# Talk:Law of Large Numbers

## The Law of Large Numbers is a Counterexample to the Theory of Evolution

You can't apply the Law of Large Numbers to a time series with a trend. That's just bad math, not a counterexample! AugustO 20:11, 14 March 2012 (EDT)

The Theory of Evolution, as it is commonly taught, does claim that some new species arose due to random fluctuations.
Man. This is so wrong I don't even know where to start. So I'm not going to because I'll get 90/10'ed out the door. It's like an infinite manifold of wrongness. Just know this, you are applying probability theory -a theory you only partially understand- to evolution, a theory you completely don't understand. --JoshuaB 20:48, 14 March 2012 (EDT)

I will explain why I believe that the law of large numbers is not a good (and probably, to be honest, misleading) counterexample to evolution: Evolutionists would argue that the hypotheses of the law of large numbers (that the random variables are independent and identically distributed) are not satisfied. I understand that the concept of i.i.d. is technical and difficult to explain, but it is nevertheless essential to the theorem. As an example, take the sample space {H,T} corresponding to flipping a fair coin once, and for each positive integer i, let Xi equal 1 if the outcome is H and 0 if the outcome is T. In other words, if the outcome is H, then $X_1 = X_2 = \cdots = 1$, and if the outcome is T, then $X_1 = X_2 = \cdots =0$. Note that $X_1, X_2, \ldots$ are all Bernoulli random variables with parameter $p=\frac{1}{2}$, so they are identically distributed. However, it is clear that the law of large numbers does not hold, as $\frac{X_1 + \cdots + X_n}{n}$ is always either 1 or 0. Therefore, independence is an essential hypothesis. In general, time series are not independent (imagine the Dow Jones index where the closing values are always independent and seeing the index go from 13000 one day to 175 the next!).

Random variables must be functions to the real numbers, so it is ambiguous what the statement "populations of species can randomly drift away from their 'mean'" is intended to mean without a quantification. Nevertheless, using height as a characteristic to measure for the sake of argument, it is clear why the law of large numbers does not hold. If we observe the height of a randomly selected member of a population each year, the observations are random variables. Nevertheless, evolutionists would provide two explanations for why the law of large numbers does not hold in this experiment. First, evolutionists would argue that factors like genetic drift allow for the events of one time period to affect the height distribution of a population in future time periods. Second, evolutionists would suggest that trends in random height suggest precisely the conclusion that the distribution of population heights is changing with each year, indicating that the random variables are not identically distributed. This suggests precisely the conclusion that the population is changing over time. By the way, looking at the statement of the weak law of large numbers, it is clear that if the random variables are not identically distributed (especially if they do not have the same mean), then the "mean" μ in the statement of the theorem is completely meaningless, mathematically. GregG 23:06, 14 March 2012 (EDT)

Folks, if it's so obvious that the Law of Large Numbers does not disprove the theory of random genetic drift -- which is central to the theory of evolution -- then it should be easy to explain in a few sentences free of jargon. Right?--Andy Schlafly 23:17, 14 March 2012 (EDT)
I'll give it a try. The law of large numbers requires the sample observations (such as heights) to come from the same distribution. Trends are seen in the heights over time. Evolutionists would argue that this may suggest that the distribution of heights in the population (and thus the population) is, in fact, changing over time (which would make the law of large numbers inapplicable to these observations). GregG 23:24, 14 March 2012 (EDT)
Andy, you ever hear of something called a "one-way hash function"? It's a cryptographic (or loosely mathematical) term for something that's easy to solve in one direction, but a real pain to solve in reverse. Sort of like cubing versus finding the cube route. Anyway, you're laying out a one-way hash argument. Your statement is simple, but the disproof would require more effort than I'm willing to expend. But in brief, the human race may have a mean height, weight, skin tone... or whatever. If you take measurements at random intervals you will find that the mean is gradually changing, not that populations are gravitating back towards the original mean. And what do we call a change over time? --JoshuaB 23:33, 14 March 2012
How about this for a short explanation. Microevolution (which has been observed to exist in the wild) relies on genetic drift. Since genetic drift it known to happen in microevolution the law of truly large numbers is either false, or it does not apply. --HHB 18:15, 15 March 2012 (EDT)

Hello. It is very easy. Law of large numbers requires that $X_1,X_2,\dots$ are independent (i.e. every finite subset of them is independent). Yet, a child has usually similar properties to an adult. Therefore Xi + 1 is not independent of Xi. It does not mean they are perfectly correlated - a child might sometimes be different from its parent. But they are definitely not independent, and therefore you cannot use the law. Using a mathematical theorem when assumptions are not fully satisfied will easily give you absurd conclusions - think what happens if you to use Pythagorean theorem in an acute triangle. --Cipe 15:54, 17 March 2012 (EDT)

The Law of Large Numbers establishes that populations revert to their averages over time. Children of extraordinarly bright or athletic parents are, on average, not so extraordinary. Nothing said above disproves this logical truth. Darwin and other founders of evolution were weak in mathematics and probability, and their reliance on random genetic drift is nonsensical as illustrated by the Law of Large Numbers.--Andy Schlafly 00:36, 18 March 2012 (EDT)
Genetic Drift wasn't described until the mid-1900s. How can Darwin have been reliant on it when proposing his theory? --RedGoliath 11:58, 18 March 2012 (GMT)
OK, fine: the other Darwinists who relied on random genetic drift (presumably to try to fit the evidence to Darwin's theory) "were weak in mathematics and probability, and their reliance on random genetic drift is nonsensical as illustrated by the Law of Large Numbers."--Andy Schlafly 10:58, 18 March 2012 (EDT)
Andy, please consider teaching a course on mathematics and probability (or science in general), explaining systematically and in detail where lame-stream science goes wrong. I admit that I am confused right now, having been indoctrinated by liberal science classes all my life, and would enroll immediately. We need the arguments to fight Darwinism effectively! Think about how we, your students, could act as multipliers! I am sure that you would do much better than the Question Evolution campaign, which I admit I am not a fan of. --FrederickT3 14:06, 18 March 2012 (EDT)
When I did teach (offline) a science class and pointed out the many flaws in the theory of evolution, one family asked me for additional copies of an inexpensive course book entitled "Evolution Cruncher." He then passed the book out to his fellow scientists at work, and it opened their eyes to all the lies they had been taught in school. There were astounded ... and grateful. My own experience in waking up to the lies taught to me in school was similar.--Andy Schlafly 15:03, 18 March 2012 (EDT)
"Children of extraordinarly bright or athletic parents are, on average, not so extraordinary." Yes. But I think that they are on average better than children of very weak people. And this is enough to show that properties of children and their parents are not independent. If they were independent, a child of two athletes would have the same distribution as child of two physically feeble people. As another example, genetic diseases exist, and a child of ill parents has larger chances to be ill as well.
Do you accept microevolution? I think your interpretation of law of large numbers disproves also microevolution. Regards, --Cipe 19:40, 18 March 2012 (EDT)
No, I don't think microevolution entails random genetic drift. Perhaps you could define the term - if it means "evolution" as that term is traditionally understood, then it is not true for the same reasons evolution is not.--Andy Schlafly 21:09, 18 March 2012 (EDT)
How does microevolution happen if not for genetic drift? --HHB 21:35, 19 March 2012 (EDT)