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awxuelong
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Math is really a beautiful system (framework?) from which we can derive ideas of beauty through symmetry and geometry, study of complex systems through calculus, and also of creativity. | ||
- How would I define creativity? | ||
o Imagine you’re an enthusiastic pursuer of truth. In front of you are a some numbers and two operators: + (ordinary addition) and * (ordinary multiplication). Science, or the discovery of knowledge, is analogous to discovering new numbers. You randomly add two numbers, 1 and -1 and discover 0. Then you add 1 to 1 and obtain 2. Repeating this process you discover all the integers. From God’s point of view, addition and multiplication over integers is closed in this set, therefore you can’t discover anything beyond the horizon of integers, even though you can discover a lot. You can find patterns, such as properties of commutativity, transitivity and distributivity. | ||
o Creativity, in this scenario, would be proposing another operator such as division. Having this new operator in your arsenal of tools to perceive reality, you can now compute a new class of numbers, the rationals and thus discover the set of all real numbers. | ||
o The infiniteness of numbers is analogous to the infinity of knowledge. | ||
Further creativity would be introducing the square root, and this tool extends our perceptual horizon to encompass the realm of complex/imaginary numbers. | ||
A different civilization, using a different set of symbols to encode numbers, may make similar discoveries, i.e., numbers obtained following the same principles of computation using + and *, discovering commutativity, transitivity and distributivity. This underlies/represents the universality of knowledge. | ||
o I’ve ignored letters, phonemes, words to simplify this overly-idealized world to get my ideas on what is creativity across. |
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