His oldest, closest friend

I happened upon an interesting phrase in a story, “Signal” by John Lanchester, from the New Yorker (3 Apr 2017):

“Michael wasn’t my oldest friend and he wasn’t my closest friend, but he was older than any of the ones who were closer and closer than any of the ones who were older, ….”

This is an odd way to describe a friendship, but it is precise. However, the more I thought about it, the more dissatisfied I was.

The description has three parts: (1) Michael is not the oldest friend, (2) not the closest friend, and (3) is older than the closer friends and closer than the older friends (the “oldest-closest” criterion).

Let’s say that the “oldness” and “closeness” of all the friends, including Michael, can be represented by numbers (e.g. age for oldness, and frequency of communication for closeness). Then they can be depicted in a plot like the following:

older_closer_1.png

Michael (the red point) is neither the oldest (#1), nor the closest (#2), as the description from the story goes. If we continue with condition #3 (“older than any of the ones who were closer and closer than any of the ones who were older”), that would be equivalent to drawing vertical and horizontal lines that intersect at Michael’s point on the plot, and seeing that there is no one in the quadrant to the upper-right, which represents potential friends who are both older and closer than Michael.

But here’s the problem: If we pick another point on the graph, representing a friend that is not Michael, we find that we can draw the quadrants for not-Michael, and also find that the “older and closer” quadrant is empty!

older_closer_2.png

That means that the position is not exclusive to Michael: there are potentially other friends who could fit that description.

To explore the scenario, I wrote a small function in R to identify friends who fit the “oldest, closest” criterion (#3) when given a set of points.

# function to find the oldest, closest friends
findOldestClosest <- function(d) {
  outOldest <- NULL
  outClosest <- NULL
  for (i in 1:dim(d)[1]) {
    ol <- d$oldness[i]
    cl <- d$closeness[i]
if (length(which(d$oldness > ol & d$closeness > cl)) == 0) {
      outOldest <- c(outOldest,ol)
      outClosest <- c(outClosest,cl)
    }
  }
  return(data.frame(oldness=outOldest,closeness=outClosest))
}
# Example
oldness <- runif(n=50,min=0,max=100)
rr <- runif(n=50,min=100,max=200)
closeness <- rr - oldness
d <- data.frame(oldness,closeness)
# Plot the example data
plot (d$oldness, d$closeness,main="Finding the oldest & closest friends",xlab="Oldness",ylab="Closeness")
d.oldestclosest <- findOldestClosest(d)
points (d.oldestclosest$oldness,d.oldestclosest$closeness,col="red")

The points are randomly generated but in such a way that the older friends are less close, to emphasize the issue at hand. The points highlighted in red meet the “oldest, closest” criterion:

oldest_closest_plot1

This shows us first that there are several potential Michaels. In addition, the very closest friend (uppermost point) and the very oldest friend (rightmost point) would meet the “oldest-closest” criterion (#3). However, we know that Michael is not one of them because of conditions #1 and #2.

The only situation where only a single friend would fulfil the “oldest-closest” criterion is when the friend is both the oldest and the closest, but as noted above that option has already been ruled out by conditions #1 and #2.

Therefore the only way that Michael can be the only friend matching all three conditions is if the only persons in the “younger & closer” and “older & less close” quadrants were the closest friend and oldest friend respectively, as shown below. Everyone else would be younger and less close to the narrator than Michael.

older_closer_3.png

If Michael is indeed in a unique situation, he is still somewhere in the middle of the spectrum of friendship.

Why describe this friendship in such a convoluted way? Perhaps that was the writer’s intention: to convey a sense of emotional distance through the circumlocution, and hint at his ambivalence about him.

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