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January 28, 2009



True. Links to wikipedia don't help a lot here :)
But still, exponential often means, by extension, "growing faster than n"...
Which is a true problem for twitter.
If you consider that the number of messages you send every day is also growing with n (because the more contacts you have the more you are interested in sending them updates), it comes to n^3 right?


The growth of the Twitter is very likely to be exponential, but the explanation is wrong. Moreover, in a realistic world, users are poorly interconnected. Usually, there is a bunch of leaders whose auditorium grows constantly and the rest of users, who have a couple of friends forever. Therefore, the traffic will grow almost linearly with the number of users. On the flip side is the total number of users AND the number of posts that grow exponentially.


Indeed, this isn't the first place I've seen this error.
I'm afraid that in the popular usage exponential is going to be used to mean anything that's substantially more than O(n) (probably doesn't include O(n log n) but does include O(n^2)).
Even before this, most "exponential" growth was probably just the exponential part of a logistic growth curve anyway.

Maybe it's time to create a new word that means "literally" exponential?

Chris Bird

Weighing in my (mis) understanding of exponential.

In my naivity, I had thought that linear growth was O(n), that geometric was
O(n^^a) and that exponential growth was O(a^^n).

However, I don't think that is correct any more :-(. So what is growth of the form O(a^^n) called?

(I am taking ^^ to mean "raised to the power of" in the above)

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