Happy Patriots’ Day!
Or, as someone might call it, happy Marathon Monday; in less than a couple of hours the Boston Marathon will kick off at Hopkington to finish around noon at Boylston St in Boston.
The Boston Marathon is that attainable, and yet so hard to achieve, goal that justifies all the hours spent on training. It’s the only marathon in US (that I know of) to require strict qualifying times to the participants ― 3:10, for me.
While waiting for the gun, I thought to write down an analysis I did a year or so ago, half in just, half serious.
In the last few years, the world record for the distance has been constantly broken, and among elites times people could only dream of few years ago are becoming more and more ordinary. Ryan Hall commented on last week Rotterdam Marathon on his twitter feed:
Some impressive results today. 2:04 is becoming more commonplace.
and, of course, we all have in mind Haile Gebrselassie in Berlin in 2008 breaking his own record by 30 seconds with an incredible 2:03:59.
After Geb broke the 2:04 wall for the first time, people started wondering once again whether humans are able to run a marathon in less than 2 hours, and honestly I think no one really knows.
As a physicist, when I see an array of numbers I look for a correlation, if any, among them ― it comes with the job. Just by looking at the data, I noticed that records were broken by tens of minutes in the early days to then being broken by a handful of seconds. What it could be described as now it’s getting harder and harder to me smells like an exponential law.
With this in mind, I copied the marathon world records and interpolated them versus year by an exponential law, and this is what I found:
and the exponential function is evident. The asymptote is at 1:56:53, which means that ― if this could be extrapolated into the future ― a sub 2 hours marathon is humanly possible.
What’s surprising is that a correlation between record and year seems to exist. I thought a bit about it: people are born with more or less predisposition to run ― a pace that could be jogging for someone might be running hard for others ― and this predisposition is randomly given but not on a flat distribution. Possibly the distribution is closer to a Gaussian, or bell curve, so that very few people are born being able to run at an elite-level and the number of those decreases exponentially: they’re in the tail of the Gaussian. This is obvious, but it doesn’t justify the correlation between world record and year; what I think it’s happening is that the predisposition ― number of people vs velocity they’re predisposed to run ― follows an exponential distribution, while the distribution for people being born with this predisposition at any given year is mostly flat. By adding the two together we have an exponential distribution for the world record vs the year …
All this analysis is, of course, not serious and I don’t really believe in the power of predictability, that this interpolation seems to suggest.
A theoretically sound limit of the time is 141μs, that is the time lapsed for an object moving at the speed of light to travel 26.2 miles (or 42.195km).