Intelligent Design - Introduction
Fri Sep 20 16:44:15 EDT 2002
This course will last 10 weeks. Your instructor is
Stuart D. Gathman, who can be
emailed at firstname.lastname@example.org.
In addition to the book
Intelligent Design, by William Dembski, Stuart will be providing
supplementary material on
the web at
Copies of web material will be available at each class.
Information and entropy are two sides of the same coin.
Dembski sticks to the concept of "specified complexity", which I and others
call "information", because it is in many ways more intuitive than entropy.
Entropy is the absence of information.
Because that which may be known of God is manifest in them; for God hath shewed
it unto them. Romans 1:19 KJV
game was used at the beginning of class to illustrate
intelligent design. The 16 boggle cubes displayed the letters
GODFIRSTLOVEDYOU in that order. Is it possible that this combination
came up from a random throw of the dice? Or are you pretty certain that
someone arranged them?
The Boggle game has about 1024 combinations.
(616×16! permutations. There are 2 or 3 duplicated letters
each permutation, so divide by 2!⋅3! or more.) For a continuous system like
ideal gas molecules,
the collection of all possible states is called "phase space". Information
theory measures complexity in bits. If a system has N states, the complexity
in bits is log2N. For the Boggle game,
1024≅280, so that 80 bits, or 10 bytes suffices
to remember a particular state. (A byte is 8 bits.)
How many of these combinations form intelligible sentences? If we restrict
ourselves to row ordering, we can take the number of intelligible 16
letter sentences and multiply by 4 for rotations. To estimate the number
of intelligible 16 letter sentences, consider that english text
is generally compressible by about 50%. 16 letters × 5 bits per
letter = 80 bits ≅ 40 bits compressed.
Divide by the total
number of combinations to get a measure of entropy. For a continuous system,
this measure would be the fraction of phase space. In the case of Boggle,
240 × 4 rotations ÷ 280 yields an entropy
for intelligible boggles throws of ½38.
It is important to notice that the criterion of "intelligible" for Boggle
combinations is "a priori" - defined beforehand. Taking whatever was
thrown as a sign of intelligence simply because repeating it is improbable is
akin to an archer painting a target around wherever his arrow happens to land.
This is the mistake commonly made by proponents of
The Bible Code. As
Boggle players know, finding words in text arranged as a grid is not
all that difficult. For a Clue By Four to smack Bible Code fanatics with,
you can find hidden messages in any reasonably large piece of literature,
What makes certain Boggle combinations "intelligible"? What makes
the special states of a continuous system used to measure entropy special?
The word intelligent literally means "to choose between". It comes
from the Latin inter "between" + legere "to choose".
When certain possibilities for a system are chosen as "special", these
chosen possibilities are a fraction of all possibilities. This fraction is
the entropy of the system. The more precise and specific the choosing,
the fewer possibilities are chosen, and the lower the entropy. Also,
the more total possibilities, the lower the entropy.
The Emperors New Mind, Roger Penrose does a back of the
envelope estimate of the entropy of the Big Bang based what we know
of the choices made in the formation of our universe that make human
life possible. He comes up
with ½1080. His conclusion: "Even God couldn't
be that precise."
Entropy and Disorder
Engineers don't normally compute total entropy. An accurate figure for
total entropy requires enumerating all possible states of a system
as well as enumerating chosen states. We usually don't know enough
about a system to compute total entropy. Instead, engineering deals
with change in entropy, which is directly related to heat flow.
Imagine that we select a Boggle cube at random, and turn
it to a random face. The chosen message will degrade. If we keep
doing this, it will eventually be no longer recognizable. Each random turn
increases entropy, because after N turns, the special set now includes all
combinations that are reachable from our initial choice in N random moves.
As the number of random moves increases, all Boggle combinations become
equally likely - a condition of maximum entropy.
While most people equate entropy with disorder, we now see that it
measures how far a system has departed from its chosen condition.
We can calculate the number of computer bits needed to record which
possibilities are chosen. If our choices select C out of N possibilities,
the entropy is C/N, and the
number of bits needed to specify our choice is
-log2(C/N) = log2(N/C).
The more total possibilities there are, and the more specific the
choices are, the more bits are needed to specify the choices.
The information needed to specify choices is what Dembski calls complex
Laws of Thermodynamics are mathematical laws that govern any
dynamic system in any universe where certain configurations are
chosen as "special". However, they are poorly understood by most people when
stated in terms of entropy. They are easier to understand when stated
in terms of information - complex specified information, that is.
In a closed (no outside interference) system,
- Total entropy can never decrease, total information can never increase.
- Any "internally irreversible" change increases entropy, and destroys
information. Memory is an "internally irreversible" change, so if you
remember the event, it is irreversible.
- Change is inevitable (or at least, no one would be able to remember
it stopping). Therefore, entropy will inevitably increase to its maximum,
and all information will be eventually obliterated.