Shevek (shevek) wrote,
Shevek
shevek

Today, I get to use my maths degree in anger. It is actually relevant to my job that I know the axioms of a metric space.

Is the ability to visualise the operation and state of a machine learning algorithm a trait of dyslexia? I suspect so, even though it's a continuous space (often of functions), and I'm more used to managing discrete spaces (data structures). I like to think of dyslexia as a continuum between symbolic and spatial thinking, and I treat it as an advantage, rather than a disadvantage. I also think teaching methods today are too biased towards the symbolic methods - it's perfectly possible to grasp (and teach) topics including advanced group theory, almost anything in computing, analysis, game theory, and so forth visually. I think I had most trouble with the subjects for which I couldn't build an effective visual model. I flew through metric spaces, because it was all about intersecting epsilon-balls, and once you have the proof that the order of the measure doesn't matter, it's just like ... hm. Symbolic vocabulary runs out at this point. It's just like filling in an n-dimensional space with balls which might be square? Um. If you can visualise dense and separable sets and completion of a space... um. Let me draw you a picture.

It's odd that I've been working as a statistician for a while now, and I didn't specialise in stats - although, the statistics I'm using is mostly basic and can be gleaned from the textbooks smeared around my desk and a basic understanding of the theory. It's mostly to make sure that the work we are doing is valid, robust, significant, and so forth, which can be done from the fundamentals. The teaching of statistics is VERY symbolic, and some of the standard presentations are very hard to grasp. It wasn't till I picked up an engineering textbook that the poisson distribution was explained as a special case of the binomial, and then it all made sense. What's far more important in my job now is a really solid grounding in algorithms and machine learning theory.

I think people get more use out of a degree than is often believed.
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