The Beauty of Monte Carlo - through casinos, code, coffee and the Cosmos

What's beautiful about it, you ask? Well, it's a beautiful part of Monaco, and has a legendary casino 😎

And for a computer scientist, it's beautiful in a way many other fundamental algorithms are.

Neural networks mimic synapses in our brains in a simple way. You excite the nodes, and out comes magic that remains somewhat mysterious to its designer. Their fundamental architecture is a lot simpler than most people might realize.
Simulated annealing is a classic algorithm that essentially mimics heating, banging and cooling metal atoms in the hopes that it will create a stronger sword. And it just will, the atoms magically realign to your will with no knowledge of what's going on, just "feeling" their neighbors.
Stable diffusion methods in some of today's AI is an extremely counterintuitive example of this that bends even tenured professor minds. You essentially degrade perfectly good training data iteratively into uniform noise, and out comes an inexplicable ability to "conceptualize".

Like many similar algorithms, Monte Carlo does not care much about what you are doing. You can generally approximate anything with it, although it has been in most heavy use when the problem cannot be mapped to a closed-form mathematical expression. Specialized algorithms are usually quicker at specialized things, like just approximating the number π. But today's information era is all about not specializing unnecessarily, and letting the data speak. As good as everything being mentioned in our current AI zeitgeist is statistical machinery. The implementation is simple and deals with large fuzzy things, not exact things, and the methods are "hopelessly" general.

What Monte Carlo lets you do here is to put love into your fuzziness, and trust that as you are building what might look to be an unstable tower of modeling fuzz, it has this magical property of improving. When scientific researchers encounter a surprising generality like this, they stop to ask if it reflects something fundamental about nature. You can approximate everything with Monte Carlo, and it's hopelessly general and fuzzy, and we stop to think: Why is statistical AI crushing IT today, how can our brains do what they do, and why is quantum mechanics our dominant fundamental theory? Do you know what else is fuzzy like these guys, and is by definition approximating our everything?

Reality

You might have heard of one the greatest remaining scientific mysteries today, which pops up as emergence, the particle-wave duality, the measurement problem, or the uncertainty principle. And you've probably also heard about our most successful, predictive and detailed model of reality today itself, quantum mechanics. This is a statistical discipline of physics where we see that everything in fact seems to be:

Distributions: "Particles" are actually a so-called wavefunction, pretty much the stuff you are used to seeing in iQx Plans. When we make an observation about a particle's wavefunction, a piece of the universal wavefunction, we say that the wavefunction has "collapsed" and "become a particle". And we have no solid ideas for what's really going on there, how to solve the measurement problem and wavefunction collapse problem, or if they relate to our interpretation of things rather than being some final math problems.
Scenarios: What we might call a "particle" is actually just a deterministic scenario that beyond proof does not paint the whole picture. This is where we run into these braintwisting dualities mentioned above, and the fact that your mind can only sense statistical summaries of reality. It has to "collapse" information into the ~20 ms thinking rate we have and compress as much of the relevant data it acquires into itself for each "snapshot".
Generalization: These little particles "approximate" the very mind you are using to read this bulletpoint. This is a mindblowingly specialized activity for the general little things you are made of to do! And as our final bullet point teases below, your mind itself could be seen as an emergent phenomenon. It exists in the sense that it makes sense to something, and the thing it's making sense to is itself, which is where it truly gets interesting.
Approximation: Emergent phenomena like the one we call "temperature" is not exactly a real thing. This is just a concept that makes sense to us with the sizes we have, and the collapsed view of reality we have access to. We have temperature tools built into our minds, and temperature only "exists" in the sense that it happens to makes sense for us who happen to exist.

So enjoy your Monte Carlo, cogito ergo sum, and know that it is magically powerful, akin to a perfect cup of beans and water collapsed into coffee, perhaps on the boardwalks of Monte Carlo ☕️🖤