The first thing that struck me in the video (90 minutes documentary) was the immense forces at play on a universal scale, the almost incomprehensible extent of the universe and the unfathomable distances and time scales involved. We are all very aware of this aspect of the universe. The next thing that caught my attention was the immense cosmic dance giving rise to supremely exotic phenomenon occurring almost with a mundane regularity in the universe. From the devilish grasp of Black holes to the concept of cataclysmic Supernovae and immense energies of the Quasars to galactic collisions, nature plays the game of destruction and beauty at a level we can hardly comprehend and she plays it with the virtuosity of a Horowitz gently stroking the keys of a grand Piano. But these were not the things that impressed me the most about this video. It was something else.
Einstein once said that the most surprising thing about nature is that it's comprehensible. And if you think about it, its rather disconcerting and very astonishing. You see, nature is not obligated to make sense. The fact that a few equations on a piece of paper can accurately describe phenomenon as weird as gravitational lensing and stellar implosion is nothing less than startling. I do not have much idea about Quantum theory but I have read a bit about Einstein's gravitation and all I can say about it is that its a triumph of human intelligence. I do not want this to be a geeky post so I will go straight to the essence of it all. The only assumption in Einstein's theory is the constance of the speed of light. Its hardly a theory of physics. Its pure mathematics. Its just a geometrical statement. And whats seriously weird is that the final equation was found by a guess since there are infinite other equally correct such equations. Einstein's equation just happens to describe the universe with a scary accuracy.
I find it strange that nature and mathematics are such close bedfellows. Why is it all so simple and so logical ? Why does nature dance to the tunes of purely mathematical laws and relations ? I am not sure if I am communicating this idea well enough. You see, mathematics is a very rigid discipline in which if a+b=c then there is no way a+b=d unless c=d. If, on the other hand, we represent two physical quantities by a and b and then try to find a+b, nature is not obligated to give us c as an answer, but it does. An example would be the conservation of energy. Saying that energy is conserved in a physical system and that 2+2=4 (always) in a mathematical system have a deep connection because we have chosen to describe nature via mathematics. But in the end they are two very distinct entities. The fact that we never see a violation of conservation of energy and that we never find that 2+2=5 somehow signifies a deep inter-dependence of the most basic natural laws and the most fundamental mathematical tenets. And this thinking rests on the sole fact that physical reality and mathematics form two ends of a very interesting spectrum. While physical reality is the ultimate truth which does not depend upon anything else for its sustenance, mathematics is the sole discipline which does not seek to explain anything and which does not depend upon any other science. Everything in between including physics, chemistry, biology either serve to explain the physical reality or emanate from mathematics or both. I find it interesting that the two fields which are just not obligated to be connected end up getting so closely tied together. Which makes me think that if there is such a thing as an ultimate truth, an ultimate reality, the only way it will be found would be in the abstract dance of purely mathematical symbols. And when you think about it, you would wonder if its all too obvious that within the infinite relationships between purely mathematical concepts, there would be one relation that would be the statement of the ultimate truth. Its just that humanity is just not intelligent enough to zero in on it, as yet.
Addendum: Well, thinking a bit more upon the topic, I have realized a rather grim possibility. If we take it that nature and mathematics are closely tied to each other and that all natural laws, howsoever deep, are ultimately expressible mathematically, we will soon reach a dead-end. A brilliant mind, with the name of Kurt Godel, gave a landmark theorem called the Godel incompleteness theorem which proves that a mathematical system cannot be both complete and self-consistent. In other words, a mathematical system that seeks to explain everything must necessarily be inconsistent and vice-versa. I wonder if it has ramifications in our understanding of reality.