Wednesday, December 5, 2012

Gain Application Probability

Statistics are being used in the arguments about biological origin and evolution. Advocates of Intelligent Design Theory (ID) are prominent among those attempting to link probabilities of events with mathematical proofs of biological information but they are not the only ones. This post, though dated 12/5/12, is an update (8/27/13) and a new compendium, called Biological Information: New Perspectives, was just released and can be read online here.  The book is an overview of the work being done to align biology with information theory which uses probabilities in trying to understand biological systems. Its authors are both ID and non-ID advocates. 

I have a new theory that I present here, but like all new theories, it needs some more work.  In fact, I've come back to re-write this post several times and instead of re-writing it another time, I'm going to eventually post about it again. But, if you are so-inclined, read on.  Then catch up with a newer post called GAP Theory that should appear Nov. 2013.

Mathematics can be applied to reality. Probabilities in thermodynamics and chemistry predict quantities and actions of energy and mass. They exist and behave in a certain way that can be measured.  But human judgment and mathematics are two different things. People rely on their own judgments about many subjects without being experts in probability theory.

It's pretty hard to imagine converting all of nature into strict mathematical terms.  Evaluating a pattern is done by humans and therefore has subjective elements.  Perhaps Information Theory does and will reveal certain hidden secrets about biology.  But I doubt if even chaos theory could give all the answers.

Some examples might be helpful.  A straightforward one goes like this:  someone "blindly" picks all red balls from a bag which contains equal numbers of red and black.  After about 20 times a pattern emerges that is different from the expected 1:1 ratio.  One might suspect the red and black balls have unique surface features which allow discrimination.  Maybe the red surface is more sticky.  But in another example, consider a different type of situation. For a while my husband and I went to the store and they didn’t have any fresh grapefruit. The produce people could not answer our questions of why they were not there, so I looked on the Internet to understand. I found that some of the Southern US produce had been damaged by storms, and Mexico had droughts that affected their exports. What was the probability that a grapefruit would be available by the next time we went to the store? Wouldn't even the experts in distribution have trouble being precise due to the unpredictability of long-range weather? Even though they have their formulas, in certain circumstances they still incorporate judgments.  It is of a different nature than pulling balls from a bag at a particular place and time. 

Included in human judgment is the sense that the extreme complexity of  biology is improbable and not random. (Some would argue here that neo-Darwinian evolution is not random due to “natural selection of the fittest,” but nature needs something worth-while to select first, which is claimed to come from random mutation.)   And yet there exist many things with very low probability, including every hand you get in a card game.  This is where critics come in and say low probability doesn't prove design. Design advocates then refer to "specificity," meaning that specific molecules are needed to perform biological tasks and that the exact combinations of these molecules are extremely improbable.

Specificity implies different values placed on equally probable outcomes. As in the grapefruit example above, I don't think we can always know exact probabilities.  And yet the concept of probabilities still might give us some insight to whether nature itself could have come up with biological function and complexity. In some cases, an evaluation of probability can affect how a person judges an event.  I'd like to talk about putting value on similar probability outcomes.  I'll call it “Gain Application Probability” (GAP).

If you have only one second to toss a coin and it takes 1 second to toss it, you will either get heads or tails (no edge landings or double half-second flips allowed). Each outcome has a probability of one half, and one of the possibilities will occur. In this example, nothing is special about either unless one outcome is assigned to a prize. If a football team calls heads and the coin lands heads, they get to choose whether they receive the ball now or later. If I say I’ll give you a hundred dollars if it lands heads, you will perceive the difference in the outcome.

Now we move on to a dice. You have only one second and it takes one second to throw. I’ll give you a prize (say, 100 dollars) if you get a 1, but not on any other number. Each outcome has one chance in six, but there is still a difference in what happens if the number 1 comes up as compared to the others. The award or denial of the prize is in a related way a measure of the outcome.

Then we take a full deck of cards. We shuffle them fairly and put them face-down on a table. You have only one second and it takes a second to draw the top card. I tell you I’ll give you a prize if the top card that you draw is an Ace of Diamonds. But now you only have one chance in 52 that the card will be the Ace of Diamonds. Is this different than tossing a coin and getting a prize if you get heads? Which would you pick to take your chances?

While we’re talking of cards, it is true that each combination in a game hand has the same probability.  But with a good grouping according to the rules of the game you are playing, you can win the hand. You might win money if there is a pot. You therefore gain with the good combination (if you play it well) more than with the bad.

Amino Acids are molecules that make up the various proteins. They have 20 different forms in our bodies and their various properties make their different combinations unique. The chances for one amino acid combination to occur might be the same as another, but if only one in 10^70 will help to break down a food molecule to produce biological energy while the others in that number don't do anything biologically active, then to me that one protein is different from the rest. If there is function for the few molecules among so many, I would apply a value of gain to those which can carry out biological tasks.

These examples demonstrate, in my term given above, Gain Application Probability. To say there is no difference between certain low probability events is to ignore the possible results. We can deliberately attach an extra benefit to an outcome or we may observe a benefit which comes naturally. We can evaluate events of low probabilities in relation to the gains they bring.

I think we can reasonably say that some improbable outcomes have more value than others. And the lower the probability and the more we gain, the greater the value. One might also be able to apply loss and neutrality to probabilities (LAP and NAP). After all, there is a losing side to a football coin toss, and many improbable events have no appreciable effect. And I suppose that zero times GAP is ZAP.

You might say Gain Application Probability is as subjective as other biological information theories (if you are a critic of these theories).  But I’m not claiming to entirely eliminate chance. I don’t even want to quantify the values of gain and loss. I think there is worth in acknowledging that values can be applied differently for different probabilistic events even when they have similar probabilities. And some outcomes are so valuable that our human judgment can take over to tell us they did not happen by chance.  So it is with functional biological materials made from combinations of molecules.

The value put upon the probability outcomes is a dimension above the science of nature.  When you have faith, you can still be scientific and yet not get bogged down by needing all-encompassing mathematical and scientific proofs.  Faith is given to us as a gift (Ephesians 2, NABRE Bible).  This is a mystery which transcends our understanding.

No comments: