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Author
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Topic: Randomness Understood
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Danpech
Member
Member # 163
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posted 31. May 2003 02:22
When you watch the sunset, you are not looking at the sun. You are looking at light from the sun.
What is randomness? I've come to the view that pure math is not the issue.
Rather, what is the perception of randomness?
Do you see the difference?
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I haven't kept up on the debate, so I don't know if I'm saying things that have already been said. My idea is that randomness is a relative thing: it depends on what you are after. It seems to me that I gain the perception of randomness in the first place only because of things that I have not identified and that do not of themselves already fit with my utilitarian purposes. A huge, 'random' pile logs may be very complex, but, unless we have certified that its organization cannot be reproduced by any algorithm, then I suppose we should assume that it is not (not) mathematically random. It is random only in the sense that it does not suit our needs: we want a log home. For the beaver, he does not care so much about the exact placement of each log; he just needs a certain over-all effect.
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A baby sees design in his mother's face, but why? Because he has the sense that relevance is everything.
[ 31. May 2003, 02:34: Message edited by: Danpech ]
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warren_bergerson
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Member # 262
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posted 31. May 2003 07:13
IMO, there are at least two clearly distinct concepts of randomness- one metaphysical and one scientific. The metaphysical concept of randomness essentially means ‘we don’t know’. Using the metaphysical concept, an event is ‘random’ if we don’t know what is going happen. The metaphysical concept of randomness is equivalent to indeterminacy.
The scientific concept of randomness, or more precisely the scientific concept of randomness used in formulating valid predictive theories, is much narrower. As used in rigorous scientific theory construction, randomness means the outcome of an event is predicted by a definable probability distribution. The result of a coin flip, the location of an electron in atom are ‘scientifically random’. The next book to be written by Lawrence Block is metaphysically random.
The immediate ‘problem’ with the concept of randomness is its use in neo-Darwinism. Originally, ‘random mutation’ was intended to mean scientifically random. As originally envisioned, if you start with a specific genetic then there exists a definable probability distribution of mutations which could occur. The original conceptualization suggested that this random probability distribution contained a very large number of possible mutations.
In actual practice, and under normal conditions, these mutational probability distribution contains very few members. If we recognize the impact or ‘error correction mechanisms’, the ‘random mutation’ probability distribution for many genes under normal conditions contains no members. For many genes there are no mutations that will survive the error correction process. for many other genes, there are only a very small number of mutations that survive the error correction process. In general, the probability distributions associated with ‘random mutation’ does not contain sufficient diversity to permit evolutionary change.
There are a number of methods of addressing this issue. The approach used in modern evolutionary theory, apparently, is to abandon the scientific concept of randomness in favor of the metaphysical. If we don’t know what mutations can occur, then, the argument appears to go, we can argue that the mutations needed to produce evolutionary change ‘COULD’ occur and ‘COULD’ be made dominant by natural selection. The use of the metaphysical concept of randomness makes it impossible to falsify a theory, but it also makes the theory non-scientific.
There are scientific techniques which can be used to address the role of mutation in genetic evolution, but they involve viewing mutations as controlled non-random events.
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Rex Kerr
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Member # 632
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posted 31. May 2003 19:34
While I agree with most of Warren's comments, I'm not sure why he states that a probability distribution must be definable in order to have scientific randomness. If he means only that in theory such a distribution exists, then the statement is not controversial. However, if he means that it must explicitly be defined, then I disagree.
Granted, if you only postulate that some probability distribution exists, your theory has less predictive power; if you can't narrow down the possible distributions, you're pretty limited in your explanatory power. For example, the lab I'm in has done behavioral experiments on egg-laying patterns; these patterns are close to linked Poisson processes, but they are not quite; despite not being able to precisely define the distribution, we still can draw important scientific conclusions from the fact that the distribution is not periodic, Gaussian, single-Poisson, etc.. Movement speeds show an even less well-defined distribution (vaguely log-normal), yet here too we can draw important conclusions, make predictions, etc..
That being said, I'd agree that one of the best scientific answers to "what is randomness" is that it is a measurable quantity that is picked from a probability distribution function. (I.e., an infinite number of measurable events would yield a density of events at each value equal to that of the p.d.f..)
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warren_bergerson
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Member # 262
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posted 01. June 2003 09:37
In order to construct a predictive stochastic hypotheses it is necessary to ‘assume’ that the relationship being described has a definable probability distribution. To actually generate stochastic predictions it is necessary to actually define, or at least approximate, the probability distribution. As Rex points out, the fit between the observed data and the ‘assumed’ distribution may be imperfect. These deviations can be characterized as noise.
Non-scientific abuses of the concept of randomness arise when the assumption of randomness is used where the evidence does not support the existence of a definable probability distribution. It will be noted that an set of ‘cause and effect’ observations will define a probability distribution. For any defined probability distribution you can ‘predict’ that future ‘cause and effect’ observations will be compatible with past observations. However, because it is possible to comply with the form of the ‘predictive stochastic hypotheses’ does not mean that sound or valid hypotheses has been constructed. If the evidence does not support the assertion that the observed distribution is repeatable, or is likely to be repeatable in the future, then the claim of sound predictive stochastic scientific hypotheses is unjustified.
Scientific randomness means that we can not predict the outcome of a specific occurrence, but we can reliably predict the probability distribution of a set of outcomes. In the absence of a definable probability distribution, we are left with the metaphysical ‘We don’t know’ randomness.
It is also important to note that not all ‘we don’t know’ random relationships will necessarily translate into stochastic relationships given enough knowledge or data. We don’t know or we can’t predict relationships may also turn out to be dynamic, where one set of conditions produce one deterministic result or probability distribution and a change in conditions produces another deterministic result or probability distribution.
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Danpech
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Member # 163
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posted 03. June 2003 02:37
The randomness I was thinking of was mostly that of static examples, such as the pile of logs. It looks random because its state is not organized to any specifications that serve us. Partly, then, this randomness is organism-specific. If a particular complexity does not serve any of the interests of a given organism, then that complexity is perceived by that organism as random (the standard coin-flipping practice, for instance).
But, this kind of randomness allows that there may be some complexities that do not serve any organism. For what little I know, it seems to me that the intersection of the patterns of different kinds of organisms, where the different organisms do not depend directly on each other for their survival, produces complexities, as by-products, that do not serve the interests of any of these organisms.
If all this is true, then there is presented to us a certain and objective distinction between intelligent and non-intelligent complexities. Further, it gives intelligent agents a sort of 'purpose' that they otherwise would not have, and which, in effect, makes them part of an irreducibly complex system that itself makes the statement, "There is a fundamental, though a very certain related, difference between teleological and non-teleological stuff." To say that there is no true, purely mathematically 'random' complexity (no complexity that cannot be defined by some algorithm) does not necessarily imply that life is the product of non-teleological entities. It may imply just the opposite.
To argue that teleology is not fundamental is to grant a teleological entity (oneself) as the objective judge.
[ 07. June 2003, 01:22: Message edited by: Danpech ]
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Mike B
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Member # 512
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posted 30. June 2003 19:57
There are events that are, to the best of our current understanding, random in that while in aggregate they the distribution can be predicted, individually they cannot. Radioactive decay is one: pair particle production is another.
There is a much larger class of events in which, if sufficient information about initial conditions is available, are individually predictable, but for which sufficient is seldom available. For example, if one started with a deck of cards in a known order, and correctly described the changes of position caused by every cut and shuffle, one would know what card was on the top. If, however, one did not know the initial configuration and did not know how the relative positions of the cards changed through shuffling, I contend that the process produces a random result. The same can be said about the throw of dice or the flipping of coins: If all the factors can be known to a fine enough level, the result is not random, but deterministic. If, as is usually the case, the information is not and possibly cannot be captured, the result is random.
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mturner
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Member # 190
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posted 01. July 2003 00:10
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Not that it should matter to anyone, but IMHO, the concept of 'random(ness)' is very different, depending upon whether you are referring to possible outcomes in the future, or to actual outcomes in the past.
You cannot understand actual outcomes in the past using the methodology for discerning possible outcomes in the future. That is, probability math only applies to possible future events, and is useless when applied to actual past events. Simply because you can only guess at the initial conditions which preceded a past event, whereas the initial conditions for a future event are present in the 'now', and may be discerned, weighed, and factored in.
In regard to actual past events, an event may be either random (irregular, anomalous, chaotic), or determined (regular, repetitious, lawful). Predictability does not enter into any understanding of a past event. It is possible, however, to empirically determine, by trait comparison, which events are anomalous, irregular, chaotic (random), and which are regular,repetitious, law-abiding (determined). Random or determined, actual natural events are always caused. The difference being that for random events the causes cannot be determined, post hoc, whereas for a determined event the causes could be so determined, whether they have actually been discovered and tested, or not. Science, including biology, is, or should be, the study of determinable events. Anomalous past events with indeterminable causation ( 'random' occurences) should not concern science, except for purposes of comparison. That is why 'randomness' is non-explanatory and non-scientific when applied to past events. It means nothing more than the superstitious cry, "It just happened, that's all!!" Which is an appeal to ignorance and the irrational. Magic, if you like.
mturner
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Mike B
Member
Member # 512
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posted 01. July 2003 15:12
quote:
Not that it should matter to anyone, but IMHO, the concept of 'random(ness)' is very different, depending upon whether you are referring to possible outcomes in the future, or to actual outcomes in the past.
I think that depends on the type of event contemplated. If one is considering a roulette wheel, for example, an examination of the results in the past can be used as a guide to predicting whether the results in the future will be random (assuming the initial conditions of each throw of the ball are effectively the same). To predict how much of a particular radioactive material in a particular sample will decay in a future time period we have to look to the decay of that material in the past.
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You cannot understand actual outcomes in the past using the methodology for discerning possible outcomes in the future. That is, probability math only applies to possible future events, and is useless when applied to actual past events. Simply because you can only guess at the initial conditions which preceded a past event, whereas the initial conditions for a future event are present in the 'now', and may be discerned, weighed, and factored in.
I see two problems with that statement: First, one can assume initial conditions for past events, and then analyze past results to see if they support (though not prove) those assumed conditions. The second is that the initial conditions of a future event may well not be any better known than those of a past event. Even if it is theoretically possible to measure all the factors that will impact what number a pair of dice will show on the next throw, in actuality that is unlikely that they will be. It is not even necessarily certain that you even know what all the factors are, let alone can or will quantify them. The net result is that the last throw of the dice and the next throw of the dice can be treated the same mathematically.
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In regard to actual past events, an event may be either random (irregular, anomalous, chaotic), or determined (regular, repetitious, lawful).
There are events that are random individually, but deterministic collectively. Radioactive decay is one example. Germination of seeds is another. There are also events in which some of the factors are random and others are deterministic.
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Predictability does not enter into any understanding of a past event.
Predictability may not (or may) be an aspect of understanding whether or not a past event occurred. I submit that it may well be important in understanding how that past event relates to other similar events, both past and future.
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It is possible, however, to empirically determine, by trait comparison, which events are anomalous, irregular, chaotic (random), and which are regular, repetitious, law-abiding (determined).
Or if they are random events that follow regular patterns at some level or another.
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Random or determined, actual natural events are always caused. The difference being that for random events the causes cannot be determined, post hoc, whereas for a determined event the causes could be so determined, whether they have actually been discovered and tested, or not.
I would contend that the causes (or perhaps better, factors) of lightening striking a particular building in the past can be at least as well determined as for many events far less random in nature.
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Science, including biology, is, or should be, the study of determinable events.
Why should it be so limited?
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Anomalous past events with indeterminable causation ( 'random' occurrences) should not concern science, except for purposes of comparison.
But how do you know if the causation is indeterminable until you have tried really hard to determine it (them)?
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That is why 'randomness' is non-explanatory and non-scientific when applied to past events.
It may not be explanatory, but it may be descriptive, at least for the data available and the current understanding of the event.
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It means nothing more than the superstitious cry, "It just happened, that's all!!" Which is an appeal to ignorance and the irrational. Magic, if you like.
It does, however, have at least as much predictive power as resort to non-detectable causers has.
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