Consider the daily trek I make from my apartment to places on campus. The eternal question beckons: which is faster — busing or walking? Here I will make a mathematical argument for why it could be the latter or former.
This Valentine’s Day, I am fortunate because I have four dates, instead of only one.
I get to hang out with my yearbook friends, many of which who are (surprisingly) single.
I get to have a night with photography, and I’ll be enjoying it with my photo team. And it’ll be extra special for me, because those who come put photography and their respects to their time commitments above Valentine’s activities.
I’ll get to do math. If not because of my problem sets due that day, then because of my own problems that I’m still working out.
And finally, if all else fails, I can still have intimate moments with tornadoes that blow harder than anything you can imagine.
Nietzsche once said that humans are the “as-yet-undermined-animal” (Beyond Good and Evil, Part 3). Now think about that for a second. What he implies is that every other being on Earth has its life cut out for it. We can, to a certain degree, predict what a squirrel does every day. Or a tiger. Or a table. They have purposes, so to speak — they have their destiny. We, on the other hand, have a large degree of autonomy; we make our own destinies.. But we use our autonomy in varied ways — some good, some questionable, and some terrible. And so we wonder about each other.
First of all, what is a square-integrable function? Wikipedia provides this definition:
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real– or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, if
then ƒ is square integrable on the real line . One may also speak of quadratic integrability over bounded intervals such as [0, 1].
The important part is seeing that if the integral of the square of a [Real-valued] function is finite, then the absolute value of the function must converge to zero at +/- infinity, by common sense.
Now the thing that really got me thinking about this was, there have been a lot of good things that have run their courses in my lifetime thus far. Continue reading →
Wow, I was 1-1 in my Conference Championship predictions. Maybe I should stop predicting against the Ravens…
The Super Bowl prediction is a tough one. Both teams are exceptionally good. Don’t look at the regular season stats; look at postseason play. Flacco has no INTs in the postseason. Rice has always been a good back. The Ravens defense is playing inspired, having won against Luck, Manning, and Brady in consecutive weeks, and with Ray Lewis having announced his retirement. The 49ers have been no slouchers either. Their offense shredded Green Bay; their defense kept the high-flying Falcons scoreless in the second half. And this is a defense that has been plagued with injuries of late.
Speaking of which, during the Conference Championships, home teams were outscored 35-0 in the second half by the teams that ultimately went to the Super Bowl. Weird eh?
So yeah, this is a tough prediction, and I simply cannot commit to either team because both are so good, and both coaches are so good. Their superior kicker, overall better health in key positions, and Flacco’s perfection thus far make the Ravens a good pick. On the other hand, the 49ers have had a tougher schedule, and the NFC has really been the superior conference this past year. Conference strength seems to be a good predictor of the Super Bowl victor, and this year, the NFC has been loaded with fairly competitive teams (Packers, Giants, Seahawks, Falcons, Bears, Vikings, Redskins, Saints). On the other hand, the AFC is more stratified, with notable tiers of greatness (during the regular season, the Patriots and Broncos were on top, followed by Texans, Ravens, Colts, and everyone else was really at a much lower level).
More on this conference thing. In fact, if you go back the last decade, the AFC has been dominated by the same few teams — the Patriots, Steelers, Colts, and Ravens to some extent. As for the teams that have gone to the playoffs in the past 5 years: the Chargers, Broncos, Texans, Jets, Patriots, Colts, Bengals, Ravens, and Steelers. The NFC has been more varied — the Cardinals, Saints, Giants, Cowboys, Falcons, Vikings, Bears, Packers, Eagles, Seahawks, Lions, and Panthers have all gone to the playoffs sometime in the past 5 years. And in fact, 4 of the last 5 Super Bowls have been won by NFC teams — the Steelers and Patriots of yesteryear have clearly declined over time, and the AFC is reshuffling its elites. Meanwhile, the NFC seems to circulate its elites and talent throughout the conference — so many teams are near the top, that any slight perturbation shifts the Lombardi candidate to another team. So the teams have more preparation, because they know their competition is stiff.
Okay, back to the Super Bowl. The kicker thing is really bothering me for the 49ers. And it’s really hard to predict against the Ravens again after getting burned three times. But regardless of the victor, you know this is going to be a competitive game — sibling rivalry at its best.
Final Score: Niners 17, Ravens 16. Very low confidence.