<<<<I don't believe it is possible for you to get your head around these facts that everyone who has studied the Bernoulli process (think infinite sequences of random bits) and all related topics would agree on. The barrier is psychological, the arrogance to think you must be right even when you have no familiarity with the subject and all those who do say otherwise.>>>>
The barrier to your understanding is indeed psychological. It's one thing to have an infinite series of 7s but where the components of an infinite series are unpredictable, there can never be closure so it's incorrect to claim that it is possible to define such a series. Your problem is that you can't conceive the reality. You're stuck in your imagination.
Claiming that I'm being arrogant is pretty arrogant of you, actually, although here, you're noted for arrogance. If you had the intelligence to try to discuss it and understand it from the pov I'm describing, instead of laying down the law, you'd get a bit more credit than you do.
Oh and the missing word is "inconsistent". If your idea is inconsistent with itself, then your idea doesn't mean anything.
Does True Randomness Actually Exist? ( ^&*#^%$&#% )
Your intuition is wrong and leads to a worthless dead end. I have explained why.
The theory of the Bernoulli Process is part of the formal, axiom and deduction based, self-consistent body of mathematical truth.
Of course, you should understand it is an abstract topic (like say the subject of Number Theory, first developed by Euclid) because there is no such thing as an infinite sequence in the physical world. Is this part of your intuitive problem? If you want to study physically realisable (or closely approximable) things, stick to finite sequences.
There are genuinely two ways of looking at this.
You are concentrating on the hypothetical results, made doubly hypothetical by the idea that you can discuss them as a mathematical possibility that is highly unlikely. My viewpoint is not as a series of hypothetical results but as a series of hypothetical coin tosses, on which there never can be closure.
Your refusal to see it the other way is a failure and an inability, albeit bolstered by the beliefs of others, which doeesn't speak well of all your past efforts in conversations we've had. There may have been occasions where you've been right and I've been wrong but our discussions have been wide-ranging indeed and especially noteable for your orthodoxy. However, there have been so many differences of opinion that it seems inconceivable to me that you have always been correct. Indeed, I can recall episodes where your logical-deductive ability has been poor. I do accept there will have been times when I've been mistaken.
However, to stick to your guns over such a thing as this, when you can do no better than "mathematicians agree with you" doesn't mean very much. I am an original thinker ... maybe that cannot be denied. I have seen no evidence that you can think for yourself. I have also seen no evidence that you possess a particularly high IQ. You may be very clever .... but definitely clever in a different way from me. It's clear that you value home territory too highly but also that you tend to claim everything as home territory. It means that you will never be able to have a conversation with anyone on equal terms. Either you will be talking down to people or, in a small minority of cases, you will defer to them as having more knowledge than you. So far as raw intelligence goes, you appear not to know what it even means.
Bear in mind that this is a reply to your personal attack.
There are genuinely two ways of looking at this.
There are always multiple ways of looking at things. Often one of them works and is useful (eg the unique mathematical theory of the Bernoulli Process) and others are not (find your own example).
You are concentrating on the hypothetical results,
We are discussing infinite sequences of random results. These are abstract and not physically realisable. That should be clear.
made doubly hypothetical by the idea that you can discuss them as a mathematical possibility that is highly unlikely.
I correctly describe the mathematics. The set of possible outcomes is the set of functions from the natural numbers to the set with two elements {H, T}. This is also described as the set of infinite sequences of elements each of which is H or T.
This set can be made into a measure space in a unique way that respects the 50-50 probabilities of the individual flips. i.e. you start with the assumption that the a set of flips where the first n elements are specified has probability 1/2^n.
This extends uniquely to the Borel sets on the space, giving a unique measure which defines the probability of all measureable sets of sequences of results. [This part is technical and will seem a bit opaque to non-mathematicians].
My viewpoint is not as a series of hypothetical results but as a series of hypothetical coin tosses, on which there never can be closure.
You are confused between the starting point of uncertainty and the results. You would not be confused if there were only a finite set of flips, but for some reason you have difficulty understanding that in the abstract object, there is nothing different about all of the flips being specified. Perhaps it would help if I point out that there is no real time in the abstract object, just a set of labels 1, 2, 3, ... for the flips. You can think of the flips as being simultaneous without changing anything, just like for a finite number of flips.
There is some similarity to the concept of the continuous probability distribution on the interval [0, 1]. A sample from this distribution is a random real number. As a binary number it is a specific INFINITE sequence of bits (to be precise, we have to exclude either representations ending in a sequence of 1s or those ending in a sequence of 0s, just like with 9 and 0 for decimal expansions). The probability of any specific real number being sampled is zero, but it makes no sense to believe that all possible real numbers are impossible results, since that would mean that no result is possible. [As an example of something with non-zero probability, there is probability 1/4 of the result being greater than 3/4. This corresponds to an infinite set of possible results, an interval of length 1/4].
Infinite object are unintuitive. But mathematics can still deal with them.
AOK so can you please describe how the theoreticians' belief, that an unpredictable infinite series being described meaningfully, as in this case, as consisting only of T but zero H, materially affects results so that not being able to describe it so will necessarily produce different results for their calculations?
will you two please tone down? its somewhat disturbing to see you rubbing on each other like that.
on another note, I thought this thread died a long time ago, probably its a good time to update the OP with some clarifications.
will you two please tone down? its somewhat disturbing to see you rubbing on each other like that.
on another note, I thought this thread died a long time ago, probably its a good time to update the OP with some clarifications.
I don't like personal attacks. In the past when they've all gone one way, I've retaliated and have been accused of starting attacks. That's not true though. If I'm personally attacked I'll reply as I see fit, within reason.
<<<This extends uniquely to the Borel sets on the space, giving a unique measure which defines the probability of all measureable sets of sequences of results. [This part is technical and will seem a bit opaque to non-mathematicians].>>>
It seems more opaque to non-philosophicals. An infinite series is not measurable, anyway. It can only be statisically predicted.
ok, here goes:
Nov. 7. 2022 Addendum:
When I started this thread and coined it with the term “true randomness”, it seemed self explanatory to me. perhaps that wasn’t the case and there’s a need for clarification.
you probably heard that randomness is a feature of our world, proven by modern physics. notably by Bell experiments, Atom decay, Heisenberg and so on. and i’m happy to confirm, that is absolutely true!
Wait. What? so why do I question randomness if it was already proved to be true? Well, I didn’t. that was the whole point. I questioned “True Randomness” (TR in abbreviation)
what is the difference you ask? well, a whole lot! and simply put, it just comes down to definitions. Over the years randomness was defined in many ways which gave it different meanings. mostly along the lines of predictability, causality, chance, the lack of information, entropy, etc.
Let's take a look at a traditional definition which is along the line of predictability. basically if an action outcome is unpredictable, then it must be random. right? kinda, because if no one can predict an outcome, it’s absolutely random for practical purposes like engineering, banking, encryption and such. this sort of randomness was proved to be true, and we have working products like computer chips that do just that, regardless if it has underlying deterministic process or not, we can be assure that some events will always be unpredictable/random to a physicist trying to make precise predictions.
Moving on. now let’s look at a modern definition along the line of “the lack of information” for example. if you write down a string of random numbers, and ask me to guess them, they are 100% random for me and at the same time 100% determined for you. Wait, what? that doesn’t sound “truly random” at all! exactly. And more important for this topic, it tells us nothing about determinism nor “true randomness”. (it’s actually a good definition that I like for some purposes, but not for a thread about determinism)
Now we finally get to “True randomness” TR, which is the subject of this topic, and i would define it loosely as being the opposite of causal determinism, or something along that line. I couldn’t care less as long as the concept itself is finally understood.
Wrapping up… asking if true randomness exist, is exactly the same as asking if determinism is true. and unlike popular belief among hobbyists philosophers, and physicists alike, the truth is that the jury is still out on this one, and we simply can’t make this call objectively. for or against determinism. that’s the fact of the matter. sorry! We just don’t know, and all we can really say objectively is that our world is mysterious regardless if it happen to be deterministic or not. to overly simplify, it actually comes down to which philosophical interpretations of QM you looking at. some are deterministic and some are not.
It also happen that objectively speaking, none of the interpretations is considered superior to the others because all of them make excellent predictions. While all of them also have serious problems. and i mean really serious problems. yea, our world happen to be more mysterious than anyone ever imagine. isn’t that awesome?
If you want to learn more about it, I suggest you ignore a lot of the nonsense being said on my thread, and learn directly from the experts in the following link.
Causal determinism in Quantum mechanics
I hope this clarification will pour some light on the topic of True randomness vs Determinism. and hopefully this will bring an end to yucky arguments.
thank you for taking the time. be happy, and keep it real
It's already been discussed quite deeply. I think that a deterministic universe has to be designed to give the appearance of TR. Why? Why use more computing power than the universe can contain, in order to pretend that randomness exists? For what? We've been discussing solving chess on another thread and it turns out that computing capability is quite an issue.
The brain couldn't evolve in a deterministic environment. I won't go into the explanations but it would have to be designed, so determinism just means design. I'm not going there. Just because something is capable of being roughly imagined doesn't mean it can then be a possible reality. I think it would defy the way the universe actually works.
The brain and entire human body would have to be designed with all the vestages of primitive, evolved organs, to convince us that we evolved. Therefore that goes for the entire animal kingdom, even though we can correlate evolutionary changes with environmental conditions in some cases. Such an elaborate hoax sounds rather like the stuff of mental illness. Perhaps there's cause for concern about educated people who take this seriously then? Not those who haven't the intellectual means to consider it but the educated ones??
Deductive thinkers only won't be able to reach any conclusions because they require premises. We can do better than deduction, however.
Oh, and Ockham. I wonder how many thousand or million unsupported hypotheses determinism requires, as opposed to one? I'm not a hobbyist one btw. I was considered real.
AOK so can you please describe how the theoreticians' belief, that an unpredictable infinite series being described meaningfully, as in this case, as consisting only of T but zero H, materially affects results so that not being able to describe it so will necessarily produce different results for their calculations?
We can't stop being able to describe it. With N the natural numbers, it is the function
f: N -> {H, T} such that f(n) = T for all n in N
It's just one of an uncountable number of possibilities, of equal standing to all others.
I feel that subconsciously you are thinking (correctly) that the single element set containing just the sequence that is all tails is of probability zero, whereas other sets of outcomes have greater probability. This is true. But those sets are uncountable sets of elements each of which has probability zero as well.
There are also uncountable subsets that have probability zero. For example, if r < 0.5, then for any number m, the set of sequences such that the proportion of heads in the first n flips is less than r as long as n > m.
Is that true if r=0.5? I hypothesise so. I do so because I would expect to be able to prove the proportion of heads crosses 0.5 an infinite number of times with probability 1.
I was trying to ask what possible, material difference believing what you believe about infinite series can make to the mathematical results. As usual, you haven't answered a tricky question.
I can't interpret your question in a way that has an answer.
It's all about the mathematical facts. The mathematical facts may have applications or not, as usual.
(See what you think about the bit I added at the end of my last post. Maybe it will be an interesting question).
@1
"statistically If you throw a dice 12 million times it will fall 2m times on each # right? so how exactly is this random? wouldn't you expect a random spread?"
Wrong. First of all, you throw a "die", not a "dice". Secondly, if you throw a die a large number of times, it will land on each face APPROXIMATELY 1/6 of the time. The larger the number of throws, the closer to 1/6 those numbers get, never to reach exactly 1/6 with certainty. But your statement, while true "for all practical purposes"....is mathematically false.
Look up the concepts of limits and asymptotes.
I can't interpret your question in a way that has an answer.
It's all about the mathematical facts. The mathematical facts may have applications or not, as usual.
(See what you think about the bit I added at the end of my last post. Maybe it will be an interesting question).
I'll try to rephrase. You and I disagree about whether it is correct to claim that an infinite series of coin tosses can have no heads, for example.
Disregarding the rather obvious fact that it wouldn't happen, it might be considered a statistical possibility but that is only if it makes logical sense to state as a proposition. I think it doesn't make sense, so that the proposition "an infinite run of tosses may contain no heads" is incorrect, in itself, as a logically valid proposition.
However, I'm trying to ascertain whether it makes any practical difference. I have sometimes believed I've seen inconsistency within your statements allthough you are very quick to point it out in others. Here you have seemed to have evaded my question, which is an important one. I personally would be very surprised if a person's private belief, regarding the meaning of a proposition, could alter its mathematical outcome.
So can it? Because, if it can't, then it would seem that your claim that mathematicians agree with you can have no practical basis. Your insinuation that the accuracy of the mathematics is tied up within this problem would seem to be a bit of a red herring, would it not?
@1
"statistically If you throw a dice 12 million times it will fall 2m times on each # right? so how exactly is this random? wouldn't you expect a random spread?"
Wrong. First of all, you throw a "die", not a "dice". Secondly, if you throw a die a large number of times, it will land on each face APPROXIMATELY 1/6 of the time. The larger the number of throws, the closer to 1/6 those numbers get, never to reach exactly 1/6 with certainty. But your statement, while true "for all practical purposes"....is mathematically false.
Look up the concepts of limits and asymptotes.
if you drop it in a vacuum it will never land 
I'll go on record here.....In an infinite series of coin tosses, it is a statistical certainty that the results will be exactly 50% heads and 50% tails. I'm talking an INFINITE number of tosses....not just some large number.
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Your arrogance is ridiculous!
It is interesting that it blinds you to the simple reasoning that your belief that a sequence of all heads is "impossible" would apply to every single other specific sequence of results, but coming to the conclusion that ALL sequences of results are impossible means you have gone wrong somewhere! [It's an informal example of reductio ad absurdum].
Please do explain why you can't understand that.
If you wanted to learn about the subject, the wikipedia article on the Bernoulli Process is quite readable. A refresher on random variables and basic probability would be a good idea first.
Oh, a personal attack. You can't help it. Anyone who disagrees with you gets the same.
Your personal attack doesn't alter who is correct. If you are incapable of thinking about it, you'll never change your opinion. The real question is "why do you have the obsession that you must always be right about everything?"
I'm not being arrogant. I'm just being correct. The idea of "all the coin tosses in an infinite series of them" is