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Evolution: Technically Random?

T'ai Chi said:
Take any non-trivial function f, and calculate f(something random). Won't the output f be random?
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Correct me if I'm wrong, but isn't the very definition of a function the set of outputs given a certain set of inputs, such that there is one and only one output for any given input?

If so, the output cannot be random. It is determined by the input. The input may be random, but from the function's point of view, it is just an input, regardless of how it was generated. Thus, we end up with exactly the world we have, despite the fact that the chances against ending up with what we have are astronomical.

(The inputs, in this case, consist of such a huge number of initial conditions that I'm not sure there is any point in discussing it.)
 
Claus said:
No, it can't even be considered stochastic even from the environment angle. The environment influences the process. Is a process that is influenced random?
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I'm assuming there are random factors in the environment. For example, cosmic rays impact the Earth in a way that is random relative to the Earth. Because there are random factors, the environment is a stochastic process.

Hammegk said:
Hmm. Most of it appears anything but random; very highly and precisely ordered in fact.
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Yet, if there are random factors, then the overall process of the universe is stochastic.

T'ai may be mathematically technically correct here, although I'm not entirely sure. But, as many people have said, such technical correctness can be horribly misleading.

And I still don't understand why you care, T'ai.

~~ Paul
 
aggle-rithm said:
Correct me if I'm wrong, but isn't the very definition of a function the set of outputs given a certain set of inputs, such that there is one and only one output for any given input?

If so, the output cannot be random. It is determined by the input. The input may be random, but from the function's point of view, it is just an input, regardless of how it was generated. Thus, we end up with exactly the world we have, despite the fact that the chances against ending up with what we have are astronomical.

(The inputs, in this case, consist of such a huge number of initial conditions that I'm not sure there is any point in discussing it.)
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multi-valued functions may have more than one output for a given input. Though not technically functions, the usage is widespread.

http://mathworld.wolfram.com/MultivaluedFunction.html
 
aggle-rithm said:
Correct me if I'm wrong, but isn't the very definition of a function the set of outputs given a certain set of inputs, such that there is one and only one output for any given input?

If so, the output cannot be random. It is determined by the input. The input may be random, but from the function's point of view, it is just an input, regardless of how it was generated. Thus, we end up with exactly the world we have, despite the fact that the chances against ending up with what we have are astronomical.

(The inputs, in this case, consist of such a huge number of initial conditions that I'm not sure there is any point in discussing it.)
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I think you it's possible to fiddle your way around this.
given the set of inputs I, allow an additional input t, a 'ticker', that increases by one each time the function is called.
If the function varies with the ticker we can call it 'random'.
That is f is random if there exists some t1,t2 such that.
f(I,t1)!=f(I,t2)

The question tai chi posses is then: Is g(I,f(I,t)) random?

Does there exist t1,t2 such that g(I,f(I,t1))!=g(I,f(I,t2)) ?

The obvious answer is; Sometimes yes. Sometimes no.

Edit: Oh, and someone's beaten me to it with a pre-existing work around.
 
T'ai Chi said:
One wonders how nuclear bombs go off.


Who wonders that?
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By your tenets, you. A function based on random variables is random. Therefore, the bomb might go off or might not go off. Nobody can predict the outcome. So you say.


Well, I'd first venture to say the theoretical population geneticists might have an equation or two worth considering. Actually, maybe even three base equations, given that there are three principle forms of selection. Whoa, who would've thought of maybe diving into the research or the textbooks to unocover how it might work.


I'm sure they do.

I'm sure each one would involve some random terms, hence the output would be unable to be predicted with certainty beforehand, hence deserving the title of random.
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Like I said, nuclear bombs involve some random terms, too, "hence the output would be unable to be predicted with certainty beforehand..." You may recognize that quote.
 
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By your tenets, you.


Your response would be stronger if you didn't put words in other peoples' mouths.

I said nothing about nuclear bombs, and I don't "wonder how they go off". I also don't wonder how animals evolve.


A function based on random variables is random.


For non-trivial functions I agree.


Like I said, nuclear bombs involve some random terms, too, "hence the output would be unable to be predicted with certainty beforehand..."


But there certainly are various bomb outputs that one cannot predict with certaintly, for example, the precise effects of one. The strength of delayed effects that can damage for hundreds of years' time come to mind.
 
T'ai Chi said:

By your tenets, you.


Your response would be stronger if you didn't put words in other peoples' mouths.

I said nothing about nuclear bombs, and I don't "wonder how they go off". I also don't wonder how animals evolve.


A function based on random variables is random.


For non-trivial functions I agree.


Like I said, nuclear bombs involve some random terms, too, "hence the output would be unable to be predicted with certainty beforehand..."


But there certainly are various bomb outputs that one cannot predict with certaintly, for example, the precise effects of one. The strength of delayed effects that can damage for hundreds of years' time come to mind.
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Please quote me properly, rather than with colors, etc. I am quoting back to you exactly what you said. Here you seem to be saying that the basic outcome of the bomb is not in question. Do you claim that the bomb is a trivial function of the underlying poisson distributions? If so, please explain with evidence. If not, then the bomb contradicts your universal assertion.
 
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Paul C. Anagnostopoulos said:
T'ai, after all this, I'm begging you to explain why it matters.

~~ Paul
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If people are saying that to call evolution random is false (or worse), yet calling it random can be defended as being reasonable and correct, then I think that is interesting to point out in terms of a logical argument.

You know, something for a dinner table discussion.
 
Well, it is wrong to call it "random." You gotta say "random process" or something.

What people are really saying is "When you say 'evolution is random,' you are incorrect." That is most certainly the case for almost everyone who utters the phrase "evolution is random."

~~ Paul
 

Here you seem to be saying that the basic outcome of the bomb is not in question.


I don't think it is really in question if the bomb goes off or not. But I don't think the occurrance of evolution of an organism is in question either.

As I've mentioned, there are various bomb outputs that cannot be predicted with certainty.
 
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The problem is that calling evolution "random" or a "random process" is misleading even if technically correct. Most people who call evolution random are creationists or people ignorant of evolution, who interperet the randomness to be on par with that of a tornado passing through a pile of debris and forming a mercedes. Evolution is the non-random selection of randomly generating varieties. Natural selection such the opposite of random that it makes evolution a non-random process even though it has a random component.
 
CACTUSJACKmankin said:
Natural selection such the opposite of random that it makes evolution a non-random process even though it has a random component.
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I see what you're saying, but everything I've seen with a random component can be described as random.
 
Sure, I can describe the output of a true random number generator as random, and I can describe a sequence of a million 1s with a 0 thrown in as random, but I'm not doing my listener any great service by equating the two in this manner.

The phrase "hidden agenda" is coming to mind.

~~ Paul
 
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T'ai Chi said:
I see what you're saying, but everything I've seen with a random component can be described as random.
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Everything physical has a random component.

However, most things at a macro scale aren't random. They follow the laws of physics. Those laws may be statistical at their foundation, but the outcome is nonetheless predictable.

So, when you ask Is evolution random?, you need to specify your perspective. From a biological perspective, no, it is not. From a perspective of quantum mechanics it is random, but that's not generally a useful perspective for discussing evolution.

So the answer, for all practical purposes, is no.
 
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