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Chaos Theory
*January 29, 2009*

*Posted by pjd4891 in Mathematics, Metaphysics.*

3 comments

3 comments

In today’s class, we discussed how fluid dynamics is not researched thoroughly even though it is one of the most important fields. It is applicable for a wide variety of disciplines. Ocean flow could be mapped more accurately, which has a direct correlation to world temperature, air flow, and pressure. Turbulence has chaotic properties. Since turbulence is so chaotic, can we even accurately map ocean flow?

The Coastline Problem was formulated by Mandelbrot in the 1960’s. We discussed this in class. If you keep zooming into the coastline, the length will approach infinity. As you zoom in, the coastline appears more jagged, because you are focusing on smaller and smaller particles. What is the smallest particle we can focus on? Is there anything smaller than a quark? Chaos theory says you cannot have infinite accuracy, so the must be something smaller than a quark.

These fractal examples appear chaotic, but when you make a small change (zooming in), it shows massive changes.

Wikipedia defines a fractal as:

- It has a fine structure at arbitrarily small scales.
- It is too irregular to be easily described in traditional Euclidean geometric language.
- It is self-similar (at least approximately or stochastically).
- It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
- It has a simple and recursive definition.

The Julia set is an interesting example as well:

We discussed that chaos theory states that we cannot accurately understand the universe. Chaos theory questions science at the core. Since we cannot make accurate predictions, what is the goal of science? How can we achieve the goal of science?

All through school, we are taught simplified versions of natural events. I do not believe that mathematical functions exist for all natural events. I think we can get closely model the flow of the ocean, but not completely accurately. There will always be factors that we will have no way of predicting or testing. Life is not supposed to be predicted and science tries to do just this. It tries to rid human lives of emotion in order to give an objective view of how the world works. While science has shown progress throughout time it may be progressing towards something that may not be the correct answer. But then this also gets into the problem with the idea of what is correct and what isn’t. I think science has no self analytical skills in certain circumstances and that it may not see the error of its ways.

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Gödel’s Incompleteness Theorems
*January 23, 2009*

*Posted by Greg in Mathematics, Philosophy of mind.*

4 comments

4 comments

Blah balha

–Evelyn Brister

I’d like to hit two main points in this blog post. First of all, I’d like to discuss Gödel‘s second incompleteness theorem a bit; second, I’d like to see if I can start an actual argument about the philosophical implications of these theorems.

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