Sampling is not the way randomness is usually modelled in mathematics, partly because mathematics is deterministic and so you can’t model randomness in this way
As a matter of fact, it is modeled this way. To define probability function you need a sample space, from which exactly one outcome is “sampled” in every iteration of probability experiment.
But yes, the math is deterministic, so it’s not “true randomness” but a pseudo-randomness, so just like with every software library it’s hidden-variables model rather than Truly Stochastic model.
And this is why, I have troubles with the idea of “true randomness” being philosophically coherent. If there is no mathematical way to describe it, in which way can we say that it’s coherent?
Like, the point of many-worlds theory in practice isn’t to postulate that we should go further away from quantum mechanics by assuming that everything is secretly deterministic.
The point is to describe quantum mechanics as it is. If quantum mechanics is deterministic we want to describe it as deterministic. If quantum mechanics is not deterministic we do not want to descrive quantum mechanic as deterministic. The fact that many-words interpretation describes quantum mechanics is deterministic can be considered “going further from quantum mechanics” only if it’s, in fact, not deterministic, which is not known to be the case. QM just has a vibe of “randomness” and “indeterminism” around it, due to historic reasons, but actually whether it deterministic or not is an open question.
As a matter of fact, it is modeled this way. To define probability function you need a sample space, from which exactly one outcome is “sampled” in every iteration of probability experiment.
No, that’s for random variables, but in order to have random variables you first need a probability distribution over the outcome space.
And this is why, I have troubles with the idea of “true randomness” being philosophically coherent. If there is no mathematical way to describe it, in which way can we say that it’s coherent?
You could use a mathematical formalism that contains True Randomness, but 1. such formalisms are unwieldy, 2. that’s just passing the buck to the one who interprets the formalism.
Do you actually need any other reason to not believe in True Randomness?
I think I used to accept this argument, but then came to believe that simplicity of formalisms usually originates from renormalization more than from the simplicity being Literally True?
As a matter of fact, it is modeled this way. To define probability function you need a sample space, from which exactly one outcome is “sampled” in every iteration of probability experiment.
But yes, the math is deterministic, so it’s not “true randomness” but a pseudo-randomness, so just like with every software library it’s hidden-variables model rather than Truly Stochastic model.
And this is why, I have troubles with the idea of “true randomness” being philosophically coherent. If there is no mathematical way to describe it, in which way can we say that it’s coherent?
The point is to describe quantum mechanics as it is. If quantum mechanics is deterministic we want to describe it as deterministic. If quantum mechanics is not deterministic we do not want to descrive quantum mechanic as deterministic. The fact that many-words interpretation describes quantum mechanics is deterministic can be considered “going further from quantum mechanics” only if it’s, in fact, not deterministic, which is not known to be the case. QM just has a vibe of “randomness” and “indeterminism” around it, due to historic reasons, but actually whether it deterministic or not is an open question.
No, that’s for random variables, but in order to have random variables you first need a probability distribution over the outcome space.
You could use a mathematical formalism that contains True Randomness, but 1. such formalisms are unwieldy, 2. that’s just passing the buck to the one who interprets the formalism.
Do you actually need any other reason to not believe in True Randomness?
Any argument is just passing the buck to the one who interprets the language.
I think I used to accept this argument, but then came to believe that simplicity of formalisms usually originates from renormalization more than from the simplicity being Literally True?