The concept of "hidalgos"

Yesterday my wife and I walked through a beautiful forest near Madrid with our friends Peter and Mary. My friend confessed that, due to the crisis, his workload has dramatically diminished. So he surfs through the Web during work-time.  Unfortunately, his Company provides a limited number of credits for internet access, but luckily some official sites are available through the Intranet. The web page of the Spanish Language Academy is one of them... and he has discovered an incredible treasure therein: a plethora of glistening jewels, the speeches pronounced by the members of the academy at the time of their entrance in the institution. He recommened to me the one by Luis María Ansón, who is a well known Spanish journalist. A "right-wing" journalist was the label that my mind had associated to him, because I am sort of left wing... But no, no, no label should accompany such man, what a stupid mistake that would be! What a wonderful, enthralling speech he pronounced and can be tasted here!

Anyhow, this is not the subject of this post. The subject is how some people, by not working, work much more than others, for what really matters, which is not so much living surrounded by an abundance of consumer goods but by the abundance of goods. Yes, I want to feel good, whatever that means. Certainly, the fantastic meal in a Galizian restaurant that we had afterwards made me feel well. But walking uncomfortably under the rain and hearing wise words about love and death also gave me pleasure, a still pleasure, which is probably more profound and more lasting.

Another friend of mine was fired a few years ago. He exhausted the unemployment allowance and now lives on a meagre monthly amount, probably scratched out of scarce savings and family contributions. He actively seeks a new job, to no avail so far, although he is an intelligent and well educated person, to the point  that it is also a great pleasure for me to talk with him. He would probably prefer another life and would not like what I am going to say now, but I do think it and can share it with nobody in this public but clandestine blog, which nobody reads: his current existence has an aesthetic appeal. Ortega y Gasset coined the concept of this type of person, by recovering the figure of the Spanish "hidalgo", like Don Quixote: a poor noble man, somoene with as high self-dignity as low income, who manages to survive out of thin air, by reducing the workings of its body and hence his or her energy expenditure to the minimum...

Yesterday we also talked during the meal about something similar: a scientific TV program that narrated the story of a French speleologist, who survived in a dark cave without any food and almost without water for 35 days. That was possible because the human brain knows how to, under exceptional circumstances, ralentize bodily activity so as minimize its needs and feed upon superfluous fat and muscle, following a wise hierachy of priorities... Thus when the guy was rescued, his body had paid the bill but his brain was intact and in excellent health.

A naughty mind would on this basis take advantage to criticize the Spanish way, resorting to the topics that accuse us of much siesta and fiesta and little work. That would be most unfair. If my friends are little productive for the market, I am also a Spaniard and I more than compensate for both of them, with my compulsory work activity. This is not about nationalities, it is a universal topic. The Spanish hidalgo may exemplify my point very well, but there are instances of this everywhere, ranging from the Indian yogi to the English gentlemanly scientist, ala Dr Livingstone. In this time of crisis, where the market strives to rule us as a merciless dictator, there may also be advantages: we may have more lucidity than in the epoch of bonnaza and be able to appreciate those apparently non-tangible goods which make us feel tangibly good.

Can Cinderella be violated?

The previous post ended with a question: when a physicist plays with clocks and rods and kinematic concepts like time, displacement, velocity, acceleration… what is his or her Cinderella, that is to say, the practical purpose that he or she has in mind?

Seeking an illustration for the answer, I reviewed the problems posed in a standard physics book. Unfortunately, the questions stopped at the abstract level. They asked, for example, about the velocity of a projectile after the lapse of a time interval. However, they would have been more amusing (and probably more pedagogical) if they had spoken out any reason why that velocity may matter. For instance: will the projectile fired by the villain arrive “in time” to hit the heroine, before the latter receives a warning message from the hero? We could think of many analogous situations and, in my opinion, in all of them should we find the same leitmotiv: they sound like causality. The shape of the question may be whether an agent causes an effect or whether it avoids it or how many times it does it…; all those are variations over the same theme, which is the old story about causes and effects.

So causality is the Cinderella of motion concepts. This is the essence, the “spirit” of these notions, which –as you can appreciate- is, paradoxically, a pretty material thing: our pious Cinderella is a practical goal, made of tangible matter.

Thus we have identified the end. The means, as commented in the previous post, is the physical instrument with which we measure: in my metaphor, it is Cinderella’s slipper; in the context of kinematics, it is clocks and rods (or, if we take a modern stance, based on Special Relativity, electromagnetic waves with which you measure both space and time). In between those two elements, there lies the third ingredient of concepts: the  logical reasoning explaining how, on the basis of what the instruments have measured, you can find the solution to the problem at hand.    

Given this, how come that, according to certain interpretations, causality (our lovely Cinderella!) can be violated?

So… you have a challenge, you need to find Cinderella, you get hold of one of her slippers as a clue for unmasking her identity, you start playing with this instrument and… the mother of all wonders! Just because of these manipulations, you suggest that… somewhere else, Cinderella may be suffering some nasty effect… she is negated, she is somehow vexed, she is breached …

Yes, it sounds ridiculous but that is the nature of intellectual process leading to the fantasies that put in question causality. It is a simple epistemological error. You invent a concept for solving a problem and in the end you get so entangled in the intricacies of the idea, you fall so much in love with it, that you become sort of fetishist: you forget your problem and feed on the instrument.

I will finish with another metaphor borrowed from the philosopher Eckhart Tolle. Concepts are pointers at solutions to practical concerns. For instance, a signboard with an arrow pointing to Rome. However, you do not remain there, gazing at the arrow. That may be entertaining if the arrow is beautifully drawn. But it is not the aim. And for sure you would never pay attention to the bizarre idea that, because of the very existence of the signboard, Rome may be set on fire.

Slippery concepts

I have a model to explain what a concept is. It is a very pragmatic one. It has three elements and they are all tainted by empirical / practical features:

a) An end. This is the practical concern, the solution to any problem of day-to-day life that is nagging you.

b) A means. In physics, this is the instrument with which you carry out measurements and obtain values.

c) The logical link between the former two, the reason why you think that b) is a clue that solves a). This should also be tested in practice: it is good if it works.

To put it graphically, a concept is like Cinderella’s slipper. Yes, I believe that fairy tales have, amongst other things, an epistemological value. Especially, Cinderella’s tale may be interpreted as a metaphor of knowledge-seeking. Those wanting to improve their Spanish and being patient enough to read a long and verbose philosophical joke... can find a development in www.idearemos.com (sorry, this site is not available any more).  But in the end the metaphor is simple: 

a) The Prince has a problem: he needs a wife and a (future) queen.

b) After several failures, he hits on an idea: he puts glue on the stairs of the palace so that a piece of his beloved, a model of her foot, gets stuck therein.

c) For a number of reasons, he thinks this is a good clue for catching Cinderella, that the slipper adequately “mirrors” the girl who satisfies his needs.

Please note what a modest approach this is. We do not “know” what reality is. We just solve problems. We do not even “describe” nature. Strictly speaking, we only describe the results of our measurements, that is to say, the score of our interaction with nature. Somehow, this is downsizing science and art to the level of technique. We, the self-called knowledge-seekers, are just crafty detectives.

And, getting to the point, I believe that Einstein’s theory of Special Relativity brilliantly exemplifies and illustrates this approach. See this quote from “The Meaning of Relativity”:

The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy. I am convinced that the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori. For even if it should appear that the universe of ideas cannot be deduced from experience by logical means, but is, in a sense, a creation of the human mind, without which no science is possible, nevertheless this universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of the human body. This is particularly true of our concepts of time and space, which physicists have been obliged by the facts to bring down from the Olympus of the a priori in order to adjust them and put them in a serviceable condition.

I would not find it strange if Einstein had read Cinderella (specifically, the version of the Grimm Brothers, in beautiful German) the day before drafting this passage. He wants the idea of time to be fed with real, empirical input. Ideas are enrooted in sense perceptions or, if you want to be more precise, objective measurements. They are built upwards, not the other way round. Why? Because only this way do concepts play their function of “mirroring” a practical problem and providing the solution thereof. The process goes as follows: the measurement embraces the concept and the concept embraces the solution, just as clothes embrace the form of the human body… In particular, if time is relative, because it depends on the state of motion of the reference frame, that is it. No more discussion. We must put up with that constraint and feed our equations and geometric pictures with relative time measurements. We just need to re-adjust the latter so that they are consistent with the real nature of their raw material. That is what the Lorentz Transformation and other related equations do.

Let us remark the difference with Newton’s assertion:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Newton was wrong in arguing that mathematical time should be the non-measured one. The equations must be alimented with the real value, otherwise they will not lead to a sensible solution to the real problem!

Hence… should we thus ban the very idea of "absolute time" from our vocabulary? Should we refuse to even discuss what it may at all mean? Should we reject it as an inexistent slipper? I do not think so. That would be misunderstanding what I explained before: how concepts work, how slippers serve for catching Cinderellas. Yes, slippers may be "ideal", purely mental constructions, too, when that comes helpful in finding the beloved solution to our concerns. But what is our practical goal when we play with clocks and rods? What is the physicist's Cinderella...?

Why a light-clock ticks, a Darwinian explanation

In the previous entry I mentioned that why-questions are legitimate, but they have a humble goal: "explaining" is just zooming in and looking at the details of a process, showing step by step how it conforms to general principles.

A good example of this (in the domain of Special Relativity) is a very frequently asked question: why does the light work, why does the photon or light pulse hit the mid-point of the top mirror and bounce back to the mid-point of the bottom mirror?

The standard answer goes as follow: "Otherwise the Principle of Relativity would not hold: you would be able to ascertain whether you are in motion by measuring the degree of deviation of the light beam; in other words, the laws of physics would not be the same in all reference frames, since the same experiment (shining light upwards) would render a different outcome in different vehicles". That is true, although it is fun to develop how the mechanics of the process conform to such principle.

Of course, light, not being a sentient being, does not "choose" the right direction. Light is "imposed" its direction by the emitter. How?

Well, sometimes it is said that the emitter "aims" at the target, but I am not sure this is the right expression. If by that we mean physically orienting the light source in the appropriate direction, that is not accurate. Let us imagine that we have two identical laser guns pointing upwards, one on a train and another on the station. When the former passes by the latter, at a given instant, the two guns are perfectly lined up (top with top and bottom with bottom) and the same happens with the remote targets of the photons. Hence the two guns have the same orientation. A different thing is that, after this instant, the targets move away from each other and, in spite of that, each photon hits its own objective.

"Aiming" may, however, be an acceptable description if we mean by that using the light source, the apparatus for firing photons, in a different manner: we produce photons omnidirectionally but the gun automatically selects those that turn out to possess the appropriate direction. The gun is a tube, a reproduction at small scale of the path that the photons must afterwards follow in the outside world. If a any of them reaches the exit hole of the gun, it is because it has already followed the good path, the one that will enable it to ultimately hit the top mirror of the clock. The smaller the hole, the better it will perform this sort of Darwinian process, where only the fittest photons survive.

This is quite apparent if we think of a "classical" source, like an incandescent bulb. Electrons bound to atoms are excited by collisions. After a short while, those electrons spontaneously relax and emit energy in the form of photons, with multiple arbitrary directions. If that is all, they go out in a spherical wave. But if we add a tube, then we sieve the photons to select only the apt ones and can thus create a more or less directional (non-diverging) light beam.

If we consider instead a "modern" source like a laser gun, the process is peculiar but not different in its essence. The laser ray can be made extremely thin, very directional. A reason for this is that here the phenomenon of "stimulated emission" intervenes. When the electron is excited, we do not wait until it releases its photon in a random direction. We hit it before with another photon that already has the right direction. The consequence is that the emitted photon is coupled with the incident one, in several respects, including direction. But how did we manage to create those clever incident photons? Again, initially, we had to generate them omnidirectionally. It just happens that the physical display of the instrument favours that there are soon many apt photons, by virtue of a selection mechanism: there are two mirrors, one at the bottom and one at the top of the gun; the photons with an "evolutionary advantage" (those moving in parallel to the tube) keep reflecting back and forth, the others are absorbed by the walls; the reflecting photons act thus as "teachers" for the new-born photons to move in the successful direction, we could say that they introduce culture and nurture into the play…;  finally, the top mirror is a half-silvered one, so when the number of fit photons calling at its door is very high, the mirror lets them out, in the form of an intense and thin beam. Hence this a clever trick to attain "direction" out of chaos, but with limitations: even laser rays are to some extent "non-directional" or "diverging", insofar as the gun cannot be made infinitely thin or long…

Why-questions are dirty

I will share in this Blog some reflections on Physics (and in particular Special Relativity) that I also post in www.physicsforums.com, although here I will also be including comments on broader topics.

I intend to publish only ideas that are as widely acceptable and as little speculative as possible, but I do not guarantee that the scientific parts of this site are reliable, since I am no authority in this field.

The title of this first entry gives the tone of the series. I am addressing why-questions, admitting (half-jokingly) that they are "dirty"... because, yes, that has been the conclusion of a recent discussion in Physics Forums: to ask "why" is legitimate, but it simply means focusing on the details of a process, getting your hands dirty with the mechanics.

I have often complained, with regard to a number of Special Relativity issues, that the standard solution simply resorts to Einstein's postulates: this is so and so because the Principle of Relativity so requires, for example. I thus cried: that amounts to describing how nature works, but not explaining why it works that way. I was responded: you will find no scientific explanation that is not purely that, a description of how nature works.

When confronted with this answer, I was struck by my own complaint. I had written many pages defending the opposite of what I had just affirmed. I have been even more radical. I hold that we do not even describe nature. We interact with nature, we annotate the score of this sort of fight (we measure) and we interpret our measurements as clues for solving day-to-day problems. That is all.

What happened, then? Why did I speak against my conviction? I am afraid that the same thing happened as with my tennis. I have learnt new tricks, but in the heat of a game or a discussion, my doggish mind seeks refuge in the old routines. Realizing this helped me the trouble of losing energy in a useless fight. But I did feel that my complaint had "some" justification. So I decided to re-phrase it. I like semantics and I trust it is a powerful tool that can bring you out of a lot of trouble, both in life and in intellectual discussions.

Thus in the end we found an understanding.

I admitted that axioms like the Principle of Relativity cannot be labelled as "less profound". You cannot say that they must be put aside in favour of purportedly "deeper" truths. Granted: the more abstract that a principle is, the better it is. First, because it is beautiful in its slimness, which is the same as saying that it (probably) works. (We like handsome people because they were more apt to survive in old times. A different thing is that such evolutionary advantage may be useless today. But the idea still holds in the intellectual realm.) Second, a very elementary, fundamental principle is like a magic word, a master key that you can take anywhere to opens myriads of doors.

Yet I also found a better expression for my concern. I just wanted to descend to the details. Zoom in. Put on the working costume and stain my hands with the intricacies of the process in question, whatever it is. The helicopter view is necessary, but sometimes it is also convenient to turn into a little insect that dwells, with the devil, amongst the details. To sum up: the infamous why-questions do not lead you to a "deeper", but to a "lower" level.

I trust that this approach may be fruitful. My opponent in the discussion (now somehow siding with me…, though not for long: he is a tough guy!) commented that this way you often find connections between thing that might look unrelated before. I expect so. In particular, I intend to touch these issues, in the field of Special Relativity: why does the mechanical clock time-dilate, why does the photon hit the target in the light clock experiment, what is spacetime, why - to the dismay of book-sellers - nothing, not even faster than light travel can violate causality...?

It is not that I will always be so poetical. I promise some math and some geometry as well. But, yes, literature will be here, I will talk about Cinderella and the slipper. And I will also talk about law: when you look at the practical details, you realize that Einstein's theory is very "legal", very much in the line of that dirty art… lawyer's reasoning!