mardi 25 novembre 2014

Il faut sauver le physicien John Bell (des griffes d'un blogueur polémiste)

Une réaction personnelle à un billet de Lubos Motl  
J. Bell : a mediocre physicist ? Do you talk about the same guy who discovered with R. Jackiw (and independently S. Adler) chiral anomaly, such an important phenomenon in quantum field theory? I can agree with all your technical arguments to support QM against classical zealots but the pedagogical value of your post would be undermined in my opinion if you would not recognize the pedagogical usefulness of the Bell's theorem and if you would not make the difference between necessarily old-fashioned conceptions or terminology used by Bell in the sixties and the loosely-defined concepts of a large number of QM's contenders nowadays.

John Bell et sa plus grande contribution à la physique 
... John Bell codiscovered the mechanism of anomalous symmetry breaking in quantum field theory. Indeed, our paper on this subject is his (and my) most-cited work. The symmetry breaking in question is a quantum phenomenon that violates the correspondence principle; it arises from the necessary infinities of quantum field theory. Over the years it has become evident that theoretical/mathematical physicists are not the only ones to acknowledge this effect. Nature makes fundamental use of the anomaly in at least two ways: the neutral pion’s decay into two photons is controlled by the anomaly [1, 2] and elementary fermions (quarks and leptons) arrange themselves in patterns such that the anomaly cancels in those channels to which gauge bosons – photon, W, Z – couple [3]. (There are also phenomenological applications of the anomaly to collective, as opposed to fundamental, physics – for example, to edge states in the quantum Hall effect.)
R. Jackiw, november 2000

Le mot de la fin à Richard Feynman et Alain Aspect
Chaque fois que l’on se replonge dans le problème que nous venons de présenter, on ne peut s’empêcher de se poser la question : y a-t-il un problème réel ? Il faut reconnaître que la réponse à cette question peut varier, même pour les plus grands physiciens. En 1963, R. Feynman donnait une première réponse à cette question dans son fameux cours de physique48 : « Ce point ne fut jamais accepté par Einstein… il devint connu sous le nom de paradoxe d’Einstein-Podolsky-Rosen. Mais lorsque la situation est décrite comme nous l’avons fait ici, il ne semble pas y avoir quelque paradoxe que ce soit … ». Deux décennies plus tard, Feynman exprimait une opinion radicalement différente, toujours sur la situation EPR : « nous avons toujours eu une très grande difficulté à comprendre la vision du monde que la Mécanique Quantique implique … Il ne m’est pas encore apparu évident qu’il n’y ait pas de problème réel… Je me suis toujours illusionné moi même, en confinant les difficultés de la Mécanique Quantique dans un recoin de plus en plus petit, et je me retrouve de plus en plus chagriné par ce point particulier. Il semble ridicule de pouvoir réduire ce point à une question numérique, le fait qu’une chose est plus grande qu’une autre chose. Mais voilà : – elle est plus grande … »
Alain Aspect
We must be grateful to John Bell for having shown us that philosophical questions about the nature of reality could be translated into a problem for physicists, where naive experimentalists can contribute. 
Alain Aspect (Submitted on 2 Feb 2004)

vendredi 31 octobre 2014

Faites moi peur (ou Vous voulez me rassurez) ...

//Le blogueur fête aujourd'hui Halloween à sa manière en convoquant quelques physiciens qui n'hésitent pas à parler du scénario cauchemardesque (nightmare scenario) de la physique des hautes énergies, à savoir pas de phénomènes au delà de ceux prévus par le Modèle Standard observables au LHC. Le but est évidemment de se rassurer en montrant que ses mêmes physiciens réfléchissent sur ce qui pourrait faire avancer leur discipline.

... Monsieur Shifman
String theory appeared as an extension of the dual resonance model of hadrons in the early 1970, and by mid-1980 it raised expectations for the advent of “the theory of everything” to Olympic heights. Now we see that these heights are unsustainable. Perhaps this was the greatest mistake of the string-theory practitioners. They cornered themselves by promising to give answers to each and every question that arises in the realm of fundamental physics, including the hierarchy problem, the incredible smallness of the cosmological constant, and the diversity of the mixing angles. I think by now the “theory-of-everything-doers” are in disarray, and a less formal branch of string theory is in crisis [a more formal branch evolved to become a part of mathematics or (in certain occasions) mathematical physics]. 
At the same time, leaving aside the extreme and unsupported hype of the previous decades, we should say that string theory, as a qualitative extension of field theory, exhibits a very rich mathematical structure and provides us with a new, and in a sense superior, understanding of mathematical physics and quantum field theory. It would be a shame not to explore this structure. And, sure enough, it was explored by serious string theorists. 
The lessons we learned are quite illuminating. First and foremost we learned that physics does not end in four dimensions: in certain instances it is advantageous to look at four dimensional physics from a higher-dimensional perspective... A significant number of advances in field theory, including miracles in N = 4 super-Yang-Mills... came from the string-theory side...
... since the 1980s Polyakov was insisting that QCD had to be reducible to a string theory in 4+1 dimensions. He followed this road... arriving at the conclusion that confinement in QCD could be described as a problem in quantum gravity. This paradigm culminated in Maldacena’s observation (in the late 1990’s) that dynamics of N=4 super-Yang- Mills in four dimensions (viewed as a boundary of a multidimensional bulk) at large N can be read off from the solution of a string theory in the bulk... 
Unfortunately (a usual story when fashion permeates physics), people in search of quick and easy paths to Olympus tend to overdo themselves. For instance, much effort is being invested in holographic description in condensed matter dynamics (at strong coupling). People pick up a supergravity solution in higher dimensions and try to find out whether or not it corresponds to any sensible physical problem which may or may not arise in a condensed matter system. To my mind, this strategy, known as the “solution in search of a problem” is again a dead end. Attempts to replace deep insights into relevant dynamics with guesses very rarely lead to success.
(Submitted on 31 Oct 2012 (v1), last revised 22 Nov 2012 (this version, v3))

... Monsieur White
In his overview talk[1] at Strings 2013, David Gross discussed the “nightmare scenario” in which the Standard Model Higgs boson is discovered at the LHC but no other new short-distance physics, in particular no signal for SUSY, is seen. He called it the “extreme pessimistic scenario” but also said it was looking more and more likely and (if it is established) then, he acknowledged
“We got it wrong.” “How did we misread the signals?” “What to do?”.
He said that if it comes about definitively the field, and string theorists in particular, will suffer badly. He said that it will be essential for theorists who entered the field most recently to figure out where previous generations went wrong and also to determine what experimenters should now look for.
In the following, I will argue that a root cause has been the exaggeration of the significance of the discovery of asymptotic freedom that has led to the historically profound mistake of trying to go forward by simply formulating new short-distance theories, supersymmetric or otherwise, while simultaneously ignoring both deep infra- red problems and fundamental long-distance physics.
In his recent “Welcome” speech[2] at the Perimeter Institute, Neil Turok expressed similar concerns to those expressed by Gross. He said that
“All the {beyond the Standard Model} theories have failed ... Theoretical physics is at a crossroads right now ... {there is} a very deep crisis.”
He argued that nature has turned out to be simpler than all the models - grand unified, super-symmetric, super-string, loop quantum gravity, etc, and that string theorists, especially, are now utterly confused - with no predictions at all. The models have failed, in his opinion, because they have no new, simplifying, underlying principle. They have complicated the physics by adding extra parameters, without introducing any simplifying concepts.

(Submitted on 5 Jun 2014)

vendredi 24 octobre 2014

De l'art de mesurer la constante de Hubble en cherchant notre place au milieu de nulle part

La longue marche vers une "cosmologie de précision"

The plots below show the time evolution of our knoweldge of the Hubble Constant H0, the scaling between radial velocity and distance in kilometers per second per Megaparsec, since it was first determined by Lemaitre, Robertson and Hubble in the late 1920's. The first major revision to Hubble's value was made in the 1950's due to the discovery of Population II stars by W. Baade. That was followed by other corrections for confusion, etc. that pretty much dropped the accepted value down to around 100 km/s/Mpc by the early 1960's.

The last plot shows modern (post Hubble Space Telescope) determinations, including results from gravitational lensing and applications of the Sunyaev-Zeldovich effect. Note the very recent convergence to values near 65 +/- 10 km/sec/Mpc (about 13 miles per second per million light-years)... Currently, the old factor of two discrepancy in the determination of the cosmic distance scale has been reduced to a dispersion of the order of 10 km/s out of 65-70, or 15-20%. Quite an improvement!
One major additional change in the debate since the end of the 20th century has been the discovery of the accelerating universe (cf. Perlmutter et al. 1998 and Riess et al. 1998) and the development of "Concordance" Cosmology. In the early 1990's, one of the strongest arguments for a low (~50 km/s/Mpc) value of the Hubble Constant was the need to derive an expansion age of the universe that was older than, now, the oldest stars, those found in globular star clusters. The best GC ages in 1990 were in the range 16-18 Gyr. The expansion age of the Universe depends primarily on the Hubble constant but also on the value of various other cosmological parameters, most notably then the mean mass density over the closure density, ΩM. For an "empty" universe, the age is just 1/H0 or 9.7 Gyr for H0=100 km/s/Mpc and 19.4 Gyr for 50 km/s/Mpc. For a universe with ΩM=1.000, the theorist's favorite because that is what is predicted by inflation, the age is 2/3 of that for the empty universe. So if the Hubble Constant was 70 km/s/Mpc, the age of an empty universe was 13.5 Gyr, less than the GC ages, and if Ωwas 1.000 as favored by the theorists, the expansion age would only be 9 Gyr, much much less than the GC ages. Conversely if H0 was 50 km/s/Mpc, and ΩM was the observers' favorite value of 0.25, the age came out just about right. Note that this still ruled out ΩM= 1.000 though, inspiring at least one theorist to proclaim that H0 must be 35! The discovery of acceleration enabled the removal of much of this major remaining discrepancy in timescales, that between the expansion age of the Universe and the ages of the oldest stars, those in globular clusters. The introduction of a Cosmological constant, &Lambda, one of the most probable causes for acceleration, changes the computation of the Universe's expansion age. A positive ΩΛ increases the age. The Concordance model has an H0=72 km/s/Mpc, an Ω= 1.0000... made up of ΩΛ=0.73 and ΩM=0.27. Those values yield an age for the Universe of ~ 13.7 Gyr. This alone would not have solved the timescale problem, but a revision of the subdwarf distance scale based on significantly improved paralaxes to nearby subdwards from the ESA Hiparcos mission, increased the distances to galactic globular clusters and thus decreased their estimated ages. The most recent fits of observed Hertzsprung-Russel diagrams to theoretical stellar models (isochrones) by the Yale group (Demarque, Pinsonneault and others) indicates that the mean age of galactic globulars is more like 12.5 Gyr, comfortably smaller than the Expansion age.
John P. Huchra, Copyright 2008
Les derniers pas...
The recent Planck observations of the cosmic microwave background (CMB) lead to a Hubble constant of H0=67.3±1.2 km/s/Mpc for the base six-parameter ΛCDM model (Planck Collaboration 2013, hereafter P13). This value is in tension, at about the 2.5σ level, with the direct measurement of H0=73.8 ± 2.4 km/s/Mpc reported by Riess et al (2011 R11). If these numbers are taken at face value, they suggest evidence for new physics at about the 2.5σ level (for example, exotic physics in the neutrino or dark energy sectors...). The exciting possibility of discovering new physics provides strong motivation to subject both the CMB and H0 measurements to intense scrutiny. This paper presents a reanalysis of the R11 Cepheid data. The  H0 measurement from these data has the smallest error and has been used widely in combination with CMB measurements for cosmological parameter analysis (e.g. Hinshaw et al. 2012; Hou et al. 2012; Sievers et al. 2013). The study reported here was motivated by certain aspects of the R11 analysis: the R11 outlier rejection algorithm (which rejects a large fraction, ∼ 20%, of the Cepheids), the low reduced χ2 values of their fits, and the variations of some of the parameter values with different distance anchors, particularly the metallicity dependence of the period-luminosity relation... 
[The] figure [below] compares these two estimates of H0 with the P13 results from the [Planck+WP+highL (ACT+South Pole Telescope)+BAO (2dF Galaxy Redshift and SDSS redshiftsurveys)] likelihood for the base ΛCDM cosmology and some extended ΛCDM models. I show the combination of CMB and Baryon Acoustic Oscillations [BAO] data since H0 is poorly constrained for some of these extended models using CMB temperature data alone. (For reference, for this data combination H0=67.80±0.77 km/s/Mpc in the base ΛCDM model.) The combination of CMB and BAO data is certainly not prejudiced against new physics, yet the H0 values for the extended ΛCDM models shown in this figure all lie within 1σ of the best fit value for the base ΛCDM model. For example, in the models exploring new physics in the neutrino sector, the central value of H0 never exceeds 69.3 km/s/Mpc. If the true value of H0 lies closer to, say, H0=74 km/s/Mpc , the dark energy sector, which is poorly constrained by the combination of CMB and BAO data, seems a more promising place to search for new physics. In summary, the discrepancies between the Planck results and the direct H0 measurements... are not large enough to provide compelling evidence for new physics beyond the base ΛCDM cosmology.

The direct estimates (red) of H0 (together with 1σ error bars) for the NGC 4258 distance anchor  and for all three distance anchors. The remaining (blue) points show the constraints from P13 for the base ΛCDM cosmology and some extended models combining CMB data with data from baryon acoustic oscillation surveys. The extensions are as follows: mν, the mass of a single neutrino species; mν + Ωk, allowing a massive neutrino species and spatial curvature; Neff , allowing additional relativistic neutrino-like particles; Neff +msterile, adding a massive sterile neutrino and additional relativistic particles; Neff+mν, allowing a massive neutrino and additional relativistic particles; w, dark energy with a constant equation of state w = p/ρ; w + wa , dark energy with a time varying equation of state. I give the 1σ upper limit on mν and the 1σ range for Neff . 
(Submitted on 14 Nov 2013 (v1), last revised 8 Feb 2014 (this version, v2))

"cosmologie de précision" : un terme à prendre avec des pincettes 

Chercher notre place au milieu de nulle part...
Tel pourrait être le propos de la cosmologie dans une perspective anthropologique. Mais ce blog ci n'est pas le lieu pour ce genre de débat. Le blogueur préfère laisser la parole de fin à une grande dame de l'enseignement de l'astronomie en France Lucienne Gougenheim en espérant que ce qui précède illustre bien l'actualité de sa conclusion générale extraite d'un exposé pédagogique sur la constante de Hubble et l'âge de l'Univers daté de 1996

  • La distance n'est pas le seul paramètre qui conditionne la valeur de H0...
  • La nature de la chandelle standard est complexe ; même quand nous avons une bonne connaissance théorique de la propriété qui sert de critère de distance, il convient de discuter l'importance des différents paramètres dont elle dépend.
  • On ne passe de la connaissance de H0 à celle de d'âge de l'univers que dans le cadre d'un modèle cosmologique.
  • ...un problème complexe ne peut se comprendre (et en conséquence se résoudre) que par la prise en compte de l'ensemble des paramètres dont il dépend...

mardi 9 septembre 2014

Shut-up and calculate* ... or converse before speculating ?

(A message of) the last of the pioneers of particle colliders

... I may be the last still around of the first generation of pioneers that brought colliding beam machines to reality.  I have been personally involved in building and using such machines since 1957 when I became part of the very small group that started to build the first of the colliders.   While the decisions on what to do next belong to the younger generation, the perspective of one of the old guys might be useful.  I see too little effort going into long range accelerator R&D, and too little interaction of the three communities needed to choose the next step, the theorists, the experimenters, and the accelerator people.  Without some transformational developments to reduce the cost of the machines of the future, there is a danger that we will price ourselves out of the market.
Burton Richter (Stanford University and SLAC National Accelerator Laboratory)
Wed, 3 Sep 2014

The high-energy colliders may not reach to heaven (and high-luminosity ones?)
In early 2015 the LHC will begin operations again at about 13 TeV compared to the 8-TeV operations before its recent shutdown for upgrading. 
The LHC itself is an evolving machine.  Its energy at its restart next year will be 13 TeV, slowly creeping up to its design energy of 14 TeV.  It will shut down in 2018 for some upgrades to detectors, and shut down again in 2022 to increase the luminosity.  It is this high-luminosity version (HL-LHC) that has to be compared to the potential of new facilities.  There has been some talk of doubling the energy of the LHC (HE-LHC) by replacing the 8-tesla magnets of the present machine with 16-tesla magnets, which would be relatively easy compared to the even more talked about bolder step to 100 TeV for the next project.  It is not clear to me why 30-TeV LHC excites so little interest, but that is the case.  
A large fraction of the 100 TeV talk (wishes?) comes from the theoretical community which is disappointed at only finding the Higgs boson at LHC and is looking for something that will be real evidence for what is actually beyond the standard model. Regrettably, there has been little talk so far among the three communities, experimenters, theorists, and accelerator scientists, on what constraints on the next generation are imposed by the requirement that the experiments actually produce analyzable data... 
The most important choice for a new, higher energy collider is its luminosity, which determines its discovery potential.  If a new facility is to have the same potential for discovery of any kind of new particles as had the old one, the new luminosity required is very roughly proportional to the square of the energy because cross sections typically drop as E-2.  A seven-fold increase in energy from that of HL-LHC to a 100-TeV collider therefore requires a fifty-fold increase in luminosity.  If the luminosity is not increased, save money by building a lower-energy machine where the discovery potential matches the luminosity.

String theorists ideas on physics might be popularized only in science fiction magazines ;-)
If you have seen the movie Particle Fever about the discovery of the Higgs boson, you have heard the theorists saying that the only choices today are between Super-symmetry and the Landscape.  Don’t believe them.  Super-symmetry says that every fermion has a boson partner and vice versa.  That potentially introduces a huge number of new arbitrary constants which does not seem like much progress to me.  However, in its simpler variants the number of new constants is small and a problem at high energy is solved.  But, experiments at the LHC already seem to have ruled out the simplest variants.    
The Landscape surrenders to perpetual ignorance.  It says that our universe is only one of a near infinity of disconnected universes, each with its own random collection of force strengths and constants, and we can never observe or communicate with the others.  We can never go further in understanding because there is no natural law that relates the different universes.  The old dream of deriving everything from one constant and one equation is dead.  There are two problems with the landscape idea.  The first is a logic one.  You cannot prove a negative, so you cannot say that there is no more to learn.  The second is practical.  If it is all random there is no point in funding theorists, experimenters, or accelerator builders.  We don’t have to wait until we are priced out of the market, there is no reason to go on 
There is a problem here that is new, caused by the ever-increasing mathematical complexity of today’s theory.  When I received my PhD in the 1950s it was possible for an experimenter to know enough theory to do her/his own calculations and to understand much of what the theorists were doing, thereby being able to choose what was most important to work on.  Today it is nearly impossible for an experimenter to do what many of yesterday’s experimenters could do, build apparatus while doing their own calculations on the significance of what they were working on.  Nonetheless, it is necessary for experimenters and accelerator physicists to have some understanding of where theory is, and where it is going.  Not to do so makes most of us nothing but technicians for the theorists.  Perhaps only the theory phenomenologists should be allowed to publish in general readership journals or to comment in movies. 

*A propos ... 

mardi 26 août 2014

Peut-on mettre un peu d'ordre dans le processus de sélection des théories physiques?

De la cohérence observationnelle à la cohérence mathématique... 
My first point is that the conditions of theory choice should be ordered. Frequently we see the listing of criteria for theory choice given in a flat manner, where one is not given precedence over the other a priori. We see consilience, simplicity, falsifiability, naturalness, consistency, economy, all together in an unordered list of factors when judging a theory. However, consistency must take precedence over any other factors. Observational consistency is obviously central to everyone, most especially our experimental colleagues, when judging the relevance of theory for describing nature. Despite some subtleties that can be present with regards to observational consistency (There can be circumstances where a theory is observationally consistent in a vast number of observables, but in a few it does not get right, yet no other decent theory is around to replace it. In other words, observational consistency is still the top criterion, but the best theory may not be 100% consistent.) it is a criterion that all would say is at the top of the list.
Mathematical consistency, on the other hand, is not as fully appreciated... Mathematical consistency has a preeminent role right up there with ob- servational consistency, and can be just as subtle, time-consuming and difficult to establish. We have seen that in the case of effective theories it trumps other theory choice considerations such as simpleness, predictivity, testability, etc 
My second point builds on the first. Since consistency is preeminent, it must have highest priority of establishment compared to other conditions. Deep, thoughtful reflection and work to establish the underlying self-consistency of a theory takes precedence over finding ways to make it more natural or to have less parameters (i.e., simple). Highest priority must equally go into understanding all of its observational implications. A theory should not be able to get away with being fuzzy on either of these two counts, before the higher order issues of simplicity and naturalness and economy take center stage. That this effort might take considerable time and effort should not be correlated with a theory’s value, just as it is not a theory’s fault if it takes humans decades to build a collider to sufficiently high energy and luminosity to test it. 
Additionally, dedicated effort on mathematical consistency of the theory, or class of theories, can have enormous payoffs in helping us understand and interpret the implications of various theory proposals and data in broad terms. An excellent example of that in recent years is by Adams et al. [15], who showed that some theories in the infrared with a cutoff cannot be self-consistently embedded in an ultraviolet complete theory without violating standard assumptions regarding superluminality or causality. The temptation can be high to start manipulating uninteresting theories into simpler and more beautiful versions before due diligence is applied to determine if they are sick at their cores. This should not be rewarded... 
Finally, I would like to make a comment about the implications of this discussion for the LHC and other colliders that may come in the future...  
In the years since the charm quark was discovered in the mid 1970’s there has been tremendous progress experimentally and important new discoveries, including the recent discovery of a Higgs boson-like state [20], but no dramatic new discovery that can put us on a straight and narrow path beyond the SM. That may change soon at the LHC. Nevertheless, it is expensive in time and money to build higher energy colliders, our main reliable transporter into the high energy frontier. This limits the prospects for fast experimental progress. 
In the meantime though, hundreds of theories have been born and have died. Some have died due to incompatibility of new data (e.g., simplistic technicolor theories, or simpleminded no-scale supersymmetry theories), but others have died under their own self-consistency problems (e.g., some extra-dimensional models, some string phenomenology models, etc.). In both cases, it was care in establishing consistency with past data and mathematical rigor that have doomed them. In that sense, progress is made. Models come to the fore and fall under the spotlight or survive. When attempting to really explain everything, the consistency issues are stretched to the maximum. For example, it is not fully appreciated in the supersymmetry community that it may even be difficult to find a “natural” supersymmetric model that has a high enough reheat temperature to enable baryogenesis without causing problems elsewhere [21a, 21b]. There are many examples of ideas falling apart when they are pushed very hard to stand up to the full body of evidence of what we already know. 
Relatively speaking, theoretical research is inexpensive. It is natural that a shift develop in fundamental science. The code of values in theoretical research will likely alter in time, as experimental input slows. Ideas will be pursued more rigorously and analysed critically. Great ideas will always be welcome. However, soft model building tweaks for simplicity and naturalness will become less valuable than rigorous tests of mathematical consistency. Distant future experimental implications identified for theories not fully vetted will become less valuable than rigorous computations of observational consistency across the board of all currently known data. One can hope that unsparing devotion to full consistency, both observational and mathematical, will be the hallmarks of the future era.

James D. Wells (Submitted on 3 Nov 2012)

(Encore) un philosophe dans la soupe du physicien

Ne pas oublier que la physique découle de la philosophie naturelle... 
"... theoretical physics has not done great in the last decades. Why? Well, one of the reasons, I think, is that it got trapped in a wrong philosophy: the idea that you can make progress by guessing new theory and disregarding the qualitative content of previous theories. This is the physics of the “why not?” Why not studying this theory, or the other? Why not another dimension, another field, another universe? Science has never advanced in this manner in the past. Science does not advance by guessing. It advances by new data or by a deep investigation of the content and the apparent contradictions of previous empirically successful theories. "
By John Horgan | August 21, 2014

mercredi 18 juin 2014

Un philosophe (apporte son grain de sel) à la table du physicien

Le spectacle de la Nature est un banquet où la soupe phénoménologique se doit d'être riche en modèles mathématiques variés
Où le blogueur essaie d'argumenter sur la nécessité de comparer les différents modèles mathématiques proposés par les physiciens pour comprendre et explorer plus avant la réalité, en le faisant à sa manière habituelle* c'est-à-dire par une citation de texte:
From the times of Niels Bohr, many physicists, mathematicians and biologists have been attentive to philosophical aspects of our doing. Most of us are convinced that the frontier situation of our research can point to aspects of some philosophical relevance - if only the professional philosophers would take the necessary time to become familiar with our thinking. Seldom, however, we read something of the philosophers which can inspire us. The US-American philosopher Charles Sanders Peirce (1839-1914) is an admirable exception. In his semiotics and pragmaticist (he avoids the word “pragmatic”) thinking, he provides a wealth of ideas, spread over an immense life work. It seems to me that many of his ideas, comments, and concepts can shed light on the why and how of mathematization...
 The quality of a mathematical model is not how similar it is to the segment of reality under consideration, but whether it provides a flexible and goal-oriented approach, opening for doubts and indicating ways for the removal of doubts (later trivialized by Popper’s falsification claim). More precisely, Peirce claims
  •  Be aware of differences between different approaches! 
  • Try to distinguish different goals (different priorities) of modelling as precise as possible! 
  • Investigate whether different goals are mutually compatible, i.e., can be reached simultaneously!
  • Behave realistically! Don’t ask: How well does the model reflect a given segment of the world? But ask: Does this model of a given segment of the world support the wanted and possibly wider activities / goals better than other models?
I may add: we have to strike a balance between Abstraction vs. construction, Top-down vs. bottom-up, and Unification vs. specificity. We better keep aware of the variety of Modelling purposes and the multifaceted relations between Theory - model - experiment. Our admiration for the Power of mathematization, the Unreasonable effectiveness of mathematics (Wigner) should not blind us for the Staying and deepening limitations of mathematization opposite new tasks.

*Remarques transtextuelles (ou portrait du blogueur en métacognition)
Quelque part dans son Moi profond, le transcyberphysicien se rêve en soldat inconnu de la guerre épistémologique que se livrent les défenseurs des différents modèles scientifiques de la gravitation quantique (théories des supercordes, gravitation quantique à boucles, piste tensorielle, géométrie spectrale non commutative...); mais à travers son discours basé essentiellement sur un usage immodéré d'extraits de ses propres lectures, il se voit aussi comme une sorte de Sancho Panza: (son Ça en somme ;-) infidèle compagnon de route virtuel d'un célèbre blogueur de sciences polémiste (et parfois triste sire) dont il relate parfois les tribulations dans le métatexte de ce blog.