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I no longer understand my PhD dissertation

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Re: I no longer understand my PhD dissertation

#11

Post by closure »

This does not surprise me in the least.

Math was always extremely easy for me growing up. Up through my first differential equations class I found almost everything trivial to learn (the one exception is that I always found proving things difficult).

I made the mistake of minoring in math and that slowly killed my enjoyment of it. Once I got to differential geometry and advanced matrix theory it all just became too abstract and I just wanted to get away from it.

For several years after college I would routinely pull my advanced calculus text out and do problems "for fun". After a while I stopped doing that. Within a few years of no longer being exposed to math, I found it all incredibly foreign and challenging, to the point where I would say I have a bit of an aversion/phobia to it.

I'm trying to reverse that now by tackling a topic I'm interested in but have previously avoided due to the math-heavy nature of it - type theory.

Hopefully I can find the joy in math again through this.

I think my point is that you can lose competence in math very very quickly through lack of constant exposure.

The same is probably true of programming but I hope to never end up in that position.

Re: I no longer understand my PhD dissertation

#12

Post by jholman »

All of these arguments are arguments for replacing the mathematics curriculum with video gaming. Games require generalized problem solving (arguably better-generalized than math, and arguably better-transferrable to other domains). Games build character: grit and tenacity, cautious optimism, etc blah blah etc. And games are fun (for many more people than find math fun).

Guess math teachers should start learning to play League of Legends and Pokemon.

Alternatively, I guess we need better reasons than those to teach a subject.

Re: I no longer understand my PhD dissertation

#13

Post by tluyben2 »

jedberg wrote: post #3

> Beyond scarcely stretching the boundaries of obscure mathematical knowledge, what tangible difference has a PhD made to my life? The same thing a bachelors degree does for everyone else. You've proven that you can start, stick with, and complete a task that takes multiple years and a complicated set of steps.

Which feels like a 'life is suffering' weirdness. I did it and never needed my diplomas for anything. Maybe I benefited somehow but I was a coder and entrepreneur before that; I had a software company before uni. It was over 20 years ago and in hindsight I find it pretty pointless and a waste of time. Maybe I became a better problem solver on some level but unless you are going into research or are not a self starter I would not recommend it.

Re: I no longer understand my PhD dissertation

#14

Post by csense »

TLDR: The author independently re-discovered what you may know as Old Code Syndrome.

I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition.

This guy's basically in the position of a fairly new developer who's just been asked to do non-trivial update of his own code for the first time. All those clever one-liners he put into his code made him feel smart and got the job done at the time. But he's now beginning to realize that if he keeps doing that, he's going to be cursed by his future self when he pulls up the code a few months later (never mind five years!) and has zero memory of how it actually works.

I'm not intending to disparage the author; I've been there, and if you've been a software developer for a while you've likely been there too.

Any decent programmer with enough experience will tell you the fix is to add some comments (more expository text than "it is obvious that..." or "the reader will quickly see..."), unit tests (concrete examples of abstract concepts), give variables and procedures descriptive names (The Wave Decomposition Lemma instead of Lemma 4.16), etc.

Re: I no longer understand my PhD dissertation

#15

Post by pmarreck »

closure wrote: post #11

This does not surprise me in the least. Math was always extremely easy for me growing up. Up through my first differential equations class I found almost everything trivial to learn (the one exception is that I always found proving things difficult). I made the mistake of minoring in math and that slowly killed my enjoyment of it. Once I got to differential geometry and advanced matrix theory it all just became too a…

> type theory

Not sure if related to your username, but I have a book on it (that was recommended to me here, in fact) on this topic, which I was curious about due to its implications in the programming field

Re: I no longer understand my PhD dissertation

#16

Post by MicroBerto »

My response is that for every 100 of these types of papers, one of them may prove to be pivotal or inspirational in something truly groundbreaking and functionally useful. For this reason, I am all for 100 different people spending their time doing things like this, because eventually one of them will make an impact that is greater than 100x the efforts of 100 normal men.

It's just a different kind of "brick in the wall" - only the diamonds in the rough can turn out to be hugely important for something else in the future.

Re: I no longer understand my PhD dissertation

#17

Post by zarkov99 »

closure wrote: post #11

This does not surprise me in the least. Math was always extremely easy for me growing up. Up through my first differential equations class I found almost everything trivial to learn (the one exception is that I always found proving things difficult). I made the mistake of minoring in math and that slowly killed my enjoyment of it. Once I got to differential geometry and advanced matrix theory it all just became too a…

The same is indeed of true of programming, at least in my experience. I took a management/consulting detour that lasted about 18 months and getting back into programming was quite though. I could not focus, could not hold the problem in my head, could not go from design concepts to implementation details. It took me a solid 6 months to get back to my former level.

Re: I no longer understand my PhD dissertation

#18

Post by eru »

closure wrote: post #11

This does not surprise me in the least. Math was always extremely easy for me growing up. Up through my first differential equations class I found almost everything trivial to learn (the one exception is that I always found proving things difficult). I made the mistake of minoring in math and that slowly killed my enjoyment of it. Once I got to differential geometry and advanced matrix theory it all just became too a…

> (the one exception is that I always found proving things difficult)

Proofs are at the heart of math. Everything else is something different.

Re: I no longer understand my PhD dissertation

#19

Post by chipsy »

It speaks to how finite we are around "knowledge." At the moment we reach understanding, we experience a sophomoric feeling of confidence. But as it fades farther and farther from our working memory, we become less fluent and more hesitant. The emerging pattern becomes one of "I can understand these interesting concepts, but it takes a lot of work and they don't last, so I have to choose to understand practically and situationally." And then in the end our bodies and personalities turn out to control our minds more than we might want to believe, as we turn away from one problem and towards a different one on some whim, never able to view the whole.

As I recognize this more in myself, I am more inclined to become a bit of a librarian and develop better methods of personal note-taking and information retrieval, so that I lose less each time my mind flutters. At the moment that's turned into a fascination with mind maps - every time I need to critically-think through a problem I start mapping it. In the future I might look into ways of searching through those maps.

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