The Number E: Your Eddington Number


For some of our more highly educated readers, the name Sir Arthur Eddington may be of some familiarity. But for most it won’t be.

Sir Arthur Eddington was a 20th-century astrophysicist most commonly known for his work on Einstein’s theory of relativity. Basically, he was one of those super smart guys who spent his career developing theoretical knowledge about stuff most of us will never understand.

However, Sir Arthur Eddington was also an avid cyclist, and he developed theoretical concepts around his bike as well; most notably, the number E (also called the ‘Eddington Number’).

Eddington’s number E (not to be confused with Einstein’s ‘e’ of e=mc2)  is defined as the largest number E, where you have ridden the distance of E on at least E different occasions. In simpler terms, if throughout your riding career, you’ve ridden 30 miles on 30 separate days, your number E is 30. Likewise, if you’re an amateur bike rider, and you’ve only ridden 1 mile, 1 time in your life, your number E is 1.

Sir Arthur Eddington, however, had a number E=84. That means in his life, he’s had 84 days of riding at least 84 miles! Especially impressive considering he was doing his riding in the early 1900’s, before derailleurs had developed much, meaning at most he had two gears on his bike.

I was introduced to Sir Arthur Eddington by a friend of mine who was reading a book on, you guessed it, astrophysics (he’s one of our more educated readers). It’s tough for me to be exactly sure what my number E is, I would estimate it is somewhere is the high 30’s or low 40’s.

And while for most riders, it is very difficult to know exactly what your number E is, it isn’t hard to guess.  However, the most impressive part of the number E is increasing it.

Unlike a personal best, which measures a single moment of achievement, the number E is intended to measure a person’s overall cycling acumen. By structuring the number E to include both distance and time, Eddington effectively controlled for a single day of excellence.


Einstein and Eddington were close contemporaries. What do you think Einstein’s number E was?

The Challenge of Improvement

So, how does one go about pushing their number E upwards? The long answer: diligence. The short answer, though, is units.

The definition of the Eddington number has two variables: distance and occasions. However, defining these variables is left rather open-ended.

Think about 20 miles by bike. Certainly not a titan distance, but a solid ride in any event. Now, if we simply change the units involved, and turn 20 miles into 20 kilometers, we have drastically shortened our ride (20km = 12.42 mi).

Now think about this in the context of an Eddington number of 20. If that E=20 refers to 20 miles, you would have had to have ridden a minimum of 400 miles (and likely more) to get there (20 miles * 20 different occasions = 400). However, if, instead E=20 referred to kilometers, the distance would be 248.54 miles after converting km back to miles.

Thus, if your interest is in pushing your number E upwards, measuring in kilometers is certainly the way to do it.

In any event, conjecturing at your own E number, and ways you can push it even just a bit higher, is a touch of fun and makes you think about your whole history with a bike. And if you want to go ahead and inflate your number a bit to challenge yourself to keep getting higher, go ahead. After all, in the words of Sir Arthur Eddington himself, “The mathematics is not there till we put it there.”