I was just on Skype with my friend Jonathan, who is also in a long-distance relationship. His is between Vancouver, BC and Germany. Mine is between Eugene, OR, and Vancouver, BC. We started coming up with a scheme for measuring the difficulty of a long distance relationship. Here are the major factors we came up with:

1) Financial impact of making the trip

2) Number of travel hours separating the couple

3) Amount of time difference between locations

To that I’m going to add,

4) The availability of high-quality video chat.

5) Number of days left before final reunification.

Obviously, any such attempt will result in a major oversimplification, but I’m thinking we should stick with easily measurable factors. For example, the communication ability of each partner plays a huge part in the success of a LDR, but is difficult to measure, so I’m leaving it out. If the couple prefers not to fly for ethical or other reasons, it will factor in, too, but I’m leaving that out as well. And so on.

So, how do we calculate this index? Generate numbers for each factor:

1) Cost of a round trip, divided by the combined income of couple.

2) Number of hours travel, round trip, by that mode of transportation.

3) Number of hours difference between locations, plus 1. So if you’re in the same time zone, you get a 1 here, and if you’re eight time zones off, you get a 9. The plus 1 is just to make a no-time-zone-difference a nonzero number, for calculating the index.

4) I’m going to estimate that having good video chat makes LDRs ten times easier, so if you have it, you get a 1 and if you don’t, you get a 10.

5) The number of days left before final reunification.

Let’s try those elements in the following equation:

difficulty of long distance relationship = (cost of trip/combined income) x number of hours travel x number of hours difference x number of days left x video chat

It’s a start. Let’s see what kinds of numbers it gives us, using about what Reanna and I have left to go–a little over a year: For Bill Gates, the index would range between about .01 to maybe 30, depending on the difficulty of the trip, or between .1 and 300, without video chat. For someone poor, with a long, difficult trip that costs their yearly salary and no video chat, the index would be about 600,000. If this very unfortunate couple had 10 years to go instead of a year, they get 6,000,000. I know, that doesn’t sound like much of a relationship, but I’m looking for the upper end of the scale.

Reanna and I get about a 30. Not too bad, I guess, though it goes up to 300 when I’m at Not Back to School Camp, which is way out on the information-dirt-road. So we get a range of 30-300, which is the same range as Bill Gates’ worst-case scenario–if he had to take his private Lear jet to the central Asian steppe every time he wanted to see Melinda.

OK, here’s where you can help me out, if you want. There are certainly several problems with this scale. Here are two, off the top of my head: First, the range of .01 to 6,000,000 is too big to think very clearly about. How hard is my 30 compared to Bill’s .01, or Mr. Unfortunate’s 6,000,000? Other than “somewhere inbetween,” it’s difficult to say. The equation needs some kind of transformation to produce easier numbers, say between 1 and 100. Second, some things aren’t working out with the math. As it is, if a couple is *very* poor, even a 10-day LDR with an easy trip comes out harder than Bill’s 10-*year* LDR with a very difficult trip, as long as Mr. Unfortunate doesn’t have Skype. That can’t be right. If any of you are math people, what do you think? Third, there are other factors that should be included but are difficult to operationalize, like communication skills and depth of commitment. Any ideas, conceptual people?

June 8, 2010 at 7:17 pm

what if instead of multiplying by number of days until the final reunion, you just added that number to the end. that’d give you a nice y=mx+b equation. it would also make the scale smaller. the only problem would be if the number of days is actually more important than would be reflected that way. you could use number of months instead of days… too bad i left my graphing calculator at home.

June 9, 2010 at 12:44 am

Hmm. That may help, Maya. I will try it out. Thanks!

June 8, 2010 at 8:38 pm

I think you’ve been taking too much science lately! How is this helping you or our relationship to know these things? Or do you just consider this an enjoyable brain exercise and nothing more?

Oh, and I say if you have poor communications, you’ve got the wrong partner, long distance or otherwise.

humbly,

your mom

June 8, 2010 at 8:45 pm

typo: “you or your relationship”.

As far as you and I are concerned, I don’t think our relationship as mother and son has not suffered due to infrequent communication. We’re solid.

I’d like to hear what your post means to you in plain English. What does it tell you about your relationship with Reanna?

June 9, 2010 at 12:42 am

Oh, this is just me having fun, Mom. This is what I do for a relaxing break from school work.

Love,

Nathen

June 9, 2010 at 8:19 am

Ah, just as I suspected.

June 10, 2010 at 12:34 am

You’d have to take the logarithm of the difficulty index to get a more compact scale, this would also emphasize the differences at the low end of the scale relative to the high end.

As for the problem of a ten day skypeless ldr being worse than gates’ ten year one… I think you just have to play around with smaller skype factors.

June 11, 2010 at 5:17 pm

One change needed for your formula is that if any of your factors are zero (no video chat for instance), your multiplication result collapses to zero (zero times anything is zero). The minimum score in any of the rating factors needs to be 1.

June 17, 2010 at 3:35 pm

I’ve written a long reply, so instead of a comment here I blogged it.

June 21, 2010 at 3:11 pm

Nathen!

OMG GEEK OUT. Here is how I would do the formula…

I’m not in a long distance relationship, so take these with a grain of salt. Also my math is rusty.

Taking a log of everything keeps the scale down to a manageable size, but doesn’t properly weight the factors. Some things increase the difficultly linearly, some exponentially, some logarithmically. Actually, I don’t think any of these things are logarithmic, but they might be.

For instance, I think the days remaining should be linear or exponential. A two year LDR should be at LEAST twice as difficult as a one-year. I’m going to go with a linear: #days/356. six months would be 0.5, two years would be 2.

I would propose lumping time difference and video chat together… they’re both about ease of communication.

If the time difference is 12 hours, it doesn’t matter if both people always have video chat… it’s going to be hard to communicate.

So… how about availability of skype on a 0-12 scale, with time difference subtracted.

i.e: contact factor = 1-(12 + skype availability – hours difference)/24

So if skype is unavailable and there is no time difference it’s 0.5.

If skype is unavailable and there is a 12 hour time difference (worst case) it’s 1.0.

If skype is always available, but the time difference is 12 hours, it’s 0.5.

I would do cost/income as an exponential. Since a cost/income ratio of 1 means it’s basically impossible to visit, that number should be huge. For lack of a better number, I’ll use 10 as the base. 10^(cost/income) which has a range of 0-10. Travel time multiplies this number. Range is 1 to 10

tt = travel time

co = cost of trip

in = combined income

vc = video chat availability on a 0-12 scale.

td = time difference

tr = time remaining in years

so:

Travel Factor = tt * 10^(co/in)

Communication Factor = 1-((12+vc-td)/24)

Duration Factor = tr

Difficulty = tr * tt * 10^(co/in) * (1-[{12+vc-td}/24])

Range is still 0 to infinity still, but values should be much lower, and maybe more meaningful?

Guesstimating you and Reanna’s numbers, I scored you at 0.4244 on this scale.

Fun!

June 21, 2010 at 10:23 pm

Wow! Thanks for all the thinking, Cory!