# Shallit on Information Theory

Since I am still getting caught up on my blog reading after my trip to the big conference, I have only just noticed Jeffrey Shallit’s interesting post on information theory. He writes:

Creationists think information theory poses a serious challenge to modern evolutionary biology — but that only goes to show that creationists are as ignorant of information theory as they are of biology.

Whenever a creationist brings up this argument, insist that they answer the following five questions. All five questions are based on the Kolmogorov interpretation of information theory. I like this version of information theory because (a) it does not depend on any hypothesized probability distribution (a frequent refuge of scoundrels) (b) the answers about how information can change when a string is changed are unambiguous and agreed upon by all mathematicians, allowing less wiggle room to weasel out of the inevitable conclusions, and (c) it applies to discrete strings of symbols and hence corresponds well with DNA.

All five questions are completely elementary, and I ask these questions in an introduction to the theory of Kolmogorov information for undergraduates at Waterloo. My undergraduates can nearly always answer these questions correctly, but creationists usually cannot.

The questions? Well, you’ll just have to link on over to Jeffrey’s blog for those.

He is right, of course, about creationists not really understanding the mathematical and scientific machinery they throw around. I have seen more than one creationist pontificate about how genetic mutations always lead to a decrease in information, without ever bothering to say how they propose to measure information in the first place. They do not seem to grant that if a point mutation from x to y leads to a loss of information, then the reverse mutation from y back to x would have to increase information.

The reason is not hard to spot. They are not really interested in applying the often complex machinery of modern mathematical information theory to the problem of understaning evolution. It is just jargon to them, useful for making dopey, Gee Whiz!, style arguments sound scientifically rigorous.

They treat thermodynamics the same way. They might blather about entropy and the second law, but in the end they are not really using any of the machinery of the subject. They are not evaluating any integrals, or calculating the change in entropy in going from one state to another, or describing reversible processes that model some biological phenomenon.

Likewise for probability theory. They are forever assigning small numbers to physical objects or processes and then, by multiplying the small numbers together, producing smaller numbers still. These smaller numbers are said to represent the probability of a whole sequence of events happening one after the other. I know from experience they have no interest in trivial details, like establishing the independence of the events whose probabilities are being multiplied.

Mathematicians and physicists have worked very hard to produce useful systems of abstract machinery. Probability theory, information theory and thermodynamics are fantastically useful, but it can be difficult to master their subtleties. The fact is that we have copious evidence from various branches of biology and geology that biological evolution has occurred, and that natural selection has a big role to play in the process. If some abstract mathematical model says otherwise, then so much the worse for the model.

1. #1 Blake Stacey
January 12, 2009

They are not really interested in applying the often complex machinery of modern mathematical information theory to the problem of understaning evolution. It is just jargon to them, useful for making dopey, Gee Whiz!, style arguments sound scientifically rigorous.

Which makes correcting or even responding to their arguments rather difficult. I mean, where do you even begin?

I have an essay on some physics crankery which addresses this issue, but the MT interface is still being too glitchy for me to work on it. m Sigh! An old post of mine touches on the problem, though.

2. #2 Jason Rosenhouse
January 12, 2009

Yes, it can be very frustrating to respond to their arguments. It is worth the effort, though. I have learned a lot about mathematics and science just from doing the research necessary to understand why the creationists are wrong. It is sort of like chess, where you learn more from your blunders than you do from your good moves. Only here it is the creationists blunders from which I am learning.

3. #3 Norman Doering
January 12, 2009

Jason Rosenhouse wrote:

Yes, it can be very frustrating to respond to their arguments. It is worth the effort, though.

Sure, you can educate yourself, but what about them:
http://normdoering.blogspot.com/2008/12/why-they-want-to-silence-us.html

4. #4 ngong
January 12, 2009

Here’s an ID response to Shallit: http://blog.coincidencetheories.com/?p=740 . The gist of the argument seems to be that Dembski is talking about information contained in a “message”, whereas Shallit is talking about a code, and there’s supposed to be some difference in mathematical treatment in the two situations.

I’m not qualified to raise an argument. I’d be curious how folks familiar with information theory dissect this.

5. #5 ngong
January 12, 2009

Here’s an ID response to Shallit’s argument: http://blog.coincidencetheories.com/?p=740 . The gist seems to be that Dembski is talking about messages, while Shallit is talking about code, and the mathematical treatments of the two cases are different.

I’m not qualified to respond, but I’d be curious how folks with an understanding of information science would. I do note that the blogger seems to regard Kolmogorov as some sort of esoteric figure, which is somewhat bizarre for someone who purports to be on top of information theory.

6. #6 Tyler DiPietro
January 12, 2009

It’s sort of funny to watch William Wallace flail in that thread. Guy hadn’t even heard of Kolmogorov, amazing.

7. #7 Tyler DiPietro
January 12, 2009

“The gist seems to be that Dembski is talking about messages, while Shallit is talking about code, and the mathematical treatments of the two cases are different.”

Dembski talks about the probability of given “events”, and his mathematical treatment is something short of rigorous (see Elsberry and Shallit’s lengthy critique). Neither Kolmogorov or Shannon talk about messages or codes except insofar as they’re talking about the information contained in strings, it doesn’t appear that the blogger has a very deep understanding of the subject.

8. #8 ngong
January 12, 2009

I assume Dembski is ultimately arguing against certain events occurring in a string of DNA, which would seem to fall more into the category of “code” than “message”. In which case, Shallit is more in touch with Dembski’s line of reasoning than Wallace.

9. #9 Tyler DiPietro
January 12, 2009

Actually, what he’s calling the “message” isn’t the precise meaning of “message” in Shannon theory. Simply put:

A message is a string of numbers, e.g. 10010010 that is transmitted between sender and receiver. Due to noise, there is a certain probability that digit will be transmitted incorrectly (you’ll get a zero where you should have gotten a one, or vice versa).

An encoding remedies this situation by reducing the probability of error. Say, for instance, that instead of sending the digit once through the communication channel, you send it three or four times consecutively. The corresponding decoding would involve selecting the digit that represents majority of digits present in a segment of three or four.

What Wallace is talking about is the meaning associated with the message, which is a mathematically irrelevant detail.

10. #10 Jason Rosenhouse
January 13, 2009

ngong –

The post you linked to is guilty of precisely what I was describing above. The word “information” means something different in mathematics than it does in everyday life. The mathematical version has nothing to do with meaning, which is why a random string of letters can be said to contain a large amount of information. Creationists, like the fellow to whom you linked, pretend they are using the formal mathematical version since it lends phony rigor to their arguments. In reality they are using the everyday meaning of information.

11. #11 abb3w
January 13, 2009

Blake Stacey: Which makes correcting or even responding to their arguments rather difficult. I mean, where do you even begin?

In the case of the Second Law of Thermodynamics, I inform them that they are obviously mistaken, since the paper “Natural Selection for Least Action”, by Kaila and Annila (doi:10.1098/rspa.2008.0178) shows how Evolution is a direct mathematical consequence the Second Law of Thermodynamics.

To which they predictably go, “Wait… what?” in highly amusing manner.

From what I understand, there is considerable parallel in the mathematics between Information Theory and Thermodynamics. Presumably, some Creationism opponent with professional-level knowledge of Kolmogorov information theory could write up a paper to overview deriving the heart of Evolution from the Information Theory expression of entropy as well, and get that paper also published as a peer-reviewed article.

12. #12 Raymond Minton
January 13, 2009

What’s really a riot is that people who believe the world had a supernatural origin, and who subscribe to other doctrines that are most charitably described as preposterous, can say that evolution violates natural law (and do it with a straight face, at that!)

13. #13 Paul Murray
January 13, 2009

From what I understand, there is considerable parallel in the mathematics between Information Theory and Thermodynamics.

It’s the link between these two that banished Maxwell’s Demon.

Information and entropy are measured in the same units – Joules per Kelvin. You can understand the second law in terms of information: “information, once created, is never destroyed (although it can be dispersed to a point where it’s difficult to recover)”.

In the act of wiping off a blackboard, for instance, the patterns of chalk on the board alter the velocity of the duster as it wipes, which means the eddies kicked up in the air by the arm of the wiper are subtly different to what they would have been if there were no writing on the board. Ultimately, it all turns to heat. Thermal motion, then, is information packed down as densely as it can possibly be packed.

It’s all good fun, and relatively easy for a non-scientist to understand.