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When Benoit Mandelbrot wrote a simple computer program to map z -> z^2 +c and to his amazement discovered something intricate and beautiful that nobody knew was

by dTal 4y ago

When Benoit Mandelbrot wrote a simple computer program to map z -> z^2 +c and to his amazement discovered something intricate and beautiful that nobody knew was there, where was the "tool"? Why should such an abstract structure, with no apparent practical application, speak so profoundly to the cortex of a primate evolved for hunting animals and gathering fruit?

injidup 4y ago
Because "shiny"
- dTal 4y ago
  You have moved the question into the word "shiny". What is "shiny"?
ahelwer 4y ago
I like to think of it this way. Compare mathematical axioms and rules of logic to the starting configuration and rules of a board game, let's say chess. All moves in chess follow from the very simple rules of chess. Every possible board position, no matter how complicated, can be reduced to iterated applications of the simple chess rules. It can result in beautiful play that exhibits extraordinary human ingenuity reaching (arguably) the same heights as any art form! Yet, we don't think the rules of chess are a product of the divine simply because we can see something transcendent from their application. Simple rules can lead to complicated and beautiful behavior. Doesn't mean anything beyond that.
lizknope 4y ago
In high school we used Newton's method to solve polynomials. Then we got an equation and just a slight change in the starting point gave a different solution. We started plotting everything on graph paper. Then we wrote a program in MathCAD to calculate the numbers for us and plot it. Then we wrote a program to plot the solutions. Then we added color to the program. It was then that our teacher told us that we had created a fractal. We then played around with fractint, learned about some real world cases of fractals, a little about chaos theory and weather prediction. I loved it all. The best part was rather than our teacher just saying "here is a fractal" we "discovered" it on our own each day over the course of a week. https://en.wikipedia.org/wiki/Newton_fractal https://en.wikipedia.org/wiki/Newton_fractal https://www.fractint.org/ https://www.fractint.org/
ukj 4y ago
When you ask “why?” questions you always get religious/philosophical answers. I cannot tell you why stuff amuses me, all I can tell you is that it amuses me. For all we know the awe and profundity comes from the sense of discovery. But what if the a sense of discovery and a sense of invention feel exactly the same?
- dTal 4y ago
  >When you ask “why?” questions you always get religious/philosophical answers No, that's silly. Most things have a reason. "Why" is a useful word in English outside of religion and philosophy. You only get to the end of the chain when you hit the limits of theoretical physics: https://www.youtube.com/watch?v=36GT2zI8lVA https://www.youtube.com/watch?v=36GT2zI8lVA > I cannot tell you why stuff amuses me, all I can tell you is that it amuses me. Do not confuse your inability to answer a question with unanswerability.
  - ukj 4y ago
    Nobody is saying it isn’t useful. Sometimes it is. Sometimes it isn’t. I am saying that in the realm of theoretical science “why?” produces only meta-theoretical (philosophical/religious) answers that may or may not be relevant to the most pertinent issue at hand: “Why are you asking ‘why’?”. All theories have conceptual dependencies. Necessary mental existents/foundations. Without dependencies (assumptions) the theory doesn’t work. Why is there a Big Bang in cosmology? Why are there elementary particles in QFT? Why is there spacetime in GR? The answer to all three is “pragmatic utility.”. If that isn’t the kind of answer you are looking for… >Do not confuse your inability to answer a question with unanswerability. Similarly, do not confuse unanswerability with your inability to answer questions. That is a good way to waste a lot of time…

by dTal 4y ago

injidup 4y ago

Because "shiny"

dTal 4y ago
You have moved the question into the word "shiny". What is "shiny"?

ahelwer 4y ago

I like to think of it this way. Compare mathematical axioms and rules of logic to the starting configuration and rules of a board game, let's say chess. All moves in chess follow from the very simple rules of chess. Every possible board position, no matter how complicated, can be reduced to iterated applications of the simple chess rules. It can result in beautiful play that exhibits extraordinary human ingenuity reaching (arguably) the same heights as any art form! Yet, we don't think the rules of chess are a product of the divine simply because we can see something transcendent from their application. Simple rules can lead to complicated and beautiful behavior. Doesn't mean anything beyond that.

lizknope 4y ago

In high school we used Newton's method to solve polynomials. Then we got an equation and just a slight change in the starting point gave a different solution. We started plotting everything on graph paper. Then we wrote a program in MathCAD to calculate the numbers for us and plot it. Then we wrote a program to plot the solutions. Then we added color to the program. It was then that our teacher told us that we had created a fractal. We then played around with fractint, learned about some real world cases of fractals, a little about chaos theory and weather prediction. I loved it all. The best part was rather than our teacher just saying "here is a fractal" we "discovered" it on our own each day over the course of a week. https://en.wikipedia.org/wiki/Newton_fractal https://en.wikipedia.org/wiki/Newton_fractal https://www.fractint.org/ https://www.fractint.org/

ukj 4y ago

When you ask “why?” questions you always get religious/philosophical answers. I cannot tell you why stuff amuses me, all I can tell you is that it amuses me. For all we know the awe and profundity comes from the sense of discovery. But what if the a sense of discovery and a sense of invention feel exactly the same?

dTal 4y ago
>When you ask “why?” questions you always get religious/philosophical answers No, that's silly. Most things have a reason. "Why" is a useful word in English outside of religion and philosophy. You only get to the end of the chain when you hit the limits of theoretical physics: https://www.youtube.com/watch?v=36GT2zI8lVA https://www.youtube.com/watch?v=36GT2zI8lVA > I cannot tell you why stuff amuses me, all I can tell you is that it amuses me. Do not confuse your inability to answer a question with unanswerability.
- ukj 4y ago
  Nobody is saying it isn’t useful. Sometimes it is. Sometimes it isn’t. I am saying that in the realm of theoretical science “why?” produces only meta-theoretical (philosophical/religious) answers that may or may not be relevant to the most pertinent issue at hand: “Why are you asking ‘why’?”. All theories have conceptual dependencies. Necessary mental existents/foundations. Without dependencies (assumptions) the theory doesn’t work. Why is there a Big Bang in cosmology? Why are there elementary particles in QFT? Why is there spacetime in GR? The answer to all three is “pragmatic utility.”. If that isn’t the kind of answer you are looking for… >Do not confuse your inability to answer a question with unanswerability. Similarly, do not confuse unanswerability with your inability to answer questions. That is a good way to waste a lot of time…