Monday, 25 July 2011

Refuting Intelligent Design: The Game of Life and Irreducible Complexity

A long time ago I wrote a blogpost about John Conway's Game of life, which used simple set of rules to make dots on a page evolve. This zero player "game" is an excellent example of how complex systems can evolve from simplicity. All we have is a grid in which each cell has two possible states dead (shaded) or alive (empty) and four simple rules:

  1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overcrowding.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

 If the system is then left to evolve on it's own given certain initial conditions highly complex patterns emerge that seem almost unthinkable with such simple rules. Here's an example.

This pattern was created by humans who worked out the initial conditions using computers. But think about what would happen if you took a huge grid containing millions of squares and kept populating them randomly while allowing the system to evolve for millions of years. Although the probability of such complex patterns forming on their own is pretty low, because of the huge timescales involved, complex patterns will inevitably develop. In fact I wouldn't be surprised if some apparently lifelike systems which replicate themselves evolved. Now if someone who had absolutely no idea of the starting conditions observed this complex system and tried to work backwards he would find find himself with an outrageously complex problem. Although this person may be able to work out how the little structures in the system function and replicate he would have little or no idea about how the system came about. 

Now think about the world as it was nearly 4.5 billion years ago when our planet was in its infancy. We had a big primordial "soup" of chemicals as the "initial conditions". The laws of physics and chemistry were the rules which our "system" which is the Earth and the primordial soup of chemicals followed. Considering the fact that the laws of physics are considerably more complex than the set of four rules for John Conway's Game of Life and that atoms and molecules have a substantially larger set of possible states that alive or dead is it not conceivable that after a about a billion years--the estimated time it took for the first life forms to appear-- by some lucky coincidence very simple prokaryotic life forms had developed?

Irreducible complexity is a concept that is very commonly used by Intelligent design proponents and creationists to justify the existence of an Intelligent Designer. They claim that in it's current state, life is too complex to have evolved by chance. This is another example of the inability of our brains to intuitively grasp extremely small probabilities. "Common sense" is often misleading when we look into the world of the very small. I think the Game of life provides an excellent example of how seemingly irreducibly complex systems can arise from some initial conditions and a set of rules. We may not have the computing power to reverse engineer evolution at present but I think the day will come soon enough.

The illusion of irreducible complexity in a bacterial flagellum. The complexity of the flagellum was shown to be reducible by  Zvonimir Dogic.

Saturday, 16 July 2011

Large Numbers and Premonitory Dreams

Ever heard of the saying "If at once you don't succeed, then try, try, try again."? Have you ever thought of approaching the problem mathematically? The idea just popped into my head today during math class. So now I shall play the role of a theoretical Mythbuster and explore the validity of age old adages using a a purely theoretical approach.

First let's simplify the problem. Let us assume that the probability of you failing horribly at something (and succeeding at it) remains constant and does not depend on whether or not you failed horribly in your previous attempt. We need to find the minimum number of repetitions of a particular task you need to carry out before the probability of success is 99%.

Mathematically this is a trivial problem which can be solved using a binomial distribution. If $X$ is the Random Variable that represents the number of successes, then $X\sim B(n,p)$ where $n$ is the number of repetitions and p is the probability of success. Let us assume for the purposes of this discussion that you are such an incredible moron at doing this task that your probability of success is only on in hundred or 0.01. We want to find n when the probability of succeeding at least once is 99%. So doing the math,
$X \sim B(n,0.01); P(X\geq 1) = 1-P(X=0) >0.99$

$n>\frac{\log 0.01}{\log 0.99}\Longrightarrow n>458.2$

Repeating the task over 458 times ought to do the trick! So this old proverb does have a mathematical basis!

Premonitory Dreams

So what does all this have to do with Premonitory dreams? As it turns out a similar concept can explain in a very simple and elegant manner why people have premonitory dreams.

There are thousands of reports every year of people dreaming about the death of a friend or close relative days before it happens. The superstitious always think of this as "evidence" for the existence of the supernatural. But despite the fact that science cannot explain individual premonitory dreams, a very simple explanation exists if you consider the population as a whole. Read this extract from an article by Michael Shermer.

We can employ a similar back-of-the-envelope calculation to explain death premonition dreams. The average person has about five dreams a night, or 1,825 dreams a year. If we remember only a tenth of our dreams, then we recall 182.5 dreams a year. There are 300 million Americans, who thus produce 54.7 billion remembered dreams a year. Sociologists tell us that each of us knows about 150 people fairly well, thus producing a social-network grid of 45 billion personal relationship connections. With an annual death rate of 2.4 million Americans, it is inevitable that some of those 54.7 billion remembered dreams will be about some of these 2.4 million deaths among the 300 million Americans and their 45 billion relationship connections. In fact, it would be a miracle if some death premonition dreams did not happen to come true! -  Michael Shermer,September 3, 2008. Why Our Brains Do Not Intuitively Grasp Probabilities. Scientific American, Retrieved from 
As we can see from this article, our brain is not very good at intuitively grasping probabilities, especially when the numbers involved are disproportionately small. This results in the intolerably widespread delusion that premonitory dreams are a result of supernatural influences. It doesn't help that most people are prone to what is called a confirmation bias. When people believe in something they tend to look for events or pieces of evidence that confirm their belief and tend to "filter out" anything and everything that contradicts their beliefs. All those who claim to be psychics take advantage of this cognitive bias. Take tarot card readers as an example. People always remember the time the street psychic predicted their promotion of pay raise but always forget the times they failed to predict anything substantial. In fact if you measured the success rate of psychic predictions you'd probably find that they are not much better than what you would expect from someone who was guessing intelligently. So in the future if you meet somebody who claims that premonitory dreams are proof of the supernatural you can gleefully prove them wrong!