"Randomness" and "probability" are just mathematical models created that happen to provide the best predictions for what happens in quantum mechanics.
no, there is an equivalent deterministic model where "randomness" is not inherent, just appears as a consequence of certain environmental constraints
"Randomness" and "infinity" are just mathematical concepts. Don't see how they are ridiculous at all. Do you have an opinion on negative numbers? Is calculus "ridiculous" since it involves a concept of infinity?
Randomness: if you know what lebesgue measure is go look up incomputable number. or sets which are not lebesgue measurable. well, the lebegue measure of a set of numbers between 0 and 1 is equivalent to the probability of choosing a number from that set out of all those numbers. since you believe in calculus (axiom of infinity + axiom of choice) then non-measureable sets exist. which means that if i throw a random dart between 0 and 1 the probability it lands in that type of set
does not exist. Not 0, not 1, not any number in between. Literally the probability of landing in that set does not exist in the mathematical universe as a whole. Probability theory is ****ing retarted anyways, just look up the bertrand paradox
Infinity: if you know what a cardinal number is, go ahead and tell me the cardinality of all the cardinal numbers.
Is calculus "ridiculous" since it involves a concept of infinity?
yes. its not real life. decent
model for dynamical systems tho
Steve while we`re here can you hook it up with a 'good definition of true mathematical randomness',
hmm laymans way: you know how you can use 7z or winrar or .zip to compress a file? a file is just a bunch of 0s and 1s. you can compress files (data) like to 10% the original size. a truly random number, mathematically, cannot be compressed at all (if it were a file). In other words, the compression would have a length equal to or greater than the original dataset (number). The only numbers which fit this property are what are know as uncomputable numbers, and they dominate the number line. (the probability you pick a uncomputable number when you randomly pick a number from the number line is 100%. Every other number you have ever encountered in your life has a probability of zero)
I think Steve was alluding to how infinity really isn`t a number and is janky anyway, algebra-wise, or to layman rather, not that it`s 'ridiculous'. Of course they are mathematical concepts, just some are more concrete than others and 'infinity' and 'randomness' are a few of the concepts that are usually diverged from their correlating constructs in reality. ON infinity, for example, it`s better to think of it as a direction, +inf and -inf on ends of the number line. This is pretty easy to imagine, just start walking around a coastline or even back and forth across the US, counting each step. You`ll keep adding one, and the number of steps will always grow, never shrink (so you know the direction) but it will also never end on a particular sum, i.e you can always take another step.
no its more like infinity doesnt exist because numbers dont exist. just abstract concepts that can do neat tricks