Saturday, March 11, 2006

How many grandmothers do you have to go back till you get to eve?

I was laying on my sofa today while my daughter was watching an extremely annoying kid's show, when I realized that it would not be hard to figure out how many generations back you have to count to get to the first homo sapiens. The answer shocked me and my wife.

If we say that on average there are 4 generations per 100 years, and human beings have been around for 200,000 years:

(200,000/100) * 4 = 8,000 generations

This can help explain why there isn't much diversity in human populations. In fact, there is more diversity in one small tribe of chimps in the jungles of Africa, than there is in our entire species. This is but one factor to take into account to explain our variation riddle, I'll save the rest for another post.

Friday, March 10, 2006

An Improbable Universe

This is the first time in a while that I've felt like blogging. So here's another entry for my die hard fan (Love you Mom!!):

I had to choose as the url for this blog because somebody already took consilience, the title of a book by biologist Edward O. Wilson which has been a big inspiration for me. So far I haven't explained what is meant by "improbable universe". For this, I will refer to Richard Dawkins's excellent analogy of the improbable occurence of a hurricane blowing through a junk yard and by chance assembling a 747 from all the parts laying around. The arrangement of matter in living systems is so improbable that there has to be some reason for it. Some people would see this as proof of god's creation, and others would say it is proof of evolution through natural selection, and still others would say that it is god choosing natural selection as his/her/it's tool for increasing the complexity of matter. I see this as proof that given enough time, all the things that are possible, however improbable, will happen.

What is the probability that the circumstances that transforms subatomic energy into matter? It must be probable because it happened. At this level of organization, subatomic particles don't have that many different behaviors. 2 or 3 at the most. Let's say that energy forming into matter requires a long permutation (order matters!) of these behaviors. How long does this hypothetical permutation have to be until it becomes impossible for this universe to exist as anything but subatomic particles? My guess is roughly 1 - the sum of all subatomic particles in the universe.

If we apply elementary probabillity theory to this stage in the evolution of the cosmos as a method of finding out how many possibillities could arise we would get 10e1000000000000000000000000000000...^3 possible outcomes. Even if the probabillity that matter would form is less than a millionth of a percent, it is still a small subset of the number of possible outcomes for this universe.

The probabillity that life would arise is smaller than that of matter forming from energy because once matter is formed the number of different behaviors increases by orders of magnitudes. Then once replicators like DNA start replicating the amount of total behaviors of all substances in the universe grows to almost infinity.

It is safe to say, that for each new level of organization in this universe, the amount of behaviors possible increases on scales we cannot imagine. If we abstract the universe into two components, actors (A) and behaviors (B), we can say that all the possible outcomes for this universe can be expressed as A^B. We can then express this iteratively to describe how outcomes increase as we move to higher levels of organization:

L = level of organization
N = number of possible outcomes

N[L+1] = A[L]^B[L]

So the probabillity (P) of any given outcome at any given level of organization can be expressed something like:

P[L+1] = 1 / O[L]

This is VERY simple math. And to tell you the truth, you now have seen nearly all of my paltry math skills. But what I'm hoping is appearent, is that for every new level of organization, the probabillity of the universe being what it has turned out to be decreases. So the Universe as we now know it, is the result of stacking statistical outliers on top of eachother.

If you read this and disagree, please post a reply. I'm pulling stuff out of my ass here. Set me straight!

Explorer Destroyer