Out of Pod Experience

It's actually you who is all to ready to be conflating "must happen" with "has a good chance of happening" on one hand, and most importantly and most egregiously, "will not ever happen" with "has a poor chance of happening".


Except that you're not going to actually be typing randomly (your typing will have very specific patterns) and you don't have an eternity at your disposal.
If you WOULD be typing really randomly (as in, equal chance to type any given letter, or better still, chance of typing any given letter closer to its normal language use frequency, like it would be more likely to happen if you use a DVORAK keyboard layout and "try" to type "randomly") and if you WOULD have an eternity at your disposal, then you WOULD in time get closer and closer to any given possible combination of letters you care to name, starting with random short words earlier, more complicated words and combinations of words later, then sentences, phrases, paragraphs and up to the works of Shakespeare or the full text of any encyclopedia.


OF COURSE I freaking agree "almost certain" is not 100%. I always did, and never claimed otherwise. But I don't care about 100% certainty, inevitability or any other thing of that sort.
You're the only one that was actually bringing actual infinity and absolute certainty into the mix. I never unequivocally said "you absolutely have to eventually get that, no alternatives", just that it is "almost certain you'll get that eventually". Which is a huge difference.

My point was about a reasonable degree of certainty (be it 10%, 50%, 90%, 95%, 99%, 99.99% or anything that can be considered reasonable OTHER THAN 100%) to obtain a certain streak of heads of a specified length or a certain text of a particular composition and length within a FINITE amount of time (whether that specific length of time is feasible or not, be it days, years, the entire recorded history, or multiples of the expected lifetime of the universe).

For ANY specific length of text (or heads streak), given a sufficiently random and unbiased text character (or coin side) selection method, and given a specific desirable degree of certainly which is always less than 100%, you can CALCULATE HOW MANY TRIES YOU WOULD NEED FOR THAT TO HAVE THE DESIRED CHANCE OF HAPPENING.
The time needed rapidly escalates with both increased desire for certainty and length of desired result, but it is always a finite number.
As long as the degree of certainty required is below 100% and the length of text/streaks is finite, the time needed for that is also finite, even if almost inconceivably long for a human being.


So, will you ever at any specific point in time be absolutely sure to have obtained the complete works of Shakespeare by random, or any other specific text or any specific length ?
OF COURSE NOT.
But you will know exactly HOW LIKELY it is to have obtained them by that point in time before checking the results.
That chance is never 0% as long as you have had at least enough characters typed.
And that chance keeps going up the more characters you add, never reaching 100%.
Eventually that chance WILL get CLOSE ENOUGH to 100% for any reasonable person to say "damn, I guess you really should have managed to get what you wanted to get in there somewhere by now".
That is, if there's still people capable of saying that or even an universe remaining at all in the first place by that time.

On the flip side, will you at any given point in time be certain you have had the letter "s" chosen at least once ?
Funny enough, the answer is the same, OF COURSE NOT, but again, you would have a very good idea of the chance of that happening.
And that chance quickly converges towards 100%, while still never reaching it, even in billions upon billions of years.

Very few things are ever exactly 0% or 100% certain.
Most things however are close enough to either, and we can be comfortable in routinely approximating them as certain or impossible, but just from a PRACTICAL standpoint in a PRACTICAL timeframe.
You say "no amount of time will change that", and that is precisely where you are wrong.
You are making the mistake of approximating something that would be practically as good as impossible in a realistic practical timeframe as actually and immutably impossible even if given a completely impractical timeframe.
The amount of time available is the ONLY factor of relevance there if the length of text/streaks is fixed.
And not only CAN we calculate exactly how much time you need for any given length of text or streaks, but it has actually BEEN calculated (approximately) in this very thread.
Experimental proof confirms it for anything that can be obtained in a reasonable time, with NO REASON to disbelieve it does scale just as well further.

Perhaps this thread has run it’s course, and this is about certain key issues (aka failings)) in statistical theory... which would require another thread to discuss. I guess I will see you all there!



* Cracks knuckles

Eternum Praetorian, let me give you a relatively straightforward statistics problem (which might look trivial at first sight but isn't quite that easy) and ask you a few short question about your answer to it.

If I want to be at least 66% sure I might have gotten at least 3 heads in a row at some point by unbiasedly flipping an unbiased coin, estimate very roughly how many throws would I have to make.
Sounds pretty simple, isn't it ?
The accuracy of the answer should easily be verifiable through practical means in a perfectly reasonable amount of time.
Heck, you could just as well make the series of specific number of throws by hand and use a notebook to record series which yielded in at least a length 3 head streaks and which ones didn't, and you can still pull off a reasonable accuracy check of the result before getting TOO bored.

If you are uncertain on how exactly to calculate that or even estimate it, feel free to err on the side of caution.
You can take whatever liberties with the approximations or simplifications you like, as long as the resulting answer is a guaranteed higher number of necessary tries, never lower.

What other variables (except "66%" and "3") should be figured into the formula which gives us an answer to the above problem, if any such variables exist ?

If any additional variables exist, why do they belong in there, in your opinion ?
Explain in as much detail as you can.

If no other variables exist, what's there to stop me from changing "66%" with "99.999%" and the "3" with "100000000" and get an answer to THAT particular question just as well ?
If nothing stops me from doing that, why exactly should the result obtained not be a finite number ?

I get it. You have no clue how to do such math. Not even how to approximate the results. If it wasn't really obvious before, it's bloody obvious now. Why do I even wonder that you can't follow the explanations either ?


You're needlessly changing the problem to something that is different from what we are actually talking about.
Instead of trying to calculate how many tosses are needed to have a certain chance of having gotten a specific string, you're shifting it to calculating the probability of NOT getting a certain string after a fixed number of tosses.


No, it's not "consistent". It's RANDOM. By freaking definition.
It's not "the same" in any way, shape or form. It's random. Again, by its very gorram definition.
It might look VAGUELY similar to what you're "used to" seeing, but that's a problem of PERCEPTION, not one of mathematical or statistical accuracy.


And here goes the completely baseless statement you keep on making.
The EXACT string of "looks something like" has PRECISELY the same chance of showing up as the same length string of 0s or the same length of string of 1s, or any other SPECIFIC combination of 1s and 0s.
There's absolutely nothing magical or esoterical about a long string of 0s or a long string of 1s, it's just RANDOM CHANCE.
The only important distinction is that there are far more possible combination that LOOK SOMEWHAT SIMILAR to what you posted in the first line, and only a couple that look like the one you posted right below.
So, of course, you're more likely to get something that looks like the former than something that looks like the latter.
But if you keep on doing it for a long, long, LONG time, EVENTUALLY, you will ALMOST HAVE (never 100% chance, but ever and ever closer to 100% chance) to stumble upon something that looks like the latter rather than the former.
How much time you need for any particular combined chance of stumbling upon it ONLY DEPENDS ON HOW MANY THROWS YOU MAKE and nothing else.

I am not responsible for your brain being unable to natively comprehend statistics on a large time scale, that's how all human brains work... but to overcome that shortcoming (because in this particular case, it can even be almost considered a handicap all humans are born with), that's what an education in statistics is good for, an education which you seem to be lacking.

I'm just gonna drop this here:
Almost surely

wat

They picked the wrong monkey/ape and the wrong hardware.
http://www.youtube.com/watch?v=3KGrXZ5pWko
There's some orangutans using iPads for fun without smashing them.

Are you saying that you don't believe that it's possible to flip 10.000 heads continuously, or to put it another way when the chance is small enough it's impossible for something to happen?

There are roughly 1.9950631168807583848837421626836 * (10^3010) combinations of 10k digits.
In order to have a reasonable but still low chance of getting 10k heads (or tails) in a row, you would need an output that's at least 2 * (10^3014) bits long, and only reach a pretty high degree of certainty for a string that's 2 * (10^3015) bits long.

There is not enough storage space on this planet to even begin to write that kind of random string.

Heck, there's not enough storage space on the planet to write down a random string that has a decent chance to reach 100 heads in a row.
You'd need 1,267,650,600,228,229,401,496,703,205,376 * 100 bits just to express all possible combos of length 100, and that is 14,411,518,807,585,587,200 TERABYTES of data.
I'm fairly certain there aren't enough HDDs, SSDs, pieces of RAM or CD/DVD/BluRay combined in the entire world to get even anywhere close to that amount of storage space.

We know exactly how LONG the string would need to be for it to have a good chance of that to happen, and it's NOT infinity.
It's an incredibly insane long number, but NOT infinity.

...

What we CAN give you is an accurate estimation of the length of random bits you need to have in order to get a decent chance of getting 5, 6, 7, 8, 9, 10, 11, etc heads in a row, and the exact same estimation formula DOES NOT CARE WHAT THE NUMBER OF EXPECTED HEADS IN A ROW MIGHT BE to give you a pretty damn good estimate.

To get N heads in a row, you need at least N * (2^N) bits just to express all possibilities, which means there's a decent chance, but still not quite high enough to be fairly sure it would actually happen, so punch that one order of magnitude higher and it should have a pretty damn good chance of happening (as in, would be surprised if it DIDN'T happen).

For N = 5, you get 5*2^5 = 160 bits ; you should have a decent chance to get 5 heads in a row with 160 bits, and if you go for 1600 bits, it should be almost certain you get 5 heads in a row (also, 5 tails in a row).

For N = 6, it's 6 * 2^6 = 384 bits for "maybe", 3840 bits for "pretty sure" to get 6 heads or tails in a row.

N = 7, 7*2^7=896 bits for "maybe, 8960 bits for "pretty sure" streak of 7 heads/tails.

N=8, 8*2^8=2,048 bits for maybe, and 20,480 for pretty sure for a 8-streak.

...

N = 15, 15 * 2^15 = 491,520 bits for "maybe" and 4,915,200 bits for "pretty sure" to get 15 heads/tails in a row.
It's already getting tedious to actually verify manually.

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N = 20, 20*2^20 = 20,971,520 bits for maybe, 209,715,200 bits for "petty sure" to get 20 heads/tails in a row.
You almost certainly can't check that manually without going bonkers.

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N = 30, 30*2^30 = 32,212,254,720 bits for maybe, 322,122,547,200 bits for "pretty sure" to get 30 heads/tails in a row.
That's already 37.5 Gigabytes of data for "pretty sure". Even a machine would take a good while to check that.

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N = 40, 40*2^40 = 43,980,465,111,040 for "maybe", 439,804,651,110,400 for "pretty sure" of 40 heads/tails in a row.
That's 50 TERABYTES of data for "pretty sure". You probably don't even have a tenth of that storage space on your own PC. It would take you a very long time to even download that and have your machine check it while it downloads.

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And you're asking for "proof" of 10k consecutives ? LOL. The whole POINT of it is that it's something UNLIKELY TO HAPPEN IN A HUMAN LIFETIME. You might as well ask for proof of evolution from an invertebrate to a mammal right in front of your eyes, both are simply not going to happen within the constraints you arbitrarily set, but have already happened in a geologic timescale.

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The burden of proof is not on us.
Logic says if something is proven for smaller numbers and there is absolutely no reason why it shouldn't apply to larger numbers, the burden of proof on those disputing the scaling up is on THEM not on us.
Or do you actually want to say you're disputing it for the smaller numbers too ?

Speaking of monkeys infinitely typing......