[tarxzvf]

Everything is pattern matching (or memorization). You can use this approach to half-automate the solution to a known existing class of problems, but how do you come up with anything new? How did Paul Cohen came up with the forcing technique? Who figured out probabilistic proofs as a possible vector of attack?

"Both these properties, predictability and stability, are special to integrable systems... Since classical mechanics has dealt exclusively with integrable systems for so many years, we have been left with wrong ideas about causality. The mathematical truth, coming from non-integrable systems, is that everything is the cause of everything else: to predict what will happen tomorrow, we must take into account everything that is happening today.

Except in very special cases, there is no clear-cut "causality chain," relating successive events, where each one is the (only) cause of the next in line. Integrable systems are such special cases, and they have led to a view of the world as a juxtaposition of causal chains, running parallel to each other with little or no interference."

- Ivar Ekeland

[gregorygoc]

I think the key to innovation is to first know what’s out there. Then you’re able to combine, twist and augment known ideas.

Special theory of relativity did not come out of nowhere. Neither did the geometry, nor algebra. It was all about humans’ curious mind and joy of exploring what’s “possible” out there.

[kiba]

There was an interview with a mathematician who used Anki and spaced repetition to learn and solve novel problems.[1]

1. https://www.youtube.com/watch?v=_RdjsVngZz8&t=1049s

[planet-and-halo]

This is such a great quote. There is a similar line in the book "Creation: Life and How to Make It." The author says that causality is a web, not a chain.

[peterburkimsher]

Yes, my thoughts follow a web pattern, not only a chain! There are chains of thought, but they jump all over the place, even in loops. And it all ends in philosophy [0].

Hyperlinks on the web are one-directional. But links are much stronger if they're bidirectional. That's possible using backlinks, or in real life, by saying "thank you".

Thank you planet-and-halo for reminding us of the web analogy. Thank you zR0x for relating the abstract maths to tangible reality. Thank you tarxzvf for suggesting that everything is pattern matching (I agree, matter & energy are finite, it's only the connections between them that we can create).

I believe that these connections hold true for dad jokes, social situations, software, maths, physics, chemistry, biology... every created thing. Let's thank our creator, and all the teachers who helped us grow.

Are there under 6 degrees of separation between everything in the universe? Or is it as few as 3.5 degrees? [1]

[0] https://en.wikipedia.org/wiki/Wikipedia:Getting_to_Philosoph...

[1] https://research.fb.com/blog/2016/02/three-and-a-half-degree....

[MonkeyClub]

> That's possible using backlinks, or in real life, by saying "thank you".

Marcus Aurelius' Meditations open with a list of lessons learned and an attribution.

Just remembered this when I read your nice note about the "thank you" -- for which, and for the ensuing recollection, thank you!

[zR0x]

Agreed. The pattern matching part is easy. That’s what bores me about math.

How can it help me reason about reality is the interesting part.

For that, one has to really practice these problems and not just hope to get a FAANG gig writing run of the mill business logic every day.