Does True Randomness Actually Exist? ( ^&*#^%$&#% )
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Nov 1, 2022
0
#3023
Optimissed wrote:
OK I'm going to have mercy and clearly explain why the probabilistic approach is insufficient. It's because probability has to deal with real numbers and infinity isn't a real number. It's a notional, abstract concept.
Furthermore, in an infinite series it would be impossible to quantify the number of tails as "all" and the number of heads as "nil" because infinity is endless. That means that you could never say that there were "no" heads in a series. You could never define, nor illustrate, nor depict an infinite series so all there is, is a vague notion that somehow it has to fulfill probability calculations that can only refer to real numbers.
I don't think that will be enough to settle it but it would be interesting to find a person who could argue that I'm wrong about this. I mean, correctly, without just repeating a mantra like ty does. Elroch and ty are quite similar but one is further down the road.
Right, if you tried to add up all the heads, and for example you punch these button on a calculator:
+
1
=
over and over, at no point does the total reach infinity.
So yes, these are abstract ideas... but that doesn't make them meaningless (and they're certainly not impractical).
roflmao nearly 2 pages of
RonaldJosephCote wrote:
I know true randomness exists because I can't match 1 powerball # in 30 yrs.
LMFAO
🤣
Nov 1, 2022
0
#3027
Optimissed wrote:
Countably infinite?
If you don't know a mathematical term, you will find it well-documented on Wikipedia or many other reference sites.
I have to point out that thinking you are in a position to argue about the mathematics without even knowing the elementary part of the subject is characteristically inappropriate.
so is ego flipping ba bas, inappropriate
Nov 1, 2022
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#3029
To put it in chess terms, knowing about cardinality and basic statistics is still a sub 1500 rating (i.e. well within hobbyist level). This isn't an argument between two sides, it's a lecture, and the ego that's on display is (far) less than what's justifiable.
Nov 1, 2022
0
#3030
And speaking of hobbyist math, there are a lot of fun YouTube channels that have maths stuff (some with very nice production, some others by actual professors) such as mathologer, numberphile, and 3blue1brown.
Frequenting channels like these along with a little self study would take a person way beyond anything discussed here so far... in other words this isn't rarefied knowledge.
sounds like mad bickering about who knows the most
Nov 1, 2022
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#3032
When a person knows nothing about the topic, it will always appear as if both sides are equally correct, and therefore to them, the disagreement will seem trivial.
I know that infinite simply means endless.
Nov 1, 2022
0
#3034
I'm not trying to make fun of you.
Sometimes on the forums, people are talking about things I don't know about, and it seems like a trivial disagreement because I can't tell who is making a good point and who is making a bad point. When that happens I don't comment because I have nothing to say 
yeah it’s a dice thing… and apparently infinitely ridiculous attempt to find an agreement? I don’t know, maybe 200 pages has such that hunch?
Nov 1, 2022
0
#3036
Optimissed wrote:
OK I'm going to have mercy and clearly explain why the probabilistic approach is insufficient. It's because probability has to deal with real numbers and infinity isn't a real number. It's a notional, abstract concept.
It's as if you have no knowledge that probability theory is applied to uncountably infinite spaces all the time. This is true every time a real-valued distribution occurs (eg for the quantum mechanics of unbound particles). It is also the case for all stochastic systems (one of which we are discussing).
Furthermore, in an infinite series it would be impossible to quantify the number of tails as "all" and the number of heads as "nil" because infinity is endless.
This is confused thinking. If you define a function from the natural numbers to the set with two elements (call them H and T) as
f(n) = H for all n
Then the definition proves the result that the value of the function is H for ALL indices.
It is almost as simple to show that the set of elements such that f(n) = T has zero elements (i.e. it is of size zero).
With all due respect, you demonstrate a lack of familiarity with the subject combined with a lack of recognition of the possibility that you lack the understanding.
they say if the BB is wrong then S&T has always been. so instead of forever its aftever (no beginning).
I once thought i luvd a guy before i ever met him. so maybe one could say '...and they lived happily ever afore' ?...not sure.
we cant comprehend that s/t doesnt have a beginning. dont mean it cant be.
Lmao does it even seem to sound to make any sense for LIFE having a beginning? I mean…. the word alone, ‘Life’, says what’s TO BE EXISTENCE, correct? Now… think for a moment on that… LIFE IS AND IT IS LOGICAL AS 2 AND 2 IS and absolute THAT it’s Infinitely ITSELF. I call that whom is forbidden to be ADDRESSED HERE ON CC. He’s In A GREAT Book .
Nov 2, 2022
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#3039
Optimissed wrote:
I thought you might try to see it from the other side.
Sure, to be a little more generous, you can make up whatever rules you want, and that's how mathematicians have done it.
So if you want to define infinity or coin flips in a way that makes it impossible to flip all heads or makes it impossible to do an infinite thing infinitely many times "because there's only one infinity" then sure, you can do that too.
It's just that the rules that survive in mathematics (the ones you can find in textbooks and papers) follow two rules (this is how I see it, maybe Elroch would say this differently). I'd say the two rules are 1) They're self consistent i.e. the new thing you made up doesn't break anything that came before it and 2) They're functional i.e. the rules are rigorously defined and can be used to solve a problem.
So one major problem when making things up on your own while talking about fundamental things (like multiplication, or flipping a coin, or common uses of infinity) is that you're going to sound like an enormous idiot to someone who uses the standard set of rules to solve simple problems.
Another problem is something I alluded to before, and that's math is self consistent. You can make things up if you're solving cutting edge problems, but when you make new rules for something fundamental, you unknowingly break an essentially endless amount of maths that uses that as a foundation... and when the math is very fundamental that's a problem since its efficacy is proven a million times over in engineering applications. If you want to say "infinity never ends, think about it, ooooh, it's spoooky" ok, but you can't just take away all of calculus because calculus actually works. Pratically every derrivation of every physics equation I've ever seen uses calculus, so you'll need a little more than "oooh, infinity it never ends, thiiiink about it, woooow." when talking about basic math problems like flipping a coin.
Nov 2, 2022
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#3040
And yes, infinity in statistics is very basic and is used all the time in practical engineering applications.
For example it's common to model different types of noise as a gaussian distribution (this is statistics) where you can use common statistical tools (PDF and CDF) for calculations. Continuous distributions not only contain an infinite number of elements, but you add these infinitely many things together (integration from zero to infinity).
This is all basic undergrad stuff used in real world applications, no trickery or anything like that.
Both of you are over-emphasising a statistical approach, which insists that an infinite run of heads is possible.
Well, I guess we should start with this.
Three flips:
H, H, H
or
H, T, H
or
H, H, T
Do you agree that all 3 of these are equally likely?
---
If not, this is something you can test on your own. Write out all possible sequences of 3 (there are 8 of them) and flip a coin 3 times. Put a check mark next to the sequence you got and repeat this a few 100 times (yes this would be tremendously tedious)... but you would discover that none is more likely than another.
The point is that infinite H is no less likely than any other specific infinite sequence.
Actually this is kind of fun, we can calculate the probability that a sequence of coin flips will contain an equal number of heads and tails with this expression (x is the number of flips)
(x choose x/2) / (2^x)
And taking the limit as x -> inf that expression = 0, meaning in a sequence of infinite coin flips, we expect there to be an unequal number of H and T with probability of 1, which is initially unexpected (at least for me, but makes sense to me in hindsight).