It's the sort of question for contexts without obvious resolutions: in the third row of the dollar store after close, for example, trimming your pubic hair with a pair of safety scissors. And it's the sort of question best raised after the fact, as the consequences of your answer reveal themselves: to pass the silences in your first eHarmony drinking date, maybe, while the person across from you twists a napkin and you look at your phone without comprehending the time. It's the sort of question that goes well with, "Am I going to have to pay for this?"
Yet before it crowns America's Greatest Thinker, the New York Mills Regional Cultural Center wants to know: "Which should you trust more, head or heart?" So what are they really getting at, and why? Head is a lot of things - some 25, according to the [?Wikipedia]. Head is the Wikipedia. It is all the information you've learned, and most of the shit you've heard. Head tells you to stop on red, to not pinch that person's ass on the metro. It tells you that the universe is probably expanding and that it could someday end, but also that it's nothing to worry about. It says "Use a condom" and "Snickers satisfies hunger." It's right most of the time, and when we discover that it is not, we do our best to correct it.
The prompt asks, "Are we at war in Iraq today because of an emotional response to 9/11 or because the facts warranted our involvement as a correct course of action?" Personally, I continue to assert that it "wasn't me" -- and don't get me wrong, I heart New York as much as the next guy. But there's that word again. Heart (disambiguation) yields, among other things: a muscular organ, an icon symbolizing love, a popular game, a decoration for the wounded. In parlance, it is both tender and tough, and what it represents resists delineation. Though without vocabulary, it speaks to us in a language of Frankenstenian origin, through variations on the single utterance, "Mmmmmmmmmmmn," which it tints with specific saturations of grin, growl, and groan. And like the head, the heart has its opinions. Often the two are at odds. So what then?
At first the answer seems easy, as if I have always known it. I begin the notes for my essay with the following observation: "The head has a powerful grasp on the heart, to be sure, and will resort to whatever means are necessary to keep it subdued, from denial and doubt to outright guilt. It will ask: 'Did the heart give us fire? Did the heart give us the wheel?' Perhaps not. But realize it was the heart that refused to be satisfied with darkness, the heart who first longed to wander. So the head is ultimately benign, an otherwise inert instrument; it may become great or terrible only at the heart's behest, and it is only the heart that we may classify as good or rotten."
It feels right, but as I reread the words I am compelled, as if by force, to add: "Of course, the head retains some say in the matter and becomes particularly powerful in cooperation. A hundred heads in conspiracy could quiet their hundred hearts, since each voice of logic is made more convincing by each other in agreement with it, while the heart is not fortified by its kind, resigned as it is to independence, its one virtue and its Achilles' heel."
I'm not sure which to believe. (Dramatically) Dum dum dum.
Joseph Thompson, your question -- "What does it mean for two quantities to have an ultimate ratio" -- has been selected as the question of the week. Congratulations. You get nothing, unless you want to put this on your resume, which, okay, whatever. Okay, let's talk about functions for a little bit, namely functions of x with rational exponents. Alright, now it may be way out there on the x-axis, but ultimately f(x) will level off as changes to x return smaller and smaller changes to f(x) (if the exponent is between 0 and 1, vice versa if the exponent is >1). This goes along with the idea of limits, the value a function approaches, becomes infinitely close to, without touching, like hot, hot foreplay for numbers. Or, as Sir Paul McCartney summed it up, "In the end, the love you take is [proportional] to the love you make." Sure Paul, in the end. But what about at any point along the given line? Another Sir, Isaac Newton, crunched a few equations and came up with the ultimate ratio, 1: nx^(n-1), for f(x)=x^n, where n is rational, as in not irrational. So for the function f(x)=x^2, for example, the ultimate ratio would be 1: 2x for any given x. If we imagine our function as describing the movement of a particle over time x, then the ultimate ratio is a way of knowing the velocity of our particle at any specific moment, which just happens to be the first derivative of the function. Got it?
Continue to send me your questions and I might just continue to dazzle you with my answers. I've noticed already that most of you have funny names. Many representatives of the Hunt and Dover clans have written already. Keep 'em comin', Dovers. There's more where that came from. Until next week, happy thinking!
Part II: Who Hearted?