Wrong Room

Tuesday is the first day of class and, whether you've had the carpet pulled out from under you (damn last minute Axess updates) or you're just oblivious (drinking while scheduling, smudged your sticky note, etc.) you are going to walk into the wrong room at least once. What then separates the sheep from the goats will be how long it takes you to realize your error.

If you're fortunate enough to be late, you'll be the subject of somewhere between 20 and 200 inquisitive gazes. The room has thus granted the shrewd arrivee a small window of opportunity to survey the distribution of a few critical demographic features of the class population at large, and from this determine whether to get comfy or awkwardly about face and book it for the nearest Bulletin.

There are several dimensions over which you might modulate your visual search:




...or perhaps not by the faces themselves but the things in front of the faces:



If the student conglomerate fails to be conclusive, a glance at the composition of the instructor's jacket may swing your running mental probabilities:

It can prove fruitful to consider things like the density of visible body modifications (a preponderance implicates Art History), average muscle mass, proportion of intentionally coordinated outfits, and ambient smell.

With a solid combination of quick and dirty heuristics, you're almost sure to save yourself the mortification of leaping up and bolting 15 minutes into lecture when the syllabus with a surprise course title is handed out.

Physics Triumphs Once Again

Thank you, Abel, for finding something more fun to do on a Sunday afternoon than a first-order logic problem set. The traer particle system physics engine, developed by our friends at Princeton, is a package for the Processing programming language that abstracts much of the gross minutiae of the force-modeling process behind a clever object oriented API.

I extended the concept behind one of the example applets to include a *few* more particles. It's sort of fun to play with:





Here's the source. Also, the default picture I used when writing the thing. In accord with the lore of one physics instructor Tom Haff, we find it appropriate to remark, "PTOA!"

If They Could Speak

What would uninhibited logos say about their backing technology?

The Code Bomb

Statistics With Commentary

Professor Balaji Srinivasan, on...


...the essence of probability:
"Curtis flips a 50 cent piece: head equals get rich, tails equals die tryin'"

...bimodal distributions:
"One hump, two humps, my humps, my humps"

...set operators:
"Someone let loose at the U factory"

...n-choose-k combinatorics:
"Just hope you didn't pick the poisonous cracker jack"

...discretizing continuous random variables:
"In my country there is problem, and problem is random variable"

...whiteboards:
"I'll do to them what Saddam did to the Kurds"

...joint distributions:
"five little six little seven little RVs"

Venn

Inspired by row manager training.

You Can't Measure Fun

The question often arises, at a precise moment in time, which party goer is a greater asset to the general ambiance: the modest slow burn or the fashionably late social butterfly? The decision is particularly convoluted exactly when the two appear to be socially on par with each other. How shall we characterize their respective states in this crucial slice of time? First, some units with which to conduct an empirical analysis...

Let's define the dimensionless unit Gregariousness (G) of party goer x to be the amount of joy that x contributes to himself and his peers through his presence. As Gregariousness inevitably varies over time, due to influences in the social environment, it will also be critical for us to define the unit of Sociability (S) as the time-derivative of Gregariousness - that is, the instantaneous rate of change of joy-providing with respect to time.



Although party goer 1 is currently more gregarious than party goer 2, PG1 has aggregated this charisma over the course of the afternoon and evening, while PG2 has just stepped in the door. But, here we must consult our derived unit to see how they really measure up! PG2 seems to be aclimating to the firendly company at a much higher rate than PG1. We can say that, although PG1 has greater total gregariousness, PG2 has significantly higher sociability.

Since we are dealing with scalar valued data, these individual measurements allow us to make some quick calculations about the party at large:



We have earlier established that gregariousness varies according to "influences in the social environment." This is an important generalization that swings the door wide open to some very interesting analysis.
Consider modeling sociability in n-dimensional space as a function of n "social environment variables."



The resulting manifold is everywhere continuous, differentiable, and orientable, and thus integrable as a non vector-valued surface. For the example above:



Conceptually, we can resolve an individual's net gregariousness by observing how his or her gregariousness has varied according to several party variables, modeling this variation by a function, and integrating over the measurement interval. Simple in principle, but horrendous in practice, as the time component of S must either be directly parametrized by (or otherwise coerced into) the SI units of the control variables.

Searching The Dendritic Arbor

Here to augment my theory of personality classes is a rough-handed take on a few major search algorithms, as implemented by the brain. Applies to decision making, pattern recognition, problem solving, or idle musing.




Class A - The Pragmatist
Meticulously reviews all of the most basic options/choices/solutions at his or her disposal before deciding to pursue any one idea further. Rules out the possibility of barking up the wrong tree for an extended period of time, and instead decides to weigh the options before committing to a deeper train of thought. Generally slow and steady, caching many thoughts at once. Contemplative.

Class B - The Eager Beaver
Prefers to drive directly towards the silver bullet solution, complicating or evolving their current strategy at each point of re-assessment until a dead-end is reached, at which point he or she will attempt slight but successively more drastic modifications to the tail of an exhaustive train of logic before backing up, giving up, or beginning a new approach entirely. Impulsive. Gets the conversation rolling.

Class C - The Skeptic
Always weighing the value of further complicating a potential solution path against the likelihood that the solution can be found much closer and with much less effort. He or she will not do any more analysis in a current state than what they believe to be the bare minimum to move towards a meaningful and complete solution. Prefers to begin a new train of thought once persisting in the current train becomes sufficiently laborious, returning only when the new train grows more tedious still. Owns a lot of Belle and Sebastian records.

Class D - The Empiricist
Works as fast as the Beaver, but refuses to sacrifice the thoroughness of the Pragmatist. This uncompromising approach often necessitates checking and rechecking the continuity of the solution path along the way: the most obvious course is charted, then abandoned, re-charted and advanced to a deeper degree, then abandoned, and so forth. Although he or she may discover a simple, elegant, verifiable solution while the Beaver is still tumbling down a bottomless rabbit hole, it can take a painstakingly long time to aggregate a technically complicated, intricate, or nuanced solution. Patient, and tenacious. While you all went out to lunch, the Empiricist nuked a pepperoni hot-pocket and never broke stride.