(Praise) The Sun

3/23/2017
Thursday
Early Morning
Beautiful

I stood in the sitting area on the bluff by the beach, the one that faces the Sun. It was 6:30 AM, roughly, when two of my fellow students came shivering into the area. They proceeded to document their expedition, taking Snapchats of the sky when the Sun's not even up. Then, they leave, never seeing the sunrise.

Of course, I wonder if this is another marker of the shorter attention spans caused by the heightened use of social media, a facet of instant gratification.

The sunrise was fucking beautiful, by the way. As the Sun rose higher behind the horizon, clouds farther ahead of me were already hit by the sunlight, and it made the edges of the clouds glow like gold. The sky grew more and more orange. In many ways, the sunrise was like a good classical song, or a good handjob: a lot of build-up, so much that when the end is finally reached, the feeling is incredible. And indeed, when that bright, golden sliver peaked above the horizon, it felt holy.

Bonus question to the reader: though I'm somewhat criticizing the masturbatory nature of social media, how masturbatory is it to post the same experience on a blogging website, which is a form of social media?

Nothing is Clear-Cut (e.g. Math)

3/20/2017
Monday
Afternoon
Partly Cloudy, but Chilling

Of course, nothing is clear-cut. Nothing fits nicely into boxes/categories/sets we create for them, but rather things are blurry, multifaceted, and they fall into many different groups. Here is a specific example related to, you guessed it, math.

Consider the fact that the derivatives of the sum of two functions is the sum of the derivatives of the composite functions. Stated a bit more symbolically, given two differentiable functions f and g, we see

(f+g)'(x)=f'(x)+g'(x).

A high-school calculus student would see this and recognize "a-ha! this is the Sum Rule!" On, say, the AP Calculus AB exam, this would be sufficient reasoning behind this fact; it was dictated in the class, and the students have memorized it, either through brute force or through much practice of finding derivatives of functions.

Of course, there is different justification for this fact from different mathematical perspectives. For example, consider Real Analysis:  calculus' rigorous, proof-based older brother. A mathematical analyst will tell you "well, the definition of the derivative is given by a limit, and since we can add limits, we can add derivatives." Moreover, the analyst could relate these limits back to sequences, and reason that the Sum Rule follows from the arithmetic of limits of functions, which follows from the arithmetic of limits of sequences.

From another perspective, consider Linear Algebra. A linear algebraist would tell you that the set of real-valued, differentiable functions form a vector space with the operations of function addition and multiplication of real numbers. Therefore, such a mathematician would say that the Sum Rule follows from the fact that the vector space of differentiable functions is closed under addition.

This is something about math that I like; you learn one thing, and it pops up everywhere, in a bunch of different fields of math. I suppose this tells us that math is less like a library, each field belonging to a bookshelf, each bookshelf containing an exhaustive list of the ideas in the field. Rather, math is like a swamp, where concepts lurk beneath the fields we've constructed.

Think different. Think DASANI.

Underrated Snack

3/7/17
Tuesday Night
Temperate, Windy

There's a lot of value in the concept of chips and dips. Some classic, popular examples are tortilla chips and salsa and pita chips and hummus. Such snacks require no heating, but just putting two different things (chips and dip) in two different bowls, and eating the dry substantial bit (chips) with a flavorful wetness (dip).

Yet, people forget their god damn roots. The simplest of all of these is right in front of us, the most basic of all chips-and-dip variants: bread and olive oil and balsamic vinegar. Dry, spongy bread soaked in savory oil and tangy vinegar is a simple staple, and should be enjoyed in larger variety. We, as a people, need to open our eyes to simplicity. We need to open our eyes to bread, olive oil, and vinegar.