9 November 2014

Good research practice

The Ethics Committee of the CNRS has published (in French only, as far as I can see) a Guide for the promotion of truthful and responsible research.

The guidelines are quite reasonable, but what drew my attention is the front cover: three ladies, a senior researcher, a more junior one and —probably— a PhD student or postdoc are huddled around a multi-well plate, each of them pointing at a different well. Note the micro-pipette in the foreground (shorthand for "this is a biology research lab"). Note also that the boss is in her street clothes and her bare hand is dangerously close to the samples. Maybe one should add to this guide rule 0.1: "Use appropriate protective equipment ?!"

Borges and Nietzsche

Borges was influenced by Nietzsche's ideas, in particular his "eternal return" (see The Doctrine of Cycles) and mentions him explicitly in some of his stories (e.g. Deutsches Requiem). What I have only recently realized is that Borges' story Funes the memorious (already mentioned in a previous post) is prefigured in Nietzsche's second Untimely Meditation1:

Imagine the extremest possible example of a man who did not possess the power of forget­ting at all and who was thus condemned to see everywhere a state of becoming: such a man would no longer believe in his own being, would no longer believe in himself, would see everything flowing asunder in moving points and would lose himself in this stream of becoming: like a true pupil of Heraclitus, he would in the end hardly dare to raise his finger.

Nietzsche's  has already been invoked in relation with Funes2, but as far as I can tell (I do not have access to the full text of the paper) only with respect to the difficulty of forming general concepts.

1. Breazeale, D., & Hollingdale, R. J. (1997). Nietzsche: Untimely meditations. Cambridge University Press.
2. Martin, C. W. (2006). Borges Forgets Nietzsche, Philosophy and Literature 30(1), 265-276.



2 November 2014

The politics of disgust

Right in time for the midterm elections we hear that liberals and conservatives react differently to disgusting images. I find it very surprising, the more so because I have never been able to understand how a single variable can account for so many orthogonal issues (citing from the paper): pacifism/abortion rights/welfare spending/torture of terrorism suspects etc.


28 October 2014

Historical event

This month, after nine years in my current (tenured) position, I finally earned more than the monthly income during my Göttingen postdoc (2002-2005).

5 October 2014

The veil of ignorance

There is something disquieting about Rawls' veil of ignorance position: participants are supposed to set aside their status, their attributes and even their personality in order to found this ideal society, whose first principle enshrines the liberty of conscience and freedom of speech. There may not be a logical contradiction between the two, but I think there is an obvious moral one.

4 October 2014

A neural basis for readiness-to-hand ?

Researchers in Munich discovered that there is a specific network in the brain for using tools (the paper appeared in The Journal of Neuroscience).
Heidegger's concept of readiness-to-hand is arguably much more general than the motor skills involved in the use of familiar objects, but I like the idea of a neural basis for a philosophical concept.

3 October 2014

Fête de la science 2014

Notre laboratoire se prépare pour la Fête de la science. Beaucoup d'activités sont prévues pour vendredi et dimanche (10 et 12 octobre), voir le programme. Pour des informations en temps réel suivre @LPS_Orsay.

25 September 2014

Solving tan(x) = x

[UPDATE: 25/09/2014 with the iterative method] This kind of transcendental equation is often encountered in physics. Undergraduate students are usually shown (or asked to draw) the graphical solution:



The numerical solutions are easily found by an iterative method using a scientific calculator (see below), but how far can one go with only pen and paper?

Expansion

Aside from the trivial solution \(x_0 = 0\), one clearly has \( x_k \simeq \frac{(2k +1) \pi}{2}\) (\(k \geq 1 \)), so we can write: \[ x_k = \frac{(2k +1) \pi}{2} - \varepsilon _k, \quad \mathrm{with} \quad \varepsilon _k < 1\] One would like to do an expansion in \( \varepsilon _k\), but of course this will not work for the tangent around its divergence points. We can however use the cotangent, since \( \tan (x_k) = x_k \Rightarrow \cot (x_k) = 1/x_k \). Using standard substitution formulas for the sine and cosine yields: \[\cot \left [ \frac{(2k +1) \pi}{2} - \varepsilon _k \right ] = \tan(\varepsilon _k) \simeq \varepsilon _k \simeq \frac{2}{(2k + 1) \pi}\] where in the last equality we neglected \( \varepsilon _k\) in the denominator. One can include it for a more rigorous treatment. Finally, we have: \[ x_k \simeq \frac{(2k +1) \pi}{2} - \frac{2}{(2k + 1) \pi}, \quad \mathrm{for} \quad k \geq 1 \, ,\] giving for the first three solutions 4.5002, 7.7267, and 10.9046, to be compared with the "exact" values 4.4934…, 7.7253…, and 10.9041…. The quality of the approximation increases with the order \(k\), since \(\varepsilon _k\) decreases (the intersections are closer and closer to the vertical asymptotes).

Iteration

Let us rewrite the initial equation by applying the arctangent to both members:
\[x = \arctan (x) \tag{1}\]
For the \(k\)-th solution, the initial estimate is: \( x^0_k = \frac{(2k +1) \pi}{2} \). Let us plug it in the right-hand side of Eq. (1) to obtain the first order estimate \( x^1_k\) and then iterate. Note that the arctangent is a multi-valued function, and the standard implementation reduces it to the first branch (the one going through the origin). We are looking for the solution sitting on the \(k\)-th branch, so we need to add \(k \pi\) each time:
\[x^{i+1}_k = \arctan (x^i_k)  + k \pi \tag{2}\]
 For the first non-trivial solution (\(k = 1\)), the sequence is: 4.71239, 4.50328, 4.49387, 4.49343, 4.49341,... with the second iteration already reaching an excellent precision!

18 September 2014

13 September 2014

False false friends

Whoever had to evolve between two related languages is familiar with the concept of false friends.
 I would argue that there is a less visible category of terms (or more precisely, of relations between terms) namely similar words that one feels are false friends but that actually have a similar meaning in the two languages: these are false false friends (FFF).
This is a subjective relation, being a false perception of one speaker.
For me, when going from French (or Romanian) to English, the FFF are mainly terms of Latin origin for which I am tempted to substitute Saxon words or other Latin terms, but which have no immediate equivalent in Romance languages:
  • salary becomes wages
  • merits deserves
  • evidentobvious
  • hypothesis assumption
etc.