Where’s your problem solving happy place?

5 10 2009

I took an algorithms exam last week.  It did not go well.  I knew it wouldn’t though since I hadn’t spent much time on the material.  The interesting thing though is the difference in the parts that went well and the parts that didn’t.  Hashing and trees were no problem while recurrence relations and mathematical induction very much were.  See the difference? It’s between the concrete and the abstract; or for me, things I can visualize and things I can’t.  I know I can do them, but I’ll need to work very hard to get those abstract things down.

This leads to my question: Where do you like to solve problems?  At abstract and theoretical layers like mathematics and theoretical physics?  Fundamental layers, like the sciences and social sciences?  Applied layers, like engineering and education?  Interaction layers, like languages, communications and tools?  Observation layers like art, music and literature?

Okay, those are all my own ad-hoc classifications ranging somewhere between the smallest things and the largest things with humans and human society thrown in.  Don’t flame me, these are thoughts in progress.  Please contribute, though.

Anyway, I probably work best and most enjoy working at the level of interaction, mainly with communications and tools.  Some of may favorite leisure reading materials are tools catalogs, both high and low tech.  Why?  I think mainly because I find the *something else* that can be done with the tools fascinating, even if I don’t want to do the *something else* myself.  As far as communications goes, I think tools like Twitter, Facebook, LinkedIn, Google Voice, and the internet in general can be and are being put to good use.  (It also helps to think of them as communications tools rather than that great buzzterm “social network tool/site/blinkyflarg.”)

So I’m here to learn: where is your problem solving sweet spot?  Or, can you help clarify what I’m trying to say?





2 responses

7 10 2009

I’m not convinced the difference in the parts of the test are strictly between concrete and abstract. Unless you tell me you can’t do high school algebra, which is quite abstract. I won’t believe you if you do tell me that, though. 😉

The place I think I excel at solving problems is in a logic-based setting with rules and a guide. This is why I like programming: (1) writing programs involves thinking logically, (2) the rules are defined by the syntax and type system, and (3) the guide is the compiler and the output, telling me when I am doing something wrong. I have come to enjoy programming in Haskell, because the type system is much stronger, meaning the rules are much stricter than those of many other languages, and the compiler has a very firm hand that smacks you when you do something silly. It also means I spend less time looking at the output, because I have more confidence in the compiler.

There are other environments in which I like to solve problems as well, including design and user interface, but my sweet spot is logic and programming.

10 10 2009

“I can’t do algebra.” Seriously. I had to get help solving a polynomial to finish out a proof. It was obvious after the fact, but very troublesome before. Okay, I’ll modify this to “I find it really, really difficult…” 🙂

You’re probably right about the abstract vs. concrete. My first thoughts were that if it can be implemented in a computer then it must be concrete. But then I looked up automated mathematical induction and realized that we’ve been have computers do more and more abstract stuff, from simple arithmetic in the early years (think census) to now, well, automated mathematical induction. (I’ve been watching James Burke’s Connections series, again.)

Maybe concrete and abstract don’t have a binary relationship.

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