Out of Pod Experience

I will not debate that perceived time can get heavily distorted in certain conditions.
I will not debate that in case the Higgs boson mechanism hypothesis is correct, we might eventually be able to manipulate mass, and in a roundabout way, possibly also time.
What I will debate however is something different - even if we do manage to achieve a pretty damn good mastery over mass and time (and maybe even space itself), the more you try to alter either one, the more energy you require, and the harder it gets to push it further. So even if we eventually might be able to manipulate time itself, I strongly doubt we will ever manage to actually "stop" it altogether.

I assure you that you will not, because true randomness does not mean all possible variations will be met. What one should expect is the occurrence of extremely simple patterns over and over again forever. Not the emergence of immensely complex reoccurring patterns.


A coin only has two sides as stated previously, and for the reasons previously stated it does not apply to larger patterns and larger variables. Ironically, I am now wonder if a binary code is actually composed of 50% 1's and 50% 0's. I wonder if this information can be found somewhere?

You are going about this the wrong way. We are dealing with the mathematical concept of "almost surely". This concept is simple: If you have an event which has non-zero probability, then this event will occur at least once with 100% probability given an infinite number of trials

Here's an example: Let's say you are rolling a 6-sided dice

What is the probability that you will NOT roll a 1 a single time when you roll the dice once? How about twice? 5 times? 10 times? 20 times? 1000 times?

You have a 5/6 ~ 83% chance to not roll a 1 with 1 trial
You have a 25/36 ~ 69% chance to not roll a 1 with 2 trials (5/6 * 5/6)
You have a 3,125/ 7,776 ~ 40% chance to not roll a 1 with 5 trials ( (5/6) ^ 5)
You have only a 2% chance to not roll a 1 with 20 trials
You have only a 6.6 * 10 ^ -80 chance to not roll a 1 at least once after 1000 trials

But we're not talking about 1000 trials, or even a large, finite number of trials. We're talking about an INFINITE number of trials. The Last Integer number of trials. An Aleph Null number of trials. We're dealing with infinite cardinal numbers here, and infinite cardinal numbers over power *ANY* non-zero finite number

Or in other words - as you increase the number of trials without bounds, the probability that an even with non-zero probability will NOT occur approaches zero. Because the probability that an event will not occur after infinite trials is zero, we say that the event will "almost surely" occur

Now the OP is dealing with an event with a much lower probability. However, the probability is STILL greater than zero so the probability that the event will NOT occur approaches zero as you increase the number of trials without bounds. It approaches zero very slowly - but it approaches it all the same

Then you are also claiming that you can flip a coin and get heads 10,000 times consecutively if you flipped it infinite times. That will not happen either. Simply... no.

Math it all you want, the coin toss thing is the best example so far. No way, no how... will you ever get 10,000 heads in a row.

It's not about any of those thing Akita, it's about the plan and simple realty of coin tossing. It does not matter how much time passes, there will never be 10,000 consecutive heads or tails because that is just not the way it works in practice and regardless of what the math says. If you were to flip coins forever, it would look remarkably like flipping coins for a year, repeated forever. You will never get the latter.



All these nerdy-math-wiz-collage graduates, and this fundamental concept of our surrounding reality cannot be grasped?


A word to the wise, math is a language and like any language created by human beings it can tell both factual and fictitious stories. Only our experience and cognitive senses can tell us which is which, and not even with a great deal of accuracy mind you.

No, infinity is infinity. The pattern of heads to tails would continue on and on into infinity. You might get 10 heads in a row, 20 heads, but never ever 10,000. Not ever, ever and ever.



Because like a fractal image descending into infinity, the seeming pattern repeats.

You're taking the fractal representation to literally. It's just a metaphor.

You might think that


Since infinity cannot be reached, sure why not lol Same difference though in the end. The random sequence will repeat indefinitely, and your not going to ever roll 10,000 heads.

Ok, we just established that each sequence of any finite number of tosses has the exact same chance of happening as any other sequence of tosses.

Let's take an arbitrary sequence of 10 tosses, like, say, 10 heads, for simplicity's sake.
We know there are 1024 possible combinations of tosses, and each of them is equally likely to happen.
After 10240 total tosses grouped 10 at a time, there's a fair chance that we have experienced a rather large number of those possible combinations of 10 tosses (with some of them not happening at all, some happening once, some twice and so on).
After 102400 total tosses (10 times more than all possible combinations strung together), there's a very good chance that every possible combination of 10 tosses has come up at least once, some of them came up many times (on average, close to 10 times each) with very few of them not having shown up at all yet.
We can safely say that after 1024000 tosses, we can be almost certain that each and every specific possible combination has almost certainly shown up at least once (on average about 100 times each), and that includes our "10 heads in a row" initial choice. The chance of any particular sequence NOT showing up is the one bordering near zero this time.

If we go with a single person with the full-time-job of tossing the coin once every second for 8 hours a day, 5 days a week, 50 weeks per year, 1024000 tosses would require only a bit over 7 weeks to complete.
So, in about 7 weeks, we have almost certainly managed to flip 10 consecutive heads at least once, and on average, we have flipped 10 consecutive heads about 100 times.
Ok, in fact, on average, we would have been flipping even more than 100 times the 10-heads string, so it would happen even sooner than 7 weeks, because we would reset the sequence every time we would get a tail, but let's assume for the sake of argument for this entire post that we don't do that, because "the error" is in your favour anyway.

Let's go for 20 tosses.
1,048,576 combinations, so in order to get on average about 100 times a 20 consecutive heads toss and almost guarantee at least one, we'd be needing 1,048,576,000 throws, which would require the same "full time job coin tosser" to keep doing it for about 145 years.
He might not get to live that long, but you never know, on average it would only need about 14.5 years for one of those to happen, so he might get lucky.

How about 30 tosses ?
1,073,741,824 combinations, tossing about 1,073,741,824,000 times to almost guarantee one 30-consecutive-heads toss (and on average about 100 of them), or 149,130 years.
Well, I guess ONE single person is unlikely to be able to do it, but he might still get lucky while he's still alive. But take 150k people and in one year, you're almost guaranteed to have at least one of them make it (in fact, probably about 100 of them will make it within a year).

Hmm, let's go a bit faster and try 100 tosses.
1,267,650,600,228,229,401,496,703,205,376 combinations, ouch, now that's a number.
Going by similar rules, 1,267,650,600,228,229,401,496,703,205,376,000 total tosses to almost guarantee at least one 100-heads toss streak.
Uh-oh, the poor person we're talking about would be needing about 176,062,583,365,031,861,318,986,550 to make that many tosses... hmm, guess that's about 12,804,551,517,456,860 times the current estimated age of the universe, oh my !
Even if we take the approximate 7bil population of the planet Earth and make them full-time coin-tossers, that's still about 1,829,221,640 times the age of the universe until we can safely say at least one of them has managed to make a 100-heads coin toss (and about 100 of those have happened on average).
Or, to put it another way, we need about 18,292,210 times the age of the universe for all the people in the world today working full-time (assuming they could maintain their numbers for that long) as coin tossers to have a reasonable chance of one of them having tosses a 100-heads streak.
We can all agree that practically speaking, that is what you would already call "impossible".
But it's still not "infinite time".

What about 10000 consecutive heads tosses ?
1.995*10^3010 combinations, we want 1.995*10^3013 tosses, that's about 2.77*10^3006 years, divided by 7bil people that's around 3.958*10^2999 years, divided by the age of the universe (13.75bil years) that's still 2.8788*10^2989 times the age of the universe.
And after THAT much time has passed, we can be ALMOST certain that AT LEAST one 10000-heads streak has happened, and that on average, chances are about 100 sets of 10000-consecutive-heads tosses have happened.
That's an awful truckload of time, and far, far, far past anything anybody halfway sane would even begin to consider calling possible. But it's quite calculable, and quite finite, thankyouverymuch, so certainly not "infinity" just yet.


Hey, what about 1 billion consecutive heads tosses ?
My calculator croaks if I try to calculate that (it can't even handle calculations for 100k consecutive heads), as it has way too many digits, but you can be fairly sure that it's still a finite number.
Hilariously large, I agree, but still nevertheless finite.

...

Yes, some things have a very low chance of ever happening in a realistic timeframe, but to say that "it would never ever happen" is downright wrong. Anything with even the slightest chance of happening will eventually almost certainly happen. It just takes a ludicrous amount of time (even more than could practically exist in some cases). But always less than "infinity". That's kind of infinity's thing, you know, anything finite, no matter how large, is always smaller than infinity.