Does True Randomness Actually Exist? ( ^&*#^%$&#% )

The example of Math proving something to exist, by making predictions which led to discovery misses a critical point.  What proves the existence is direct, verifiable observation along with empirical evidence. The Maths only led us in the right direction to look. The maths helped us understand a phenomenon that was not well understood. We use a tool - mathematics to search in the right direction. 

If it's wanted, in hindsight after the discovery to state- well then, the Maths are what proved something previously unknown exists, it's not an issue. But I'll beg to differ and state the math merely represented a clue as the equations will likely be revised, new numbers added/subtracted.

A good example, very simple indeed, of what you're talking about is the discovery of new elements after simple maths helped us understand the likely properties of undiscovered elements from the Periodic Table of Elements after it was invented.

The appropriate reasoning here is Bayesian reasoning.

It is necessary to start with an a priori viewpoint about the possible behaviour of the coin. This is just a fact about reasoning: if you start nowhere, you can't get anywhere. But where you start becomes less and less important as you get empirical data. Note that there is no way to avoid this general picture if you wish to make inferences about the real world. You need to start with some tentative viewpoint and then modify this as you obtain empirical information. Nothing else is possible.

In Bayesian reasoning, the starting point is a distribution of possible models for the behaviour of the coin which is fairly neutral. Assuming coin tosses are independent, there is one model for every possible probability of heads. You can think of this as there being an unknown fact which is the probability of heads coming up, and the possibilities correspond to all the real numbers between 0 and 1.

At any step in time, your state of belief is a distribution which tells you how likely it is that the true probability of heads is any specific value. As you see real flips, Bayesian inference provides a single correct way to update your belief (in an analogous way to what ordinary logic does this when you receive a boolean fact from which you can infer other things).

The process looks like this, where I started with what is called an "uninformative prior" -  a state of belief which is very neutral and unassuming, then flipped a biased coin 1000 times. The curves indicate the state of belief about the probability of heads at different times. It gradually headed towards a strong peak centred near the true probability of heads (which was 0.75).

If anyone instinctively dislikes this, I suggest trying to find an alternative way to obtain knowledge about the real world from empirical data!

There is a distinction to be made. Maths that verify and Maths that make predictions in the context of new discoveries.

Maths that verify are complete equations, arrived at after the empirical evidence is in. 

Maths that make predictions begin as incomplete. The empirical evidence needs gathering, the maths usually are refined, new observations and measurements are made and perhaps a discovery is made. Perhaps it is of the thing being looked for, or the new discovery may be something quite different.

To state after the discovery, that the original predictions proved the existence of something, represents a given viewpoint. Perhaps a matter of semantics, but I think it's far more than that.

math is a function of arithmetic. not the other way around. and u know it ! itsa never been a unitless universe. and thats why u cant prove, the human construct, that 5 is greater than 3 w/outta unit. 

and quit high-talking him....u derivative of acceleration !

1. Idea

Bayesian reasoning is an application of probability theory to inductive reasoning (and abductive reasoning). It relies on an interpretation of probabilities as expressions of an agent’s uncertainty about the world, rather than as concerning some notion of objective chance in the world. The perspective here is that, when done correctly, inductive reasoning is simply a generalisation of deductive reasoning, where knowledge of the truth or falsity of a proposition corresponds to adopting the extreme probabilities 1 and 0.

5. Objective Bayesianism

For some Bayesians, degrees of belief must satisfy further restrictions. One extreme form of this view holds that given a particular state of knowledge, there is a single best set of degrees of belief that should be adopted for any proposition.

I'll suggest Elroch's reasoning  fit's the bill. 

Key terms are "interpretation of probabilities" and "rather than as concerning some notion of objective chance"

I take it the extremist always believes in "interpretation of probabilities" for all observations of the world and believes their interpretation is always best. In an ideal situation, complete agreement by all of an interpretation is the theory, as using such logic results in but one valid conclusion.

how went everyone this great

total comments worth

Actually I don't. What I described was the fact that there is a correct way to modify your beliefs based on evidence. The reason this is not the same is that there is no way to objectively choose prior beliefs. There are ways to do so that are regarded as good, and there are some that have desirable invariance properties, but this is not enough to say they are definitive.

In practice, the more evidence you have, the less prior beliefs matter, but it is only in the limit that (with a mild assumption) they don't matter at all.

Doing a search now, I find this in the Stanford Encyclopedia of Philosophy:

"In the limit, an Objective Bayesian would hold that rational constraints uniquely determine prior probabilities in every circumstance. This would make the prior probabilities logical probabilities determinable purely a priori. None of those who identify themselves as Objective Bayesians holds this extreme form of the view. Nor do they all agree on precisely what the rational constraints on degrees of belief are. For example, Williamson does not accept Conditionalization in any form as a rational constraint on degrees of belief. What unites all of the Objective Bayesians is their conviction that in many circumstances, symmetry considerations uniquely determine the relevant prior probabilities and that even when they don't uniquely determine the relevant prior probabilities, they often so constrain the range of rationally admissible prior probabilities, as to assure convergence on the relevant posterior probabilities. Jaynes identifies four general principles that constrain prior probabilities, group invariance, maximium entropy, marginalization, and coding theory, but he does not consider the list exhaustive. He expects additional principles to be added in the future. However, no Objective Bayesian claims that there are principles that uniquely determine rational prior probabilities in all cases."

<<If anyone instinctively dislikes this, I suggest trying to find an alternative way to obtain knowledge about the real world from empirical data!>>

I instinctively disliked it because I would assume that the only way to make a biassed coin work is to allow it to fall each time you toss it, since catching it in midair would automatically prevent any bias. I always catch them in midair ... otherwise they get lost.

The British spelling of biassed is biassed; the American is biased. You're a Brit, using a spell-checker which nominally has a "British" vocabulary which seems to have been programmed by a person who is ignorant of all British spellings.

<<Mathematics is about abstract truth (often not about numbers). Adding up is about arithmetic.>>

That is, of course, an interesting question. Perhaps there isn't a "true" answer. Certainly, mathematics is taken to involve all forms of manipulation of ideas about numbers where variables are used as symbols. But it would be possible to do simple arithmetic like that. So, perhaps, mathematics starts at a point where the going gets difficult enough for there to be a need for generalised methods. But this can't mean that such a point is the same for everyone. I can't do it now but back when I was ten or eleven I could perform quite complex multiplication and divisions apparently instantaneously and probably faster than you could do them on a calculator, because I had derived mental methods to perform them, including the ability to wipe an area in my mind, write a long number on the screen, perform maybe two other tasks and then come back and read the number, and wipe the screen. Also I was performing two calculations simultaneously. I was using arithmetic at points where others would be resorting to mathematics. 

So there is no clear-cut point at which arithmetic becomes maths, and so that means that there is no absolute difference as depicted.

^ Sophistry.

Mustang: "The formula may predict 1 in 100 Gazillion, no matter the possibility exists - therefor it could have happened"

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what do you mean? some things can be predicted with math, others can not. but the possibilities are crucial. can you give a real life example?

how many flips it took your software before it detect a bias approximation of say 0.7-0.8?

An example is Life arising from non-life. A recurring topic in Elroch's thread. Basic reasoning in support goes something like there are only two possibilities. One is dismissed, that of ID. The simple fact that life exists is evidence that's it's possible. There are several estimates of the chances of random DNA or RNA combining in such a fashion. All the best guesses make for astronomical odds. 

So my point is, it really doesn't matter how great or small the odds are. A priori beliefs often determine conclusions, not the Maths in play. If something is 50/50 - easy to believe in the possibility. But where is the line made where doubt creeps in, the odds become so long so it it becomes thought to be near impossible? This will be different for everyone. Therefor, mathematical possibilities are not all that crucial in this case. The chances of life arising by random chances. the 100's of necessary combinations in exactly the right order, again are astronomical as best guessed by the experts. Included is the belief the necessary building blocks formed in the 1st place. Yet ,life is here. Perhaps if live arose in this manner, the experts have got it all wrong in calculations. This explains why my belief Maths (abstract) are not proof of probabilities for events that are not observed nor measured, but only speculated on (abstract). Math is but a single tool, one of many to be used in attempts to understand what is unknown.

life is here. no one knows how. but dont let probability & math theory trick u.

just like the 50-50 thingy. okay. I'm gonna play the lottery tonite. I have a 50-50 chance of winning. either i am or im not.

Might say Life is not a Concrete example - what's needed is something substantial as in a type of particle. The two examples really are not all that different, when realized we too only have best guesses about the creation of matter (The BB). It could be all wrong, yet some steadfastly believe it is the only answer to explain how the universe started and importantly, how it is behaving today. Thing is, perhaps there never was a starting point. The mind comes to believe in such things as a beginning and an end as absolute. 

This goes to point out the minds rationalizations regarding randomness, trying to make sense of something in such a fashion that satisfies our "conditioned minds."

our minds are conditioned cuz they taught us that in skool. u'll be way-WAY better off if u unlearn e/t u learned in skool.  

so okay. throwing math theory out the window (which is a pretty good place for it), take random # generation....the very-VERY basis for stats & probables. the higher the sample pool the higher # of samples needed to reach parity, right ? iows, they're directly proportional, right ? (if u dont believe me then try it empirically) and if u can remove time then u'll get there. Problem: u cant remove time. its unioned to the space needed to generate these random #'s. so, darn. 

try it 4urself s/t. frumma a test, u'll find that there's NO PROOF u'll ever reach parity from, say a, roulette wheel (38 #'s. or 37 if ur in France). its ALL justa accepted theory by so-called booknose poindexters. wut ur gonna find is the more #'s in the pool the greater chance u'll never get to parity. common sense here. forget theory.

ok. ask a kindygardner. they'll say idk or probably not. and e/t u ever needed2know u learned in kindygarden, right ?