Philosophy of random

more or less... A random Nuber Generators use is it, that it's spit out Numbers are unforeseeable.

Right, 123456 can happen in a random generator. The problem is that if you repeat this sequence of numbers it won't be random any more because in a random sequence you can't know what will be the next number, but here you know exactly what will be the next number, so it is not random

Its not random cause it has a specific pattern.....

Yes random is unforeseeable/unpredictable , cos you can see this circuit you know what it's generating so it's not random cos you know for certain what's the next number. If this circuit was a black box then these numbers would be random, you're never sure what's the next number cos you won't know for sure, even tho it went 1 to 1 billion sequentially it still could be a extremely unlikely fluke! Like also flipping a coin billion times and getting tails every time... unless of course the coin is rigged like this circuit is ;)

I've retitled this circuit , it itself is not a random number generator :P but the numbers its generating are potentially random if you don't know the circuit is hardwired to produce this 'specific pattern'... i probably sound like a bumbling fool now :P

take any set of numbers, if you can find an algorithm that matches it then you may think its not random, you can see the pattern. or if its compress-able through a zip program on your computer then that program has seen repeating patterns in the set it can use to compress. So you might infer that a truly random numbers set would be something that is not compress-able? But no, the point i'm trying to make that something with a pattern and something without a foreseeable pattern are just as random as each other. Actually if you had a sequence set that cant'be compressed by your program then those numbers might have been specifically chosen not to fit an obvious pattern that the algorithm can see... so ironically making those number not random!! :P you guys getting my drift?

Randomness should be viewed as a matter of scale. Much like in physics where one can treat a large curved surface as locally flat or calculations over long line segments which are finite but behave as infinite close up. The flipping of a single coin is always random in the sense that the outcome is unpredictable yet over a large sampling

the total outcomes are predictable according to their probabilities. It's safe to say that a hundred samples of ten flips would yield many different outcomes that are not predictable, but a large enough sample would most likely yield a 50/50 split between heads and tails (according to probabilities). So, in terms of a Black Box (algorithms hidden from the observer) then small samplings of generated numbers can be considered random. Generate ten numbers then reset the machine to generate a new set and so on. Over a large sampling a pattern is most likely to occur as it does in nature, but small sampling can be treated as somewhat random, or pseudorandom.

Yay someone to talk to, thanks maxmax. To back up what you're saying , Taking a lot of samples from the black box to test if is random, statistically would expect an almost even distribution or 50/50 if it's coin flippings. The more samples we take the flatter the line gets. If it's otherwise then we suspect it's not random, right?

What my beef is if that statistical line was not smooth , it spiked here and there...whose to say that's not random?! It still can happen, even though how unlikely it is . Our universe exists because of a fluke like this :P

Also if we flip this coin over and over and we tails every time, there's another reality that splits off at every toss where we may get heads. We just happen to witnessing the reality where we tails over and over. I think you know where am going with this ;) just trying to say no matter how unlikely the results are, there has to be a reality where it happens ;)

Quantum mechanics entanglement and schrodingers cat is all about this. But I'm not trying to talk about subatomic particles, just my observation of the randomness we perceive. Hope you don't think I'm going mad :P

Precisely. If the results from a million flips yields all heads, while statistically possible, is highly improbable. It is reasonable to assume the outcome has been weighted in some fashion (a black box algorithm which generates just heads, for example). However, as I stated before, this result is still statistically possible, so it is possible for our black box (which generates both heads and tails) to spit out a million heads in a row without any weighted interference or loss of integrity. The millionth plus one result could easily come up tails.

Yep and on every result the box spits out it is oblivious and independent to all the previous results , but average up all the results we get a straight line , wtf!?! LoL really but what else could it be when it's totally random?? O.o

Also, despite the predicted pattern generated by the statistical probabilities, the black box in question can indeed be a random generator. A predictable pattern does not infer a lack of randomness. I suspect we use the term pseudorandom as a position of compromise. To prove the randomness or lack of randomness of any random generator would require an infinite sampling, since any predicted pattern could change at any point, and who wants that task.

Reason why I'm thinking about this soo much cos I directly experience this in the work I do...

Yes that's what I have trouble fathoming, we get a predictable result from something that supposed to be random. I understand why logically, but still feels there's some tampering happening from the universe at large :P maybe I'm looking at it all wrong

I like your definition on pseudo random being somewhat a compromise ;)

Could be a version of the anthropic principle. The universe exists and evolves because of local randomness and by extension, so do we. On the large scale, these wild fluctuations of randomness balance out and lead to the relative stability of the universe. Without both conditions being met there would be nobody to ask the question. It's a weak argument, I know.

Anthropic principle makes sense to me, it's the most likely outcome if there are many universes ( approaching infinity), the conditions are just right in our universe for us to exist to ponder these questions... It's inevitable ;)

Or were you trying to answer why we perceive this order in randomness on a large scale with the anthropic principle? Yeah it could be related in some abstract way

I only bring it up in response to your feeling of tampering by the universe. We could objectively and quantitatively answer why random events form large scale distributions using thermodynamics, but this skirts your initial statement. I think you make a good point when you say that a sequential set of numbers can indeed be generated from a random number generator. Like you said, it's a rare event, but the possibility exists. It would be reasonable for any observer to subjectively assume the generator is weighted, when we know it not to be. As long as the result falls within the possibility distribution, it can still be considered random. If a truly random generator generates a definite possibility distribution, is it fair to conclude that any real world application of the simulated random number generators presented in EC are not random, even if they generate a similar distribution?

Wow I'm blown away with your deep understanding on this subject! Let me absorb what you just said and I'll get back with a reply :P

...I'm having a blonde moment

Lol

Okay maxmax. Your last argument , if a (pseudo) RNG in EC can match the possibility distribution of real randomness , it's still not considered really random? I'd say yes that's correct the EC RNG is not random. I gotta be careful now how I word your question , and I think I sound like I'm contradicting myself from earlier posts. Also I'm confused with the 'possibility distribution' , is it the same as probability curve. If it was really random wouldn't that possibility distribution be flat? You can get your algorithm to match a flat distribution , or just have it count sequentially . Instead of some fancy algorithm we just had a large array pre-populated with random values, again I don't think that counts as random either. But they all can be used as a compromise depending on how many samples you need before they start repeating

Thinking about the possibility distribution , the position of subatomic particles like electrons are described by there probability curve. There paths are not random but they are not definite either, or is it weighted random? Or am I really loosing the whole concept here?!? And take PI, 3.1415... leading to infinity but never repeats, but not random, would it's probability curve be flat I wonder?

Let me know if I'm waay off the mark, maybe over-confusing matters :P sometimes need to take a step back for some fresh air ;)

No, I believe your conclusion is correct and well put. I guess we could build a black box which generates an equivalent number of states on the order of possible configurations for a finite universe (or possible different configurations of multiple universes), say an LFSR with adequate non-linear combinations of elements and accurately call it random, but then it's size would always exceed the size of the Universe, so not really possible. My error is injecting quantum mechanical thinking into an inherently deterministic process.

As for Pi, I the occurrence of each number is near equivalent, so it's the probability distribution is flat.

And sorry, I meant to say probability distribution (or curve). My bad.

Actually thought 'possibility distribution' was fitting in the context here, gives it a more multiverse like understanding in an abstract way ;)

Well since your touching on thermodynamics entropy , I want to come back to that flat distribution line that's been bugging me. I suspect I got this really wrong like comparing apples to oranges but... how is it that we get an ordered flat distribution from chaotic randomness (decrease entropy?!?) when everything else goes from ordered to chaos (increase in entropy), how's the universe allowing this? I know I'm making the wrong comparison somehow

We have to distinguish what were analyzing here. If we are comparing the occurrence of specific numbers which occur in calculating Pi, this distribution will be flat because Pi is fixed, it has no other "state". If, on the other hand, were analyzing coin flips (for the sake of simplicity) or any other system which generates multiple states, we will get a standard Guassian distribution or bell curve, since we're analyzing all possible configurations of states. A coin flipping "machine" would be equivalent to a box containing two distinct gases. The most unlikely configuration of states, corresponding to the most ordered configuration (least entropic) would be one where there is no mixtures of gases. Each gas occupies one side or the other. This would correspond to a run of coin flips which yields all heads or all tails. These possible configurations lie a the ends of the probability distribution. The most likely configuration of gas molecules, corresponding to the least ordered configuration (most entropic) would be one where both gases are equally distributed within the box. This corresponds to a run of coin flips which yields a mixture of heads and tails. These configurations lie toward the centre of the probability distribution. All other configurations lie to the right or left of the peak. The bell curve

Is the normal distribution of all possible configurations of states where entropy always increases.

In this type of analysis, we would always get a Guassian distribution. A flat line would definitely indicate a serious statistical anomaly.

I wish it was that simple dylanmissuwe, but there's something called 'Quantum Mechanics' that says otherwise . If the world was that simple then how would 'free will' be possible?

Maxmax, everything you last said makes sense , sort of :P but I can't see how to relate it to my question about the entropy of randomness decreasing on large scale. BUT now to think further about it, I'm comparing entropy with statistical outcome...which ain't the same two things, is that the error of my ways? Oh and happy new year :)

No need to apologise my congenial friend ( always wanted to use that word :P ) you've been a great help with your patience :) I'm understanding the meanings of 'frequency of occurrences' and 'appearance of consecutive sequence' and the Gaussian bell curve. But not understanding the meaning of 'counting single states' Yet. But don't worry gimme a day to think about it before ask you to elaborate even more ;)

Let me reword the above , it should say understanding the Concept of...

Lol. Happy New Year to you as well.

Vsauce talked about this: https://youtu.be/9rIy0xY99a0

It might be better to idealize the situation. Consider a box containing marbles marked one to ten. Each marble represents a particular state. In addition, we have ten empty slots to be filled from left to right as we draw each marble. In this case, each number can be drawn only once so the odds of drawing any particular number is one in ten. On the second draw the odds of choosing any other particular number is one in nine and so on until all slots are filled. On each run, each number (or state) appears only once so the frequency at which each number appears is the same for each run (crudely simulating a large sampling). Each run of ten draws creates a specific configuration of numbers (or states). Now the specific configuration where the slots are filled from left to right with the the consecutive sequence of 1 to 10 is unique, there is only one way we can fill all the slots this way. On the other hand, there are many more ways to configure all ten numbers that are not consecutive sequences. While it's possible to draw the numbers consecutively from 1 to 10, the odds of drawing them in a non-consecutive fashion is much greater. In this case, the consecutive sequence is in a more ordered configuration of states than is the non-consecutive sequences. In terms of entropy (which in essence represents the amount of randomness or disorder present within a system), the disordered (more random) configurations dominate, as would be expected in a system where entropy always increases. So while it's possible to pick out a consecutive sequence and seemingly violate the laws of thermodynamics by creating an ordered configuration of states and thus decreasing the system's entropy, it would normally require many runs to achieve thus creating many more disordered states increasing the overall entropy. Interestingly enough, if you drew a consecutive sequence on your first try, there would still be no violation. While you would decrease the entropy of this particular system, the energy expended in realizing this system (building the box, marbles, the energy you expend while manipulating the system) increases the overall entropy of the Universe.

Ok dylanmissuwe, we'll just dismiss nearly a century of quantum mechanical theory because Vsauce said so. Get off YouTube and pick up textbook. You might learn something.

Maxmax don't pass judgement on the vsauce video just yet ;) check it out it's making sense :) it's not bad

Again...I'm absorbing your last write up ...

Actually I should give vsauce a lot of credit, got me thinking deeper about a lot of things I'd take at face value before

I agree, it's a great video but dylanmissuwe's initial statement is both a misinterpretation of what's being said as well as a misinterpretation of quantum theory. The suggestion from Vsauce that nothing is random is purely rhetorical. The whole subject itself is far more complex than can be condensed into a short video. I can only encourage dylanmissuwe or anyone to seek out some deeper understanding on this subject and apologize for my harshness. I'm old school. Books rule.

I suspect there is also some confusion about the relative exclusivity of the leading theories. It should be made clear that classical theories such as Einstein's general relativity theory are intrinsically deterministic since they are not statistical in nature, while quantum mechanics is purely probabilistic, statistical both in theory and in practice. We can only apply quantum theory and thermodynamics to address the question of randomness in the universe.

I know i'm wrong. I typed that comment before i watched the video.

Hey, no problem. Thanks for the link. The video was very compelling.

Can't argue with that, books are the best source for hardcore science. But I don't have the attention span anymore, especially for the hardcore maths that go with it. It's easier watching scientific educational vids that sum up (or skim over) the subject of interest , even if it's not as indepth

Yes good find dylanmissuwe , it touches on QM from 8mins in the video

Also linked to it is the video from veritasium that's very interesting too, touches so much of we been talking about above :) http://youtu.be/sMb00lz-IfE

Interesting thread! Back to the question, can we decide for a black box if its a random generator or just a fake? - I think the question is already wrong ;-) - Why? Cuz, we never can say any rule in our universe is TRUE. We only can say, so far it looks true cuz we never saw it was false. But for this "black box" we also can not say its FALSE. So whatever sequence it generates we can see it as random or not. How bad is that?

okay thanks hurz for throwing that curve ball , mind blown ! ;)

This you are talking about is what we take as fact is based on our observation of it? Cuz we have tested theory's by our observed experiments? Am I on the right track??

I agree, hurz. But we must accept some level of objective reality. Say, for instance our Universe is just a giant computer simulation like the Matrix, where the perceived randomness is just a complex algorithm within the simulation. If there was no way to show that our Universe was a simulation, would it truly matter whether it was a simulation or not. The programmed randomness would be the ultimate expression of randomness within our "reality". We can only ask how random something is compared to that ultimate expression of randomness. I realize it's a circular argument, but we must accept some rules as true, at least tentatively, within the scope of testable reality.

Have you heard that theory that if some time in the future if a matrix like simulation is possible, then there should be many many MANY virtual realities simulations running, and so infer that the likelihood of us existing for real is unlikely and that it's more likely we are part of one of these virtual reality matrixy simulations !! LoL I don't buy it of course , don't believe computers of that complexity are possible in this universe, they are constricted to the physical laws of this universe ... But another universe hmm maybe :P

...so maybe the physical laws we observe in this simulated universe aren't actually the real laws of the computer's real universe it exists in ,LoL??? Food for thought or just baloney?

I'm on a roll here ... or maybe those many simulations are a metaphor for the multiverse :P

And maxmax , yeah observing randomness could be testing the finer nuances and limitations of the simulation we could be living in

Hmm, now I got this eerie feeling that these thoughts of mine aren't actually mine!?! Makes great SciFi tho :P

Back to seriousness. To reiterate maxmax , classical Newtonian and relativistic einsteinium physics is deterministic, 'cause and effect' at its heart . Quantum mechanics breaks cause and effect, there is no underlying coherent mechanisms we have found...yet , this is where randomness is derived. The smallest indivisible unit of space time is believed to be the Planck length , the ultimate resolution of this universe and all other multiverse. There is massive void from the Planck length to the fundamental building blocks (quarks) , a void in comparison the known universe to an atom is similar to an atom to the Planck length!! It just could be there is cause and effect happening near the Planck length, so many high energetic frequencies set in motion from the beginning of the universe creating the complex almost incoherent world at the quantum level. From here our coherent world is derived we see around us. Our deterministic physics is an illusion derived from the quantum world which in turn is derived from much simpler very basic cause and effect from much deeper... Somehow I feel ;)

Meant to write Einstein not einsteinium above. Rereading it I guess I could have expressed the idea better, but maybe let the numbers speak for themselves ;) Planck length:10^-34 , atom:10^-9 , known universe:8.8x10^26 meters (give or take 50 feet :P ) just googled it

Broken due to new update

Fixed it ;)