Statistics is the kind of scientific course of study that has appealed to me on certain levels. I was a big baseball fan as a kid, still am, and learned how to do all the math involving batting averages and ERA and so on. Later I studied how the Strat-o-matic game company compiled its realistic baseball player cards and was able to devise my own formulas to make a similar game for myself. This is all pre-computer, of course. Now one could easily use a home computer to do what it took me many, many hours to create back then.
I became an avid reader of Bill James back around 1980 or so. He published the Baseball Abstract which used statistics to analyze various baseball players and strategies to either support or debunk widely held beliefs. Fascinating stuff. His efforts led to the formation of the Society For American Baseball Research and as an enthusiast, I became a sabermetrician. I did publish a paper that evaluated the greatest catchers of the 20th century using some SABR formulations and some work of my own. It may sound boring to you, but a lot of fun for me and some like-minded individuals.
My wife accuses me of being a math brain, since I can do all sorts of calculations in my head. But these are simple add/subtract/multiply/divide functions and frankly I am not all that great at math. I aced Algebra classes but began pulling down B’s as I moved up the ladder to Geometry and Trig/Calculus because I didn’t really find the raw numbers all that interesting. I only took one mandatory college math class and then avoided higher math altogether after that.
Therefore, I am not going to portray myself as a math expert and will depend on the testimony of others to help explore the odds concerning evolution. I does behoove me to lay the groundwork, however, and that will be easy enough.
A common American coin, such as a nickel, has a “heads” side and a “tails” side. Logically, one would think that the odds are 1:2 against a heads flip since half the time one would expect to see tails showing at the end of the flip. Research has indicated that many factors can throw off this perfect ratio of 1:2, including sleight of hand of the flipper. Is nothing sacred???!
Still, discounting biased flippers and the occasionally unbalanced coin, one would expect heads to come up one out of every two flips. Each flip carries the same odds, so for heads to come up twice in a row, the math is 1:2 times 1:2, or 1:4. This ration continues exponentially, so that for a coin to come up heads five times in a row, the odds against that happening are 1:32. You can see that carrying this out would make getting heads, say, 100 times in a row very unlikely. Below is a formula taken from Ion Saliu’s Probability pages:
“The probability of binomial distribution = inseparable events, multiple trials
The formula is also known as the probability of repeated trials. What is the probability of tossing exactly 5 heads in 10 coin tosses? M successes in N trials is yet another definition for this type of probability problems. The formula relies on factorials (!) and combinations C.
BDF = —————— * pM * (1 — p)N — M
(N — M)! * M!
or, using a simpler equation of combinations C(N, M):
BDF = C(N, M) * pM * (1 — p)N — M
BDF = the binomial distribution probability;
p = the individual probability of the phenomenon (e.g. p = 0.5 to get tails in coin tossing);
M = the exact number of successes (e.g. exactly 5 tails in 10 coin tosses);
N = the number of trials (e.g. exactly 5 tails in 10 coin tosses = number of trials).”
I remember reading a study on self-replicating machines that included the work of John von Neumann and others. One source thought that the minimum number of “parts” needed for a self-replicating machine was 800. But his premise was based on several false premises. Recent studies indicate that self-replication begins at a minimum of 500,000 “bits” or components.
One wonders whether such a machine, or an organism capable of doing the same, could have occurred by chance?
By the accepted laws of probability, any event that has a calculated probability of less than 1:10 to the 50th power is considered an impossibility. Scientists throughout various disciplines acknowledge this. It is not a controversial assertion. Controversy enters in when we attempt to apply this number to evolution.
Evolution requires mutations within the genetic code. Without mutations, the genetic code remains unchanged. Within the genetic code of all organisms are numerous “choices” that allow for variation within kind. This makes it more likely that the organism will continue to survive when changes in environment occur. For instance, there is code with the Finch allowing for both larger and smaller beaks. Conditions cause either larger or smaller beaks to be “selected” since the trait best suited to the survival of the bird will tend to survive and mate. Variation within kind is understood and used by breeders to, for instance, make smaller and smaller little dogs that people like Paris Hilton can stuff into their purses. Dogs as fashion accessories!!!!