Snowflakes are important because they are, each and every one, the result of a causal process, and are, each and every one, different. You can predict exactly when snow will form, but it is impossible to predict the shape of any one snowflake. Understand this and you understand the interplay between strictly deterministic causality and chaos theory. The fine grained variability that limits what can be predicted. The fine balance between order and disorder as each flows into the other. It is the fundamental entropic flow of all existence.
And rainbow - well, they are curved because light travels in straight lines. There, in front of our eyes, the visible evidence of quantum theory - the paradox of light being both a wave and a particle. Which, of cause, results in Heisenberg's uncertainty principle - that if you know the speed of a particle, you must be uncertain about its position, or if you know the position you must be uncertain about its speed - you cannot know both about the one and the same particle.
Now throw in Godel's incompleteness theorem - not even numbers work, they are not provably consistent - and Turing's halting problem - that you cannot know if a program will stop or not in advance of running it; and the result -
now why should I do the thinking for you?
Embrace the uncertainty, love the chaos, wonder at the creativity that results.
And rainbow - well, they are curved because light travels in straight lines. There, in front of our eyes, the visible evidence of quantum theory - the paradox of light being both a wave and a particle. Which, of cause, results in Heisenberg's uncertainty principle - that if you know the speed of a particle, you must be uncertain about its position, or if you know the position you must be uncertain about its speed - you cannot know both about the one and the same particle.
Now throw in Godel's incompleteness theorem - not even numbers work, they are not provably consistent - and Turing's halting problem - that you cannot know if a program will stop or not in advance of running it; and the result -
now why should I do the thinking for you?
Embrace the uncertainty, love the chaos, wonder at the creativity that results.
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