Intelligent Design - Information Theory

Last updated Fri Nov 1 17:11:39 EST 2002

Information and the Law of Entropy

This chapter is concerned with an informal demonstration of the law of information - which is the dual of the law of entropy. The basic principal is: in a closed system, information can be destroyed, but not created. By "information" in this context, we mean "complex specified information", or CSI. All CSI in a closed universe had to be present at the beginning. If CSI has been added since the beginning, then the universe is not closed.

Measuring Information

Information is the reduction in uncertainty associated with an event. The probability of a realized event is one measure of information, but an inconvenient one. Smaller probabilities signify more information, and probabilities are multiplicative. The probability of A & B is A × B.

For this reason, information is measured in bits. For a probability P: bits = -log2P. The reason for a base of 2 is that the smallest unit of information is considered to be a bit - the knowledge that one of two possibilities of equal probability was realized. This measure of information is a measure of complexity. Information can also be specified.

Where does CSI come from?


Manfred Eigen claims that CSI comes from algorithms and natural laws. While this is mathematically impossible (not merely in conflict with observation), let's look at the touted source of this information: Chaos. Chaos refers to the fact that simple deterministic functions in mathematics or systems in physics can have chaotic behaviour. Chaotic behaviour is deterministic, but completely unpredictable. It is not even predictable in principle, because computing its behaviour requires infinite precision.

Does chaos produce CSI? It certainly produces complexity. However, the specification for all that complexity is, and by the basic principle of chaos itself can only be, exactly the deterministic function or system which produces it. So chaos can produce complex information, but not CSI. It plays a role indistinguishable from Chance.

In general, laws and algorithms can preserve existing CSI, or destroy it. Chaotic laws and algorithms can generate complexity, but not CSI.


This horse has been beat to death, but monkeys at typewriters do not produce sonnets. There is a vanishing small chance that they might, but then there is a vanishing small change that my glass of water might spontaneously turn into ice and steam. Emile Borel proposed 10-50 as lower bound on probability. Anything less likely that this can be considered impossible for all practical puprposes. Dembski proposes an stricter bound of 10-150 based on the number of elementary particles in the observable universe, its duration, and the Plank time.

Chance can generate complexity, but not CSI. In fact, Chance tends to destroy CSI.

Chance and Necessity?

Chance and Necessity form what is called a Stochastic process. Stochastic processes cannot generate CSI. The gist of the proof is that all Stochastic processes can be decomposed into a function with random and deterministic variables. The random variable cannot generate CSI as we have already seen. And the function operating on a sample of the random variable cannot generate CSI.

Mutation and Selection?

Darwin's mutation-selection mechanism is a Stochastic process and cannot generate CSI. Genetic algorithms cannot generate CSI. Random mutations can only destroy CSI. Their combination cannot produce CSI either. The law of information is as complete general as the law of entropy. It doesn't matter what the specific random or deterministic processes are.

The Law of Conservation of Information

The upshot of all this is that just as entropy can only increase, so CSI can only decrease (in a closed system). In light of this knowlege, you can still be a Naturalist or Deist. You simply posit that the universe sprang forth (or was created) with all the CSI needed for its evolution already present. What does not fly is the current Evolutionary Dogma claiming that CSI is created out of nothing by the mutual action of Chance and Necessity. This is the sort of tired optimism from which perpertual motion and vacuum energy inventions are born.

Information Theory and Evolution

While positing that all CSI came with the Big Bang is consistent, it is scientifically unsatisfying. We would like to know how the CSI was transferred into things like living cells. The ways that we know about include Inheritance with modification, Selection, and Infusion. (Contrary to Dogma, Mutation adds no CSI.) Inheritance passes on a randomly selected mix of CSI from both parents. Selection conveys CSI from the environment, killing off ill adapted genetic configurations. Infusion is the addition of CSI from outside the organism. For instance, bacteria exchange plasmids to acquire antibiotic resistance, and genetically engineered plants and animals acquire new CSI from researchers.

Evolutionary theory needs to be reformulated in light of the science of information.