I am not a philosophy student but am very fascinated with the chaos theory. It is said that a chaotic
system is not a random system. Also, it explains that a small change in the input could produce a
huge change in the output, hence it being called the 'butterfly effect'. Correct me if I am wrong. My
question is: Every event or action, however small, can produce a specific outcome. Although we're
not able to predict it precisely, there is still a cause and effect situation happening. If that's the case,
does that mean that there are no such things as coincidences?
However, when you say "specific outcome", you are not being clear. Specific in what sense?
Definite? Definitely known? Observable? Predictable? Strictly speaking, it is not accurate, on the
quantum level, at any rate, to say that every action will certainly produce a reaction, because of
quantum uncertainty... zero-point energy, if nothing else. But you are going further than that when you
say that an action produces a "specific" outcome, if by that you mean one unique to an action. Why
should that be true? So when you talk about "cause and effect" situations, you have to be careful.
That being said, yes, chaos theory is a deterministic theory, within the purview of Newtonian
mechanics (although that doesn't have to be the case), and so is a causal one. But,so what?
Newtonian mechanics isn't the last word, right? In other words, chaos theory, a branch of non-linear
dynamics, is a subset of mechanics which is concerned with very complex systems, i.e., recursive
systems. You can find non-linear, recursive, systems anywhere, and you don't have to be Newtonian
to do that, although that's pretty much where it's applied now, as far as I know.
So what does all this have to do with coincidence? Well, I don't have the slightest idea. Perhaps when
you can come up with a definition of "coincidence" which is a mathematical treatment applicable to
physics you might be able to answer this question. But the normal sense of the term "coincidence"
just means something vaguely like a surprising repetition or similarity. Chaos theory has to do with
very hard-core mathematical models, not with feelings of surprise. So your question is mixing
categories of ideas or concepts, like apples and oranges. Chaos theory is simply not relevant to
coincidence, as that latter term is normally employed.
That's a brain-twister. Toss a dime or a dice. The outcome of tossing a fair dime is with necessity
equal probability of heads and tails. But you cannot tell what the outcome will be in a single toss. So
what is it — is it necessity or is it coincidence? That's explains the "butterfly effect": Two or more very
large developments are of "nearly exact" equal probability as is a knife standing on it's point: There
must be any one outcome, but neither before nor afterwards can anybody prove what outcome there
will be, since by sheer logic two or more or an infinity of outcomes are likewise probable, neither
having any provable priority. What one has to accept then, is the necessity "by definition" of equal
chances of "head or tail", which has nothing to do with the "uncertainty principle" or any physical
effect but with "the logic of symmetry". By definition "symmetry of form" includes "symmetry of
behaviour and outcomes". You cannot evade that conclusion. So the paradox is: Statistical outcomes
are by necessity unpredictable.