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Every mathematician has only a few tricks (2020)

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Re: Every mathematician has only a few tricks (2020)

#71
post #7

Earlier quoted context omitted.

“The most successful people have failed more times than you have tried”

Success is relative. If the goal is to never fail, never try is the best strategy. Also the most sure path to finish in the 1% wealthiest is to start in its network. When the game is set to make 99% of players considered as losers in its own terms, the best strategy to have fun at scale is to not care about the highlighted goal. Keep awareness of how rules actually apply, take shortcuts if it feels safe and preferabl…

> always respect human dignity even when nasty players try to make a dirty move against you

What a gem of a quote. A great way to avoid becoming a bitter person.

Re: Every mathematician has only a few tricks (2020)

#72
post #50

Earlier quoted context omitted.

The most brilliant software developer (an EE PhD) that I have ever worked with has been using the singular value decomposition (SVD) to solve an enormous number of linear algebra and numerical computing problems in engineering software. The SVD seems to be useful for many engineering computations if you know how to apply it.

What are some interesting things he has used the SVD to solve?

Model reduction (for control systems), numerical precision control for matrix operations, eigenvalue computation, etc. as far as I understand.

Re: Every mathematician has only a few tricks (2020)

#73
post #70

Earlier quoted context omitted.

Success is relative. If the goal is to never fail, never try is the best strategy. Also the most sure path to finish in the 1% wealthiest is to start in its network. When the game is set to make 99% of players considered as losers in its own terms, the best strategy to have fun at scale is to not care about the highlighted goal. Keep awareness of how rules actually apply, take shortcuts if it feels safe and preferabl…

I am having trouble thinking of situations where the only good outcome is being the top 1%. There are, to be sure, often power-law benefits to being exceptionally good, but to use your own example, being in the top 5% or 10% of wealth is nothing to sneeze at. It's all a spectrum. With that said, I think you make some good points about the perspective people should have about competitive goals. Most contests are not s…

This wasn't to mean that ending up in the top percentile of whatever metric is a good outcome, simply that those who advocate the game and its rules will generally tell what is supposed to be valuable and praised as part of the game framing. My point wasn't to tell that taking blindly this or that outcome as a desirable one is advisable.

For the second paragraph, we seem really aligned on the developed points.

Re: Every mathematician has only a few tricks (2020)

#74
post #69

Earlier quoted context omitted.

Success is relative. If the goal is to never fail, never try is the best strategy. Also the most sure path to finish in the 1% wealthiest is to start in its network. When the game is set to make 99% of players considered as losers in its own terms, the best strategy to have fun at scale is to not care about the highlighted goal. Keep awareness of how rules actually apply, take shortcuts if it feels safe and preferabl…

>Success is relative. If the goal is to never fail, never try is the best strategy. This is dangerously not true, if you never try, then you are guaranteed to fail to live up to your potential, which is one of the greatest failures of all.

Sorry if it wasn't clear and explicit enough, but this wasn't meant to be an advise to not try anything. Just an extrem example of what it might be logically concluded when starting from unsound grounds. Never fail is not a sound goal.

That said living up to our potential is not very much better per se. Or at least it seems far too vague to be aptly considered. What forces are going to define what it is to tap relevantly in our potential?

Re: Every mathematician has only a few tricks (2020)

#75
post #34

Earlier quoted context omitted.

My dad was also an Engineer. He was also a Fortran fan. Once he asked me to explain OOP. After I explained the basics he said it was useless and never looked back.

Get your dad a copy of the classic Scientific and Engineering C++: An Introduction With Advanced Techniques and Examples by John Barton and Lee Nackman . It was written to introduce C++ to Fortran programmers using examples from scientific/mathematical domains. The fact that it is old (from 1994) makes it better suited for folks from Fortran (or other languages) since there is none of the complexity of "Modern C++" t…

Unfortunately he has left our presence and is now probably getting to grips with the universe being mostly hacked together with Perl.

Re: Every mathematician has only a few tricks (2020)

#76
post #25

Earlier quoted context omitted.

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

A popular naming convention in Mathematics is to name things after the second person to discover them. The first person is Leonhard Euler.

Leonhard Euler (https://en.wikipedia.org/wiki/Leonhard_Euler) is the only reason i believe in "extraterrestrial life" which are "more intelligent" than us :-)

List of topics named after Leonhard Euler - https://en.wikipedia.org/wiki/List_of_topics_named_after_Leo...

Re: Every mathematician has only a few tricks (2020)

#77
post #75

Earlier quoted context omitted.

Get your dad a copy of the classic Scientific and Engineering C++: An Introduction With Advanced Techniques and Examples by John Barton and Lee Nackman . It was written to introduce C++ to Fortran programmers using examples from scientific/mathematical domains. The fact that it is old (from 1994) makes it better suited for folks from Fortran (or other languages) since there is none of the complexity of "Modern C++" t…

Unfortunately he has left our presence and is now probably getting to grips with the universe being mostly hacked together with Perl.

Nope ;-) He would tell us that the world is a simulation implemented using Fortran Coarray SPMD.

Re: Every mathematician has only a few tricks (2020)

#78
post #4

One of the answers links https://www.tricki.org/ , which describes itself as a 'Wiki-style site with a large store of useful mathematical problem-solving techniques.' no longer maintained, but looks neat.

Thank You for pointing that out; that is indeed nice!

Re: Every mathematician has only a few tricks (2020)

#79
post #70

Earlier quoted context omitted.

I am having trouble thinking of situations where the only good outcome is being the top 1%. There are, to be sure, often power-law benefits to being exceptionally good, but to use your own example, being in the top 5% or 10% of wealth is nothing to sneeze at. It's all a spectrum. With that said, I think you make some good points about the perspective people should have about competitive goals. Most contests are not s…

This wasn't to mean that ending up in the top percentile of whatever metric is a good outcome, simply that those who advocate the game and its rules will generally tell what is supposed to be valuable and praised as part of the game framing. My point wasn't to tell that taking blindly this or that outcome as a desirable one is advisable. For the second paragraph, we seem really aligned on the developed points.

Yes. An interesting corollary is that we should pay close attention to what games we have an inherent advantage in, and double down. Much higher chances of reaping those power-law benefits. I speak, frankly, mostly to myself here: I am naturally pretty bad at almost all human skills (although I’ve of course worked hard to build up at the competencies required to be a functioning adult and partner.) But for the one or two things I am naturally good at, it all comes so very easily, it’s effortless and free and I have built my life around them.

Re: Every mathematician has only a few tricks (2020)

#80

Earlier quoted context omitted.

Yeah for that you need Euler’s method… I mean of course Runge-Kutta. … By that I’m of course referring to rk4. … I mean, you have a point. Joking aside I think having a few basic numerical methods like say Newton, rk4, brent root, monte carlo simulation etc in your general toolbox of techniques you know how to do can make you unreasonably effective in a wide range of situations. Just yesterday I had to solve a proble…

If you know some basic composition methods, Euler, RK and all the higher order methods can be easily constructed as you need them. But there are still many applications where you for example want to use symplectic methods instead. If you know about those+composition, you can at least solve more or less all of classical newtonian dynamics. But if you go to quantum mechanics or field theory (or quantum field theory), y…

PDEs are PDEs, regardless of where they come from Newtonian or quantum. Would you care to elaborate why you think quantum requires a new kind of numerical analysis?
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