Feynman: 'Greek' versus 'Babylonian' mathematics

“In mathematics and theoretical computer science, we read research papers primarily to find research questions to work on, or find techniques we can use to prove new theorems.” This is why figuring out an elegant, concise, and powerful set of mathematical models which apply to multiple domains, and then devoting effort to simplifying, organizing, and explaining those ideas in an accessible way is so important. Incentives for researchers are mostly to push and prod at the boundaries of a field, but in my opinion mathematical ideas are only of marginal value in themselves; more important is the way they help us understand and interact with the physical universe, and for that building communities, developing effective languages and notations, codifying our understanding, and making it accessible both to newcomers and to outsiders is the most important task for a field, and perhaps for our society generally. Just like with software projects or companies, the most “success” comes from helping a range of other people solve their problems and extend their abilities, not from making technically beautiful art projects for their own sake (not that there’s anything inherently wrong with those). Perhaps more generally, while theorem proving has overwhelmingly dominated pure mathematics and related fields for the past 80–100 years, and has been an important tool since Euclid, theorem proving is only one way of approaching the world, and in my opinion is a mere tool, not an end in itself.

> What is simple and clear about Python? .. it's really a pretty complex language with a deep ecosystem Here's a helpful video from Feynman that kinda explains it: [VIDEO] Python language (ditto Perl, Ruby..) uses Babylonian approach, while the languages with more fundamental building blocks (like say Scheme, Haskell..) are more like Greek approach. So Python it is not simpler as a language per se, but it is simpler to mold onto the problem. At least that's my explanation why people (myself included) like to use it, despite well understanding there are more elegant (mathematically) languages out there.

> causality is still a strong axiom The "causality axiom" is a nice (or trivial) statement in philosophy. But as far as we know, there's no such axiom in any mathematical theory proved to match physical reality, and nothing so clear cut in modern theoretical physics at all afaik... Also, physics isn't that much built on axioms, in general: [VIDEO] (Summarizing Feynman: you still get from time to time cases where you can prove something from "axioms", but then you also find it to still hold in contexts where the axioms don't apply, or even to not work in others where they do apply... and the latter is the case where you have to remake your theory to match reality ) But my main point is that considering something impossible simply because our puny ape brains can't fathom them is preposterous!

Here's the part of the lecture mentioned in the article: [VIDEO] Feynman was an excellent communicator, it's rare that having an intermediary "explain" what he was saying adds more than it takes away.

There is no such thing as "bottoms up" in mathematics, I think a relatively broad examination of mathematics might be useful so that you can discover what is relevant to the subjects you are actually interested in. I learned this the hard way. Here you have Feynman talking on this: [VIDEO] Finding a real world use case for the math you learn will be crucial if you self-study to keep yourself motivated to keep going.

By linear I did not mean the order in which you study, but rather how your understanding builds up, as in, how much time you put in, and how much you grow. For example if your native language is subject verb object (cows eat grass) it is quite linear to learn subject object verb (cows grass eat) languages (e.g. Japanese), you put in time, and you make progress. There are other subjects where when you get stuck you cant move on, and the pedagogy and androgogy systems we have came up with for math/physics and etc are getting better and better to understand what people don't understand and how to move them further. Which on its own is quite problematic when you have a class of 30 kids and you are moving with the 'average' kid which does not exist. In the same time, programming is fairly new, and teaching it is still evolving, educators still disagree on what is important and in which order (reminds me a bit of this Feynman video about 'Greek' versus 'Babylonian' mathematics [VIDEO] ) There was a great example someone used, the amount of people who get confused by the equal sign, and some actually never go through understanding references and values for many years: x=5 y=x x=6 print(y) and a=[] b=a a.push(1) print(b) Now I am teaching my daughter and I spent about 3 days per week just on pointers and strings (We even made a card game we play from time to time [LINK] ), and I can see when she is stuck and what exactly she is stuck on, but how can you do that with 30 kids, when the