fun fact: that something has 0% probability of happening doesn’t necessarily guarantee that it won’t happen. consider the following example:
you take a needle and throw it some random distance. now you measure the distance of the needle’s tip to you. assuming that the distance is exactly one well-defined real number, then each of these numbers must have a probability of 0% of occurring, since there’s infinitely many possible numbers and if you divide 100% probability of “any of them” by the (infinite) number of possibilities, you’re gonna arrive at 0% for each possibility. but one of them must still be the measurement outcome, despite having a 0% probability.
That isn’t how that works. Throwing a needle doesn’t yield infinite probabilities. Nor does any action. Statistics are always calculated within human, useful limits. It is never fully free of context.
An unpredictable event like “where will this hurricane take my paper plane” may have a lot of potential outcomes, but “a lot” is way, way less than infinity. If you’re standing in China you’re not gonna throw a needle with your human arm and have it land in France.
Nor are very very small numbers equivalent to 0. The needle will land at 1 position. That means there simply must have been at least a 0.0…1% chance for it to have landed there. Not having enough context to calculate exactly how many zeros would be “correct” is not the same thing as there being infinite possibilities
Probability doesn’t live in the real world, it’s maths and maths is full of actual infinities. The probability of a specific event in a continuous probability space is like the area of a line: zero. We can’t make actual zero-width lines in the real world but they’re very simple mathematical objects
Yeah, well, not that it matters, but this thing you’re saying here:
Statistics are always calculated within human, useful limits.
, is not some great truth lol, it’s just what we usually do in the real world to make decisions.
Statistics in math, sure as fuck can, and often are calculated to mathematical abstractions that make “no sense”, because the abstractions many times, are the point.
The abstract ideas of 0.0… …01 == 0, and the chance of something in the physical world landing exactly somewhere being 0% (< clean and true 0), are actual truths, that just point to a breakdown of the system of measurement and communication, in some true way.
The “chance for the needle to land precisely there is 0%”, for example, just says “the physical world we measure, has an infinitely subdividable infinity of submeasurements”.
There’s math that calculates and compares those infinities with other infinities and such nerdy shit, that’s honestly beyond me. Just don’t be an asshole when something if foreign to you.
fun fact: that something has 0% probability of happening doesn’t necessarily guarantee that it won’t happen. consider the following example:
you take a needle and throw it some random distance. now you measure the distance of the needle’s tip to you. assuming that the distance is exactly one well-defined real number, then each of these numbers must have a probability of 0% of occurring, since there’s infinitely many possible numbers and if you divide 100% probability of “any of them” by the (infinite) number of possibilities, you’re gonna arrive at 0% for each possibility. but one of them must still be the measurement outcome, despite having a 0% probability.
That isn’t how that works. Throwing a needle doesn’t yield infinite probabilities. Nor does any action. Statistics are always calculated within human, useful limits. It is never fully free of context.
An unpredictable event like “where will this hurricane take my paper plane” may have a lot of potential outcomes, but “a lot” is way, way less than infinity. If you’re standing in China you’re not gonna throw a needle with your human arm and have it land in France.
Nor are very very small numbers equivalent to 0. The needle will land at 1 position. That means there simply must have been at least a 0.0…1% chance for it to have landed there. Not having enough context to calculate exactly how many zeros would be “correct” is not the same thing as there being infinite possibilities
Probability doesn’t live in the real world, it’s maths and maths is full of actual infinities. The probability of a specific event in a continuous probability space is like the area of a line: zero. We can’t make actual zero-width lines in the real world but they’re very simple mathematical objects
Yeah, well, not that it matters, but this thing you’re saying here:
, is not some great truth lol, it’s just what we usually do in the real world to make decisions.
Statistics in math, sure as fuck can, and often are calculated to mathematical abstractions that make “no sense”, because the abstractions many times, are the point.
The abstract ideas of 0.0… …01 == 0, and the chance of something in the physical world landing exactly somewhere being 0% (< clean and true 0), are actual truths, that just point to a breakdown of the system of measurement and communication, in some true way.
The “chance for the needle to land precisely there is 0%”, for example, just says “the physical world we measure, has an infinitely subdividable infinity of submeasurements”.
There’s math that calculates and compares those infinities with other infinities and such nerdy shit, that’s honestly beyond me. Just don’t be an asshole when something if foreign to you.