15 December 2008

The h factor

Academic and research administrators have an interest in reducing one's work into a single number. Ideally, they claim, they could use a single number to decide whether researcher A is better than researcher B. The actual reasons behind such claims are that the majority of administrators (academic department chairmen, directors funding agencies, heads of laboratories, etc) cannot understand each researcher's work, and also want to minimize their time in giving a judgment: they can, with the click of a button, order researchers in a line a button and finish their work in five minutes.

In fact, there is a "science" being developed, called "bibliometrics" (see here, here, here and here) aiming at producing such indices. The most (in)famous of these indices is the h factor (not the x factor--this is a TV programme--see below). The h factor is defined as follows: If a researcher has n papers cited n times each then his or her h factor is at least n. In fact the h factor is the largest such n.

For example, if a researcher has written one paper which is cited 1000 times and 9 other papers which are cited once each then his h factor is 1. If researcher B has written 3 papers, each cited twice, then her h factor is 2. Hence B is better than A (an administrator would conclude).

A recent report by Robert Adler (Probabilist of the Technion–Israel Institute of Technology), John Ewing (Executive Director, American Mathematical Society, and Peter Taylor (Probabilist, University of Melbourne) show that "citation data provide only a limited and incomplete view of research quality, and the statistics derived from citation data are sometimes poorly understood and misused; [r]esearch is too important to measure its value with only a single coarse tool". It's an interesting read.

However, I admit that the report may not be as much fun as an x factor episode:

Just to make things clear, the guy in this video is not looking for an h factor, but an x factor. (Some colleagues tell me it's more or less the same thing though.)

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What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant