Somewhere there’s a someone for everyone
Somewhere there’s a someone for me
Though I may be lonely now
I’ll see it through somehow
To someone’s heart I know I hold the key
–Dean Martin, “Somewhere There’s a Someone,” 1966

But was old Dean right in his assertion? The fact that he spoke in such certainties when mathematics and modern physics seem to tell us, in stereo, that the only certainty in the universe is the lack thereof is unnerving to me. His words beg the question: is there really a someone? Somewhere? For me?

Perhaps even in this very university?

There is only one way to find out. As both an engineer and a student of applied mathematics, I am inclined to believe that this problem, like nearly every problem worth solving, can be investigated numerically.

Let us begin with the basics. First of all, based on observations of my peers, seems obvious to me that maintaining a relationship with someone outside of the University of Maryland community would be an exercise in futility, mainly for pragmatic reasons of logistics. There are currently 36014 students, undergraduate and postgraduate, enrolled at UMCP.

As I am heterosexual and unwilling to engage in polyamory, love triangles, torrid affairs, or disputes with big linebacker boyfriends, I will narrow the dating pool to women not currently in relationships. Like any statistical analysis, we must work under a number of basic assumptions:

• -Despite the fact that some students commute, some are in classes, dorms, programs, etc. physically located such that they and I will almost certainly never cross paths, etc., let us assume I am equally capable of meeting every UMD student.
• -approx 50% of persons are currently in a relationship at a given time. (53% according to [1])
• -approx. 50% of student body is female (49% according to online statistics).
• -Every matriculating and graduating class does not vary significantly.
• -All determining factors are independent.

This means that at any given time, ¼ or 25% of UMCP students are “datable.” To find a suitable fit within this pool, we must impose further constraints, based on the following overarching assumptions:

• -Attractiveness, viewed holistically as a combination of physical and personal traits, is distributed normally.
• -Intelligence (which is inherently difficult to define) is distributed normally, and is correlated significantly with IQ and SAT scores, so as to justify the assumption of a causal relationship.

Clearly, in order for me to enjoy, or even consider initiating a relationship, the other party must be attractive, both physically and in terms of her personality. To diffuse the argument that could be made that my standards are too high, let us say that for a girl to interest me, she must fall a mere three-fourths of a standard deviation above the mean. This is not being picky; a full 22.66 percent of the area under a normal distribution falls above z=0.75. This narrows the potential girlfriend pool to 25% * 22.66% = 5.665% of UM students , or 2041 girls (rounding up, to be optimistic)

Likewise, in order for me to enjoy a girl’s companionship, she must be reasonably intelligent. Let’s say one standard deviation above the mean, corresponding to an IQ score of 115 or an SAT score of 1100, based on the distributions of both. Unfortunately, UM’s admissions department is dodgy in issuing these statistics. The best I could get is “The middle 50% of admitted students scored between a 1240-1380 on the SAT last year.” [2] Based on these data, the standard deviation of SAT scores is then 70 / .675 = 103.704. Assuming the mean and median are close (which they should be, given the size of the population and the assumption of normal distribution), we find:

1310-1100 = 210
210/103.704 = 2.0250
Probability for z-score -2.0250 = (1 -0.0987)= .9013

Meaning that based on the assumption that a causal relationship exists between intelligence and SAT score, 90.13% of University of Maryland students are intelligent enough to hold a meaningful conversation with. Combining this statistic with previous findings, we find that 5.665% * 90.13% = 5.1059% of UM students meet my criteria. Still, this reduces the number of potential girlfriends to 1840 girls (again rounding up).

A prospective girlfriend must also find me attractive, again through some arbitrary combination of physical and personal traits I possess that she finds desirable. We must then narrow the pool of potential partners further.

Assumptions:

• -I am of average attractiveness, both physically and personally.
• -The average woman has the same standard for attractiveness as I: 3/4 of a standard deviation above the mean.
• -Attraction is independent. The odds I like a broad do not affect the odds she likes me. (Although my use of the word “broad” probably does.)
  

Using previous calculations, we find the probability corresponding to the area beyond z = 0.75 = 0.2266. Combined with the previous result, we find that 5.1059% * 22.66% = 1.1570% of UMD students would be suitable relationship material. In other words, at any given time, there are 417 women on campus (again rounding up).

We must make one final assumption in our analysis: my intelligence will not be a factor in attraction. Fortunately, I have the benefit of being intelligent. Therefore, we can assume the probability of my being sufficiently intelligent for a given woman approaches one. So my intelligence does not narrow the dating pool further.

At first glance, having 417 potential girlfriends on campus is an amazing statistic. In comparison, the average introductory math lecture (MATH140-246) has about 200 students [3]. In other words, the population is large enough to fill two lecture halls. As a matter of fact, if we assume the distribution of class registration is even, it is likely that I have a potential girlfriend in my own mathematics lecture! If only I could meet her…

…And therein, as wrote the Bard, lies the rub. Of course, the key component of striking up a relationship with someone is meeting the person in question. Thus, the odds of my having a relationship with a given student depend not only on probability of compatibility, as determined previously, but also by the probability of me meeting them during my college career. I have 140 Facebook friends at Maryland. A count reveals that 73 are people I did not know from high school. I have been a UMD student for 3/4 of an academic year. Assuming I continue to meet people at this rate and graduate on time, I will have gotten to know 219 new individuals in my time at Maryland. Each of these individuals is assumed to have the same 1.1570% chance of being a potential girlfriend. This means that over the course of my college career, I will meet 0.01157 * 219 = 2.584 potential girlfriends. That’s actually a lot better than I expected. Now, should I also spend 2 years of grad school here, I will have met 324 people in my experience, meaning I will meet 3.8 potential girlfriends. Even better. Better still is the fact that, even should these calculations be adjusted drastically upward or downward to account, it is almost certain that my estimation is correct in terms of order of magnitude. In other words, I am almost certain to meet between one and ten potential partners in my career at Maryland. Perhaps we can rest assured in taking the advice of a dead alcoholic Italian, and conclude that somewhere, there is almost certainly a someone for everyone.

To the innumerate (or, as it were, less numerically inclined) among the readership, I offer that, in restricting the dating pool, it is the assumption that attraction is independent that is the real killer. Were we to assume, on the other hand, that being attracted to someone else makes them more likely to find you attractive—that is to say, if we account for “chemistry,”—the individual’s options get a lot wider. Note also that the most significant assumption is that you have a chance of meeting everyone. If, for some reason (cough the Greek system cough) limit your initial dating pool, your chances shrink significantly, although it could be argued that individuals within the now-limited initial pool are perhaps more “compatible” with the individual in question, and, needless to say, the need to discriminate based on intelligence is no longer an issue. And if you are reading this, fratboys, please do not beat me up. It’s not my fault that your father was never there for you. It’s not my fault you enjoyed it when your uncle touched you that special way. It’s not my fault someone “accidentally” called the cops on your last party just because this chick I like was there and I couldn’t get in the door.

Okay, maybe that one is my fault. But I digress.

On the other hand, the fact that I perform analysis such as this on problems such as these seems to speak volumes about why I can say, with almost complete certainty, that I will never have a girlfriend.

Sources:

[1] www.epjournal.net/filestore/EP05612631.pd
[2] UMD enrollment statistics, http://tinyurl.com/43mx9
[3] UMD class schedule, http://tinyurl.com/4azvq7