[yor_on]

Are you telling me that we can't define a smallest chaotic system to experimentally define its 'determinism'
And therefore it becomes deterministic?

Ah well

I think I would say that any system unable to be deterministically defined have a very little probability to be proven deterministic, other than theoretically. After all, we should use experiments to define theory, not the other way around.
=

On the other hand, theory do define experiments, to test a theory. and that's what I would like to see here Determinism being proven by carefully chosen initial parameters. Otherwise it seems to me that no matter how small those initial parameters are we still won't prove a systems determinism, although we can show a 'deterministic' constant repeating itself. So one might then be able to say that even though outcomes are unpredictable, its pattern is mathematically predictable.

Doesn't it remind you about the discussion of 'free will' too? I know it does to me, statistical trends relative individual choices..

[Pmb (OP)]

I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.

[yor_on]

Yes, afraid you're right Pete. Maybe we should split it?
You better talk with a moderator, to agree on where, as you're the originator of the thread.

[dlorde]

I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.

You may be right; but perhaps the direction of the thread is evidence that the difference between randomness and chaos (which involves both physics and maths) is a topic that's hard to grasp?

Personally, I'd rather have a live thread than a dead one - unless someone has some other hard-to-grasp topic to discuss?

[yor_on]

Wrote this, and thought it made sense at the time

"One can think of it this way maybe, the pattern of a thousand tails is no more uncommon that any other combinations of set patterns like tail - tail  - head, if repeated over and over, for a thousand flips. Which then just should make one thousand tails, or heads, uncommon, because it is so easy to recognize for us. That will make the one defining it as being 'reset' with each new flip the one making most sense.

What i mean is that if you count the way a pattern evolve over time, flipping a coin, then all patterns possible should have a equal chance of evolving, singling out no pattern as the one, more probable. And a pattern would then be whatever way you found head and tails arrange themselves over a thousand throws."

Still think it makes sense, but read this..

"In contrast, you wouldn’t expect all of the dice to be 4 at the same time, or otherwise assume one particular pattern.  That would be a very unlikely and low entropy outcome." http://www.askamathematician.com/2011/12/q-why-does-the-entropy-of-universe-always-increase-and-what-is-heat-death-of-the-universe/

So a unordered sequence is then more probable?
What makes it so?

Stupid question
You got a larger probability (number) of 'unordered sequences' than 'ordered'. Then again, we are the ones defining them as ordered or unordered, isn't that so? We mark them, and so define them.

In 'reality' no pattern should be more probable, as I think?
Maybe it's a stupid question, but there seems a slight difference to me? What we define as a probability relative a logic. Or maybe it's just me not thinking it through.
=

(Sorry Pete, forgot, still, this is a rather good thread I think, 'organically growing' if you see how I read it.)

[CliffordK]

I think there was a moderator discussing the numerical theory.  Anyway, if more posts are on that subject, we can split, if not, I'll leave it alone.   Certainly there would be benefits of discussing probability and numerical theory.  And, I'm quite rusty on my factorials and "Choose" equations.

I saw this puzzle online.
What is next in this series? 1, 4, 10, 19, 31, _   (no need to post the answer here).

It reminds me of the old SAT questions (Scholastic Aptitude Test).  Anyway, there may be benefits of discussing how to approach determining an unknown sequence or series.

Another, more well known series:
1, 1, 2, 3, 5, 8, 13, ...

[bizerl]

I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.

That's a shame Pete, because I really wanted to talk about the Monty Hall problem again. I got all excited because after reading this thread, I finally get it. But I'll address the topic first and say that Maths never really bothered me much at the fairly low levels I studied it at.

What always baffled me was "particle" physics and what a "particle" actually consists of. I think that trying to simplify it diagrams of an atom made of billiard balls actually makes it harder to grasp on a deeper level of what is actually happening.

Now, Monty Hall. I find it interesting that you can think of the situation of 100 doors, where you are asked to choose a door, but then you are asked to decide whether the door has the prize, or a goat. Probability at that stage would say that you've probably chosen a goat, which is why when you are given the opportunity to change in the original scenario, you would.

What interests me is that if at the stage of having 98 goats staring out of opened doors and 2 closed doors, one of which has a prize, someone new enters the studio and is asked to choose a door, would he (or she) be given any advantage by asking what the previous person chose?

[damocles]

From bizerl:

What interests me is that if at the stage of having 98 goats staring out of opened doors and 2 closed doors, one of which has a prize, someone new enters the studio and is asked to choose a door, would he (or she) be given any advantage by asking what the previous person chose?

The answer to that is yes -- it is extra information that modifies the odds from 50:50 to 99:1.

From pmb:

I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.

I apologize Pete for my part in this, although I think you can see that Probability and Combinatorics is a part of Maths that both fascinates and confuses many people.

One part of advanced Maths/Physics that confuses me is how to relate the character tables of say trigonal groups like C_3v or D₃ to that of the underlying C₃ group (there are other examples of the same sort of thing where a degenerate representation might consist of a pair of complex conjugates or a conventional E type representation with a character of 2 for the identity.)

[evan_au]

I just discovered the Khan Academy, https://www.khanacademy.org/

This covers a number of areas of Maths & Science in a progressive and clear manner (I needed a statistics refresher).

...although I am puzzled about how & why they combine "Science & Economics" into a single category??

[damocles]

I just discovered the Khan Academy, https://www.khanacademy.org/

This covers a number of areas of Maths & Science in a progressive and clear manner (I needed a statistics refresher).

...although I am puzzled about how & why they combine "Science & Economics" into a single category??

The reason for this is because physics and econometrics are the major areas of application of advanced mathematics, and because (at least in Canberra) there were a huge number of postdocs in physics at ANU who could not find employment in physics when their contracts ran out, but they were easily able to move across and develop the field of econometrics with jobs in the public service (perhaps explaining why econometrics has not turned out to be particularly successful). I do not know about the situation in other countries, but can imagine it was much the same.