By the Numbers: Grace

the above is a subset of the people of the world we live in, plotted onto a graph that shows their likely level of 'goodness' at any instant, on a scale from 0 to 10.

so you don't cheat, steal, kill or fornicate with animals. most people would say that you are a decent human being -- a nice, pleasant, good person. by golly, you don't even cuss or download mp3s or dance in public (want a medal?). you read the Bible, the Koran and the Torah every night before bed, pray before every meal and visit to the bathroom, kiss your mom goodnight and leave a 16.7% tip minimum for every service rendered. hallelujah! praise the Lord because you always say, 'praise the Lord' after something good happens.


this next graph shows the same numbers as seen in the previous graph, but in the context of God.

our 'goodness' compared to others, in the context of God, is negligible; our 'goodness', in the context of the truly Good, is nothing. still, in our decrepitude, God reaches down to offer saving grace for all who accept it. no one receives any more or any less than the other.

By the Numbers: Compatibility

ever wonder how those matchmaking sites find people to make matches?

i always thought it'd be something like this:

Matchmaker 1: okay, it's your turn to throw the darts.

Matchmaker 2: so we're putting the green ones together?

Matchmaker 1: and the blues. try to get them in the nostrils.

Matchmaker 2: don't we have to send these photos back?

alas, this is not the case (because matchmakers cannot throw darts). in actuality, they use the power of maths to hook you up with someone compatible.

they don't even know me; how can they possibly find someone that matches? you might ask.

when you sign up with a matchmaking service, you undergo rigorous psychological testing to determine your personality in finite, objective terms; it's a questionnaire. the results of your test are plotted into a vector generator. a vector is like a coordinate (x, y), but has an anchor at (0, 0), thus forming a line. the vector of your personality, lets call it [y1, y2, y3, ... yn], is then dropped into a databank of other desperate lonely folk's personality vectors and a computer runs them through a stiff algorithm: the dot product.

finding the dot product between two vectors is quite fun. you take the number in the first dimension from one vector and multiply it with the number in the first dimension of the other vector and add it to the product of the numbers in the second dimenion and the third and so on:

x dot y = x1y1 + x2y2 + ... xnyn.

this is equivalent to the product of the two vector's magnitudes (lengths) and the cosine of the angle between the two:

x dot y = |x||y|cos(theta).

the computer solves for the angle and uses it to determine the strength of compatibility. really small angles between two vectors mean that they are very similar, and therefore compatible. angles of around 180 degrees are also considered compatible since opposites attract. the computer then compiles a list of candidates for each person based on the data.

By the Numbers

i heard about an excellent discussion that was held in a math class today. technically, it was a private conversation, but who's counting?

anyway, the issue up for discussion was this: is it okay for a 16 yr old girl to date a 27 yr old guy?

knee-jerk answer says: EW.

but it's math class, so it should have a mathematical answer. fortunately for everyone who doesn't want to look like a skeevy perv, there is a simple equation people use to determine the Socially Acceptable Dating Age Range:

y = 0.5x + 7,

where x is Your Age and y is The Other Person's Age. this equation determines the lower bound (the youngest) that you can date and still be considered socially acceptable. conversely, the upper bound can be found by inverting the function:

y = 2(x - 7).

for those of you with low Mathema-logical aptitude, here is a lovely graph i whipped up for you:

therefore, it is pretty sketchy for Peter Petrelli to be dating Claire Bennett, and extremely sketchy for a 16 yr old girl to be dating a 27 yr old guy.