Re: Randomness
- From: Leonard Evens <len@xxxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 17 Nov 2005 10:09:44 -0600
Kippers wrote:
> John Bode wrote:
>
>>The word "random" gets tossed around a lot on t.o., and I just want to
>>make sure I'm understanding and using the term as intended.
>>
>>An event is random if previous events do not affect or predict future
>>events. A coin toss is random because previous tosses do not affect or
>>predict the next toss (assuming a fair coin, anyway). Tossing 50 heads
>>in a row does not change the probability that the next toss will be
>>tails.
>>
>>Genetic mutations are random because previous mutations do not affect
>>or predict future mutations (e.g., a deletion of a nucleotide does not
>>change the probability of a future deletion in the same region).
>>
>>Selection is not random because previous selections *do* influence
>>future selections. The composition of the population changes with each
>>generation, which changes the probability of a particular trait being
>>passed on.
>>
>>I've noticed that some Creationist arguments seem to confuse randomness
>>with probability, notably the "tornado in a junkyard" analogy.
>>Chemical reactions are random, but not all possible reactions are
>>equally probable.
>
>
> I would say there is no such thing as ultimate randomness, we just call
> something random when we have no chance of predicting the outcome or no
> understanding of the mechanisms involved in determining the outcome. A
> coin toss is not really random, it depends on the coin itself, the air
> it is tossed in, the way it is tossed etc, there are so many factors
> involved that we cant predict which way it will land so we just call it
> random.
>
The term 'random' has a fairly precise meaning in the area of
mathematics called probability and statistics. Even so, there are some
subtleties. But its use more generally may be quite different. A
comprehensive discussion can be found at
http://en.wikipedia.org/wiki/Random
One confusing thing is how we can describe a phenomenon which is
completely predictable in principle as random. For example, according
to Newtonian mechanics many phenomena are completely predictable based
on initial conditions. In practice, we can never know the initial
conditions accurately enough to make the predictions and even if we did,
we can't do the calcuations accurately enough anyway. So such phenomena
are in practice unpredictable in detail, although they may be
predictable in broad characteristics. When can we say such a system
is random? This is a question which is still an active area of
research. One criterion is that its statistical behavior looks like
that of a truly random system following one of the standard probability
distributions. A similar example is the (pseudo) random number
generators used in computer programming. These are usually based on
fixed algorithms so the results are completely determined once one
specifies a seed to start. But for good random number generators the
statistical distribution of the numbers produced comes close to that
expected from a truly random process following some standard probability
distribution such as the uniform distribution or normal distribution.
In philosophy/theology, the question of free will and how it can be
consistent with God's foreknoweldge is a vaguely related question.
Under quantum mechanics, it gets more complicated. Quantum mechanica
theories tell us how a mathematical construct called a wave function
propagates. The result is again completely determined by initial
conditions and related parameters. But if you make measurements, the
results vary following a probability distribution based on the absolute
value of the wave function. So the theory is deterministic, but
measurements are random. Of course that doesn't mean they are
completely unpredictable since they do follow statistical laws.
Predictions made from modern quantum mechanics are among the most
accurate known to science, which belies the identification of randomness
with being totally unpredictable. Just how the deterministic wave
function produces random measurements has been a bone of contention from
the beginning of quantum theory. There are a variety of solutions, but
none are entirely satisfactory. Also, since physicists have yet to
produce a theory combining gravitation with the other forces, it is
possible that such a theory may change how we think about the problem.
Biology is seldom accurate enough to be considered deterministic in the
sense of Newtonian mechanics. That is, we can often predict broad
general features, and certain things like what can happen to DNA are
severely retricted by structure. But statistical theory has been used
extensively for population biology and also for tracing origins via DNA
analysis. The issues raised above about theoretical predictability vs
"true" randomness, I think, are moot.
.
- References:
- Randomness
- From: John Bode
- Re: Randomness
- From: Kippers
- Randomness
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