An interesting discussion has sprung up on the xkcd forums regarding the observation that most named mathematical constants tend to be small, usually not more than 10 and often between 0 and 1. There does not seem to be a good a priori reason for this, so I think it would be interesting to get some expert opinions on whether this is more about mathematicians' preferences on what constants deserve names or whether it actually reflects some meta-mathematical principle. For example, I think one can come up with good arguments why constants like e, pi, phi, and even things like the Feigenbaum constant ought to be small, but constants like the twin prime constant seem to me more about mathematicians' preferences.

But this question might be too philosophical. What do you think?

There are bigger very interesting constants, like the order of the monster group. As computational power goes up, the magnitude of the constants also will go up.

By contrast, in physics, the fundamental constants are very big, or very small, etc..

This question is clearly philosophy. It is not research mathematics, which is the topic of MO.

I think very few working philosophers would regard this question as part of their bailiwick. To me, it seems like a mixture of mathematics, history and sociology.

I also find the question rather interesting, especially compared to many soft questions we've seen recently on MO. So I am mildly in favor of it being posted.

Some possible exceptions: -163, 691, 1729, 196883, 10^10^10^963

Mildly against. I wouldn't vote to close it, but it strikes me as to vague to be interesting.

@Pete Clark. The order of the monster is also an interesting constant. It is(from wikipedia)

246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71

which is, 808017424794512875886459904961710757005754368000000000

or approx. 8 · 10^53.

I meant to say, in physics/chemistry there are big constants, like the Avogadro number, or very small numbers, like the Gravitation constant.

Why initially math had only smaller constants, is a consequence of limted computational possibilities of the days in which these numbers took center focus. This was not the case in other sciences, which connected more directly with what is happening in nature.

Delving into such questions is clearly philosophy. Philosophy can embrace math, meta-math, sociology and math-science relationships. I think it is best addressed by a philosopher.

@Sam Nead: Unless you're going to correct me on points of Geordie slang, I think not ;)

@Emerton: don't know about the literal origins of the word. I suspect it is essentially a "dialect" version of knackered" - which in turn came from "horse knacker" and "knacker's yard", I always thought; the knacker's, rather than, erm, the knackers.

The meaning when I've heard it used is "bust" or "broken" through damage or wear (so much the same as the longer word): "that heater's knacked, man" and so forth. I just like the monosyllable better than "knackered", it seems to fit the mood of exhaustion...

But I fear we've gone rather off-topic ;)

Dear Yemon and Andrew,

I have to agree with your definition, and conclude that uncouth Australian kids (or, at least, this one) merged the two words, "knacker's" and "knackers", unthinkingly. (For example, we used the verb "to knacker" in the context of sports, playground fights, or other situations with the potential for such an injury, and in particular spoke of someone being "knackered" in such a context; this seemed to be based on the specific meaning of "knackers", but at the same time, certainly led to the victim being broken in a more general sense as well.)

Since I don't know what a Gordie is (and since I apparently cannot read the native language of the author of http://en.wikipedia.org/wiki/Geordie ) I humbly withdraw the suggestion.

@Andrew: I see that you haven't lived in the ITV coverage area in a long time. http://news.bbc.co.uk/2/hi/entertainment/7776059.stm