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Firstly in the scientific sense, random means: lacking predictability.Quote:
Originally Posted by bbshriver
But aside from that, evolution kind of does have an aim or purpose namely, to produce an organism better adapted to it's environment than it's ancestors. This "aim" is determined by the evolutionary process itself and if you want to think of the process of evolution as a sort of "god" that's peculiar but up to you. However, it certainly doesn't require any kind of intelligent designer.
:tu nice :tuQuote:
Originally Posted by Jimbo
Yes, I think it is misunderstanding. Scientific terms are very precise. For example a scientific theory is not 'just a theory' term used in common language, with the meaning that it may or may not be true. In science this is called hypothesis. A theory is something that has predictive power in a well defined domain.
A common way for development of science is to apply the same rules that can predict stuff to outside the domain of their established applicability.
If they still have predictive power, you've just expanded your understanding.
If not, it doesn't mean that your theory is wrong in its original domain. It means that it is restricted to it and you need something else for the new one. A phenomenon is considered understood in science not when you know who created it, but when you can explain it in terms of other, simpler phenomena and be able to predict what is going to happen if such and such happens. The modern understanding of nature, is that everything is probabilistic, i.e. the only observable knowledge is statistical.
You can't guarantee that when you point a flash light at me the photons will end up on my retina every single time. You can only predict the probability of it and then make enough experiments and verify that the ratio of the ones who end up there and the ones who don't match your theoretically calculated number.
That's why no reasonable scientist will have problem with a religious belief that God created it all the way it works. That doesn't explain anything and in scientific terms is a completely empty statement.
For example "And God said, Let there be light: and there was light." has no scientific value whatsoever. Democritos's view of light is quite not the same as that of Newton, whose wasn't at all like the one of Einstein, whose wasn't the same as the one of Feynman either. Of course, the reason you can use a cell phone or the internet is Feynman's quantum electrodynamics. I don't know if you would consider it an 'explaination' of the phenomenon light, but it can certainly predict what will happen with any electromagnetic radiation including light under any condition it has been observed so far.
In other words, God saying the light into existence may be nice poetry or the way it happened, but it's irrelevant to understanding how the light propagates inside a wave-guide. Perhaps God made an atheist understand how light works, so that other men can make waveguides. Or may be the atheist understood it by the power of his own intellect. At the end of the day it's everybody's personal choice whether to believe in God or not and if yes in which particular one.
So, yes, there is a lot of misconception about science, scientific methods and proper terminology and passing hypothesis like 'intelligent design' as 'scientific theory' in high school is not going to improve the situation. I have no problem whatsoever with people being taught intelligent design, as long as it is labeled properly.
Would you be happier with "the same evolutionary process that gave rise to monkeys also gave rise to man"?Quote:
Originally Posted by Russel Baldridge
And thus "Expected Value" has no meaning?Quote:
Originally Posted by trewornan
I'm not entirely sure I understand the question but certainly a random variable would not have an Expected Value, that doesn't make the phrase meaningless - just not applicable.Quote:
Originally Posted by ScottS
Most random variables (r.v.s) have an expected value defined as its first moment. Those random variables that do not (e.g. a Cauchy r.v.) usually do not have one because the integral or sum defining its first moment is not defined mathematically (e.g. non-finite integral).Quote:
Originally Posted by ScottS
The random variable that arises from throwing a (fair) die and recording the number on the upper face is usually how most intro. probability courses explain it. If X denotes the r.v., it can take values 1, 2, ...., 6, each with probability of occurrence on any one throw of 1/6. So 1/6th of the time we'd expect to get a 1, 1/6th of the time a 2 and so on. The expected value of X is therefore 1/6(1+2+3+4+5+6) = 21/6 = 3.5. When the r.v. takes any value in a continuum (as opposed to a discrete or countably infinite set) the sum becomes an integral.
So anyway, just because something is random does not mean we can't do anything with it.
James.
I see what you mean. But the predictability you're talking about applies to the distribution of results not the individual results themselves. Each individual result still lacks predictability, you don't know what value each roll of the die will produce because it's random.Quote:
Originally Posted by Jimbo
This is precisely what I was talking about with regard to evolution. The individual mutations may be random the overall process and end result are not.
I think I know where this conversation is going. I'll get my cat, you make the box and somebody call Schroedinger for instructions. :D
Sure, but that is basically what I said, and then said that it was being misinterpreted. What's your point?Quote:
Originally Posted by ScottS
(can't tell if your trying to correct me or make a snide remark)