I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to have time to write while I'm away, I'm taking the opportunity to re-run some old classic posts which were first posted in the summer of 2006. These posts are mildly revised.
Back when I first wrote this post, I was taking a break from some puzzling debugging.
Since I was already a bit frazzled, and I felt like I needed some comic relief, I decided to
hit one of my favorite comedy sites, Answers in Genesis. I can pretty much always find
something sufficiently stupid to amuse me on their site. On that fateful day, I came across a
gem called Information, science and biology", by the all too appropriately named
"Werner Gitt". It's yet another attempt by a creationist twit to find some way to use
information theory to prove that life must have been created by god.
This article really interested me in the bad-math way, because I'm a big fan of information theory. I don't pretend to be anything close to an expert in it, but I'm
fascinated by it. I've read several texts on it, taken one course in grad school, and had the incredible good fortune of getting to know Greg Chaitin, one of the co-inventors of algorithmic information theory. Basically, it's safe to say that I know enough about
information theory to get myself into trouble.
Unlike admission above, it looks like the Gitt hasn't actually read any real
information theory much less understood it. All that he's done is heard Dembski presenting
one of his wretched mischaracterizations, and then regurgitated and expanded upon them.
Dembski was bad enough; building on an incomplete understanding of Dembski's misrepresentations, misunderstandings, and outright and errors produces a result
that is just astonishingly ridiculous. It's actually a splendid example of my mantra on this blog: "the worst math is no math"; the entire article pretends to be doing math - but it's actual mathematical content is nil. Still, to the day of this repost, I continue
to see references to this article as "Gitt's math" or "Gitt's proof".
Gitt starts his article by thoroughly butchering an introduction to Shannon
information theory. I'll just let that breeze by; no sense belaboring the obvious. After
his botched introduction, he moves on to the rubbish that I'll focus on.
The highest information density known to us is that of the DNA (deoxyribonucleic acid)
molecules of living cells. This chemical storage medium is 2 nm in diameter and has a 3.4 NM
helix pitch (see Figure 1). This results in a volume of 10.68×10-21
cm3 per spiral. Each spiral contains ten chemical letters (nucleotides), resulting
in a volumetric information density of 0.94×1021 letters/cm3. In
the genetic alphabet, the DNA molecules contain only the four nucleotide bases, that is,
adenine, thymine, guanine and cytosine. The information content of such a letter is 2
bits/nucleotide. Thus, the statistical information density is 1.88×1021
This is, of course, utter gibberish. DNA is not the "highest information density
known". In fact, the concept of information density is not well-defined. Without a good definition, it's meaningless: How do you compare the "information density" of a DNA molecule with the information density of an electromagnetic wave emitted by a pulsar? You can't: it's meaningless to compare. This is just a sign of the kind of nonsense to come: Gitt is a guy who doesn't believe that he needs to be bothered with trivial little details like
definition. He's a big idea guy!
Anyway... we can define a kind of information density as bits per cubit centimeter. Of course, that's still not well-defined; how do we decide what's a bit? Naively it
seems obvious, but when you think about it in detail, you'll realize where the ambiguity comes in. Is a bit a specific chunk that can be one of several options - as in the segments
of DNA? Is a bit the magnetic alignment of a bit of iron? Is a bit the charge of an ion? Any of those are perfectly plausible definitions of a unit of information encoded into a physical
form. Depending on how you define it, you can come up with a number of different "highest information density known to us".
Consider, for example, the information density of a crystal, like a
diamond. A diamond is an incredibly compact crystal of carbon atoms. There are no perfect
diamonds: all crystals contain irregularities and impurities. Consider how dense the
information of that crystal is: the position of every flaw, every impurity, the positions of
the subset of carbon atoms in the crystal that are carbon-14 as opposed to carbon-12.
Just take the impurities, and look up the density of a diamond. Assume that there's one
non-carbon atom per billion in the diamond - that's probably on the low-end of the number
of impurities. Use its position in the diamond lattice as a bit indicator. Assume that the
impurity encodes only one bit - even though you could encode quite a lot more. Now, work
out the "information density" of the diamond.
Considerably denser than DNA, huh?
After this is where it really starts to get silly. Our Gitt claims that Shannon
theory is incomplete, because after all, it's got a strictly quantitative measure of
information: it doesn't care about what the message means. So he sets out to "fix"
that problem. He proposes five levels of information: statistics, syntax, semantics,
pragmatics, and apobetics. He claims that Shannon theory (and in fact information theory
as a whole) only concerns itself with the first; it's incomplete because it doesn't
differentiate between syntactically valid and invalid information, much less attempt to reason about the higher levels.
Let's take a quick run through the five, before I start mocking them.
- Statistics: This is what information theory refers to as information content, expressed in terms of an event sequence (as I said, he's following Dembski); so we're looking at a series of events, each of which is receiving a character of a message, and the information added by each event is how surprising that event was. That's why he calls it statistical.
- Syntax: The structure of the language encoded by the message. At this level, it is assumed that every message is written in a code; you can distinguish between "valid" and "invalid" messages by checking whether they are valid strings of characters for the given code.
- Semantics: What the message means.
- Pragmatics: The primitive intention of the transmitter of the message; the specific events/actions that the transmitter wanted to occur as a result of sending the message.
- Apobetics: The purpose of the message.
According to him, level 5 is the most important one.
Before moving on, I'll just briefly note: formulating things this way is assuming
the conclusion. What he wants to prove is that all real information includes
a message which was sent with intent and purpose - and thus can't be created by
anything other than an intelligent sender. But he's already assuming in his definition of information that it must have these components - including the intention of the sender and the purpose of the message.
Throughout the article, he constantly writes "theorems". He clearly doesn't understand what the word "theorem" means, because these things are just statements that he would like to be true, but which are unproven, and often unprovable. These aren't theorems. In math, the word "theorem" means something very specific. A theorem isn't just "a statement that I think is true", or "a statement that I want to specifically label because it's important". A theorem is a proven statement. If
you don't show a proof for it, it's not a theorem. No matter how obvious it seems, no
matter how straightforward, it's not a theorem if you don't have a proof.
Now let's look a few examples of his so-called theorems. I'm quoting the
entire theorems here - a series of them and the start of the discussion
that follows. This is really how he presents "theorems". This comes
from his section on what he calls the syntax level of information.
Theorem 4: A code is an absolutely necessary condition for the representation
Theorem 5: The assignment of the symbol set is based on convention and
constitutes a mental process.
Theorem 6: Once the code has been freely defined by convention, this definition
must be strictly observed thereafter.
Theorem 7: The code used must be known both to the transmitter and receiver if
the information is to be understood.
Theorem 8: Only those structures that are based on a code can represent
information (because of Theorem 4). This is a necessary, but still inadequate,
condition for the existence of information.
These theorems already allow fundamental statements to be made at the level of
the code. If, for example, a basic code is found in any system, it can be
concluded that the system originates from a mental concept.
How do we conclude that a code is a necessary condition for the representation of information? We just assert it. Worse, how do we conclude that only things that are based on a code represent information? Again, just an assertion - but an incredibly strong one. He is asserting that nothing without a
structured encoding is information. And this is also the absolute crux of his argument: information only exists as a part of a code designed by an intelligent process.
Despite the fact that he claims to be completing Shannon theory, there is nothing to do with math in the rest of this article. It's all words. "Theorems" like the ones quoted above, but becoming progressively more outrageous and unjustified.
For example, his theorem 11:
The apobetic aspect of information is the most important, because it embraces
the objective of the transmitter. The entire effort involved in the four lower
levels is necessary only as a means to an end in order to achieve this
After this, we get to his conclusion, which is quite a prize.
On the basis of Shannon's information theory, which can now be regarded as
being mathematically complete, we have extended the concept of information as
far as the fifth level. The most important empirical principles relating to the
concept of information have been defined in the form of theorems.
See, to him, a theorem is nothing but a "form": a syntactic structure. And this whole article, to him, is mathematically complete.
The Bible has long made it clear that the creation of the original groups of
fully operational living creatures, programmed to transmit their information to
their descendants, was the deliberate act of the mind and the will of the
Creator, the great Logos Jesus Christ.
We have already shown that life is overwhelmingly loaded with information; it
should be clear that a rigorous application of the science of information is
devastating to materialistic philosophy in the guise of evolution, and strongly
supportive of Genesis creation.
That's where he wanted to go all through this train-wreck. DNA is the highest-possible
density information source. It's a message originated by god, and transmitted by each
generation to its children.
And as usual for the twits (or Gitts) that write this stuff, they're pretending to put
together logical/scientific/mathematical arguments for god; but they can only do it by
specifically including the necessity of god as a premise. In this case, he asserts that DNA
is a message; and a message must have an intelligent agent creating it. Since living things
cannot be the original creators of the message, since the DNA had to be created before us.
Therefore there must be a god.
Same old shit.