Posts tagged with "mathematics"

Why is it that makes mathematics so inscrutable?

It reminds me of my naive days at university learning computer science. I held Perl in high esteem, although I never knew it well. Because of its opaqueness it made me feel like I was in an exceptional group of people.

A couple years later, during my first job after my education and having not touched Perl since, the company I worked for contracted with an individual to develop a web application. After the application was created, and in use, the business owner desired to continue development on it and so asked me if I could continue its development. I cautiously accepted the task. Upon opening the project I immediately knew I would not be able to productively continue development of the project. I went back to the business owner and told him the web application is beyond my ability. That given time I could figure it out, but it wouldn’t be an efficient use of my time. I felt defeated. It was later that I learned Perl is considered a write once read never language.

From then on I began prioritizing the readability of applications I create. I still often do not succeed in this goal, to the extent which I would like, but I am very mindful of this quality.

I’m undetermined if this quality is of less importance with AI coding agents. I don’t think it is less important. It still seems very helpful to coding agents to have well structured and readable codebases. Additionally, it still seems important for humans to be able to read and understand the code as the application is being built by the coding agent, to both direct and correct the generated code.

Mathematics to me is like Perl. Instead of welcoming people into the world of mathematics it feels mathematicians have created walls around their knowledge keeping people out. It is true symbol use is of value to those intimiate with its usage, but it is a barrier for all other audiences.

I was reviewing Bayes’ Theorem. At first site the equation appears intimidating. But if you understand the equation it is fairly simple. Because of the way it is written our brains needs to go through several layers of translation, mapping each piece to their meaning, which is then mapped to the scenario at hand. It seems better to me to present the equation written out, have one less translation, and less prior knowledge needed. Others unfamiliar with the equation will immediately gain an initial understanding of what it means, instead of feeling defeat.

Probability of A given B = Likelihood B assuming A * Prior belief about A / Sum of likelihood of B for all scenarios

Edit:

It seems David Bessis is of a similar mind, A Mind-Blowing Way of Looking at Math (with David Bessis).

The issue with mathematics is it’s something that manifests itself in a horrible way. It’s on paper, on the blackboard; you see cryptic symbols, formulas; and this is impossible to make sense of. But, how you interact with that—how you gradually tune your intuition to build up meaning for the symbols—is the real art of mathematics.

Math books are written in a certain way that follows a certain logic that is called logical formalism. It’s a kind of recipe for building mathematical objects, but the words make no sense to you when you open them, so you can’t read them.

That was what I call the tourist menu. He was showing me the tourist menu with the kind of very formal dishes that nobody really wants to eat, but they look like it’s a fancy place. And, he was presenting his research mathematics the same exact way.

And, when I told him, ‘Please repeat. Repeat it as if I had some disability, as if my brain was damaged. Because I am jet-lagged, I’m tired, whatever, I’m stupid, I’m a slow thinker. Please be as simple as you can, I don’t understand anything.’ So, when I did that, I gave him the permission to serve me the true menu, the thing for the locals—how he really himself looked at his mathematics. And he was using different words and describing the situation using very simple images, examples. And it was a different thing.