3 ms·

And this is what gets me about Feynman, why I am a huge admirer of his work. Take a look at the footnote. An offhand comment of how to calculate the square ro

And this is what gets me about Feynman, why I am a huge admirer of his work. Take a look at the footnote. An offhand comment of how to calculate the square root of any N using a short iterative loop that you can compute by hand. I'm no mathematician (clearly) but I had no idea that this method even existed. I've just had to try it out. And it's a footnote! I have the book of Feynman's computation lectures and they're dated, but most of the theory is still relevant and his writing remains accessible to anyone.

SamReidHughes 7y ago
That loop is known as Newton’s method, applied to square roots, it is very well known and taught in intro calculus classes.
grey--area 7y ago
Here's the method that's being applied: https://en.wikipedia.org/wiki/Newton%27s_method https://en.wikipedia.org/wiki/Newton%27s_method It's an iterative method for finding x such that f(x)=0 for a given function f, in this case f(x) = x^2 - N, where N is the number you want the square root of. The special case has such a simple expression, though, that I'm tempted to commit it to memory. Edit: Another nice example, for when you have access to a calculator that can compute powers but not logarithms: a' = a - 1 + x/c^x will converge the base-c logarithm of x (though it will converge slowly if you start very far from the solution).
- fastbeef 7y ago
  At it's core, it's also what drives Carmack's Fast Inverse Square Root (https://en.wikipedia.org/wiki/Fast_inverse_square_root https://en.wikipedia.org/wiki/Fast_inverse_square_root). Yes, yes, I know Carmack didn't invent it.
- acqq 7y ago
  The method in question was known for millennia before Newton, it is believed to be known to Babylonians: https://en.m.wikipedia.org/wiki/Methods_of_computing_square_roots https://en.m.wikipedia.org/wiki/Methods_of_computing_square_...
chrisbrandow 7y ago
There are many stories of how Feynman did fairly profound work in an offhand way. Two that I can remember: 1. A number of times, young professors would visit with him when they were in town to give a lecture, and would discuss a recent result they had come up with, and Feynman would say that reminded him of something, pull out a sheet of paper from his drawer, and say effectively, "yes, looks like your result is correct". 2. A more specific version of that was captured in the link below, when Feynman worked out blackhole radiation on a blackboard with some grad students over lunch. The blackboard was erased and the result lost until Hawking published the same result a year later, propelling him to fame (deserved, of course). http://nautil.us/blog/the-day-feynman-worked-out-black_hole-radiation-on-my-blackboard http://nautil.us/blog/the-day-feynman-worked-out-black_hole-... He was a gifted theoretician with an ability to see how/why things worked and had the mathematical ability to express that understanding rigorously.

SamReidHughes 7y ago

That loop is known as Newton’s method, applied to square roots, it is very well known and taught in intro calculus classes.

grey--area 7y ago

Here's the method that's being applied: https://en.wikipedia.org/wiki/Newton%27s_method https://en.wikipedia.org/wiki/Newton%27s_method It's an iterative method for finding x such that f(x)=0 for a given function f, in this case f(x) = x^2 - N, where N is the number you want the square root of. The special case has such a simple expression, though, that I'm tempted to commit it to memory. Edit: Another nice example, for when you have access to a calculator that can compute powers but not logarithms: a' = a - 1 + x/c^x will converge the base-c logarithm of x (though it will converge slowly if you start very far from the solution).

fastbeef 7y ago
At it's core, it's also what drives Carmack's Fast Inverse Square Root (https://en.wikipedia.org/wiki/Fast_inverse_square_root https://en.wikipedia.org/wiki/Fast_inverse_square_root). Yes, yes, I know Carmack didn't invent it.
acqq 7y ago
The method in question was known for millennia before Newton, it is believed to be known to Babylonians: https://en.m.wikipedia.org/wiki/Methods_of_computing_square_roots https://en.m.wikipedia.org/wiki/Methods_of_computing_square_...

chrisbrandow 7y ago

There are many stories of how Feynman did fairly profound work in an offhand way. Two that I can remember: 1. A number of times, young professors would visit with him when they were in town to give a lecture, and would discuss a recent result they had come up with, and Feynman would say that reminded him of something, pull out a sheet of paper from his drawer, and say effectively, "yes, looks like your result is correct". 2. A more specific version of that was captured in the link below, when Feynman worked out blackhole radiation on a blackboard with some grad students over lunch. The blackboard was erased and the result lost until Hawking published the same result a year later, propelling him to fame (deserved, of course). http://nautil.us/blog/the-day-feynman-worked-out-black_hole-radiation-on-my-blackboard http://nautil.us/blog/the-day-feynman-worked-out-black_hole-... He was a gifted theoretician with an ability to see how/why things worked and had the mathematical ability to express that understanding rigorously.