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Poor explanation of 'random'

  1. Aug 14, 2009 #1
    It seems to me that when 'randomness' is referred to, the explanation is always describing what 'random' behavior is not. I would equate 'random' with: no history, no dependence on intial conditions, no pattern, no predictable order. It only argues that 'random' behavior or outcomes are based on something other than what is listed above. So, my question is: what 'is' randomness, without descriptions of what it is not???
     
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  3. Aug 14, 2009 #2

    Hurkyl

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    In probability theory, a "random variable" is simply a probability measure on some space -- a function that, among other properties, assigns a real number from 0 to 1 to each "event" of the measure space.

    (e.g. one might consider the discrete space {1,2,3,4,5,6}, and the measure P that assigns to each subset S the number |S|/6)



    In complexity theory, the "Kolmogorov complexity" of a string is its shortest representation (according to some reasonable scheme). It turns out (I hope I state this properly) that for any computable property Q, the proportion of incompressible strings that have property Q is the essentially the same as the proportion of all strings that have that property.

    In particular, this means incompressible strings have no "features" that make them stand out from other strings, and so this makes for a good measure of randomness.

    Unfortunately, this system is only really applies in bulk -- it cannot be used in any reasonable way to talk about individual strings.
     
  4. Aug 14, 2009 #3
    Randomness is simply a word that is defined in terms of a negative. There are many such words -- such as "unkind", "antisocial," "atypical"...the list goes on. By definition, these words are defined in terms of the lack of something else. So what?

    Randomness exists mostly only in Utopian statistical theory. The only potential source of randomness so-far known to man is in quantum theory...so this could be used as a positive example of randomness, but it doesn't change the fact that it is impossible to re-define a word that is defined in terms of a negative in terms of positive(s).
     
  5. Aug 14, 2009 #4

    ideasrule

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    Alright, but how about a system that behaves almost exactly like a system that has no history, no dependence on initial conditions, etc? Chaotic systems have such sensitive dependence on initial conditions that, for all practical purposes, they behave like a random system would.
     
  6. Aug 14, 2009 #5
    A random event has no deterministic cause - not just no cause that we know of, but no cause period that can exactly explain the effect.
     
    Last edited: Aug 14, 2009
  7. Aug 14, 2009 #6

    DaveC426913

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    How can such an event occur at all then?
     
  8. Aug 15, 2009 #7
    macro chaotic systems are deterministic in principle, just not in practice. But, this doesn't seem to be 'random' as it is defined here, as future behavior is based on the initial conditions (in chaos theory), it's just not predictable. I think true randomness can have no ties to initial conditions, if it did, and the behavior of the system is dependent on these initial conditions, then this seems to be the cause, and therefore the system becomes determined (in principle).
     
  9. Aug 15, 2009 #8
    If there was a 'how', it wouldn't be random.
     
  10. Aug 15, 2009 #9
    In addition to JoeDawgs response... who said random events occur at all? :)

    Besides many (but not all) quantum physicists, of course.
     
  11. Aug 15, 2009 #10
    Correct... unless you consider that random events may be bound by initial conditions. Events with no definite cause may still be bound by preconditions, even if they are not determined by them. Such situations are proposed by some interpretations of quantum mechanics, for example.
     
  12. Aug 15, 2009 #11

    DaveC426913

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    My point is, it could not occur in the first place. A penny cannot fall - randomly or otherwise - if it has not first been tossed.
     
  13. Aug 15, 2009 #12
    It seems, then, that you believe in deterministic causation in nature. In this case, no event can be truly random. We can still have the word "random" and use it approximately in 2nd order macroscopic statements of cause and effect. We say that a coin flip is random, but it's understood that if we could have complete knowledge of the toss it would be, in principle, possible to determine the outcome ahead of time. This is the classical mechanized world view.

    QM is more fuzzy about random events occurring at the basic physical causal level.
     
  14. Aug 15, 2009 #13

    DaveC426913

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    I believe that the reason for decay of a nucleus will eventually be explainable. If the decay or any other random subatomic event truly had no causal event, then what is to stop it from decaying into multiple hydrogen atoms, or into a pot of petunias? See, there are causal rules around decay; it happens virtually the same way every time. The fact that the time delay (of an individual nucleus) doesn't seem to follow a rule suggests simply that we don't know it yet.
     
  15. Aug 15, 2009 #14
    At the quantum level we have absolutely no idea what forces are at play, and we can't predict what outcome will occur with any level of certainty at all. Arguments can surely be made for an assumption of determinism in nature... but it may be harder to get there than would initially be expected.

    Niels Bohr, based on Kantian ideas of the primacy of classical properties, simply denied that there is any underlying level of determinism to be uncovered. David Bohm, assuming the primacy of deterministic natural laws, came to the conclusion that such laws exist but we can in principle never know what they are. According to Bohm, we can only reveal lower and lower levels of an infinitely recursive reality, but we can never explain anything in terms of the deepest level of reality.
     
  16. Aug 15, 2009 #15

    DaveC426913

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    Agreed. But that is not tantamount to saying there is no causitive agent.
     
  17. Aug 15, 2009 #16
    This is a standard http://en.wikipedia.org/wiki/Argument_from_ignorance" [Broken] If its random, then yes, it could result in a pot of petunias, but thats really not just one random event, its quite a few. The hydrogen thing involves fewer.

    So yes, there could be a pot of petunias floating somewhere around Orion's belt. But there is no frequency to random events, and the universe is big, so the fact you haven't seen it happen doesn't mean much.

    All you've said here is you don't believe in random events.
     
    Last edited by a moderator: May 4, 2017
  18. Aug 16, 2009 #17
    Well, how about this.
    Determinism means a causal event chain. A chain that develops over several stages over a period of time.
    A random event would be an event that has no event chain.
    This would essentially mean it happened instantaneously and that there is no causal process for why it happened.

    Using this definition, is there really any way to understand such an event?
    I would say no.
    I'm not going to try to say that I have all the answers, but it does seem odd to me if such events exist in the universe, either in quantum physics or any other macro/micro level.
    The only way I can see it looking random is if something is injected into our universe from another dimension, or similar, because then the process would not have started in OUR universe.
    But this is of course speculation to the extreme. Just saying.
     
  19. Aug 16, 2009 #18

    DaveC426913

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    Or how about less extreme: simply a causal event occurring in a dimension we do not have access to - a la the higher 4 dimensions of string theory.
     
  20. Aug 16, 2009 #19

    I agree. It seems without a cause to determine (in principle) the outcome, then the outcome can be boundless and without order or structure. The fact that the decay of a nucleus occurs the same in multiple events leads one to the notion that there is a form and structure to the decay and this is essentially what determines it (in principle). However, the cause may never be known. Kind of like Chaos theory. If we go far enough down the causal chain we lose sight of the initial conditions, we know the result is caused by them, but the interactions that brought the result is too complicated to understand or it is simply hidden from our knowledge.
     
  21. Aug 17, 2009 #20
    It would seem that to predict just which atom will decay and when it will decay would assume that each atomic nucleus of a particular isotope is distinctive in some way. This would imply some hidden variable(s) involving nuclear properties. Does anyone have any idea what properties these might be? For example, are there different kinds or combinations of gluons? I think we know the quark structure of nucleons, and afaik, it is the same for all nucleons.
     
    Last edited: Aug 17, 2009
  22. Aug 17, 2009 #21
    It has long been thought that quantum fluctuations at the Planck scale are indeed random and without cause, as the term is usually understood: a necessary and sufficient agent. Presently, the "new determinism" would assume there is a cause for QF. However, unless and until there is a real theory re hidden variables, I don't think we can just assert that all events require a cause.
     
    Last edited: Aug 17, 2009
  23. Aug 17, 2009 #22
    Ah, how quickly science gave up on the idea that its purpose was to uncover causal natural laws...

    "I can't figure out why I'm getting these results!"
    "Screw it. It can't be us. Nature's gotta be broken. My theory describes not only everything that could be known, but everything there is to know. Trust me. I'm that awesome."

    Edit: I'm not disagreeing with you, and I've personally argued for the standard interpretation of QM from the elevated semantic status I think it suggests we give epistemology. I just find the history of the issue to be pretty hilarious in light of the mechanized world view and all previous definitions of what it meant to be real.
     
    Last edited: Aug 17, 2009
  24. Aug 17, 2009 #23
    On another note... this very assertion has been made (and required) by all science ever performed. Science has been the search for the underlying cause. Stopping at any one level and saying "it's complete, nothing else to see here," stops all scientific exploration. The Catholics made the claim that their explanatory framework was complete and look at the wonders that did for science in the years following Christianity's rise to power.

    Unless a theory is deterministic and consistent with all experiments performed, any claims of completeness with regard to the deepest level of reality can only be explained as attempts by the theory's proponents to discredit opposing viewpoints and maintain their own social power.

    (Please note that Niels Bohr explicitly claimed that QM was not complete with regard to the real essence of the manifold in his book published in 1934. He claimed that QM was only complete with regard to aspects of our experience, which he held as prime based on a Kantian view of space-time categories. Claims to the contrary have been inconsistent with Bohr's views.)
     
  25. Aug 18, 2009 #24

    apeiron

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    The quantum zeno effect would seem to be a good argument that QM indeterminism is actually a similar story to the randomness of coin tossing.

    http://en.wikipedia.org/wiki/Quantum_Zeno_effect

    With a "random" event, we are really talking about a global level set of constraints which then leave particular localised outcomes "free". The outcomes are not completely free (no petunias), just free in terms of the global constraints and the degree of control they exert (or rather, do not exert).

    So with a coin toss, we create a binary object. Toss a ball and the outcome will always be vague. The question "which side up?" has no meaning. But a coin is geometry constrained so outcomes will be crisply definite.

    Then we also have to constrain the action of the toss. We must toss it so high and fast that we quite clearly are not controlling its flight.

    So we can see how we are manufacturing randomness by constraining an event of many degrees of freedom - but then with equal global "determination" are making a binary outcome look as much like a free or chance choice as possible.

    Now people can get worried about the micro-level causality. If we knew every Newtonian detail, we could predict heads or tails. But then this would go against the original global constraints spirit of the action. Where what we were attempting to produce was a random toss, not a controlled toss.

    Globally, of course, we would make the coin land head or tails by increasing the constraints around the process. We would toss the coin very slowly with care. Or just place it. And any process of measuring the coin toss so as to predict the outcome would also be a constraints-based tightening of the rules around the process.

    We would not be proving micro-causality IS deterministic, just that causality can be DETERMINED to a very fine degree by global or macro-causality.

    With coin tosses, at a Newtonian level of discussion, this all seems obvious. The two troubling areas are of course QM and chaos theory.

    With QM, the quantum zeno effect shows I feel that global constraints decohere local potentials. So it is not the location that self-determines in a random fashion to decay or whatever. Rather it is the context that shapes the space of what is possible. And nature can be set up so that the QM "coin-toss" is more generally constrained (the decay seems spontaneous and follows a powerlaw - probability is unaffected by passing time). Or it can be more specifically constrained as in the zeno effect.

    It would be interesting if others viewed the situation differently.

    With deterministic chaos modelling, the paradox lies in the idea that completely determined equations can produce random looking outcomes. A lot of micro-scale definiteness can produce macro-level confusion.

    But again, equations are still global level processes. And the kind of equations that work are the ones that can generate the equivalent of a coin-flip of uncertainty over all scales. There is a grain of "error" built into the process to get things started (well, not error but some particular set of initial condions so exact that we in practice could never measure reality with the infinite precision required to obtain the actual value). And then this "error" is forced - via feedback loops usually - to propagate symmetrically across all available scales.

    Anyway, the key to randomness is not to puzzle over an apparent lack of causality at some location, controlling some event, but to look upwards in scale to the nature of the global constraints that obtain. Randomness does not exist in some naked, basic and fundamental way in nature. It only occurs as a feature - a local freedom - within some larger system of constraint. Or rather as a result of what some larger system is not managing to constrain either through choice (human coin tosses) or inability (QM tunnelling, initial conditions measurements).
     
  26. Aug 19, 2009 #25
    I'm not sure what you mean to be honest.. The randomness of a coin toss is a completely subjective assessment due to our inability to understand all the variables involved.
    In the actual reality there is no randomness or freedom for the coin.. I don't understand what you mean by "local freedom?"
    Local freedom in what? In nature?
     
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