issues, into a bunch of stupid to solve compile time issues, which is generally a good thing.
The fact that this it parses comments JSDoc comments in JavaScript files is quite amazing.
Examples under typescript. Run each one of them with:
npx tsc example.ts
node example.js
Helper:
tsr() (
  # ts Run
  f="$1"
  npx tsc "$f"
  node "${f%.*}.js"
)
tsr example.ts
Some major annoyances of TypeScript:
Universal Module Definition Updated 2025-07-16
Since JavaScript devs are incapable of defining an unified import standard, this design pattern emerged where you just check every magic global one by one. Here's a demo where a Js library works on both the browser and from Node.js:
Java program Updated 2025-07-16
Riseup Updated 2025-07-16

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