Kleinman writes:
quote:
If you want to peer review my work, you had better have a good understanding of probability theory. Here's the short answer why the theory of evolution is not true, it's the multiplication rule of probabilities which makes the theory of evolution not true. For those who don't understand probability theory, it takes a much, much longer answer. It requires teaching you probability theory and how to analyze a stochastic process.
Congratulations. I'm a mathematician. My concentration was in numerical analysis (which includes probability and statistics). Rest assured that I will understand most everything about probability you care to name.
I dare say that you have no idea what a stochastic process is. For one thing, a stochastic process is an evolutionary one. One of the simplest examples is that of the Markov Chain. It is a probabilistic scenario in which you have a state that can change with a probability for each resulting state that is solely based upon the current state, not any of the previous states. It describes completely independent variables. Roulette is a good example. If you have $500 and bet on a particular number, you will either win or lose. Your odds of winning or losing are not dependent upon anything that happened previously (assuming a fair game). It also doesn't matter how you came to have $500, whether you started with that amount, worked your way up to it, or have lost your way down to it.
It seems you have confused many aspects of probability. To help us determine where you're starting from, I'm going to ask some questions. I hope you will answer them honestly.
You have a standard deck of 52 cards. You randomly choose a card.
What is the probability of having drawn the Ace of Spades?
What is the probability of having drawn an Ace?
What is the probability of having drawn a Spade?
What is the probability of having drawn a black card?
What is the probability of having drawn a card?
What is the probability of having drawn the Ace of Spades given no information?
What is the probability of having drawn the Ace of Spades given that it is an Ace?
What is the probability of having drawn the Ace of Spades given that it is a Spade?
What is the probability of having drawn the Ace of Spades given that it is a black card?
Yes, in the case of independent events, you multiply the probabilities. Rank and Suit are independent variables for cards and thus, to determine the probability of a card being drawn, you can determine it by multiplying the probability of having drawn that Rank by the probability of having drawn that Suit.
What makes you think that the evolutionary history of a population is based solely upon a series of independent events? Evolution is not a Markov Chain. What happens next is highly dependent upon what came before. Suppose you have a bin with colored balls in it, red and blue. There are 7 red balls and 4 blue balls. You reach in and draw a ball and set it aside. You then reach in and draw a second ball. What is the probability that the second ball is red?
That very much depends upon the color of the first ball you drew. There was a 7-in-11 chance of drawing a red ball the first time. If you did, then there is a 3-in-5 chance that the second ball is red. If the first ball was blue, it's a 7-in-10 chance.
Now, the chance of drawing two red balls in a row is found by multiplying the probabilities of drawing a red ball the first time by drawing a red ball the second time, but that isn't what we're asking. We're asking what the probability is of the second ball being red and you can't determine that without knowing what happened with the first one.
Do you understand how the game Yacht works? You try to roll certain combinations of dice. You have five of them and you roll them all at once. You can then choose certain ones to re-roll (possibly all of them) in an attempt to achieve the specific combination you wanted. So what is the possibility of rolling all dice the same number on the first roll? What if you can do this choose-and-reroll process three times? If you already have four 5s, how difficult is it to roll a fifth 5?
If you could be more specific about what you think is amiss in the way probability is being used in evolutionary theory, it would be helpful for us to figure out what you're talking about. After all, evolution happens to populations, not individuals, and population biology is all about statistics:
Suppose you have a single-gene trait with two alleles with perfect dominant/recessive expression. If you are homozygous for dominant allele or heterozygous, you display the dominant trait. Only if you are homozygous for recessive allele do you display the recessive trait and you always do if you are homozygous recessive. Suppose the current rate of recessive display is 1-in-1,000. Suppose that those who display recessive trait are sterile and cannot reproduce while those who display dominant trait (either homozygous dominant or heterozygous) have no difference in reproductive capability.
How many generations would need to pass in order to reduce the appearance of recessive trait from 1-in-1,000 to 1-in-1,000,000?
What is the value for p? What is the value for q?
Rrhain
Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.
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