Ciro Santilli @cirosantilli 37

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:

H = \nabla^{2} + m^{2}

(1)

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:

H ψ = i \frac{\partial ψ}{\partial t}

(2)

taking the Hamiltonian twice leads to:

H^{2} ψ = - \frac{\partial ^{2} ψ}{\partial ^{2} t}

(3)

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.

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Emscripten by

Ciro Santilli 37 Updated 2025-07-16

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TypeScript by

Ciro Santilli 37 Updated 2025-07-16

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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

typescript/inferFromInit.ts. Should fail with:
hello.ts:2:1 - error TS2322: Type 'string' is not assignable to type 'number
since TypeScript infers the type of i from first assignment as string, and we then attempt a number assignment later on
typescript/inferAfterInit.ts. Does not fail, as the first assignment cannot be computationally determined at runtime without breaking computer science.
typescript/js-from-ts/main.ts: call JavaScript file typescript/js-from-ts/notmain.js from TypeScript.
```
npx tsc jsFromTs.ts && node jsFromTs.js
```
TODO we are unable to make it typecheck that require, i.e. make that fail, but we've seen cases in complex codebases where that did happen and www.typescriptlang.org/docs/handbook/intro-to-js-ts.html has infinite information on supporting it. So... how to make it fail??
typescript/functionArgument.ts: basic argument tests
- typescript/functionOptionalArgument.ts: f(n?: number)
typescript/functionOptions.ts: f({n, s}: {n: number, s: string})

Some major annoyances of TypeScript:

destructuring assignment in function arguments requires repeating all arguments:
stackoverflow.com/questions/12710905/how-do-i-dynamically-assign-properties-to-an-object-in-typescript how to dynamically assign properties to objects without defining explicit interfaces? We really need a syntax of type:
```
const myobj = {
  i: 2,
  [s string],
}
if (something) {
  myobj.s = 'asdf'
}
```

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IP address by

Ciro Santilli 37 Updated 2025-07-16

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Video 1.

The Internet Protocol by Ben Eater (2014)

Source.

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Intel Research by

Ciro Santilli 37 Updated 2025-07-16

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"Intel Research Lablets", that's a terrible name.

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Set SVG background color in Inkscape by

Ciro Santilli 37 Updated 2025-07-16

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This is related to the underlying SVG pain point of SVG background color:

For PNG export:

superuser.com/questions/249860/how-can-i-change-inkscapes-default-export-background-color-from-yellow-to-white

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Iterative in-order by

Ciro Santilli 37 Updated 2025-07-16

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This is a bit harder than iterative pre-order: now we have to check if there is a left or right element or not:

(START) push current
if there is left:
- move left
else:
- (ELSE) pop
- visit
- if there is right
  - move right
  - GOTO START
- else:
  - GOTO ELSE

The control flow can be slightly simplified if we allow NULLs: www.geeksforgeeks.org/inorder-tree-traversal-without-recursion/

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WebGL by

Ciro Santilli 37 Updated 2025-07-16

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developer.mozilla.org/en-US/docs/Web/API/WebGL_API/By_example

HTML snippet:

new class extends OurbigbookCanvasDemo {
  init() {
    super.init('webgl', {context_type: 'webgl'});
    this.ctx.viewport(0, 0, this.ctx.drawingBufferWidth, this.ctx.drawingBufferHeight);
    this.ctx.clearColor(0.0, 0.0, 0.0, 1.0);
    this.vertexShaderSource = `
#version 100
precision highp float;
attribute float position;
void main() {
  gl_Position = vec4(position, 0.0, 0.0, 1.0);
  gl_PointSize = 64.0;
}
`;

    this.fragmentShaderSource = `
#version 100
precision mediump float;
void main() {
  gl_FragColor = vec4(0.18, 0.0, 0.34, 1.0);
}
`;
    this.vertexShader = this.ctx.createShader(this.ctx.VERTEX_SHADER);
    this.ctx.shaderSource(this.vertexShader, this.vertexShaderSource);
    this.ctx.compileShader(this.vertexShader);
    this.fragmentShader = this.ctx.createShader(this.ctx.FRAGMENT_SHADER);
    this.ctx.shaderSource(this.fragmentShader, this.fragmentShaderSource);
    this.ctx.compileShader(this.fragmentShader);
    this.program = this.ctx.createProgram();
    this.ctx.attachShader(this.program, this.vertexShader);
    this.ctx.attachShader(this.program, this.fragmentShader);
    this.ctx.linkProgram(this.program);
    this.ctx.detachShader(this.program, this.vertexShader);
    this.ctx.detachShader(this.program, this.fragmentShader);
    this.ctx.deleteShader(this.vertexShader);
    this.ctx.deleteShader(this.fragmentShader);
    if (!this.ctx.getProgramParameter(this.program, this.ctx.LINK_STATUS)) {
      console.log('error ' + this.ctx.getProgramInfoLog(this.program));
      return;
    }
    this.ctx.enableVertexAttribArray(0);
    var buffer = this.ctx.createBuffer();
    this.ctx.bindBuffer(this.ctx.ARRAY_BUFFER, buffer);
    this.ctx.vertexAttribPointer(0, 1, this.ctx.FLOAT, false, 0, 0);
    this.ctx.useProgram(this.program);
  }
  draw() {
    this.ctx.clear(this.ctx.COLOR_BUFFER_BIT);
    this.ctx.bufferData(this.ctx.ARRAY_BUFFER, new Float32Array([Math.sin(this.time / 60.0)]), this.ctx.STATIC_DRAW);
    this.ctx.drawArrays(this.ctx.POINTS, 0, 1);
  }
}

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AIDS by

Ciro Santilli 37 Updated 2025-07-16

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Goldstone's theorem by

Ciro Santilli 37 Updated 2025-07-16

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Abraham by

Ciro Santilli 37 Updated 2025-07-16

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B Reactor by

Ciro Santilli 37 Updated 2025-07-16