The physics of Ayotzinapa

Protest in Mexico City’s central square (Zócalo). Legend reads: “it was the state” (“Fue el estado”).

By Ignacio Gonzalez.

I am willing to concede that an outright denunciation of social injustice looks like an obvious misfit within this blog, however, I believe that the reader should equally grant that if the claim is properly woven with physical metaphors, then, the dissonance becomes considerably mitigated. Thus, I appeal to the reader’s tolerance to allow me this semantic transgression. I trust that if I get this through alright then perhaps by the end of it I will have gained a grain of the reader’s sympathy, but much more rewarding  than obtaining sympathy directed at the author, I hope that the reader might sympathize with the very motives underlying this topical deviation.

Then, let us get started by describing the putative “physical system” that I want to deal with in this delivery.

Defining the “Mexican system”.

Spatially, Mexico extends its territory over almost 2 million square kilometers (turning this nation into the 14th largest country in the world). The dynamics of Mexico’s physical area are of the rather static kind nowadays (although there is plenty of room for argument against this assumption) therefore, I would like to focus on a more challenging problem: the dynamical behavior exhibited by Mexico’s nearly 120 million inhabitants aptly denominated as “Mexicans”. From now on, I will refer to the group of all Mexicans by using the term “Mexican system”.

Recently, the Mexican system has been subjected to a disruptive and completely arbitrary stimulus of considerable magnitude. The disturbance has propagated rapidly throughout large parts of the system, which, in response has reacted by physically mobilizing hundreds of thousands of its component particles and propitiating ideologically-loaded verbal manifestations from millions more.

Some of the most relevant questions regarding the evolution of the system in the aftermath of this major perturbation are: will the magnitude of the emergent collective behavior so far displayed by the Mexicans continue to amplify as the time passes by? and if so, will the many reactionary waves come to a coherent state of constructive interference? Will the coherence last long enough for the reaction to gather enough momentum in order to drive the badly needed phase transition that the system needs?

Tough questions for a tough problem, perhaps we simply do not count with enough information to provide a positive or negative answer with a high degree of certainty, after all one must never forget that a good fraction of the variables that span the phase space of any social system have a remarkable talent to remain stubbornly hidden.

Ayotzinapa, the critical point?

To understand what Ayotzinapa is let us go back to the geographical space for only a moment. Ayotzinapa is a community enclaved within the mexican state of Guerrero (more internationally known for harboring the playa of Acapulco). According to the all-knowing Wikipedia Ayotzinapa was home to less than 100 people back in 2010.

Perhaps the main reason why this minuscule town occupies a discernible spot in the map it’s because it is home to the “Raul Isidro Burgos” rural Normal School where around 530 students aspired to become elementary school teachers. On the night of the last 26th of September that student body became suddenly and forcibly reduced by little less than 10 % when 43 students were abducted near the  city of Iguala (lying around 130 away from Ayotzinapa). This subtraction have sparked a massive turmoil within the Mexican system, not a minor feat for a system that is commonly labeled by many as intrinsically apathetic when confronted with similar happenings.

One cannot make sense of such an intense reaction when the event is framed only in the language of cold hard numbers. The tiny fraction of the Mexican population that these 43 of its members represent would be more economically expressed in scientific notation, but for marketing purposes I will express the figure in standard decimal scripture: the 43 missing students make up around the 0.0000003-th part of the whole Mexican system. Why is it then that the vanishing of such an infinitesimally small fraction has provoked such an over-reaching response? On the face of it, it seems like this phenomenon blatantly violates Newton’s third law of mechanics which states that a reaction over a system is entitled to cause a reaction from the system of equal intensity but with opposed direction (the “equal intensity” bit being the obviously transgressed part), could we instead be witnessing a sort of runaway “butterfly effect”? should we abandon classical approximations and jump into the framework used to describe complex dynamical systems in the verge of chaos in order to understand how this phenomenon came about? Perhaps that is not necessary, one task and one assumption might suffice to treat the problem at hand:

Task: To analyze the context around the subtraction. The inherent explosive nature of the event might be understood once its phenomenological details are inspected.

Assumption: To assume that the Mexican system is endowed with memory capabilities. As faulty as the data storing ability of the system has proven to be, a hope remains that the bits of information engraved on the collective Mexican mind might not be yet completely covered in rust so as to leave them illegible.

Why Ayotzinapa feels different.

The Mexican system oscillates along countless degrees of freedom. One of its dominant oscillations has been strictly periodical since 1934, I am referring to the presidential oscillation which completes a period every six years. The fabric that holds the system together has been degrading as successive periods come to pass. I will not pretend to be a historian, thus, I will not try to pinpoint an exact point in time marking the beginning of the structural decomposition of the authorities in charge to enforce the laws under which the Mexican system plays. Most likely the causes cannot be traced back to a single water-shedding event, however, it seems to me (and many more would agree with me up to a degree) that in the last three presidential periods the rottenness of the governmental institutions has leaked profusely and now it deeply pervades the whole of the Mexican system.

Let us focus on the number of agents forming the system. The subtraction rate ramped up during the period comprehended between December of 2006 to November 2012 when the infamous Felipe Calderon drove the system into a state of war (shockingly, this is not a figure of speech, Calderon did declare war against the drug dealers as soon as he took office. If this was ever intended as a metaphor then Mr. Calderon should know that you do do not metaphorically refer to intentions and deeds that you actually plan to carry on). The numbers vary depending on the source but by all accounts the subtraction operation performed over the Mexican system during this outrageous period was massive (over 100,000 deaths without counting other thousands labeled as “missing”). Both, Blood and pesos, were valid currency back then and one cannot safely say that the exchange rate among them has substantially subdued ever since.

When one takes a look at those numbers and contrasts them with the apparent calm with which the Mexicans seem to carry on with their lives, one might be forced to conclude that the Mexican system has developed a disturbingly robust resistance against such deadly perturbations. Or, could it be more likely that the bloodbath induced a phase transition in the system driving it into a state of stupor and indifference? was it a kind of spinodal transition where the system could have equally evolved towards a state of revolutionary uprising on the one hand, or, of fear-induced stasis into the other? Could the falling into the latter due to an almost imperceptible tweak on the initial conditions? if it is so, then, the question of why the Ayotzinapan case has demonstrated to be so outstandingly revulsive becomes as transcendental as ever.

A good part of the answer to this conundrum is neatly summarized in three proverbial words that the Mexican system has chosen as a banner for the movement: “fue el estado” (“it was the state”). The abduction, the subtraction, the kidnapping of the 43 students was performed by uniformed policemen who acted upon direct orders given by the mayor of Iguala himself (or should I say his wife? it seems that she is stealing the shameful limelight). This time, it was the undisguised state. This time there was no immediate “war” background to absorb the impact that the disappearance of 43 innocent citizens would have on an increasingly strained society. Actually, the circumstances that lead the 43 students to be transformed into victims is precisely the kind of trademark symptom of the social strain I just referred to. The students had set off to Iguala to either voice a protest against the educational reform implemented by the government (say some) or to prepare the logistics necessary for them to take part on the annual commemoration of the student massacre perpetrated by the state back in 1968 (in which case The Machiavellian irony surrounding the whole incident could not fail to be noticed).

In any case, one can easily peer into the kind of properties typically exhibited by the Mexican system that the state took into consideration before playing one more of its rapacious tactics on its own population: it could have been emboldened by its seamlessly all-forgiving nature, or fooled by its apparently incurable amnesia, or simply betting on its impossibility to wake up from the blood-induced trance of recent times… or a mixture of all the former properties plus many more that the author might be missing to list.

Well, even the most superficial evaluation of the aftermath tells an obvious truth: the reactivity of the Mexican system was seriously underestimated by the state.

The Mexican system as solid under strain.

Could it be that the ultimate physical metaphor to describe the evolution of the Mexican system’s behavior during the last decade is that of a deformable solid subjected to repetitive stress loads? Let us pose a series of propositions to confirm that the similitude between both systems can hold.

Proposition 1: A deformable solid can change its shape whenever a force large enough is applied onto it. 

Analogy: This would be equivalent to say that the Mexican system is able to change its behavior whenever it is confronted by a social stimulus of enough “strength”.

Example: If a certain place is deemed (either factually or only perceived) as dangerous or a certain time of the day as insecure for being on the street (this designation playing the role of social stimulus), then, the population would take notice and stop attending to the place in question or showing up in public at the signaled time (the pertinent behavioral change by the population). Both situations have been manifest in some parts of the Mexican territory, for instance, people withdrew themselves from Casinos after shooting incidents occurred at several such places. Similarly, as the violence wave engulfed large parts of the national territory, whole villages and cities were effectively turned into ghost towns as soon as the sun sank in the horizon.

Proposition 2: After a large enough strain has been applied to the solid a transition into the so-called plastic regime can occur, this is, the object is not able anymore to recover its former configuration even after the strain ceases to be applied (as it happens with elastic objects which can recover their shape after they have been strained). This quality endows the object with some kind of memory, its present shape keeps track or stores information about the deforming stimulus that has been applied to it.

Analogy:  It would be in extreme naive to suppose that a population can fully recover from a prolonged exposition to indiscriminate violence without even leaving a scar. The traumatizing effects of such an experience are seen and felt everywhere, individual habits can change permanently, doors that used to be left open now never go unlocked through the night. On a larger scale, the social strain imposed by cycles of violence can permanently deform the infrastructure of a city or the demographics of a nation, even if the violence eventually wanes the system is already irreversibly transfixed.

Example: Take the case of the “Barrio Antiguo” district in the northern city of Monterrey. A place that used to be buzzing with nightlife, full of bars and clubs, this quintessential meeting point essentially closed its doors after the violence reached its grounds. The busy nights that characterized the place will not come back. The Barrio Antiguo is currently being brought back to life but not by the re-opening of clubs but by the activity of newly established restaurants. Not an strictly bad turnover in itself, but, an irreversible and uncalled change of urban landscape. Much more dramatic is the draining of entire communities due to massive emigration to safer havens mainly across the north american border, or again in a stockade of irony, to the Mexico City megalopolis traditionally regarded as an epithet of insecurity by the majority of the Mexicans.

Proposition 3: Plastics break. Even the most ductile of the materials is doomed to fracture if the application of ever increasing stress loads does not wither away.

Analogy: Revolutions, overthrows, shunning of inept authorities or regulations, all of those are unequivocal manifestations that a society has been strained beyond its self-restoring capabilities, or simply, beyond its tolerance. There are several pathways that can channel a society to a breaking point, namely: flamboyant displays of corruption, stringent inequality policies. There are several directions along one can pull on a social system in order to fracture it, one of them can well be the incapability of national institutions to provide safety to its population. The rupturing process is ensured to accelerate if those same institutions are transformed from national protectors to criminal perpetrators, just as it happened to those constituting the Mexican state.

Example: Can the kidnapping of the 43 students of Ayotzinapa be the critical event that drives the Mexican system to break away from its governing class? To recover the control over its territory that has been lost to corruption and institutional degeneration? I do not know the answer to these questions but I hope with all my might that an affirmative one will satisfactorily answer both of them. If we are not at the critical point quite yet and if indeed the deformable object analogy is a good one, then, what we can do to quicken the fracturing process is to constantly refresh the memory of the system, do not withdraw the topic from the public tribune, keep on stressing.

A hope-loaded prediction.

The Mexican system is giving us encouraging signals, it is telling us that it does have a memory, that the magnitude of the abuses and atrocities to which it has been subjected has lead the system  to trespass its elastic limit long ago, that the social strain applied onto it has left perennial marks on its topology, that bit by bit, pull after pull, the Mexican system has been painfully escalating to higher and higher energy states and that maybe, only maybe, what happened in Iguala will provide the final kick that the system needs to jump over the energy barrier and complete its phase transition and never walk back through such a tortuous path.


Rewards from a failed attempt to ambush Neil deGrasse Tyson

Hayden Planetarium

By Ignacio Gonzalez

The past 18th of October Carolina, Josue and me were on a mission. We knew that if we were to successfully accomplish it then our bodies would pay the consequences dearly, undoubtedly our feet would take the highest toll. We managed to coincide in New York City after more than a year and a half from our last encounter. I was flying from Germany and they both from Mexico, not a small deal of organization, money and will had been put into the effort and we had to make the whole event count. The plan for the day was to visit not one, not two but three museums, and, we had to reach the third before 6:45 pm!… and none of us was wearing particularly comfortable shoes! It was too late to back off, the targets were set and the route planned, time had come to man-up, but much more importantly, to nerd-up. At 10:00 am sharp the doors were open: the American Museum of Natural History welcomed us!

And what a welcoming sight that was! You have not yet completely dragged yourself through the entrance door and you already need to pick up your jaw that has dropped to the floor while simultaneously your neck arches backwards in an effort to fully contemplate the figure of a towering sauropod skeleton (a Barosaurus) rising to its full frame. Luckily, if you already had the chance to walk around skyscraper-crammed Manhattan, maybe by then your anatomy is used to this uttermost anti-ergonomic posture. So imposing is the intimidating stance of the Barosaurus that one almost misses the Allosaurus which is provoking the defensive reaction in the first place. But when one does spot the (wannabe) predator, one cannot help to feel a bit of sympathy mixed with pity towards it. No matter how many dozens of razor-shaped teeth you can squeeze into your mouth, there’s no chance you’re going to take down such a leviathan. If the Allosaurus had rationalized that it surely wouldn’t have acted so cocky. But wait, not so fast! maybe the intended prey was never the gigantic long-necked dinosaur but instead its considerably smaller offspring that shies away behind the protective colossal parent. The Allosaurus was not that bold (or blatantly stupid) after all, it was just trying to get very very lucky.

We had only as much time as it took us to get our entries to contemplate that fossilized scene of Jurassic drama. Why the rush? cause we had less than 30 minutes before the big show began. You see, the American Museum of Natural History is a large place, so big that you could fit, say, a planetarium in it. And that is exactly what whoever is in charge of taking such decisions did. Thanks to an enlightened choice the Museum also serves as home for the Hayden Planetarium and it was there where we were heading. The featured space show was (and it still is) the “Dark universe” and I will be telling you in more detail about it in a moment but first allow me a slight deviation. The show is narrated by  Dr. Neil deGrasse Tyson. Chances are that the reader knows who Mr. deGrasse Tyson is, if not from his prolific scientific work as a physicist (mainly in the fields of cosmology and general relativity), or his contributions as an educator for the masses (he has authored or co-authored at least ten popular science books and he is the heir of Carl Sagan as the host of the totally refurbished version of the classic Cosmos TV series), then, at least because he has been meme-fied (or meme-rized, as you prefer) for posterity. As of right now myriads of hand-sketched deGrasse Tysons in an it-was-not-me sort of gesture swarm through the internet (open your facebook, he might be there… more than once). Tyson also happens to be the director of the Hayden planetarium but it is not that office what makes him the obvious candidate to guide us through the dark universe, probably not even his appropriate credentials were the decisive factor, surely if he had lacked that characteristic baritone voice of his then the job would have gone to another astrophysicist. On our way to the planetary dome I kept scanning the corridors looking for a sign saying something like “Dr. deGrasse Tyson office. Knock twice for an autograph. Thrice for free books” followed by an accusatory arrow but such a sighting never materialized. In a snap my hidden agenda simply vaporized, even being fully conscious of the naivety of my childish little plot I was not quite able to shake a tiny feeling of failure. However, I knew that as soon as the tour through the “Dark universe” began I would be more than compensated.

To understand the premise of the show first consider all what you can perceive with your own senses, all of that already encompasses a considerable fraction earthly and cosmic stuff. Now add to that bunch everything that you can detect aided by whichever piece of gadgetry or machinery that has ever been conceived, then your list has become immensely improved. Now you can also count electromagnetic radiation (or photons) of essentially any frequency you choose (radio waves, infrared, X-rays, gamma rays…) and a dazzling zoo of subatomic particles as entities that are perceivable. We have worked out how all those ingredients can cluster to produce a rich plethora of matter-energy states (matter and energy being ultimately interchangeable according to the über-famous Einstein’s equivalence E = mc2, where E stands for energy, m for mass and c is the speed of light). We have come to understand how liquids, solids, gases, plasmas, laser beams, rays of particles, Bose-Einstein condensates, and other rarities come into existence. And more recently we started to peer into fancy new states of matter-energy like “molecules of light“,”dropletones” and the first observed Majorana fermion. Indeed mankind has amassed a lot of physics over the last couple of centuries and with all that knowledge we have forged two powerful theoretical frameworks that together (but so far not united) span an umbrella under which we can accommodate almost every phenomenon ever registered: we have general relativity to explain gravity and the standard model of particles physics to deal with electromagnetism, the weak, the strong force and the whole cornucopia sub-atomic particles (in principle gravity could be included within the standard model but for that we still need to detect the yet unseen graviton that works as carrier for the gravitational force). The picture of the universe painted by all these couple of theories is quite impressive, but, and here comes the devastating blow to our ego as a species, it is also utterly and miserably incomplete.

Turns out that of all the stuff (matter and energy) that makes up our universe only around 5% of it can be explained in terms of our beloved theories, the remaining 95% is in a form which is totally unaccounted for by either the standard model or by general relativity. More precisely, to the best of our knowledge that 95% is made of around 27% of something called “dark matter” and 68% is an even more mysterious thing denominated as “dark energy”. One can almost hear the echo of the Nobel laureate physicist I. I. Rabi exclaiming “Who ordered that?!” as he did when he was informed about the discovery of the muon. Well, dark matter and dark energy is what the “Dark universe” show is all about, however, in this entry I will refer only to the former.

The complains start with the term “dark matter” itself. It is commonly regarded as a staunch reminder of the dull naming abilities of physicists (consider the examples: standard  model, black holes, or the quarks which come in  up, down, strange, charm, bottom and top versions… not exactly pearls of creativity). Dark matter is dark because we cannot see it, that is, because it does not emit or reflect light. Nevertheless, I cannot get rid of the feeling that “dark” does not quite work as a good label mainly because dark matter does not even absorb light which is  the single most transcendental characteristic of dark objects. Other than deflecting light due to its gravitational pull, dark matter remains supremely oblivious to the existence of photons. I think the name “transparent matter” would have been more accurate though perhaps with a weaker marketable punch, but then who asked my opinion?

The million dollar question that is begged at this point is: if we cannot “see” it then how do we even know that it is there? Well, I sort of let a spoiler slip through the last paragraph. We can be unmistakably aware of its presence due to its gravitational effects over “conventional” (or baryonic) matter as well as over light.

The first solid hints of the presence of dark matter came from the abnormal dynamics of stars within galaxies, more specifically, their rotational speed around the center of their respective galaxy. Just as the gravitational pull of the Sun causes the planets to go around it, all the stars contained within a galaxy describe elliptical orbits around their galactic center where most of the galaxy’s matter was thought to be concentrated. Furthermore, this distribution of matter should make the stars nearer to the center to go around faster than those located at the outskirts, however, this is not what is observed. The astronomer Vera Rubin cataloged several galaxies where the rotational speed of the stars is essentially the same  regardless of their distance to the galactic center. That is an astonishing fact on its own right but there were yet mor surprises in store. It turns out that the overall speed of rotation of the stars was simply too high, at those velocities the stars should get projected into the void of intergalactic space! The galaxies were spinning so fast that their gravity should be insufficient to hold them together unless: 1) Our theories of gravity had been embarrassingly wrong all along, an option too scary to contemplate or 2) There is more matter lurking in the galaxies than meets the eye (actually much more than that which we can see). It is via the option No. 2 how dark matter enters the picture and saves gravity.

More evidence. Matter and energy can bend the space around it (one of the central consequences of general relativity) and this bending can be measurable to a high degree of accuracy by a phenomenon called gravitational lensing where the light passing nearby a massive object (or collection of objects) suffers an apparent deflection due to the curved space around caused by the object itself. It is not that the light rays actually curve their path, they continue travelling in straight lines, it is that the flatness of space itself has been disrupted due to gravity! (curiously, Einstein was fully aware of this implication of his theory but he deemed the effect as to be too weak to ever be measured experimentally). Astronomers have measured the gravitational lensing due to large clusters of galaxies and determined that the amount of deflection of the light that they cause is much too large to be provoked by only the luminous matter seen in the clusters. Again, most of the matter is missing… or not, it is there but it refuses to be seen, it is dark. The list of experimental results demonstrating the existence of dark matter is very rich but I better move on rather than going through them all.

Mysteries exist to be solved, and, the more puzzling the mystery the higher the motivation to clear it out for good. Dark matter is one of the biggest mysteries of modern science, thus, it is not a surprise to have a surplus of theories competing for the “final answer” status. Physicists seem to have picked their favorite theory, one stating that dark matter is made of WIMPs! I do not mean that, over ridden by despair, physicists have resorted to loudly accuse dark matter of  having a feeble anatomy so as to at least vent out their frustration, WIMPs is actually an acronym that stands for Weakly Interacting Massive Particles. Surely the reader (as myself) cannot escape the feeling that, stated like this, this answer sounds like no answer at all. It is like living in a universe where corkscrews have not been invented and stumbling upon a bottle of wine, then, the stumbler accepts that he cannot think of any kind of known machine that would allow him to open the bottle and then theorizes that a WIBOD or Wine Bottle-Opener Device is just the type of machine that would solve the problem and walks away feeling elated for his cleverness. This is to me the same way in which WIMPs solve the problem of dark matter. WIMPs are particles with mass thus they can give rise to the gravitational attraction and they interact so weakly with ordinary matter as to almost obliterate our chances to detect them (they could be neutrinos, axions or another kind of supersymmetric particle. Only neutrinos have been detected so far), but is this not kind of reformulating the problem of dark matter but this time pretending that the act of restating it provides in itself a solution?

Then string theory  (or a family of string theories that have been amplified and re-baptized as M-theories) comes along and offers that gravitons are what actually constitute dark matter, quadrillions of them. The issue then is obvious, why if they are so numerous not a single one of them has been yet detected? String theory attempts to get away with this enigma by assuming two things: 1) Our three-dimensional spatial universe is actually a so-called brane embedded in a higher dimensional space which in principle can host many more branes, and 2) gravitons are tiny pieces of strings forming closed loops such that they do not have open ends which might anchor them to a particular brane. In this way gravitons are fundamentally higher dimensional entities that are free to travel from between branes. The only footprint they leave during their fleeting path across our brane-universe is their gravitational attraction. Interesting premise undoubtedly, but there is a deep stigma that prevents one from investing too much faith in string theories, none of them has been able to make predictions that can be experimentally tested. For a group of theories that have been around  for more than 30 years that is hardly an invigorating health signal (see Lee Smolin’s “The trouble with physics“).

As I said earlier, we do not suffer from a famine of ideas regarding the dark matter puzzle, nevertheless, I sense a strong imbalance or bias in the arguments of such theories. Briefly, what all of them basically do is to pick a particle (known or unknown) and hold it as their champion suspect for it being the stuff of dark matter. To the best of my knowledge there is not a single theory which dismisses the particle hypothesis altogether, which, leads me to ask the very obvious (and probably equally ingenuous) question: What if dark matter is actually not made of matter at all? and more importantly, if that is the case, then, of what else can dark matter be made of? Well… what about space itself? would that be a too crazy/stupid suggestion? maybe, but give it a chance for a moment.

Left to right: Me, Triceratops, Carolina, Josue

Imagine that space itself has an intrinsic and particularly intricate “curvature pattern” at a cosmic scale. How could this come to be? consider the possibility that during the very early period of expansion of the universe some regions of space “flattened” at a slower rate than others, and that the places where those regions would be located were somehow determined by the positions where the earliest clusters of matter got nucleated. Afterwards, as the universe continued to grow, the regions where matter agglomerated to form stars and galaxies co-evolved forever entangled with those primordial regions of “crumpled” space, creating a super structure of unevenly stretched space that survives nowadays. Of course, this is wild speculation. I do not attempt to provide a mechanism explaining how the clustering of matter promoted a network of spatial “wrinkles” additional to the amount of space curvature induced by virtue of the clusters’s own mass, nor I can explain why  those regions have not been yet totally flattened by further cosmic expansion. I would only like to provide a new perspective from which to look at the problem of dark matter that does not consist solely on hunting for the right kind of particle, and at the same time, raise speculation about the potentially crucial role that space itself might play in this puzzle.

Well, this is a juicy topic and it is impossible to do justice to it in a single blog entry, undoubtedly these dark matters will be routinely addressed in this space. Before finishing this post I would only recommend that if a visit to the American Museum of Natural History and the Hayden Planetarium within it is within your reach, then, do not miss the chance! Go watch “Dark Universe” and enjoy the show… oh, and the dinosaurs, enjoy the dinosaurs, they are forever cool!

On cosmic fleshy rings and other sensible nonsense

Nasa/JPL/Space Science Institute

“Circumcision of Christ” by Friedrich Herlin









By Ignacio Gonzalez

One of the many cool features of friends is that they have the sensibility to peer into our interests, scrutinize them and then come to us with suggestions, pieces of information or advice about how we can enrich them or pursue them more effectively. Over a month ago my friend Fernando Castillo exercised this sort of kindness in a spectacular manner. He stumbled upon a block of information, picked it up, and quickly realized that it might just fill in a crucial gap in the knowledge of the members of the “Manglaristas” Whatsapp chat group, a group to which I belong along with three other friends from my adolescent years.This was no ordinary block, it was a diamond worthy of a shrine and I will be forever grateful to “Fercas” for having handed it to us. Genuine selflessness!

Without more preamble, here is what all the fuss is about:

Back in the XVII century there was a Vatican librarian that went by the name Leo Allatius. Mr. Allatius was a passionate theologian and had an interest in astronomy, thus, he set up his talents to arrange a rendezvous between both disciplines. The result of the affair? a literary piece titled “De Praeputio Domini Nostri Jesu Christi Diatriba” (or for us who are not fluent in dead Latin: “Discussion concerning the Prepuce of our Lord Jesus Christ”, a great example of how the act of translation can immediately strip away all sophistication). Essentially, this work was Allatius’s shot at solving two big mysteries of his age in a single master stroke: Where did the prepuce of Jesus go after his death? and what are Saturn’s ring made of?… I am pretty sure that at this point the reader is able to connect the dots but just for the sake of completeness I will explicitly outline Allatius’s thesis: Jesus’s holy foreskin was lifted into the heavens and turned into the trademark ornament of the solar system’s poster child, or put more bluntly, the annular piece of skin had been enlarged to colossal proportions and placed around Saturn for eternity. The simplicity of the argument is only matched by its wishful naivety.

One last point about this peculiarly bizarre issue. Back in the day the quest over the fate of Jesus’s foreskin was not treated as a superfluous or morbid topic, after all, which among all the alleged holy relics could surpass in holiness an actual part of the savior’s own body? To trace back its whereabouts was a dignified “field of research” for centuries. On defense of those antique persons obsessed with circumcision leftovers, I assume that only a small fraction of  17th century businesses would not look bizarre through a 21st century lens (well, maybe this is not the best example of long-forgotten oddities, turns out that the holy foreskin hunt might not have totally died out after all).

The somewhat more subtle but by far more relevant point of the story has to do with what you might call an “intellectual dichotomy”  very characteristic of the human species: humans are capable of coming up with a “circumcisionist” theory of Saturn’s rings and simultaneously master science and engineering in order to manufacture telescopes powerful enough to observe those same rings in the first place. To achieve the latter you need an accurate understanding of (a set of ) the natural laws which govern the universe, while to conjure the former you need to perform mind-bending intellectual gymnastics so those same natural laws can be forced to conform to preconceived dogmas that have nothing to do with reality. It is even more remarkable to realize that a single person is fully capable to harbor these two essentially opposed methodologies to apply them alternatively to examine the world and come to terms with its workings.

It appears that sensical and non-sensical approaches to get a grasp on reality can cohabit a single brain without generating unbearable amounts of intellectual friction. Remember for example that the same guy that revolutionized the physical sciences by single-handedly inventing calculus on a fine summer, also invested many years of his life trying to turn less precious metals into gold as well as finding hidden messages encrypted in the Bible (I am referring to Sir Isaac Newton and not to Gottfried Leibniz, in case a clarification is needed). It is as if whichever circuitry allocated in the brain and assigned to deal with evidence-based, logic-bound kind of thinking does not make short circuit with the circuitry used for faith-based, superstitious-bound kind of thinking. I suppose that if you hold a compartmentalized view of the brain as composed of several specialized sub-units capable to act independently if so is required, then, the possibility of this chiaroscuro so inherent to the human mind is not quite challenging after all. I however have a hard time comprehending how a single mind juggles between both lands and still holds (or struggles to hold) a cohesive personality. I do not question the viability of humans shifting from a reasonable thinking mode in the morning to a superstitious one in the afternoon, so to say, I only stare mildly aghast at how their brains swiftly accomplish the shift without incurring into an “operative system breakdown”.

The key to understand why it is possible to hold a defined set of superstitious beliefs and not develop a rational/irrational split personality is to realize that this danger does not exist in the mind of the superstitious subject in the first place, instead, it is only conceivable for an observer that acts as a judge of what is rational and what is irrational according to his own internal paradigm. We humans need to make sense of stuff at any cost and it is precisely this universal impulse what forbids the holder of a non-sensical belief to even realize about the falsehood of the belief in question. Whenever you are able to realize by yourself that some tenet or idea does not make sense, you simply stop holding it as true and immediately discard it, but if you gloss over the falsehood of any given proposition then you will most likely find a way to rationalize it and make it true, even if this requires to build an ideological cathedral that defies reality. To “make sense” is as vital for a well functioning brain as water is for a human body.

The rationalization of otherwise non-sensical beliefs can be an extremely demanding mental exercise. Despite of being so there is an eagerness in many people to push their conscious minds to square the circle (an impossible geometrical feature), I believe this universal impulse can be traced back to a fundamental property of brains: to create or to complete patterns. The human brain is remarkably good at patterning, and that is alright, if it were incapable of doing so then we would have long perished as a species. Ironically the problem might be that the brain is actually too outstandingly good at this task that it quickly “sees” patterns where none are there (take for example how easily we are fooled by optical illusions). Rapid pattern recognition it is just one among many evolutionary traits with a double edge; while it enables us to make quick life-or-death decisions with incomplete information (especially important when your habitat is a predator-packed grassland) it is also to blame  for distorting our perception of the real world out there. Needless to say that our brains carry out a good deal of this sort of automatic “photoshopping” behind the plane of your awareness, i.e. subconsciously. In my view, rationalization can be seen as a conscious effort to make propositions about reality to conform to preconceived patterns or cannons, in other words, it would be like the conscious counterpart of the subconscious patterning labor that our brain performs so well.

As with patterning, rationalization is a double-edged tool. On the one hand it is essential for assimilating ideas and on the other  it vindicates false propositions by nesting them within a true, or at least more reasonable, framework. Perhaps the widest and simplest mode of rationalization consists of creating a mental bucket, label it as “fundamentally incomprehensible” and then drop all those facts and/or ideas that are deemed as impossible to understand even after only the slightest scrutiny. I apologize if it sounds condescending or unfair, but it is quite common to see how a fair amount of people do not seem bothered in the slightest degree when they regard entire domains as to be fundamentally beyond comprehension, as if enveloped in an impenetrable halo of mystery. Common examples are the beliefs about the existence of ghostly entities, wandering spirits, and all kinds of otherworldly creatures as well as with witchcraft, curses and the like. It is even worse when some domains are considered to be even beyond all scrutiny or questioning as it may happen with the literal interpretation of sacred books or religious mandates. These types of rationalization seem so lazy that it is even hard to concede that there is a process of reasoning behind them, nevertheless they definitely require a deliberate act of classification or categorization in order to separate matters that can be ultimately comprehensible from those over which any kind of inspection is meant to be futile. But do not be deceived by the ingenuity of this apparently mindless classification process, after all, it is not hard to see how to abandon all lines of inquiry over a whole class of issues can easily lead to the erection of taboos, which of course is a highly toxic practice.

There are of course much more ingenious attempts at making sense of all sorts of grandiose claims, some of which I find incredibly curious. Generally, this other kind of rationalizations consist of very  delicate intellectual constructions where many times the original propositions end up so distorted as to be essentially unrecognizable. But why the need of such a stupendous act of intellectual contortion to rationalize the unreasonable? it is necessary because the final goal is to create a map that can accommodate unfounded claims onto facts supported on as much evidence as possible. This map is solely built upon analogies, metaphors, interpretations, code-talking and other devices to strain or straightforwardly misuse language. No surprise then that once the task is accomplished we end up with and undecipherable knot where we can hardly discern the original content of whichever proposition we wanted to make sense of.

One of my favorite cases of “extreme” rationalization is Frank Tipler’s interpretation of the Holy Trinity (the Father, the Son and the Holy Spirit). You see, Tipler is a physicist and as such he took over the improbable task of reconciling Christianity with theoretical physics. Do not believe me? well, he is author of a book which is actually titled “The physics of Christianity“… there you go. There he goes away with “explaining” the virgin birth of Jesus, his ability to walk over water and even his resurrection, none of which I will touch here, instead I will elaborate a little over how he found the three Holy persons of Christianity lurking in disguise within an important cosmological concept: the singularity.

An example of a singularity is that which is thought to occur at the center of a black hole where the gravitational force has an infinite value and the laws of physics (as they are currently formulated) simply break down, this is, we do not yet know how to apply them to predict what would occur to a test particle under such extreme conditions. Other singularity is thought to have taken place at the beginning of the universe when space and time themselves suddenly arose from this singular state. Well, it is precisely the latter type of singularity the one which Tipler identifies as God (the Father) himself. Not metaphorically speaking, the point of infinite mass-energy from which the universe sprung into existence is God in Tipler’s view… alright fair enough. Then comes a second “present singularity” in his sanctified physical model and here things start to get weird(er). First of all Tipler assumes that we live in a universe contained within a much larger multiverse and then justifies the multiverse’s existence on the validity of quantum theory which he interprets as a “theory of possiblities”, this is a bold move but not yet a completely implausible one (although this is not the most popular approach to the multiverse). Then, if the number of universes living within the multiverse is infinite then there are infinite copies of ourselves inhabiting an infinite set of those universes. Each one of us (as well as our copies) are of course limited to exist within the confines of a single universe and cannot jump from one to another (no odd encounters with your own self from another universe are allowed), however, this mysterious “present singularity” can travel between universes at will, after all what good is a singularity for if it needs to surrender to physical laws? and oh, yes, I almost forgot, the “present singularity” is Jesus Christ, hopping across the multiverse to make sure that no one, absolutely no one is deprived of the chance to be saved. The third and last singularity is the point-like end of the multiverse, the final singularity created when the whole multiverse faces its death. This final singularity is only possible if you assume that the multiverse happens to be a “closed multiverse” since only this kind of multiverse will collapse back onto itself in a big-crunch style. If you are counting then you already know that this final singularity must be identified with the Holy Spirit according to Tipler’s scheme, not many options left anyway. Unfortunately for Mr. Tipler almost all theories involving closed universes and big-crunches have lost a great deal of credibility in modern cosmology since it is now known that far from contracting, the universe is expanding at an accelerating rate and there does not seem to be enough matter-energy within it in order to drive an eventual re-collapse. So, in three strokes of truly cosmic proportions Tipler merrily announces that he has proven the existence of the Holy Trinity. But again, you do not have to believe me, you can listen to it yourself.

There you have how the human hunger for sensibility has driven a man to speculate that heavenly bodies can be adorned by huge rings of flesh and another to summon a universe-hopping Jesus, better to have an explanation that none at all… right?