## how can we tell someone “be natural”? [#2]

**F**ollowing my earlier high school composition (or, as my daughter would stress, a first draft of vague ideas towards a composition!), I came upon an article in the Science leaflet of Le Monde (as of October 25) by the physicist Marco Zito (already commented on the ‘Og): “How natural is Nature?“. The following is my *(commented)* translation of the column, I cannot say I understand more than half of the words or hardly anything of its meaning, although checking some Wikipedia entries helped *(I wonder how many readers have gotten to the end of this tribune)*…

The above question is related to physics in that (a) the electroweak interaction scale is about the mass of Higgs boson, at which scale

[order of 100GeV]the electromagnetic and the weak forces are of the same intensity. And (b) there exists a gravitation scale, Planck’s mass, which is the energy[about 1.2209×10where gravitation^{19}GeV][general relativity]and quantum physics must be considered simultaneously. The difficulty is that this second fundamental scale differs from the first one, being larger by 17 orders of magnitude[so what?!]. The difference is puzzling, as a world with two fundamental scales that are so far apart does not sound natural[how does he define natural?]. The mass of Higgs boson depends on the other elementary particles and on the fluctuations of the related fields. Those fluctuations can be very large, of the same order as Planck’s scale. The sum of all those terms[which terms, dude?!]has no reason to be weak. In most possible universes, the mass of this boson should thus compare with Planck’s mass, hence a contradiction[uh?!].

**A**nd then enters this apparently massive probabilistic argument:

If you ask passerbys to select a number each between two large bounds, like – 10000 and 10000, it is very unlikely to obtain exactly zero as the sum of those numbers. So if you observe zero as the sum, you will consider the result is not «natural»

[I’d rather say that the probabilistic model is wrong]. The physicists’ reasoning so far was «Nature cannot be unnatural. Thus the problem of the mass of Higgs’ boson must have a solution at energy scales that can be explored by CERN. We could then uncover a new and interesting physics». Sadly, CERN has not (yet?) discovered new particles or new interactions. There is therefore no «natural» solution. Some of us imagine an unknown symmetry that bounds the mass of Higgs’ boson.

**A**nd a conclusion that could work for a high school philosophy homework:

This debate is typical of how science proceeds forward. Current theories are used to predict beyond what has been explored so fat. This extrapolation works for a little while, but some facts eventually come to invalidate them

[sounds like philosophy of science 101, no?!]. Hence the importance to validate through experience our theories to abstain from attributing to Nature discourses that only reflect our own prejudices.

**T**his Le Monde Science leaflet also had a short entry on a meteorite called *Hypatia*, because it was found in Egypt, home to the Alexandria 4th century mathematician Hypatia. And a book review of (the French translation of) Perfect Rigor, a second-hand biography of Grigory Perelman by Martha Gessen. (Terrible cover by the way, don’t they know at Houghton Mifflin that the integral sign is an elongated S, for sum, and not an f?! We happened to discuss and deplore with Andrew the other day this ridiculous tendency to mix wrong math symbols and greek letters in the titles of general public math books. The title itself is not much better, what is imperfect rigor?!) And the Le Monde math puzzle #838…

November 19, 2013 at 4:40 pm

Tu es bien difficile. Cet $f$ transformé en intégrale est plutôt élégant. Quant au contenu du livre, il est tout à fait passionnant, en dépit d’une violente critique dans les Notices il y a 18 mois. On en apprend beaucoup sur la société russe, l’organisation des mathématiques en URSS, et un peu tout de même sur la conjecture de Poincaré. Amicalement, Gérard Letac.

November 19, 2013 at 5:27 pm

Merci Gérard de tes commentaires et

mea maxima culpa: je n’ai lu que la critique du livre. Donc te remercie de ton avis plus profond sur le dit livre. Je reste cependant réticent sur l’emploi de symboles mathématiques ou grecs hors de contexte pour “faire” scientifique. Comme par exemple ce récent livre sur les irrationels, reviewé dans CHANCE, et imprimé comme Πhε irratiΦnals… Avec toutes mes amitiés, Christian