The n-Category Café

What do you mean by that, Mike? To calculate $n!$ mod $n^2$, to calculate $\sqrt{n}!$ mod $n$ when $n$ happens to be a perfect square but we don't know that (but that's quick to discover, isn't it?), or to extend factorial to fractional numbers with the Gamma function and calculate $\sqrt{n}!$ in $(\mathbb{R},+)/n$, or what?

Luckily this form of insanity is almost always temporary. You sound perfectly normal now.

If anyone has ever gone permanently nuts from grading, I’d be very interested to hear about it.

I assure you, she’s not normal at all.

John wrote:

If anyone has ever gone permanently nuts from grading, I’d be very interested to hear about it.

Here’s the closest reference I’ve found so far:

“University faculty are not immune from mental illness. In fact, Kilburg (1986) argued that the stresses of an academic position might actually increase the risk of mental illness among academics. No matter what, we might assume that roughly one-quarter or one-fifth of university faculty suffer from a mental illness at any one time, and that perhaps 5% or 10% suffer from an illness severe enough that it impacts their ability to complete basic occupational duties.”

Grading hard then, John? Well, it is your birthday…

arXiv:0906.2117 [ps, pdf, other]
Title: Grand Antiprism and Quaternions
Authors: Mehmet Koca, Mudhahir Al-Ajmi, Nazife Ozdes Koca
Comments: 21 pages, 12 Figures
Subjects: Mathematical Physics (math-ph)

Vertices of the 4-dimensional semi-regular polytope, the grand antiprism and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the E_{8} root system which decomposes into two copies of the root system of H_{4}. The symmetry of the grand antiprism is a maximal subgroup of the Coxeter group W(H_{4}). It is the group Aut(H_{2} plus H’_{2}) which is constructed in terms of 20 quaternionic roots of the Coxeter diagram H_{2} plus H’_{2}. The root system of H_{4} represented by the binary icosahedral group \textit{I}of order 120, constitutes the regular 4D polytope 600-cell. When its 20 quaternionic vertices corresponding to the roots of the diagram H_{2} plus H’_{2} are removed from the vertices of the 600-cell the remaining 100 quaternions constitute the vertices of the grand antiprism. We give a detailed analysis of the construction of the cells of thegrand antiprism in terms of quaternions. The dual polytope of the grand antiprism has been also constructed.

Thanks for the birthday presents, Jonathan. Yes, it’s strange and sad how we manage to make such a misery of our short stay in this wonderful universe — even California, such a wealthy place, has let itself go broke. I’m doing embarrassingly well myself right now, but that too shall pass… so the more permanent patterns of nature are somehow reassuring to contemplate.