This article is an interesting read for two reasons: firstly, and most obviously, is the discussion of the problem in question. Secondly, is because the user comments highlight the basic difference between mathemeticians, engineers, and liberal arts majors.
The mathemeticians take the problem at face value, and solve it as an interesting puzzle that is to be reasoned through. The engineers all say the problem is stupid because it makes no sense and ignores all sorts of real world considerations, like micro-fractures in the surface of the bowling ball. Then they try and come up with all sorts of other ways to solve the problem, such as vise grips, terminal velocity calculations, etc.
Some would say this indicates that engineers are better at thinking "outside the box", and that mathemeticians are not as creative. I would argue that the converse is true, that instead this shows that engineers are incapable of thinking of anything but the box, i.e. the real world. Mathemeticians have no trouble dropping the pretext of reality and imagining something simply in the abstract for the sake of an interesting puzzle that demonstrates how well you can reason through a problem. Of course they know that there are better ways to test bowling ball resilience, and that there are inherent flaws in the test, but that's not the point of the problem. Engineers, on the other hand, can't get their heads around the idea of a problem that doesn't use the normal rule set they are accustomed to, and instead, try and change the problem to better fit into the box in which they are used to thinking.
In short, Kirk thought like an engineer. When presented with a problem that didn't allow him to work within his usual frame of reference, he changed the problem so he could.
And the liberal arts majors? I'm pretty sure this comment was left by one.
So do you think like a mathemetician, an engineer, or a liberal arts major.
Interesting comparison. I don't know how to distinguish between the problem solving skills of the engineer vs the problem solving skills of the mathematician. I'd like to say that an engineer only brings to the table what he already knows, but that's simply not true. And I'd like to say that a mathematician sticks within the bounds of the problem, but I'm not sure that's true either. If mathematicians stuck within bounds, then where did imaginary numbers come from? (strange sense of about-to-be-learned sets in) The only difference that sticks out to me as far as those two groups go is the engineer needs actual results to deliver to someone, where the mathematician only needs to show that it can be done.
ReplyDeleteAs far as the people commenting on the problem, I wouldn't say so much that the people who want to test with a fresh ball every time were engineering types, because they weren't approaching the problem the way a software engineer would. They were just too small minded to work on an abstract problem. The problem could have been replaced with variables and software constructs and the solution would have been the same, but the small-minded crowd just wanted to find some reason to say that the example didn't work. My guess is that they won't work either.
I generally desire the results that a mathematician in me would produce. But given my limited flashes-of-insight* and time limitations on development, I tend to crank out engineering type solutions.
*unless I misunderstand the nature of a good mathematician, I kind of think that kind of mind needs regular flashes of insight. I found it very frustrating to see something like 8 proofs on a math test in college to be solved in an hour. From my perspective those problems required flashes of insight or they wouldn't be proofs, they'd just be "the obvious". I'm not good at producing 8 flashes of insight in an hour. At best 6.
or maybe I just don't understand the difference between the two
ReplyDeleteI almost struck up enough gumption to read the whole thing... but wayward Liberal Arts education forced me to respond to this post..
ReplyDelete"meh..."
My solution: "get an intern to figure it out and create a computer simulation proving his answer for me"
Given an endless supply of expendable labor, I can do anything.