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Is Randomness Just a Complex System We Don't Understand?

In summary, the article explores the concept of randomness, questioning whether it is truly inherent or merely a reflection of complex systems that we have yet to comprehend. It discusses the implications of perceiving randomness as a lack of understanding rather than an intrinsic quality, suggesting that advances in science and mathematics could eventually demystify what appears random. The piece highlights the interplay between chaos, complexity, and predictability, proposing that our current limitations in understanding may lead to the illusion of randomness in various phenomena.
  • #1
STAii
Well,After some time of thinking, i realised that what human beings see as randomness is simply a system that works in a very complex way that we can't understand, or that depends on too many variables so we prefer not to think about it.Take any little example, for example you throu a dice.Now our normal every day experience will say that number that will show is a random integer between 1 and 6 (supposing you have a normal dice).While if you really look at it, the dice went from your hand in a certain angle, this angle depends on how your muscles moved, which depends on the neraul signals it got from the brain, the angle in which the dice went off your hand (and how the dice was rotating for example) will show where the dice will hit the ground, now analyzing the ground you can know how the dice will rebound, and you can calculate the whole thing till youknowthe number that will show on the upper surface of the dice.Now sure since no one tries to calculate that, we just say that teh number is random.So anyone agrees with my idea ?Thanks--> That's Zargawee and Lilith, Cool Couple
 
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  • #2
Throwing a dice depends upon air resistance and turbulence, which I suppose eventually depend upon quantum randomness, and the uncertainty principle, and invoking chaos theory means that the result of this true randomness has an effect on large scale events.Though it would be possible in the vast majority of cases to predict what would happen to a huge huge degree of accuracy, it would not be correct all of the time.
 
  • #3
I feel that the debate about the existence of "truly random processes" is purely a philosophical one. Mathematically the debate makes no sense to me.Let's look at the problem of the rolling dice in a purely mathematical framework:quote:Originally Posted by Staifour-Take any little example, for example you throu a dice.Now our normal every day experience will say that number that will show is a random integer between 1 and 6 (supposing you have a normal dice).While if you really look at it, the dice went from your hand in a certain angle, this angle depends on how your muscles moved, which depends on the neraul signals it got from the brain, the angle in which the dice went off your hand (and how the dice was rotating for example) will show where the dice will hit the ground, now analyzing the ground you can know how the dice will rebound, and you can calculate the whole thing till you know the number that will show on the upper surface of the dice.
 
  • #4
Can please define 'chaotic' and tell us what is the difference between 'chaos' and 'randomness' ?Thanks in advance"No Nou Is Good Nou"--Ichi IchiNote : I Used To Be STaifour
 
  • #5
Chaotic (I think) is still a roughly subjective term. There are ways to define it but the "essense" of the term hasn't been captured.A chaotic system is highly sensitive to variations in initial conditions.The classic demonstration of chaos is governed by the following equation:f(x) = A x (1 - x) where 0<=x<=1 and 0<=A<=4The procedure is that you start with any value x between 0 and 1, then you keep applying the above function. For example, if A = 2 and we start with .4, we get the following sequence:.4.48 = 2 * .4 * (1 - .4).4992 = 2 * .48 * (1 - .48).49999872...But if we start with a number close to 0.4, we get:.41.4838.49947512.499999......Notice that the difference between corresponding terms actually decreases as you progress.This system has other interesting properties that I will skip, but I will briefly mention. For A = 2, any initial value will approach 0.5. Similar values of A will provide similar behavior, the answer approaches a particular "fixed point". But when A gets large enough, the "fixed" solution is periodic, the values you get will bounce back and forth between 2 values. Eventually it becomes 4 values, and more.But the part we're interested in is when it gets chaotic. Suppose A = 4 and we do the same thing, let us compare the iterates of 0.4 and 0.41.4 - .41.96 - .9676.1536 - .1254 (values are rounded now).5200 - .4387.9984 - .9850.0064 - .0592.0255 - .2228.0993 - .6927.3577 - .8514.9190 - .5060Notice after a few iterations, the values don't seem to correspond anymore! In this case, the 6th iterates were wildly different. This is the essense of chaos, the small variation in initial conditions eventually blows up into large differences.However, you can delay the effect by reducing the difference. For instance:.4 - .401.96 - .9608.1536 - .1507.5200 - .5119.9984 - .9994.0064 - .0023.0255 - .0090.0993 - .0356.3577 - .1375This time it take 8 iterations to achieve the same degree of error as in the previous example.Because any measurement we make has some error from the true value, if the system happens to be chaotic then long term predictions made from the measured value will be wrong. We're forced to take a step into statistical mechanics to describe whatcouldhappen as opposed to making predictions about whatwillhappen.As demonstrated, though, improving the precision of measurements allows us to make longer term predictions.In a random system (aka nondeterministic), errors build up because the system is inherently random. I would like to emphasize that randomness and chaos are totally different things that just happen to both be described with statistics. An example of an nonchaotic random system is:f(x) = x + random(-0.01, 0.01)If you carry out 10 iterations, the result can vary from x by at most 0.1, though is very likely to be closer to x. If you carry out 100 iterations, the result can vary by at most 1, but it is very likely to be closer to x.The long term behavior of these iterationsispredictable; the iterates will generally remain near the initial value.Another even better example is:f(x) = 2 x (1 - x) + random(-0.01, 0.01)Here, no matter what the error of the initial measurement, the long term behavior is very predictable; iterates will permamently remain near 0.5, though there will be a bit of fuzziness due to the random term.However, despite being totally different things, there is a blurry line between randomness and chaos when we want to make highly precise long term predictions. In the previous example our predictions will have an error of 0.01... but the same result could occur in a partially chaotic system, the overall trend of the system is predictable but there is a small bit of fuzziness due to chaos, but they could still be distinguished, increasing the accuracy of measurements would allow you to make better predictions for a longer time...Unfortunately, Quantum Mechanics makes the line even blurrier because of limits on the precision of measurements. There is a point where we can go no further and it becomes entirely impossible to distinguish between randomness and chaos.Anyways, to summarize:Chaos is when errors in measurement prevent us from making precise long term predictions.Randomness is when precise long term predictions are fundamentally impossible.(kinda sorta)Hurkyl
 
  • #6
While you were doing all that thinking, did you give any thought to quantum physics, where there is good physical evidence that true randomness exists in quantum processes, without any "hidden variables".Your argument goes back to the early days of quantum physics and experimental evidence seems to have settled it on the side of true randomness.
 
  • #7
Thanks a lot Hurkyl, i think i got it.Experimently i see a possibility for 'chaos' expectations, but if we are talking in a theoreticla world, where you get the EXACT values of everything, i don't see a chance for chaotic values, right ?HallsofIvy: Unfortunately i know almost nothing about QM."No Nou Is Good Nou"--Ichi IchiNote : I Used To Be STaifour
 
  • #8
HUP does not state that things are random; it just makes a statement about what we can measure.-----------------------------------------------------Don't ever let anybody mess with your amygdala. You might start humping a chair.
 
  • #9
Correct, if you hadexactvalues for everything, and were able to carry out exact computations, you could make exact long term predictions in a chaotic system.Hurkyl
 
  • #10
Great, so HUP cannot turn this theory down.I understand that it is impossible to get measurments that are 100% right, but let's only suppose that we can, would this theory be 'right' ?"No Nou Is Good Nou"--Ichi IchiNote : I Used To Be STaifour
 
  • #11
quote:Originally posted by STAii:Great, so HUP cannot turn this theory down.I understand that it is impossible to get measurments that are 100% right, but let's only suppose that we can, would this theory be 'right' ?"No Nou Is Good Nou"--Ichi IchiNote : I Used To Be STaifourIn a deterministic system, where every thing is known, you could calculate the outcome.
 
  • #12
That's my original idea, 'knowing all the variables', i feel some releif now althought i know this is practically impossible, but only the idea that nothing around you is random makes you feel better for sure."No Nou Is Good Nou"--Ichi IchiNote : I Used To Be STaifour
 
  • #13
Well isn't radioactive decay completely random, where you cannot predict exactly when the next decay will happen. Although it will follow a general pattern over a long term (ie. the halflife).I believe some one time pad keys are created using radioactive decay reading.Aspiring to be mediocre. :|
 
  • #14
quote:Originally posted by Hurkyl:Correct, if you hadexactvalues for everything, and were able to carry out exact computations, you could make exact long term predictions in a chaotic system.HurkylBut that would supposedly be impossible. The uncertainty principle will not allow you to know the exact values of EVERYTHING. You could know the exact position of a particle, x, but not the exact velocity, v, at the same time and vice versa. I know everyone knows that but I was just looking for comments, as usual.MajinVegeta
 

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