No stalgia

So I’m back on UT campus for the North American Summer School of Logic, Language, and Information.  I get to take nifty classes like

  • Stochastic Lambda Calculus and its Applications in Cognitive Science
  • Logical Dynamics of Information and Interaction
  • Extracting Social Meaning and Sentiment
  • Social Choice Theory for Logicians
  • Lambda: the Ultimate Syntax-Semantics Interface

at the crossroads of language, cognition, logic, and computation.  Not for the first time, I wish I had a stronger math background. Knowing what I know now, I probably should have gotten a math/stats/CS degree instead of EE.

Anyway, wandering around campus during the lunch and dinner breaks, I see the campus has remained largely unchanged. Oh, UTC has installed large plasma displays for teaching. The game shop I went to every week in Dobie Mall is gone, as has the theater, and half the food court is shut down. But the Drag is still the Drag. The buildings and grounds look the same. 24th Street is still way too narrow for a major 4-lane artery connecting campus to Mopac.

I don’t remember too much from the four years I spent here, nor do I find myself really wishing I did. This was the wrong major for me. This was the wrong school for me. Of the people I met here, there were plenty of good times, but the ones that stand out are best left in the past now. It is a past I don’t want to be hung up on.

I bring this up as I will be leaving Berkeley soon. And I realize I’ve been preparing to leave Berkeley for the best part of the year. I’ve gone from the guy with a laptop at practice to who’s that guy just sitting there? I am already missing this place, and perhaps I have unconsciously been trying to soften the eventual parting. It’s a bit strange because most seniors try cram as many experiences as they can before the next chapter of their life sweeps them away. Not that I’m a senior. Perhaps four years is not enough in a place, but eight is?

Or perhaps it is because many of the people who have made Cal special to me have or will soon be moving on.

Factor-y

I ran across a neat little trick today for factoring quadratics.

Let’s start simple: factor x^2 + 11x + 24.  To this, most people would start by finding factors of 24 because we need two numbers that multiply to +24 while adding to +11.  Well 1,24 would sum too high and 4,6 would sum just a little too low.  Nearby, 3,8 works out.  x^2 + 11x + 24 = (x + 3)(x + 8).

How about factoring 6x^2 – 11x + 10?  This is a bit more annoying because now we have to factor both 6 and 10, check pairwise combinations, and try both permutations of which factor of 6 multiplies which factor of 10.  There are a lot more combinations to check.

However let’s transform this problem into a similar problem: factor 6(6x^2 – 11x – 10) = (6x)^2 + 11(6x) – 60 = y^2 + 11y – 60, where y = 6x. This factors to (y – 4)(y + 15) or (6x – 4)(6x + 15). However, there is an extra factor of 6 in there, which we remove to get (3x – 2)(2x + 5).

In summary, we turn an annoying problem we’d solve by trial and error to one that can be solved by less trial and error. Okay, we’re replacing factoring two small numbers with factoring one large number, but we have a heuristic to guide the latter in that the sum/difference of the two factors behaves in a simple manner.

tl;dr taking the time to turn a hard problem into an easier problem may save you time in the long run.