To Paraphrase a Sermon

(Written in response to a Unitarian sermon that was trying to be spirtual about science and give the credit for the beauty of the universe to someone/thing besides humans. So this rejoinder was written in the form of a Protestant/Unitarian sermon. Unitarians aren't Protestant, but the worry alot about not being so.)

Reading #1
1. The World is All that is the Case.
1.1 The World is the totality of facts, not things

-- Ludwig Wittgenstein Tractatus Logico-Philosophicus

Hymns
All singing to be done from the IWW songbook. Just to remmind us that anarchy ain't chaos.

Reading #2
6.1 The propositions of logic are tautologies
6.11 Therefore the propositions of logic say nothing.
6.2 Mathematics is a logical method.
6.21 A proposition in mathematics does not express a thought.
6.5 When the answer can not be put into words, neither can the question be put into words. The riddle does not exist. If a question can be framed at all, it is also
possible to answer it.

-- Ludwig Wittgenstein Tractatus Logico-Philosophicus

Sermon
The Tractatus
Probably the most influential book of the 2Oth Century, and probably one of the least known or read. All of the following derive from this little 70 page book:
If you have ever said "you must define your terms", it started here.
Propaganda as we know it in the 20th Century. In other words, that words can mean what I want them to.
Cultural Relativism
Eliminating 75% of the topics in Philosophy from ever having a final answer including Ethics, Religion, etc. because the questions can not be precisely stated (because the definitions of the words cannot be agreed to) there can be no answer.
Logical Positivism
The Vienna Circle School of Philosophy
The Twenties fascination with technology as the solution to the all of the important problems and still carried over into the middle of the century. (Contrapositive of the above, if we can only precisely state the problem, we will have the answer shortly.)
The basis for building computers.

While Wittgenstein wasn't completely correct, he was very close on a number of things in particular:

Mathematics is not Science
Tautologies say nothing, because they are always true.
All statements in mathematics are tautologies. Therefore, mathematics says nothing.
Any conclusion about the real world drawn from mathematics is a metaphore created by the human mind and not a result of mathematics.


Mathematical theories merely have to be consistent.
Scientific theories have to be consistent AND fit the data.
Mathematics is not a science because it does not consider empirical data.
The real foundation of mathematics is not logic, but human neurophysiology.
There is no guarantee that another intelligent species would have a mathematics that looked anything at all like ours.

Science Does not find Truth
Contrary to what a lot of people seem to think. Science does determine truth. Scientific theories are merely models for a certain class of problems that a group of scientists consider interesting. Anything else, including perhaps some very important phenomena relevant to what they think they are interested in, is ignored. These models last for a while until interests change or the investigations lead to new areas that are outside the current models. Then new models are required. Sometimes one is lucky and there is some consistency between the old models and the new, e.g. the transition from Newtonian to quantum mechanics. Even better sometimes when confronted with seemingly disparate data, a model makes it all fall into place in a very beautiful way, e.g. plate tectonics. In any case, scientific theories are only of interest in that they are predictive and current experiments continue to confirm the theory. They do not represent TRUTH. There are many other models, some quite superior to the ones we use, that can describe the same phenomena and come to very different conclusions and find other things to be important.

What does this have to do with Fractals
First of all, fractals do make very beautiful pictures. However, fractals are a mathematical construct and therefore tautological. They say nothing. It is only in the mathematical formulation that a fractal can have an infinite distance inscribed inside a finite circle. When applied to physical systems the process is stopped well before this pecuilarity of the number line appears. (Actually, this is no stranger than the mathematical tautology that says that two transcendental numbers and an imaginary one can be combined in a very simple way yield an integer, i.e. e**-i = -1.)

However, what fractals actually tell us is that many systems are not truly random, but random in a constrained way. The random selection of next state is constrained by the current state. The next state may in fact be chosen randomly, but the range of choices is constrained by what the current state is. Take the coastline example. What fractals say about the next state in a point on the Cape is that it may randomly move inland or out to sea, but it is constrained to be within some bounds. The next state can't move the coastline to Buffalo or half way to Bermuda. In fact, what a fractal describes is in fact equivalent to the Null hypothesis. If a process is perfectly described by a fractal, then it really is random. There are no external influences.

There is a very nice biological example of this described by Stephen Gould in one of his early collections of essays, (Ever Since Darwin). A random model is created to generate the spindle diagrams or phylogenetic graphs found in many biology texts that show time on the vertical axis and number of species in a family or phylum horizontally. Gould found that a very simple random model would very closely emulate the fossil record. They then used the results of these models as the null hypothesis to indicate when a mass extinction was statistically significant (i.e. due to some external event) and when was the number of extinctions were what would be expected randomly. They were able to eliminate something like more than half of all the mass extinctions in the fossil record as not being statistically significant. In other words, the number of extinctions was about what one would expect under normal circumstances. (Gould also found that these kinds of random processes aren't as "random" as one might expect, but actually can exhibit a direction. Could it be that progress is part of the Null hypothesis?)

Fractals do the same thing for the processes they are used to model. So in some sense they say nothing in more ways than one.

But this nothing is a very important nothing. It tells when our systems are random and when they aren't. It tells us that there are different kinds of random processes. Chaos isnt as homogeneous as one might think.

Conclusion
We are responsible for seeing the world as beautiful because of our ability to selectively decide to ignore some things and find patterns in others. Nothing external made
it beautiful; WE made it beautiful. Isn't that somehow even nicer?

And oddly enough, the longer we look at the chaos the more beautiful patterns we find. But they are just beautiful patterns, they ain't truth.

Closing
6.54 My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them - as steps - to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up.)

He must transcend these propositions, and then he will see the world aright.

7. What we cannot speak about we must pass over in silence.

-- Ludwig Wittgenstein Tractatus Logico-Philosophicus