2009-02-17

Darwin's theory - the mathematical argument

Charles Darwin is perhaps one of the most influential scientists in the past 300 years. The others include Newton and Einstein. The reasoning behind Darwin's theory can explain phenomena observed in many fields in this world, including even modern business and finance.

For example, the evolution of the players in an industry mimics the various species in a habitat where new species are evolved and the fittest survives. Each thriving company would have mastered its own niche, like a thriving species does. As the environment shifts, 
The only key difference, as strategist Bruce Henderson noted, is that evolutionary path in the natural world "happen", more or less by chance of the re-shuffling of the double helix. While companies can actively pursue its strategy to chose its own path (and hence niche/competitive advantage).

In finance, one simple analogy is the stock market indices such as DJIA, where successful company phases in and the less successful one phases out, creates an illusion to us that stock price always grow (with the indices). While in reality many companies failed and many investments disappeared, but they are not reflected in your DJIA or Hang Seng.

People are often under the impression that it is possible to win against the casinos, as we often hear (directly or indirectly) people bragging how much they got from a trip to Macau or Vegas, or their friends or friend of friends, if not themselves. One often fails to notice the fact that people usually won't tell you if they lost. So you got only a biased sample of gamblers. Those who vanished after losing their lives' saving won't have the opportunity to tell you their stories, just like the out-competed species who will not live to tell you theirs.
-- the simple fact is, casino is a very profitable business. Casinos make a lot of money despite the high operating cost and heavy tax.

I can go on and on, which is why Darwin is so great, in my view.

There are many evidence supporting Darwin's theory, which you may all have read. The most important (to some, 'controversial') idea of Darwin is that Species are not stationary, they evolve, and new species will appear as a result of 'evolution'.

Here I want to lay out a simple argument, simply based on two pieces of facts
1) There are only finite number of species in history
2) Species extinct in the past, present, and also likely in future

They we can reason as below
3) If there is no new species coming into this world, the total number of species will decrease (monotonically -- to borrow a high school mathematice term)
4) When such trend continues, and unless the rate of decrease of the disappearing (extinct) species falls at certain rate (mathematically, the sum over time converges to a finite number) -- which is certain untrue at present time as we witness the lost of species much faster than any other time in human history, mostly due to the impact of human themselves -- there will be very few (or no) species left within a finite number of years.

Therefore, there are only 2 alternatives (with the caveats stated above). (A) New species emerges over time. (B) There will be very few species left in some years.

Now let's start this line of thought from a couple billion years back, when we first observed life on earth (from fossils). 
1) the total number of species in our world today is 3-30 million
2) the history of life on earth is about 3.5bn years
3) if no new species emerged since "genesis" (i.e. 3.5bn years ago), then the total number of lives back then would be 3m+(3.5bn)X, where X is the number of species extinct per year. (to be more precise, this should be an integral, as the rate is not a constant. but we can approximate)

We know that many species extinct each year in today's world. Without the human impact this rate of extinction would be much slower, however, we do see many species extinct in the past, such as the dinosaurs, the trilolites. If only on average one species extinct per year, the total number of species existed on earth 3.5bn years ago would have to be 3.5bn+3m! One has to ask, if the earth is large enough to accomodate so many species, given it could only house 30m today.

5 comments:

yan said...

That is all only valid if you assume that life is really 3.5 billion years old, of course. ;)

Sun Bin said...

Carbon 14 dating etc showed fossil of (i think) about 1 billion old, so even with 1bn year, it is the same order of magnitude...

yan said...

That's if you believe in C14 .. http://www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=3&t=37&m=1

I guess that's how these kinds of theories work - for every detailed claim you make they are going to make up some counter-claim.

yan said...

Also, you completely ignored Noah's ark.

Maybe the real question is how many species would fit on such a ship?

Jeremy said...

I have read about that Darwin did not realize the enormous potency of natural selection until he read Thomas Malthus’, an Essay on the Principle of Population exposition on the counter intuitive consequences of exponential growth — a fundamentally mathematical insight. So it looks like Darwin was not only a preeminent naturalist but also one of the greatest theoreticians of all times.