Moderated Coin Flipper

[Leumas]

It's an integer.

Which one?

It is not 1, hence the use of the symbols "<1.0"

So it is indeterministic... QED!!!

No chance involved. "Arbitrary" means you get to choose it. You might for example choose p= .99 or .9999 or .99999999, as long as the number of 9's is finite, because as you said we don't like infinite quantities 'round these parts.

Why not choose 1 which is what it will have to be if it is deterministic?

And you might choose ε= .01 or .00001 or .000000071, as long as the number of lead zeros is finite, because as you said we don't like infinite quantities 'round these parts.

Why not choose 0... which is what it has to be if it is deterministic?

The point is that for any possible choice of p<1.0 and ε>0, there is some number of throws n that meets the stated condition.

What about p=1 and ε=0... what is n then?

There is no probability so close to 1.0 and/or epsilon so close to 0 that the corresponding n becomes anything other than a finite integer.

What about 1 and 0... what is n then... if it is going to be deterministically 50% then it will have to be 1 and 0... what is n then?

That's what it means mathematically when we say a sequence of fair tosses converges on exactly 50% heads.

So what is n for EXACTLY 50% i.e. ε=0 with p=1?

The calculation of n for any given p and ε is completely deterministic, and no infinite quantities are involved either.

For it to be deterministically 50% exactly then you have to choose p=1 and ε=0 ... calculate n then please.


If you choose p < 1 and ε > 0 then you do not have determinism or convergence.... what you have is a guessing that is ARBITRARILY CLOSE and not deterministically EXACT certainty.

What is n when you want a deterministic exact p=1 and ε=0?

 

[jsfisher]

...
If it were convergent there would not be erratic divergence and oscillations and more divergence.
...

May we assume by "divergence" you mean not as close as it was before? Then by inference, "convergence" must mean closer than it was before?

You have been told what convergence means several times in this thread, and it is not what you seem to believe. It can be a very noisy path towards convergence, getting closer than further away than closer again. The only requirement is that for any degree of closeness you care to specify, there is a point in the sequence where from thereafter it always remains within that degree of closeness.

...
here are some [ B]more [ /B]facts from running [ B]Coin Flipper 4[ /B] that you did not bother to look at

No, they were looked at, but they only serve to highlight your ignorance (misunderstanding, perhaps) of what convergence means. Getting near then wandering away a bit is well within what is allowed. Short-term anomalies are to be expected. It is the long-term trend that matters.

 

[Leumas]

No, they were looked at, but they only serve to highlight your ignorance (misunderstanding, perhaps) of what convergence means. Getting near then wandering away a bit is well within what is allowed. Short-term anomalies are to be expected. It is the long-term trend that matters.

You are the one who admitted being agnostic about all this.

So the Argumentum ad Ignorantiam fallacy is yours... not mine.

And your definition means nothing... it is still definitely not p=1 and ε=0... and thus it is still oscillating arbitrarily and indeterministically.

Guessing that something is arbitrarily close to 50% is not deterministically 50% is it.

It is the long-term trend that matters.

How long?

If... as Coin Flipper 4's sample output demonstrates (see here)... after 10⁹ coin tosses it is still diverging and getting close then diverging by THOUSANDS of heads/tails away from 50-50... then when?

After 10²⁰? Infinity?

Do you know how long it will take to do 10⁹ coin tosses in REALITY?

So in REAL REALITY it remains that it is indeterministic and totally random when you want to GUESS the result of 10⁹ coin tosses.


QED!!!

 

[Myriad]

If you choose p < 1 and ε > 0 then you do not have determinism or convergence.... what you have is a guessing that is ARBITRARILY CLOSE and not deterministically EXACT certainty.

Yes, congratulations for figuring out what the term "converge" means in mathematics.

It might help to compare with this simpler example: the function y = 1/x, where x is a positive real number.

Mathematicians say that for increasing values of x, y converges on zero. You can say "but even when x is eleventy gazillion squintillion, y is still one eleventy-gazillion-squintillionth, so y can never be quite actually zero." The mathematician says, "that's true, but for any y>0 you give me no matter how small, I can give you an x for which 1/x is smaller than your y. That makes it mathematically valid to say that y = 1/x converges to y=0 as x increases."

You can call the mathematicians silly for saying this, but the mathematicians are busy using this kind of definition to make calculus work, so they probably won't notice.

Or you can say "well what if I give you y is exactly zero, what then huh huh?" and they'll just shrug and say "then that's not a y greater than zero so it's irrelevant to the definition of convergence."

Note that for values of x decreasing toward zero, the inverse is true: for any value of y you give me no matter how large, I can give you an x for which 1/x is larger than your y. That shows the function y=1/x diverges or is unbounded as x approaches 0, and that it has a singularity or goes to infinity or (if you're coding it) will throw a divide by zero error at x = 0.

 

[jimbob]

You are the one who admitted being agnostic about all this.

So the Argumentum ad Ignorantiam fallacy is yours... not mine.

And your definition means nothing... it is still definitely not p=1 and ε=0... and thus it is still oscillating arbitrarily and indeterministically.

Guessing that something is arbitrarily close to 50% is not deterministically 50% is it.






How long?

If... as Coin Flipper 4's sample output (see here)... after 10¹⁰ coin tosses it is still diverging and getting close then diverging by TENS OF THOUSANDS of heads/tails away from 50-50... then when?

After 10²⁰? Infinity?

Do you know how long it will take to do 10¹⁰ in REALITY?

So in REAL REALITY it remains that it is indeterministic and totally random when you want to GUESS the result of 10¹⁰ coin tosses.


QED!!!

No.

If you want to predict the outcome to an arbitrary confidence level (eg, 95% certain, 99% certain, 99.9% certain etc) and to an arbitrary level of accuracy (eg 1 in a thousand, 1 in a million, 1 in a billion etc) it is possible with well understood statistical techniques to state how many filps would be needed. The more accuracy and the higher the desired confidence level, the more filps you need. Note that these are proportions and not absolute numbers.

This converges on the predicted value not oscillates as there's no periodicity in any flipping between being above or below the predicted value, but the percentage difference (again a proportion) is getting smaller with increased numbers of flips.


And I am coming back to your claim that your starting process is random.

To use your card deck analogy, my understanding is that you have a large number of decks if cards, for the purposes of the analogy and to make the sun's easy, let's say 1000 decks, so 52000 cards.

You shuffle these, and lay them out in order, then take the first 10,000 cards and flip them up and put them into your look up table.


You use this look up table multiple times (people have pointed out that there were more blacks than reds in your table)

Each time you use the look up table, you run a complicated but entirely deterministic algorithm to determine what number will be picked.


And you are using this deterministic, pseudorandom algorithm to make a claim about truly random events.

You statement here implies a fundamental misunderstanding of what randomness actually is. In that you seem to be saying that it is a subset of deterministic processes. I think you are getting at some statement of perceived order... I hesitate to say entropy.

Let's say that one picks the 20th card from the right side of a shuffled and spread out deck of cards every time.

That is not just deterministic... it is not even random

If the atmospheric noise data is continuously published, you could simply request a single value and check whether that value is above or below a threshold value. That would be truly random - it *might* be biased if the threshold is set incorrectly but it would be truly random.

 

[Leumas]

Yes, congratulations for figuring out what the term "converge" means in mathematics.

And you still have not calculated n that will give a deterministic 50-50.

When you do I will also congratulate you on figuring out that you cannot have a deterministic 50-50.

So it is indeterministic by facts of reality.

I am still waiting... what is this n?

It might help to compare with this simpler example: the function y = 1/x, where x is a positive real number.

Nope... it will not help at all... 1/x is deterministic you have x you can calculate 1/x.

So this is a deceptive analogy.

Can you calculate a coin toss's outcome??

No... well then your simplistic analogy is invalid.

I am still waiting... what is this n for an exact deterministic 50-50?

 

[Leumas]

No.

If you want to predict the outcome to an arbitrary confidence level (eg, 95% certain, 99% certain, 99.9% certain etc) and to an arbitrary level of accuracy (eg 1 in a thousand, 1 in a million, 1 in a billion etc) it is possible with well understood statistical techniques to state how many filps would be needed.

Nope... 99.999999 is STILL not 100% which is what is needed to say it is deterministic.

A low probability of guessing wrong is STILL GUESSING and can be wrong so it is not deterministic.

I am still waiting for your to calculate n that will give 100% certainty that it will be 50-50.... which is what deterministic means.

Until then... QED!!!

 

[Myriad]

The n is a function of p and epsilon, as I explained.

Because a finite n exists for all p<1.0 and ε>0.0, we say that a sequence of fair flips converges on 50% heads.

The expected number of heads per fair flip is precisely .5. The outcome of any given flip is random, but the expected value is a deterministic calculation. That's where that distinction between abstract concepts (e.g. all of mathematics) and real individual events comes in, again.

When the number of events becomes large, the variation between individual events becomes less important and the statistics of the aggregate behavior become more so. Pressure and temperature are real-world measurable quantities, even though they result from (large numbers of) individually random trajectories of particles. The fact that the aggregate statistics converge on specific values with large numbers of events is the reason temperature and pressure exist.

 

[jimbob]

Nope... 99.999999 is STILL not 100% which is what is needed to say it is deterministic.

A low probability of guessing wrong is STILL GUESSING and can be wrong so it is not deterministic.

I am still waiting for your to calculate n that will give 100% certainty that it will be 50-50.... which is what deterministic means.

Until then... QED!!!

Do you use a computer?

Every charge carrier in every silicon chip occupies energy states according to Fermi-Dirac statistics. Yet even though the circuits are vulnerable to so-called "soft errors" from alpha particles and cosmic rays, it takes a very eccentric definition to claim that computers are random systems.

Similarly, pneumatics rely on the random movement of gas molecules, but the numbers are so large that their performance can be highly predictable.

Your definition of randomness is so broad as to be useless.

ETA - I see that Myriad has invoked one of the same examples as me

 

[Leumas]

The n is a function of p and epsilon, as I explained.

What is it... you have not calculated it for p= 1 and epsilon= 0 which is what deterministic means.

For any p < 1 and epsilon > 0 you do not have determinism.

So can you calculate n for determinism.

If not then coin tossing is an indeterministic random process... QED!!!

 

[Leumas]

Do you use a computer?

No... never seen one...

Your definition of randomness is so broad as to be useless.

And your definition of determinism is incoherent and contrary to reality.

 

[Thermal]

Nope... 99.999999 is STILL not 100% which is what is needed to say it is deterministic.

A low probability of guessing wrong is STILL GUESSING and can be wrong so it is not deterministic.

I am still waiting for your to calculate n that will give 100% certainty that it will be 50-50.... which is what deterministic means.
Until then... QED!!!

Oh ffs, no it doesn't. What WE can predict is not the barometer for what is or isnt determined. What WE can predict is a reflection of our knowledge, nothing more.

 

[jimbob]

.






And your definition of determinism is incoherent and contrary to reality.

No. A deterministic system is one where the same inputs produce the same outputs every time. A nondeterministic system is where this is not the case.

A truly random system is nondeterministic.

 

[JimOfAllTrades]

To avoid confusion it might be as well to point out that this convergence is only demonstrated for the relative results. That is, the proportion of results being heads converges to 50% as the number of tosses increases.

However, in terms of absolute numbers, the opposite occurs. The results actually diverge. The more often you toss a coin, the greater the likely difference between the number of heads and half the tosses is going to be.

This is what I was trying to show my post here:

Only if you add the data together and recalculate the average based on all ten runs.

Run 01 - 490 heads, 510 tails, average for heads .490
Run 02 - 510 heads, 490 tails, average for heads .510
Run 03 - 490 heads, 510 tails, average for heads .490
Run 04 - 510 heads, 490 tails, average for heads .510
Run 05 - 490 heads, 510 tails, average for heads .490
Run 06 - 510 heads, 490 tails, average for heads .510
Run 07 - 490 heads, 510 tails, average for heads .490
Run 08 - 510 heads, 490 tails, average for heads .510
Run 09 - 490 heads, 510 tails, average for heads .490
Run 10 - 510 heads, 490 tails, average for heads .510


In doing this you never get any closer to 50%. As you say it could oscillate forever and never get any closer.

But add those 10 runs together and recalculate and you get exactly 50%. (Not that you'd expect that exactly in the real world.)

Now do one more run of 1000:
Run 11 - 490 heads, 510 tails, average for heads .490

Again, you're no closer on that one run. But add that run to the previous totals and recalculate and you get 5490 heads, 5510 tails, and your overall average is .499 heads, much closer to 50/50.

So with a binary selection chosen at random, the more selections you do the closer it should converge on 50/50.

But I think your post says it more clearly.

And with that, I'm out as well.

 

[Myriad]

What is it... you have not calculated it for p= 1 and epsilon= 0 which is what deterministic means.

So? I haven't calculated it for p=repetition and epsilon=paying attention which is what practice means either. I'm not describing determinism or nondeterminism, I'm describing what it means for the cumulative results of a large number of trials to converge on a statistical expectation.

 

[jimbob]

Oh ffs, no it doesn't. What WE can predict is not the barometer for what is or isnt determined. What WE can predict is a reflection of our knowledge, nothing more.

To be fair, a subset of what we cannot predict completely is because it is truly random.

 

[jsfisher]

And you still have not calculated n that will give a deterministic 50-50.

Precisely 50/50 was never a requirement; you are confused about the meaning of deterministic if you require exactness.

 

[jsfisher]

You are the one who admitted being agnostic about all this.

I have no idea what you mean by that. I also have no idea how it would lead you to this conclusion:

So the Argumentum ad Ignorantiam fallacy is yours... not mine.

Care to explain?

 

[Leumas]

So? I haven't calculated it for p=repetition and epsilon=paying attention which is what practice means either. I'm not describing determinism or nondeterminism, I'm describing what it means for the cumulative results of a large number of trials to converge on a statistical expectation.

So you cannot do it... I suspected that much... well get someone better than you at math to do it then... until someone does it ... a coin toss remains indeterministic and random and unpredictable no matter how many times you can humanly in the life of this universe do it.... QED!!!

Thanks for trying though...

 

[Thermal]

To be fair, a subset of what we cannot predict completely is because it is truly random.

Very true. What I object to is the extrapolation of what is deterministic (but complicated) into all of natural physics.