THE FASCINATION OF PARADOX

(Learning from not understanding)

© Ioan Tenner 1990, 2010

“The thinker without a paradox is like a lover without feeling” (Kierkegaard. Philosophical Fragments)

"Sits he on ever so high a throne, a man still sits on his bottom" (Michel de Montaigne)

Raymond Smullyan, Professor of Mathematical Logic and part-time magician, writes of an incident he experienced when six years old. It was so intriguing that the child would remember it for all of his life:

“It was the first of April 1925. He was sick in bed with grippe. His elder brother, Emile has told him that morning: “Well, Raymond, today is April Fool’s Day and I will fool you as you have never been fooled before!” Raymond waited all day long for this wonderful surprise. Nothing happened. Late that night, his mother asked him: “Raymond, why don’t you go to sleep?” “I am waiting for Emile to fool me.” Mother turned to Emile and asked him to keep promise and fool the child. This dialogue ensued:

Emile: So, you expected me to fool you, didn’t you?

Raymond: Yes.

Emile: But I didn’t, did I?

Raymond: No.

Emile: But you expected me to, didn’t you?

Raymond: Yes.

Emile: So, I fooled you, didn’t I?

Raymond:?”

This is a paradox in the tradition of the Greek word (which means etymologically “beyond expectations” or contrary to accepted opinion). It is a variant of the “announced surprise inspection” or “unexpected examination” (of the kind: “this week, you will have an unannounced inspection”). One could find a similar pattern in a note you will read in a bus station, announcing that “The last bus of today will not come”.

I was captivated by paradoxes from my childhood. They looked to me like a mysterious, exotic realm of subtle thought and wit, which I hoped to understand and master one day. Like good humour, paradoxes made me think. I liked them. I also observed that paradoxes were received with suspicion or derision by many people. Paradox was considered something unbecoming and I wondered why. My interest and my gradual discovery of paradox grew from this opposition.

*

In this paper I will not try to have the last word on what paradoxes are. Leave that to the convergent thinkers.

I do not, heaven forbid, try to solve paradoxes.

I will not be criticising what is and what is not a flawless paradox.

I do not even feel bound to consider exclusively “regular”, scholarly recognised or logically orthodox paradoxes.

In the following lines I will rather consider what happens when we meet things that appear paradoxical to us. This paper claims that paradoxes are fertile and useful. They could give us more freedom in the mind.

*

What logical paradoxes are and how they work

Philosophers invented paradoxes and then worked hard to solve them and get rid of them. Akin logical “bugs” like aporias, dilemmas i ironies or antinomies ii were treated in the same way, like logical vermin.

Philosophers define paradox as, for an example:

 

“an argument which seems to justify a self-contradictory conclusion by using valid deductions from acceptable premises.” iii

“A paradox is an argument that derives or appears to derive an absurd conclusion by rigorous deduction from obviously true premises.” iv

I would say that a logical paradox creates its own world, impeccable in form, and then makes it impossible in meaning. Being self referential, it is waterproof to critical sense v and to external evidence.

We can observe that logical-mathematical paradoxes are defined by a few features (contradiction, self reference or circularity, absurd coexistence of truth and false…) and a thought process, usually deduction: the development of an argument from premises to conclusion.

Logicians are concerned by what paradoxes are and what they mean. Their main effort is to find the error and – as I said - to solve it.

This negative attitude is understandable. For logic, paradoxes announce danger, pain and paradigm shifts. As W.V.O. Quine explained:

“The argument that sustains a paradox may expose the absurdity of a buried premiss or of some preconception previously reckoned as central to physical theory, to mathematics or to the thinking process. Catastrophe may lurk, therefore, in the most innocent-seeming paradox. More than once in history the discovery of paradox has been the occasion for major reconstruction at the foundation of thought.” vi

*

By valuing paradox I seem to take issue with a very respectable attitude of logic and philosophy. A scholar like R. M. Sainsbury presents only three possible treatments of a paradox:

“(a) Accept the conclusion ... but explain why it seemed unacceptable;

(b) Reject the reasoning as faulty;

(c) Reject one or several premises, explaining why they seemed acceptable.”

As an uninhibited pragmatist and “psycho-logician” I need to observe three more de facto possibilities:

(d) Misunderstand or refuse to consider the statement altogether;

(e) Live humbly or peacefully with the paradox unresolved as any true believer does (they are the majority of World population);

(f) Transcend or transgress the frame of reference given, the one that makes the situation impossible.

We can do better than banishing paradoxes. We can put them to use.

*

Paradoxes outside the field of logic and mathematic

Academic definitions appear to consider only logical and mathematical paradoxes expressed in propositions made of words, symbols or numbers. But paradoxes are more than words in propositions. Many domains other than logic are concerned with paradoxes.

General dictionaries are inclined to give more practical and wider definitions to the term paradox:

“1. a. A statement or tenet contrary to received opinion or belief; often with the implication that it is marvellous or incredible; sometimes with unfavourable connotation, as being discordant with what is held to be established truth, and hence absurd or fantastic; sometimes with favourable connotation, as a correction of vulgar error...

2. a. A statement or proposition which on the face of it seems self-contradictory, absurd, or at variance with common sense, though, on investigation or when explained, it may prove to be well founded (or, according to some, though it is essentially true).” (Oxford English Dictionary)

Paradox [Gk paradoxon], contrary to expectation.

1: a tenet contrary to received opinion

2 a: a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true b: a self-contradictory statement that at first seems true c: an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises 3: something or someone with seemingly contradictory qualities or phases. (Merriam-Webster, 1994)

We can observe that the defining features are in this wider sense; unexpectedness, differing from common opinion on the subject matter, method or conclusion, unbelievability, amazement, absurdity, consternation, contradiction but also…the potential means to express the complexity of truth vii and wisdom. As a consequence, the public concern could be different from finding the errors and reducing paradoxes to accepted knowledge.

It may be interesting, instead of finding error, to examine the shocking newness. In the sixteenth century many people spoke of the Earth’s motion as the paradox of Copernicus and Galileo viii . Quite often, one man’s clear idea is another man’s paradox (especially when the one man’s idea is new).

A moral philosopher like S. G. Stent, finds that paradoxes are generated by our rational faculty in domains where rationality tests its limits and deep truth is sought; free will vs. determinism, soul, moral responsibility... ix

It may be worth, instead of hunting for precision, that surrogate of truth x , to uncover some hidden wisdom so often disguised in paradox xi . I believe that wisdom – which is for me the anthropocentric understanding of knowledge and experience – must often be expressed in the form of paradox; its complexity requires the gamble of contradiction and the prudence of obscure formulation.

The impression they give, of surprise and absurdity, makes paradoxes (or appearing to be paradoxical) a familiar ingredient of ridicule and of jokes – the pun that provokes laughing. In this wider cultural meaning, paradox is then a recipient or a vehicle of esprit de finesse and of humour.

If it looks like one and works like one...it is one

Let me go further and extend the discussion from paradox to paradoxical.

An extensive and openly subjective view of paradox as “everything experienced as a paradox” takes the discussion out of philosophy, into the practical province of thought and action in everyday life.

When you come to “real people”, anything could be received as a paradox if it appears as compelling but strikingly new, contrary to established opinion or belief, self contradictory, unexpected or impossible to understand.

Such a fuzzy view of paradox is less concerned with what paradoxes are but rather with “how they behave” and what they do to people.

Psychologists found real life abundant of “double binds”, cognitive dissonance, and so many other blocks that look to me very much like paradoxes with or without words.

For authors like Paul Watzlawick, as bugs in the mind, paradoxes are frequently the very form in which difficult problems are created in the mind and in which wrong solutions induce and perpetuate a crisis they are meant to prevent or resolve. Many self-perpetuating problems can be identified in such dysfunctional blind spots.

Parents, teachers, lovers and leaders give sometimes paradoxical instructions, make conflicting demands that paralyse and beat the mind when the victim is unaware and unable to discard them:

“Be spontaneous!”

“Do not read this sign!”

“Be natural!”

“Be yourself!”

“Be independent!”

“Go to your room and don’t come out until you have a smile on your face!”

“Don’t take notice of my presence!”

“You should trust me!”

“Why don’t you want to love me?”

“I want you to like me of your own free will!”

“Discipline must be freely accepted!”

“You must change the way you think!”

“Don’t think evil!”

“Please ignore my previous mail”.

Orders of this kind are impossible to obey from the very moment they are uttered. They are seemingly meaningful but contradictory and absurd. Their impact is destructive or at least destabilising. They create “double binds” as described by Gregory Bateson in the ‘950s. Such tension unresolved is a provocation to madness or at least, to duplicity and double-talk. These “games of not playing a game” create the problem they pretend to prevent. The skill to detect such paradoxical circumstances allows one not to solve them, but to cope with them or to evade them.

The prisoner’s dilemma proposed by game theory appears to generate situations of paradox as well – trust versus distrust. Common sense distrust leads the “prisoners” to act in a vicious circle, in the name of compelling prudence, finally against their interest and to their inexorable loss.

The study and the diagnosis of paradox proved also to be a gold mine of original, often paradoxical solutions to blocked situations and impossible problems. Psychologists found that prescribing paradox – making a situation as absurd as possible - can lead to the solution of seemingly insoluble situations.

Another field rich in paradoxes is art. Artists like Maurice Escher or Salvador Dali demonstrated to our eyes impossible perceptions “that can’t be, but still are”.

Image paradoxes typically called optical illusions are coercing the spectator (or the victim) to perceive things that can’t be, according to common sense; Impossible triangles, water flowing down - upwards, hands drawing each other. These are paradoxes formulated not in words but as objects and perceptions.

This is not only amazing and beautiful. It is eye-opening. I used such optical and other illusions to help people learn that seeing is not always believing. There are few such ostensive means to persuade one to become more critical with the obvious.

Literature is another source of paradoxes xii . Writers like Franz Kafka and George Orwell exposed entire totalitarian systems were words mean their contrary and where people are damned if they do and also damned if they don’t. Jonathan Swift, George Bernard Shaw, H.G. Wells with his time machine, Oscar Wilde ("Those who try to lead the people can only do so by following the mob”), Lewis Carroll, Joseph Heller (Catch 22) are a few examples of literature rich in paradox.

Private and corporate lives are crawling with the absurdity of political correctness double-talk, perverse effects, vicious circles and structural contradictions. Aren’t all these paradoxical? Paradoxes that appear as dissonant structures of people and contradictory, self-defeating relationships?

Situational and organisational paradoxes are less studied scientifically (or I do not know enough about their study). A study of organisational paradoxes identified eleven of them: stability vs. change, empowerment vs. control, people focus vs. organisation focus, consistency vs. flexibility, internal vs. external, narrow vs. large picture, means vs. ends, soft vs. hard, individual vs. group, words vs. actions and trust vs. mistrust. xiii Some of them maybe structural or stem from the self-fulfilling prophecy or compelling paradigm of a founding father. That paradox will re-create itself for a long time before being exposed as utopia or dystopia. Others are, I think, “ways to hell paved by good intentions”, group-think and perverse effects of cultural bias and politically correct hypocrisy in big organisations.

A whole political system can become a paradoxical one in which, as my mother - a historian - used to jest, even “the past is most difficult to foresee” because it will be continually falsified to fit current dogma. Under totalitarian tyranny contradiction is carefully cultivated between thought, speech and action. In such worlds good is bad, truth is lie, freedom is submission, ugly is beautiful, soldiers fight against war and everybody is born a sinner and a suspect, doomed to prove his innocence forever. Orwell and Kafka describe such tyrannies at their extreme.

Religions like Taoism and Zen Buddhism appear to use paradoxical Koans in order to produce major change by crisis in people’s mind. The stress of trying to find the meaning of paradoxical statements, differentiating things from themselves or of achieving spontaneously prescribed states of mind destabilises, it seems, to the point of producing quantum leaps of faith or of comprehension. Many sects seem to use such devices to lure people into leaps of faith.

*

While reading this enumeration, you may believe that I write here to deplore paradox for its negative instances of manipulation and suffering. However, as I announced, my goal is different. I look at how the ubiquitous paradoxes feel and “behave” because I seek to learn something useful from what they do to people. What good things could we do with such painful paradoxes?

Let me enlarge the field once more. For me, as a psychologist, if people experience something as a paradox, then, for them, it is one. I mean to say that being paradoxical will suffice for any item to constitute a “paradox” locally. You can paradox most of the people some of the time… and that is enough.

Observing this feeling of paradox I appreciate the value of such things and situations that act upon people’s minds, surprise, challenge or numb them and leave them perplexed. I also look at this traditionally disquieting field with the eyes of the teacher.

The following will then be my definition: For this paper a paradox is something (a statement but also a thought, a feeling, an object, an image, a question, an instruction, a choice, dilemma, a situation) that leads into or keeps our perception, our reason, our feelings or our action in an impasse and which invites surpassing.

The premises or perceptions leading to an experience of paradox are acceptable, plausible and necessary. My eyes or ears, my fingers, my experience, should not cheat me, and the reasoning or the perceived transformations appear to be sound and self-evident to my common sense and my intuition. They may even be compelling to logical thought (as logical paradoxes show to be). However, the meaning implied or the conclusion reached appear impossible and with no way out.

It had better be a joke. The feeling of paradox is most often irritating. It goes against my common sense. It undermines my certainty, my faith. Some simple, basic, unquestionable values and deep beliefs, about truth and reason, my very intellectual makeup must be threatened if I take this seriously. If God Almighty cannot (or can) create a stone too huge for him to lift is He almighty? I feel tired to think further. I better laugh it away. Or stone the author and burn his book. Or quit. I am so busy with other business. Living a paradox leads us through mental dissonance. It may also open us to new, reformed, belief.

In time, my own meeting with paradoxes taught me something I call fascinating: The “paradoxical” gut feeling of experiencing something “impossible” is a unique symptom. A symptom of touching one of two limits of my mind:

(1) its’ outer frontier – what I don’t know (and don’t know that I don’t know), or

(2) its’ inner foundation – the obvious, the basic “axioms” that guide my reason and my daily life.

I mean that the feeling of paradox is a “detector of the Unknown” or an “exposure of unexamined certainties”.

When I write about the outer frontier of the unknown I have in mind one of its major problems; that we usually don’t know what we really don’t know. And not only by definition. Of all people, those who need to grow and change to the better, are unaware, even totally unaware of their ignorance. How to find out the direction in which we need to seek? By what means to become aware (as Socrates made us) that we are ignorant where we believed we knew? Intuiting about what, or in what direction we are ignorant, is in my opinion precious for both the masterly teacher and the deserving learner.

The same applies to the other end, so to say, of our usual lack of critical thinking concerning the obvious. I even believe that the unexamined obvious is a worse enemy of learning and changing than unsuspecting ignorance. Received beliefs or past successes become part of our persons and certainly of our culture. People are made of their preconceived knowledge to such an extent that they feel threatened when their basic beliefs are questioned or put to test. The paradoxical way of compelling one to reconsider the “obvious” is one of the rare means to access the strongholds of the mind.

If what I claim is true it means that we have here a tool to detect that which we do not know or cannot conceive or never considered critically. Allow me the metaphor: I call it a philosopher’s stone of critical thinking xiv .

*

Let me pause and take leisure by recollecting some old examples of paradoxes:

The strongest paradox known in history is probably the one “of the liar” that of Epimenides the Cretan who claims that all Cretans are liars: a correct statement that ends up in havoc: I read: “This statement is false.” A medieval formulation of it is this imaginary argument between Socrates and Plato:

Socrates: Everything Plato will say here is false.

Plato: Socrates spoke the very truth.

If this is true, it is false. If it is false, it is true. This is not normal. This is not what I learned in school. The disciplined mind needs to solve this. For my undisciplined mind this is a provocation to ask what truth is.

Many grains of sand form a heap. If you take away one grain, it is still a heap. You keep taking grains away. When is the heap no more a heap?

I do not care to solve the vagueness problem, but it makes me think at soft water drops that pierce hard rocks. It reminds me that it is the last straw that breaks the camel’s back. The accumulation of small nothings may bring big change.

I will ask you to answer with “yes” or “no” only, the following question: “Will your first answer to this question be “no”?”. If you say “yes”, you lie. The same if you say “no”.

If you give a thought to this impasse, you realise that language is relative and limited and there must, of course, be something like language about language. There may be times when we should free ourselves from words.

An example of paradoxical ruse:

Euathlus the apprentice lawyer had a contract with his teacher Protagoras the Sophist; he would only pay a fee for the teaching if he won his first case in court. Euathlus had a clever idea. He sued the master himself to obtain free tuition. If he would lose this first case, he had nothing to pay, as agreed. If he would win, he will not pay, by force of law.

Just imagine the endless ruses this “turning a thing on itself” can inspire. And imagine the power of being able to change the frame, the context by which meaning is given.

The Zen teacher formulates koans, questions impossible to answer:

“What happens to my fist when I open my hand?”

“What is the sound of one hand clapping?”

“If a straight line is an infinite circle, then where is its centre?”

“Kuang Tze dreamed one night, he was a wonderful butterfly, enjoying the breeze in the sunny field. Then, he woke up and he didn’t know any more: was he Kuang Tze heaving dreamed being a butterfly, or was he a butterfly dreaming now that he is Kuang Tze?”

The growth solution of a koan is (maybe) to gain autonomy from the question itself. It is formulated with the intention to exasperate the learner to such an extent that he would in the end break the “catch” in a sudden illumination that all the rules can be disobeyed and transgressed in the mind. This is, in intellectual terms, a satori. Perhaps.

Religious ethic has its paradoxes too:

If God is good, all-mighty, and all-knowing, then how can

there be so much suffering and evil in the world?

This may result in scepticism and loss of faith for some or in endless theodicy to justify God’s ways for others. For me this mainly demonstrates the result when ethic meets complexity and life. It tells me that ethic choice is our arbitrary struggle with disorder in the name of being as good as we can. It means that there is as much goodness in the world as we put into it.

My favourite creation of a mild feeling of paradox is to tease you:

“I will here and now create, because I please so, a piece of truth that I challenge you to refute if you can. Here it is: ‘There are only two kinds of people: Those who believe that there are only two kinds of people, and those who don’t‘”

Let me stress this: we can create paradox. We can create and wield the magic wand of paradoxical experiences, to make people’s minds move.

*

The question that inspired this paper is: “Why is Paradox so fascinating?” It is time to ground my answer: “Because it is a master tool”. I will try to explain this through my own way of rediscovering and using it.

Paradox is fascinating for me because it makes reason bend beyond itself. I understood as I kept teaching and growing older that, in everyday life, paradox is not only a mere “bug in the mind” but also a Master tool.

Paradox is fascinating as an instance of learning from not understanding.

Carefully administered, the puzzlement induced by paradoxes enables me and the people I work with, to detect things beyond the field of what we al-ready conceive. “Just as sight recognises darkness by the experience of not seeing, so imagination recognises the infinite by not understanding it.” (Proclus Lycaeus, 412-485 AD).

I realise that this is quite a strong statement, difficult to defend. I do not want to appear mystical. I believe that understanding and using paradoxes allows a practical approach to our inner limitations, structural or caused by ready-judged ideas, stubborn received beliefs about undecidable issues, unshakeable values and other convictions, too deep or too obvious to be a likely subject of critical discussion. I will take an example from my experience xv :

How I teach by confusing people

One of my favourite classroom koans in a course of wisdom (which I disguised for many years as a “Management” course) is to lure the par-ticipants into an exercise of inventing “things impossible to imagine”. It is an exercise of creativity xvi which I dubbed “a can opener for the mind”.

First I ask several groups to compete in inventing as many possible things one can do with “bricks”.

This is a very well known and slightly worn-out classic of brainstorming and the participants have a feeling of déjà vu. Easy! Soon, most people understand the rule of the game - that we are free and legitimate in the mind to invent whatever we like, provided there are no constraints of rule, law or material limits. They discover that they can even redefine “bricks” to mean whatever they fancy.

After this first teaser, when people are pleased with themselves, I unexpectedly declare that “all this was no real creativity since we only imagined things possible to do with “bricks””. “What about some real creation,” I propose, “like inventing the same amount, but of things impossible to do with “bricks”?”

Now this is a paradox and people fall into it, regularly. They are surprised.

First, my students rush into listing a large number of “impossible” things thus contradicting themselves. I have to point out that minutes ago they accepted that “everything” was possible in the mind and they just took advantage of this freedom rule.

Now, after some work of challenge, people grow to accept that only very, very few things can be retained as impossible. For an example, stating that a thing is not what it is may be retained. This is voted by a majority’s common sense as “really impossible”. The exercise does not end with this. Now I would ask, again surprisingly: “If it proves almost impossible to find things impossible to imagine, why did we, why do we imagine so few? Where is the rest of infinity?” A very formative discussion follows, where engineers, IT experts and profit minded managers prove passionate interest for philosophical speculation and meanings of invention.

Reads confusing? All this is very confusing for people who take part in the exercise and I have to appease their feelings, as some feel suddenly lost and inferior. The important thing is that one after the other, at different speeds, people discover by means of this confusion that they have a number of basic assumptions, so obvious to them that they never considered questioning those axioms until this moment. Some feel uneasy but all learn something important. What is it? Participants are left deeply impressed after this exercise.

The unease and the confusion of paradox are privileged ways of bordering what we do not understand and becoming aware of the obvious. A Zen saying reminds that “the foot feels the foot, when it feels the ground”.

In the best Socratic tradition, the intuition of being helplessly ignorant in a field where I had no doubt, allows me to open and learn new things.

The exasperation of Paradox not only challenges people to grow more open but also gives them a hint where to go and how. It points at a frontier, a rationally conceivable limit of the unknown, of the impossible and of the necessary. The inevitable spirited discussion after my koan is about realms, rules and definitions, about what is possible and impossible. Existence, reality and the limits of the mind suddenly intrigue most un-philosophical people. They sense something we all learned to forget: that in the “meta” realm of the mind, protected with question marks, quotes, parenthesis and attention marks, one could transgress and reframe almost anything. One could be free. Nothing is impossible to imagination and to thought if there are no rules and no limitations. Error should not be ruled out from this creation process, as it could be productive. Of course, error could also result from it. Later, it may be that the result of this imagining and trespassing into the unknown and into the impossible must be tested for feasibility to be transferred into real life today.

George Bernard Shaw expresses best this enchantment of unfettered thinking in a phrase I am never tired to quote from his “Back to Methuselah”:

“People see things and ask: Why? I dream of things that never where and ask: Why not?”

The use of paradox in education, while investigating the unknown and the non understandable, grows the size of personal freedom. It multiplies choices in the mind. It emancipates people. Fascinating, isn’t it?

*

Change is something else.

Let me now look at going through change and governing change. Acquaintanceship with paradox helps here too, by developing the states of mind favourable to coping and surviving unfamiliar change.

Things that are truly new appear paradoxical. I believe that this is because they are “out of the system” of our current understanding. In fact, change itself, when it is not our mind size, is often paradoxical to our perception: if change is too small or too huge, too fast or too slow, too unimportant or too important, too far away or too close to us – we cannot perceive it or cannot respond to it. To navigate change and to create newness one must be at ease with the unfamiliar and the contradictory instead of becoming defensive or hysterical.

People who bring and help change must learn to live with the unknown, the uncontrolled and even with the irrational, untamed for a while xvii . They must be able to function even in a state of perplexity. To cope with the never-ending surprise of our world, familiarity with paradox is a necessary companion of Change. Someone mentally accustomed to live with vagueness, complexity, ambiguity, contradiction, able to survive in cohabitation with not understanding, is better prepared to produce newness and to cope with newness.

Learning to live with things unknown instead of compulsively trying to reduce Newness to something already controlled is a key to change management.

I derive from this friendly, non defensive attitude to the unknown, a practice of strategy in the terms of James Carse who suggests “preparing for surprise”, to complete our customary “preparing against surprise” xviii . Preparing for surprise means becoming accustomed with the idea that surprises – surges of the unknown - are inevitable; there are ways to respond to them rationally and optimally instead of the biological enmity to surprise hard-wired in our species.

*

Instead of a conclusion

So, I found paradox fascinating because it is useful as it achieves a rare thing – sensing that which we don’t know. What to do then, after sensing the unknown? That may be the subject of another essay. One, to examine the means of trespassing into the not yet known. The metaphor of the trespassing is simple: once we detected the unknown territories which we don’t even understand we could at least draw white maps of those unknown continents. Then, we could plan our expeditions to conquer the white map: Normal, study expeditions interrogating other peoples’ knowledge and understanding or bold personal inventions. Maybe even inventions that would make new knowledge arise from nothing. Isn’t everything possible where are no rules and limitations?

Let me illustrate the choice we face once we experienced paradox and met the unknown with an old parable:

When you have little knowledge, it is comparable with the small light of a candle. Its warm flickering creates a small space of friendly, familiar safety.

If your knowledge grows, it is like a street-light. Now you see many more things and you can walk firmly. However, the dark space of night at the confines of luminosity grows too. More things that you do not know are inevitably glimpsed.

And what happens when you become really learned? Now the space of light is great. But beyond what you know, becomes apparent and even certain huge darkness, the infinity of things you will never know. You are left alone, small and insignificant among stars lost in infinity.

The question is: “What do you chose? Despair in front of the unknown? Rebellion? Urge to reduce infinity to what you know? Seeking enlightenment from a prophet? Hiding humbly inside a large community of anonymous scientists and begging the future by faith in progress? Or do you accept with modest friendliness to do what you reasonably can and use wisely what you know while coexisting peacefully with the unknown?

*

Now let me indulge, after concluding, in another touch of self-critical vagueness. My own paper reminds me a story (And I hope that it leaves you with more questions than you had before reading it):

In days of old, in ancient Japan, the summer evenings, bamboo-and-paper lanterns were used, with candles inside. Someone offered such a lantern to a blind man who wanted to go home after a visit.

“I don’t need a lantern. Light or darkness is all the same to me”.

“It is not for you my friend. Without one, someone else may run into you on the road.”

The blind man started off with the lantern and before he had walked very far a passer-by run squarely into him.

“Why don’t you look out where you walk? Can’t you see my lantern?” said the blind man.

“How could I? Your candle has burned out while you walked, my poor man,” answered the stranger.

*

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