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Big ideas do not come only from leisure. The arduous, mundane work is a vital part of the process. You can't skip the worrying phase. You work, and work, and work some more to get some understanding.

The eureka moments will emerge once you have prepared your mind.

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Ideas come to us when we have a specific problem but we do not focus on solving the problem directly.

It’s not at all obvious how to go about thinking up some new twist on these things. A new idea can feel like a remarkable discovery

*Henri Poincaré, the father of chaos theory and the co-discoverer of special relativity, relates his own discovery. "the idea came to me, without anything in my former thoughts seeming to have paved the way for it.”*

*The Irish mathematician, Sir William Rowan Hamilton, had a similar...*

The first phase of solving can be described as “worrying” about a problem or idea. It evokes anxiety and gives the impression of productivity.

But, overthinking can lead to a dead end. The key to solving the problem is to take a break from worrying. Focus your attention on some other activi...

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How do Eureka moments happen? They do feel contingent & magical, arising in consciousness on their own. But looking at the history of breakthrough ideas there seem to be a rough 2-phase process:

- An initial period of
**concentration**, study, tinkering aka “worrying” abou...

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*Where do ideas come from? That’s a big question. Here’s a smaller one: Where do mathematical ideas come from? I’ve wondered about this from the time I first contemplated being a mathematician until long after I officially became one.*

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There is a lot of math behind how the Golden Ratio is calculated. But designers, artists, and photographers aren’t usually high-level mathematicians. To benefit the algebraically disinclined, let’s keep it simple.

The Ratio is approximately **1.618 to 1**. It’s approximate bec...

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