The Feynman Lectures on Physics: Algebra (1963)

[jihadjihad]

One thing I will always appreciate about Feynman as a teacher is that he never shies away from telling you why things work the way they do. I've spoken with a lot of people who "hate math" and it's almost always because they never had a teacher that went into the whys and wherefores behind equations, tables, graphs, etc.

Here we have a plainspoken yet rigorous explanation of what algebraic operations actually mean (addition is iteratively adding 1 b times; multiplication is iteratively adding a b times; exponentiation is iteratively multiplying by a b times, etc.).

I wish more students would have the chance to build up such intuition, for such intuition is the key to keeping oneself interested in math and not finding that one "hates" it.

[djmips]

It is thought that multiplication is better explained to mean scaling a by a factor of b. This is better illustrated by a diagram. I believe that 3Blue1Brown covers this graphically in several videos. For one, it better unifies division with multiplication as an inverse scaling.

[acpetrov]

I stopped enjoying math for about this reason. My university tried to teach with proofs, which to me is about as far from an intuitive understanding as possible

Looking for recommendations on lectures / course that goes over linear algebra in this way

[curiousgal]

I'm sadly now convinced that that approach only works for "simple" concepts. For instance I am yet to find a single book, course or teacher that can explain measure theory in a way that cultivates intuition.

[mr_gibbins]

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.

[chrisbrandow]

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-...

He was a gifted theoretician with an ability to see how/why things worked and had the mathematical ability to express that understanding rigorously.

[grey--area]

Here's the method that's being applied: 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).

[SamReidHughes]

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

[jameshart]

There’s something delightfully physicsy about deriving Euler’s identity, which famously deals with the irrational and the imaginary, by brute force calculation using log tables and fudging the fifth decimal place. But the approach of sneaking backwards into the algebraic continuation of e^x by actually doing the arithmetic is a great way to viscerally get that it’s all just the same set of mathematical tools.

[michelpp]

If you can find it an audio recording of this lecture is also available and it is one of the best lectures in the series. Feynman really brings forward the "soul" of algebra and the illustrates how powerful the art of abstraction is. Audible has all the audio lectures for sale, which is how I got them on my kindle, and I have also seen them floating around the net in other formats. I wish Caltech would release the audio material like they did the books!

[arunix]

The article has a link to a page which has the audio:

http://www.feynman.com/the-animated-feynman-lectures/

[enriquto]

The Feynman lectures is one of my favourite books ever. Yet, this chapter specifically is the least enjoyable for a mathematician. Somehow I find he's trying to explain very simple concepts using way too many words, which is the opposite style of the rest of the book.

[jonjacky]

It's deliberate. In his book The Character of Physical Law, Feynman discusses some differences in how physicists and mathematicians approach math.

[xref]

I was reading the 1993 bio Hard Drive about Bill Gates recently (great to go back and read old books centered on tech, really makes you remember why people hated Bill/Microsoft...and he’d barely gotten started!) and it mentions several times that Gates would watch these lectures in what he considered his “down time”

[gerbilly]

My high school math teacher taught us a class where he followed this general outline, building up the number systems based on which equations we couldn't solve.

Now I know where he must have gotten it from.

I think it must have been around grade 10 or 11.

[mrcactu5]

He does a numerical computation of the complex powers of 10 (to five decimal places) and they still are on the unit circle. And this was done in 1963.

[smcl]

This specific Feynmann Lecture popped up very recently either here or on lobste.rs. I have since bookmarked the "FLP" series as I really want to come back to it, but I'm curious if there is any significance to why the Algebra lecture in particular was submitted a couple of times. Is it just coincidence, or was it a particularly good one?

[tim333]

It's one of my favourites. Aside from Feynman's clear and enthusiastic style, I find it's remarkable you can start from counting 1,2,3 and by a bit of reasoning come up with logs, complex numbers and:

>This, then, is the unification of algebra and geometry.

I can't help wondering if you could go further and come up with some physics.

[StephenDaedalus]

It recently went rather viral https://twitter.com/Adam8Hasan/status/1137081098381484032

[BucketSort]

I bet it has something to do with the build up to Euler's formula, which is famous for blowing people's minds.

[sooheon]

The first paragraph seems to address this: because it's enjoyable.