Gödel
Godel's incompleteness theorems are fundamental to understanding the limits of scientific and mathematical knowledge and the power of self-reference.
"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense." -Kurt Gödel
It proves the Taoist saying by demonstrating that we can never universally determine what is true using the language of mathematics.
The tao that can be described is not the eternal Tao.
The name that can be spoken is not the eternal Name
-Lao Tzu
Gödel, Escher, Bach should be considered required reading for a full understanding of metaculture.
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Gödel and Fractals
The implications of Gödel are metaphorically represented by the fractal boundary between the black and the color in the Mandelbrot set. Consider the black areas of the Mandelbrot to be the Truth--theories about the universe that can be proven, and are consistently true when tested. All of the colored areas are incorrect ideas--imprecise estimations that are often true in simple cases but break down when you consider more complex variables.
Visualizing it this way, it becomes clear that why truth is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more complex variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of reality.
Consider Newtonian physics versus Relativity. Newton's laws of motion predicted the behavior of matter at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our fractal picture of reality, revealing new, complex patterns that were not visible with Newton. Quantum mechanics further enhanced the picture, allowing us to model the behavior of subatomic particles. The more we learn about the complexity of the universe, the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.
Gödel proved that universal truths are impossible. The truth is infinitely complex, and science can only continue to refine our models to create closer approximations of the true laws of physics.
The same logic also applies to ethics, which is why every "moral absolute" has a thousand exceptions when you consider all the possible external factors.
Incomplete Videos
Here's a basic explanation of Gödel's incompleteness theorem if such a thing exists.
A free online course from MIT is available to help get the most out of this seminal work.
Technically this is based on another book by Hofstadter but it does a good job explaining a lot of the concepts of recursion and consciousness that are in GEB.