The math of Occam's Razor

Let's do some back-of-the-envelope math, to represent Occam's Razor, why it's a thing, and why it matters.

I don't really care about the exact year William of Ockham was born, and the 'razor' part is obviously a metaphor. I do care about the "WHY" and "HOW" of it.

The popular version, that I refer to, is something like this:

The simplest explanation, all other things being equal, tends to be true

But why?

I mean most of us kinda get it, and use it, maybe unknowingly in day to day life. Others knowingly throw it out the window, refer to it as some outdated philosophy or something. But it's not! Let me show you real quick.

Example: moon landing

Many of the astute netizens will be aware that there is a weird phenomenon that has gained a lot of traction: many people don't believe the moon landing was real. They believe it was a hoax. This is not about blaming them - I happen to personally know one such person, and I love and respect them despite this. But let's just take a look at what this model requires to be true, and how likely it is to be true.

• Cinema tech and props never-before seen anywhere, to create the videos of the falling feather vs hammer, the moon dust, the low gravity, etc. Just this alone is like, 10% probable at best. I mean we can't measure because we don't have a statistic, but how often do we see a movie out-perform our expectations in terms of effects, hmmm?
• One of the most powerful rockets ever built, actually being built, and launching somewhere. Many people saw it, and felt the shockwaves of the rocket. Any explanation of that would be extremely unlikely to be true. 1%?
• The cherry on the cake: the thousands of people who worked on this, and the supposed thousands who would have to work on a fake movie production. If a secret is known by 2 people, it's no longer a secret. Ask any police detective and they'll tell you how easy it is to drive a case to court once you've got the actual guilty people in questioning and they don't ask for a lawyer. If there are many people - they will talk. Oh they will SING! Sure, some of it might be labeled as lies or BS, might be burried in the noise, but there was no "noise". The messaging was consistent - we went to the moon. No controversies. The likelihood that any one person would spill the beans is like 50%. At 1000 people, this becomes impossible to keep.

All of them had to be true for the moon landing to be a hoax. Multiply the finger-in-the-wind estimated probabilities together, and you get the roughly estimated probability that it was a hoax.

Aaand that boils down to ... 0.1 * 0.01 * ... how much is 0.5 to the power of a f8ck ton? Well, it's 1/(2¹⁰⁰⁰). And how much is that? It's an insanely huge number. How huge? Remember the paradox - if you could fold a piece of paper 50 times, it will be thick enough to get to the moon. Yeah, ironic isn't it? Because this isn't 50 times, but 1000. 1000 is bigger than 50. In exponential math, that's a lot. It's more than there are atoms in the universe probably. IDK, I didn't count the digits. Oh wait, I did! It's 302 digits. It's 1 with 301 digits after it.

If you were to fold a paper that's 1 atom thick, 1000 times, it would be the thickness of 10²⁹² meters, and for y'all non-metric folks out there, that's a bit more than 10²⁸⁸ miles.

Well how big is that? Well, the diameter of the observable universe is about 10²⁷ meters, so 10²⁹² is roughly 10²⁶⁵ observable universes. Still not getting it. What does that number mean?

Well, if we were to fill the observable universe with the densest thing that is not a black hole (neutron star stuff), we would need fewer neutrons than this number. By a lot.

In other words: This number be big.

Which means that 1/(that number) is the closest thing to zero you have ever seen in the real world.

Back to the moon

What this means, is that the probability of 1000 people knowing about the biggest hoax ever, keeping quiet, is so close to zero that calculators having enough digits to calculate that probability didn't even exist when they landed on the moon. Even if I tried to be extremely conservative and say that the chances of 1 person spilling the beans is only 1%, that still makes it less than 0.01% chance that they would all keep quiet.

Back to Occam's razor

Occam's razor, again, refers to situations where you are considering versions that require you to take a lot of leaps of faith. Those leaps of faith are probabilities that you can estimate. The reason they are "leaps" is because they're very low.

When you have to do that, the version you're considering is just nonsensical. If you really want to consider this hypothesis, you have to work really really hard on eliminating these leaps of faith, showing that the probability isn't low, by actually showing that it's happening.

And when you have a readily-available version that relies on tried and tested technology, that is well documented, reliable, and replicatable to a very high degree of success, you get the opposite - a very high probability that this combination is correct.

Fewer leaps of faith = higher chances that it's correct. And some leaps of faith are just astronomically ridiculous, and that's an understatement.

Small disclaimer

Mental maths, especially like this, on probabilities, isn't the right way to do it. It's a heuristic thought process, that assumes that those factors are independent, and that we can actually perform such operations of multiplying the probabilities. These aren't numbers that you should put on any paper like that, and this is the best example of how not to write a paper. However, if you apply this same process to 2 competing hypotheses, you will be better off than not doing it at all.

This just sits in a comfy place between heuristics and analytics.

What next?

Try applying it to every day life where you see conspiracy theories:

• how likely is for a lonely amateur shooter far far away to hit the just tip of Trump's ear on purpose?
• how many people would've had to stay quiet about the setup of the 9/11 attack? (seriously, the "number of people" is usually the killing blow to any hypothesis that rely on this leap of faith)

Or, is it more likely that it did actually happen according to the official versions?