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Feynman wrote in his autobiography that much of his success came from having different mathematical tricks than most of his peers. So when they were stuck, he could sometimes make progress.
His style was always the same, he just mastered it really well.
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For me, it's tracing code/pipelines to figure out how a result was produced, typically in the context of that result being wrong somehow. Go To Definition is the most useful function in any editor. I'm always surprised by how frequently colleagues don't think to do this and are left helpless.
This reminds me of my further theory that everyone needs one 'heavy' and one 'light' technique. The 'light' technique is something that often works well as a heuristic and can be an effective unit of iteration. The 'heavy' technique is something that you can fall back on in difficult cases, something that can reliably solve hard problems, even if it's slow. Sometimes the heavy technique is: just ask someone else. ;)
I’m not a software developer anymore.
Feynman wrote in his autobiography that much of his success came from having different mathematical tricks than most of his peers. So when they were stuck, he could sometimes make progress.
Feynman wrote in his autobiography that much of his success came from having different mathematical tricks than most of his peers. So when they were stuck, he could sometimes make progress.
Interestingly, one of his famous tricks of computing complex integrals by parameterizing[1] and then differentiating under the integral is known as “Feynman’s trick” in his honour spite of it having been invented by Euler over 250 years before. [1] https://zackyzz.github.io/feynman.html
Earlier quoted context omitted.
This reminds me of my further theory that everyone needs one 'heavy' and one 'light' technique. The 'light' technique is something that often works well as a heuristic and can be an effective unit of iteration. The 'heavy' technique is something that you can fall back on in difficult cases, something that can reliably solve hard problems, even if it's slow. Sometimes the heavy technique is: just ask someone else. ;)
> Sometimes the heavy technique is: just ask someone else. ;) For a lot of people I know, this is the light technique!
She's incredibly intelligent, but more importantly she's a phenomenal social networker. She always has someone to call to ask about any question or solve any problem that comes up in life, and she's great at connecting these people with each other when they have problems of their own - so they all want to help her with whatever she needs, just to gain access to a pool of people they themselves can talk to.
What do you do with a skillset like that? I honestly don't know - something in leadership, probably, something where finding the right people and setting them to work is the most important skill of the job.
My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…
Earlier quoted context omitted.
> Sometimes the heavy technique is: just ask someone else. ;) For a lot of people I know, this is the light technique!
You jest, but that's how my sister gets through life, and it's always fascinated me. She's incredibly intelligent, but more importantly she's a phenomenal social networker. She always has someone to call to ask about any question or solve any problem that comes up in life, and she's great at connecting these people with each other when they have problems of their own - so they all want to help her with whatever she n…
Found it really hard to adjust to that. I'm the kind of person that prefers to research things on my own, find hard references and understand context. But there, this was the wrong approach.
My dad (an engineer not a mathematician) would use Newton-Raphson[1] to solve basically any problem that wasn’t very obviously linear. When I was a kid, some of my first programming memories were my dad getting me and my brother to implement Newton-Raphson in basic on an HP85a, getting me to implement Newton-Raphson in rpn on an HP calculator, debugging my dad’s (genuinely revolting) basic program[2] which wouldn’t r…
Relatedly, I've found Newton-Raphson is a great example of an algorithm where Knuth's "I have only proven it correct, not tried it" rears its head very prominently. The obvious implementations can work flawlessly on toy examples and then fail miserably on real-world examples.