I realized something today. I do not learn advanced concepts well. This is a known problem. There's probably a lot of reasons why this is, and I have a decent idea about a few of them, but today I thought of a new one.

I am pretty smart. Or at least all the tests always said I was, and looking around for the past 20+ years affirms that. The key problem I've had for some time is that I might be a little too smart, and it's led to problems later in life.

I remember when I was young my father (a mainframe programmer) would get calls late at night when a program went bad. He'd sit there, right after being awoken in the middle of the night without a computer and quote line numbers to the guy on the phone regarding what code to fix. My childhood memory wasn't quite that good, but spelling tests are easy when you can recall the image of the word in the spelling book.

The other thing that made schoolwork easy was the ability to pattern match and do kind of extrapolation. A sentence's grammar is something of this type followed by a different type, followed by... fits mentally right in with algebra behaviors. And that's usually how I'd learn new things. The new thing follows this pattern, or the new thing behaves like this known thing.


So these sort of things were great in school. Most of (US, public) school is just memorizing and regurgitating things. The rest is learning pretty similar concepts in a vaguely different form.

Now as an adult, they're kind of sucky. My memory is mostly gone. I'll remember the shape of the license board in FFX or where we left off in the last D&D campaign or the ID of the user I worked on yesterday or who the Steelers quarterback was when they tied Atlanta... but not reliably anymore. And code? No way. It doesn't fit into the shape or pattern or however my memory likes it.

And as it turns out, mapping new concepts into old concepts only goes so far. It goes a hell of a long way mind you, but eventually you need (a few) new concepts to really know something different. And it's hard to get them when you've never needed to.

Perhaps more significantly, I have problems communicating certain things to people. I'll tend to describe coupling oddly for example. That the data organization should line up like a tree; just as actual personnel organizations and areas of responsibility; just as a graph of sciences and their interactions or a game's tech tree. I tend not to make any distinction between any of them, and the abstract concepts of relations, interactions, parents, 'weak' sort of ownership are all still sort of there even if they're not commonly used in that particular tree. And that leads to problems sometimes when other people just don't think of them that way.


Anyways, as I was saying, I realized something today. Another facet of learning problems I have is when people abstract stuff for me. I was looking at the wikipedia entry for Limits in category theory and my brain shut off. Not exactly surprising. But this time I realized why I hate greek lettering and the general 'blah is defined as blah op blah to blah blah blah op' that is universal to higher math resources and not a few programming language books/articles/guides. I can't conceptualize greek.

I just can't form a symbol in my head to represent the first element of the relation/equation. X is fine. I know what X looks like, what it sounds like, and reading it I can get a handle to 'some placeholder named X'. Greek? Can't do it. Things that I'm not sure are placeholders, or are some new abstract concept I don't know? Can't do it.

Further, I don't learn by taking an abstraction and specializing it to cases. I learn by taking hard examples (which give me nice solid things to use as symbols/images while thinking) and extrapolating them into the general case. So compare that wikipedia article to this haskell tutorial regarding list comprehensions. That tutorial is what kinda set off the light bulb for me today. It was the first thing I thought of after my brain rebooted. It's the same sort of math gibberish I have problems with, but it starts with an example. No problem at all learning what it is and even the mathematical notation it's based off of.

It starts with a nice set as the visual symbol and then edits it as the tutorial goes along describing what the example comprehension is/does. It describes what everything is in the example, and relates it back to the mathematical roots so that mentally I can make that footnote. It then does progressively more complex things, but always again from an initial state. It works fantastically for me; someone who starts with a known concept and maps new concepts to it, expanding or adapting the original concept as needed.