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Collapsing into beauty


Baby Astronaut
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I'm reposting this from a post made long ago in a thread not far away:

 

One philosophical thought I'd like to contribute, which I suspect many in this community might already privately harbor, is that mathematics which detail existence is reducible far beyond its usual framework into very simple components.

 

One reference I can point to is E=mc2.

 

I believe all mathematics can achieve this simplicity or better. However, if even one variable were off, an increase of complication ripples through the framework until it nears its current state.

 

The variable I mentioned has many faces. Conclusive evidence is one -- and what if it turns out to be incorrect? When Einstein proved that energy and matter were one and the same, I would imagine it had a ripple effect that simplified other formulas. Consequently, a lot of divergent theories may have been collapsed into a simpler framework.

 

The leap of insight with electromagnetism most probably accomplished a similar thing.

 

I've noticed in researching mathematical origins that the authors of certain formulations had used personalized notations. The implications of this leads me to hope a few will realize that our mathematical architecture in its formal state might need a complete overhaul and redesign, in order to accommodate new explanations for reality which might be lurking just beyond its range yet within the grasp of a less complicated system of notation.

 

One day, computers will be able to rearrange the math system by tinkering around with many variables in novel ways, until it hits an approach that collapses a lot of formula notations down to unforeseen sizes.

 

The Lounge is a good place for this to discuss, as I want mathematical laymen to join in the conversation, as that's what I am! :)

 

And a couple of links for discussion that could be relevant to this idea:

 

Mathematicians Want to Say Goodbye to Pi

 

and

 

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