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On Meaning

Gödel, Escher, Bach

GodelDouglas Hofstadter’s Gödel, Escher, Bach is a fascinating exploration of how consciousness can arise from inanimate matter. It's an intellectual tour-de-force, covering a fantastically diverse range of subjects, including mathematics, art, music, molecular biology, neuroscience, Zen Buddhism, extraterrestrial life, computer science, and artificial intelligence.

At the core of Hofstadter’s beliefs about consciousness lies the idea of a “Strange Loop”:

“The "Strange Loop" phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started.”

Hofstadter cites the Epimenedes Paradox - the statement “this statement is false” – as an example of a one-step Strange Loop. He spends a large part of the book discussing Gödel’s Incompleteness Theorem, which can be thought of as the translation of the Epimenedes Paradox into mathematical terms.

“Gödel says that no sufficiently powerful formal system can be perfect, in the sense of reproducing every single true statement as a theorem... The fact that truth transcends theoremhood, in any given formal system, is called "incompleteness" of that system.”

A “formal system” is a system that has a set of axioms and can generate statements by following a set of rules. A “theorem” is just a statement made by the system (including the axioms). “Sufficiently powerful” means a system that has the ability to make statements about itself.

While Gödel’s Theorem is about mathematical systems, an analogy can be drawn with the English language. This can be thought of as a system with a set of axioms (words) and a set of rules (grammar) for combining those words into sentences. Sentences can be constructed that are true (“the sky is blue”) or false (“ice is hot”). Gödel’s Incompleteness Theorem is analogous to saying it is impossible to create a book that contains every true statement that could be made in English, regardless of how large that book is.

The gist of the proof is as follows. Consider the sentence, “This sentence is not in this book”. Would that sentence be found in our hypothetical book, or not?

Suppose it was in the book. In that case, the sentence is untrue. But since we have said that the book only contains true statements, this is impossible. Therefore, the sentence must not be in the book. But in that case, the book must be incomplete, since we know the sentence is true, yet is not contained within it!

Hofstadter also notes that whether a statement is true or false is not inherent in the statement itself – it depends entirely on the interpretation we choose for the symbols. For example, consider, “the sky is blue”. This is only true if we interpret “the sky” as “the sky on planet Earth”. Were we to interpret “the sky” as “the sky on Mars”, the statement would be false. This mapping between the symbol “sky” and the concept of the thing above our heads is called an “isomorphism”. Indeed, the only thing that gives the inherently meaningless squiggles S-K-Y meaning is our recognition that they refer to the thing above our heads. As Hofstadter puts it, “Meaning is an automatic by-product of our recognition of any isomorphism”.

Whether a system is internally consistent also depends on the interpretation chosen for it. For example, consider a system with “1p1q2” as an axiom. We might choose to interpret p as “plus” and q as “equals”. Now suppose we decided to create a new system by adding the axiom “1p1q4”. Isn’t this new system inherently inconsistent? We might think so, since not only is 1+1 not equal to 4, we now seem to have two axioms that disagree with each other. However, we only have a problem because we have retained the same interpretation for the symbols p and q. Reinterpret the symbols appropriately (for example, by reinterpreting q as “less than or equal to”), and our system is consistent and meaningful once more.

Later in the book, Hofstadter offers a great visualisation of a multi-level Strange Loop:

“Think of chess. Clearly the rules stay the same, just the board position changes on each move. But let's invent a variation in which, on your turn, you can either make a move or change the rules [according to some constraints]...

Now we have two layers of rules: those which tell you how to move pieces, and those which tell how to change the rules... You could even express rules and metarules as positions on auxiliary chess boards...

Now we can have any number of adjacent chess boards: one for the game, one for rules, one for metarules, one for metametarules, and so on, as far as you care to carry it. On your turn, you may make a move on any one of the chess boards except the top-level one, using the rules which apply (they come from the next chess board up in the hierarchy). Undoubtedly both players would get quite disoriented by the fact that almost anything - though not everything! - can change...

Now it is possible to go considerably further in removing the pillars by which orientation is achieved. One step at a time... We begin by collapsing the whole array of boards into a single board. What is meant by this? There will be two ways of interpreting the board: (1) as pieces to be moved; (2) as rules for moving the pieces. On your turn, you move pieces - and perforce, you change rules!... The distinction between game, rules, metarules, metametarules, has been lost. What was once a nice clean hierarchical setup has become a Strange Loop... There are still different levels, but the distinction between "lower" and "higher" has been wiped out.”

Hofstadter argues that consciousness arises from a similar tangling of different levels in the brain:

“My belief is that the explanations of "emergent" phenomena in our brains - for instance, ideas, hopes, images, analogies, and finally consciousness and free will - are based on a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being itself determined by the bottom level. In other words, a self-reinforcing "resonance" between different levels... The self comes into being at the moment it has the power to reflect itself.”


Krista Tippett on Understanding Others

BecomingWiseKrista Tippett’s podcast On Being seeks to illuminate what it means to be human, through conversations with scientists, artists, theologians, activists and teachers. In Becoming Wise: An Inquiry into the Mystery and Art of Living, Tippett summarises what she’s learned from these conversations, and offers her views on how to foster understanding in our communities.

The key, says Tippett, is asking good questions.

“It’s not true what they taught us in school; there is such a thing as a bad question. In American life, we trade mostly in answers—competing answers—and in questions that corner, incite, or entertain. In journalism we have a love affair with the “tough” question, which is often an assumption masked as an inquiry and looking for a fight... My only measure of the strength of a question now is in the honesty and eloquence it elicits…

Questions elicit answers in their likeness. Answers mirror the questions they rise, or fall, to meet. So while a simple question can be precisely what’s needed to drive to the heart of the matter, it’s hard to meet a simplistic question with anything but a simplistic answer. It’s hard to transcend a combative question. But it’s hard to resist a generous question. We all have it in us to formulate questions that invite honesty, dignity, and revelation.”

Tippett starts each episode of On Being by asking her guest to describe the spiritual background of their childhood. It’s typical of her approach, inviting people to answer her questions through the story of their lives. Tippett explains why:

“In Collegeville, discussion about a large, meaty, theological subject began by framing it as a question, and then asking everyone around the table to begin to answer that question through the story of their lives: Who is God? What is prayer? How to approach the problem of evil? What is the content of Christian hope? I can disagree with your opinion, it turns out, but I can’t disagree with your experience. And once I have a sense of your experience, you and I are in relationship, acknowledging the complexity in each other’s position, listening less guardedly. The difference in our opinions will probably remain intact, but it no longer defines what is possible between us.”

“The human soul [is like] a wild animal in the backwoods of the psyche, sure to run away if cross-examined,” says Tippett. More open, indirect lines of questioning are a better way to reach understanding.

Our discomfort with others’ suffering, or a desire to find common ground or a fix, can be an obstacle to understanding. Tippett tells of the mayor of Louisville’s initiative to embed compassion in the social fabric of the city. According to one African American pastor, “the greatest breakthrough was having a politician who was willing to sit with people’s pain—just that. Not, in the first instance, to present a policy or a fix—but to acknowledge that damage has been done and dwell with it, let it be in the room, accompanied, grieved—lamented”.

These obstacles aren’t only present when seeking to improve understanding between groups. They operate at a personal level too. Tippett recounts the experience of Quaker author and teacher Parker Palmer while battling depression:

“I had folks coming to me, of course, who wanted to be helpful, and sadly, many of them weren’t. These were the people who would say, “Gosh, Parker, why are you sitting in here being depressed? It’s a beautiful day outside. Go, you know, feel the sunshine and smell the flowers.” And that, of course, leaves a depressed person even more depressed, because while you know intellectually that it’s sunny out and that the flowers are lovely and fragrant, you can’t really feel any of that in your body, which is dead in a sensory way. And so you’re left more depressed by this “good advice” to get out and enjoy the day. And then other people would come and say something along the lines of, “Gosh, Parker, why are you depressed? You’re such a good person… You’re so successful, and you’ve written so well.” And that would leave me feeling more depressed, because I would feel, “I’ve just defrauded another person who, if they really knew what a schmuck I was, would cast me into the darkness where I already am.””

But one person was different, willing to simply be present, without offering advice:

“There was this one friend who came to me, after asking permission to do so, every afternoon about four o’clock, sat me down in a chair in the living room, took off my shoes and socks and massaged my feet. He hardly ever said anything. He was a Quaker elder. And yet out of his intuitive sense, he from time to time would say a very brief word like, “I can feel your struggle today,” or farther down the road, “I feel that you’re a little stronger at this moment, and I’m glad for that.” But beyond that, he would say hardly anything. He would give no advice. Somehow he found the one place in my body, namely the soles of my feet, where I could experience some sort of connection to another human being. And the act of massaging just, you know, in a way that I really don’t have words for, kept me connected with the human race.

What he mainly did for me, of course, was to be willing to be present to me in my suffering. He just hung in with me in this very quiet, very simple, very tactile way. And I’ve never really been able to find the words to fully express my gratitude for that, but I know it made a huge difference. It became for me a metaphor of the kind of community we need to extend to people who are suffering in this way, which is a community that is neither invasive of the mystery nor evasive of the suffering, but is willing to hold people in a space—a sacred space of relationship—where somehow this person who is on the dark side of the moon can get a little confidence that they can come around to the other side.”


Einstein’s Dreams

Einsteins Dreams“There is only one cause of unhappiness,” says Anthony DeMello in The Way To Love. “The false beliefs you have in your head, beliefs so widespread, so commonly held, that it never occurs to you to question them.” Whether it’s the belief that happiness requires money, or marriage, or children, there are certain ideas that our parents and culture have instilled in us so deeply that we consider them axiomatic, not beliefs at all.

Similarly, we take the laws of the physical world for granted. When we drop something, it falls to the ground. When our car is moving, we must brake to stop it. Time flows from the past to the future. All these things are so obvious, we rarely give them any thought.

In Einstein’s Dreams, physicist Alan Lightman asks us to reconsider time. The novel is a collection of vignettes, each describing how life might be if time behaved differently to the way it does in our world.

What if time wasn’t a straight line, from future to past, but bent back on itself in a circle? What if effect sometimes preceded cause? What if the passage of time brought increasing order? What if there was no time, only images? What if we only lived for one day? What if time was a sense, like sight or taste? What if it was a visible dimension? The number of alternatives Lightman considers is dazzling.

Some scenarios are chilling. What if the texture of time was sticky, causing certain people and places to become stuck at a certain moment, never to break free?  

“The tragedy of this world is that no one is happy, whether stuck in a time of pain or of joy. The tragedy of this world is that everyone is alone. For a life in the past cannot be shared with the present. Each person who gets stuck in time gets stuck alone.”

Or suppose there was a place where time stood still from the perspective of those outside it.

“Who would make pilgrimage to the center of time? Parents with children, and lovers…

Some say it is best not to go near the center of time. Life is a vessel of sadness, but it is noble to live life, and without time there is no life. Others disagree. They would rather have an eternity of contentment, even if that eternity were fixed and frozen, like a butterfly mounted in a case.”

Einstein’s Dreams is an intellectually interesting series of thought experiments, but some of the vignettes offer insight on the way we live our lives in this world too. Consider a world in which time works as it does in our world, but people have no memories.

“Late at night, the wife and husband do not linger at the table to discuss the day’s activities, their children’s school, the bank account. Instead, they smile at one another, feel the warming blood, the ache between the legs as when they met the first time fifteen years ago. They find their bedroom, stumble past family photographs they do not recognize, and pass the night in lust. For it is only habit and memory that dulls the physical passion. Without memory, each night is the first night, each morning is the first morning, each kiss and touch are the first.

A world without memory is a world of the present. The past exists only in books, in documents. In order to know himself, each person carries his own Book of Life, which is filled with the history of his life. By reading its pages daily, he can relearn the identity of his parents, whether he was born high or born low, whether he did well or did poorly in school, whether he has accomplished anything in his life. Without his Book of Life, a person is a snapshot, a two-dimensional image, a ghost…

With time, each person’s Book of Life thickens until it cannot be read in its entirety. Then comes a choice. Elderly men and women may read the early pages, to know themselves as youths; or they may read the end, to know themselves in later years.

Some have stopped reading altogether. They have abandoned the past. They have decided that it matters not if yesterday they were rich or poor, educated or ignorant, proud or humble, in love or empty-hearted— no more than it matters how a soft wind gets into their hair.”

Or consider a world where people live forever:

“Strangely, the population of each city splits in two: the Laters and the Nows.

The Laters reason that there is no hurry to begin their classes at the university, to learn a second language, to read Voltaire or Newton, to seek promotion in their jobs, to fall in love, to raise a family. For all these things, there is an infinite span of time. In endless time, all things can be accomplished. Thus all things can wait. Indeed, hasty actions breed mistakes. And who can argue with their logic? The Laters can be recognized in any shop or promenade. They walk an easy gait and wear loose-fitting clothes. They take pleasure in reading whatever magazines are open, or rearranging furniture in their homes, or slipping into conversation the way a leaf falls from a tree. The Laters sit in cafés sipping coffee and discussing the possibilities of life.

The Nows note that with infinite lives, they can do all they can imagine. They will have an infinite number of careers, they will marry an infinite number of times, they will change their politics infinitely. Each person will be a lawyer, a bricklayer, a writer, an accountant, a painter, a physician, a farmer. The Nows are constantly reading new books, studying new trades, new languages. In order to taste the infinities of life, they begin early and never go slowly. And who can question their logic? The Nows are easily spotted. They are the owners of the cafés, the college professors, the doctors and nurses, the politicians, the people who rock their legs constantly whenever they sit down. They move through a succession of lives, eager to miss nothing.”

Or what if, Lightman concludes, time was a nightingale?

“Trap one of these nightingales beneath a bell jar and time stops. The moment is frozen for all people and trees and soil caught within.

In truth, these birds are rarely caught. The children, who alone have the speed to catch birds, have no desire to stop time. For the children, time moves too slowly already. They rush from moment to moment, anxious for birthdays and new years, barely able to wait for the rest of their lives. The elderly desperately wish to halt time, but are much too slow and fatigued to entrap any bird. For the elderly, time darts by much too quickly. They yearn to capture a single minute at the breakfast table drinking tea, or a moment when a grandchild is stuck getting out of her costume, or an afternoon when the winter sun reflects off the snow and floods the music room with light. But they are too slow. They must watch time jump and fly beyond reach.”


Lightness and Weight

UnbearableWhat’s better: a life of lightness or one of weight? So asks Milan Kundera in his novel The Unbearable Lightness of Being.

Our culture is schizophrenic. On one hand we are told to value selflessness, self-sacrifice and duty. We are urged to marry, to raise children, to contribute to our communities. Those who avoid commitment are criticised as immature and selfish.

“Necessity, weight and value are three concepts inextricably bound: only necessity is heavy and only what is heavy has value.”

On the other hand, our culture of individualism encourages us to do what makes us happy, to follow our bliss, to put ourselves first. If we’re dissatisfied with our marriage, we don’t need to work on it, we can just get a divorce.

Knowing whether to pursue lightness or weight isn’t easy. We cannot look to others for guidance. One person’s lightness is another’s weight. To Franz, the secrecy surrounding his affair with Sabina was heavy. To Sabina, that secrecy was light: it kept their relationship free from the judgement of others. When Franz leaves his wife, and the gaze of the world falls on them, their relationship becomes joyfully light to Franz and unbearably heavy to Sabina.

Moreover, many of our most important decisions – whether to marry, for example, or have children – are transformative experiences. We cannot know whether we should pursue them until we are already committed, because the experience itself changes us in a fundamental way.

 “The goals we pursue are always veiled. A girl who longs for marriage longs for something she knows nothing about. The boy who hankers after fame has no idea what fame is.”

Faced with such difficulties, we shouldn’t be too hard on ourselves if we find we don’t know what we want:

“[Tomas] remained annoyed with himself until he realized that not knowing what he wanted was actually quite natural. We can never know what to want, because, living only one life, we can neither compare it with our previous lives, not perfect it in our lives to come. Was it better to be with Tereza or to remain alone?...

Any schoolboy can do experiments in the physics laboratory to test various scientific hypotheses. But man, because he has only one life to live, cannot conduct experiments to test whether to follow his passion or not.”


Searching for Meaning

Viktor Frankl was an Austrian neurologist and psychiatrist who survived three years in German concentration camps during the second world war. In Man’s Search For Meaning he analyses his experiences in the camps and provides a template for finding meaning in life, even under the most difficult of circumstances.

Frankl believed that life is not a quest for pleasure or power, but a quest for meaning. However this is not a search for an abstract meaning of life, but for a specific meaning of our particular life at a given moment in time. Meaning may vary from person to person and from day to day. Moreover, not only must we create this meaning, we have a responsibility to do so:

“Ultimately, man should not ask what the meaning of his life is, but rather he must recognise that it is he who is asked…

Life ultimately means taking the responsibility to find the right answer to its problems and to fulfil the tasks which it constantly sets for each individual.”

How might we do this?

“The perception of meaning… boils down to becoming aware of a possibility against the background of reality or, to express it in plain words, to becoming aware of what can be done about a given situation.”

Where might we look for meaning? Frankl saw three possible sources:

1. Work

The most obvious source of meaning is by achieving or accomplishing something: by creating a work or doing a deed.

2. Love

The meaning of love is about helping another human being realise their potential:

“By his love he is enabled to see the essential traits and features in the beloved person; and even more, he sees that which is potential in him, which is not yet actualised but yet ought to be actualised. Furthermore, by his love, the loving person enables the beloved person to actualise these potentialities. By making him aware of what he can be and of what he should become, he makes these potentialities come true.”

3. Suffering

The attitude we take toward unavoidable suffering can also be a source of meaning. The suffering must, however, be unavoidable – seeking meaning in avoidable suffering is merely masochistic.

Frankl describes how many prisoners in the camps occupied themselves with thoughts of happier times to make the horrors of the present less real. But:

“In robbing the present of its reality there lay a certain danger. It became easy to overlook the opportunities to make something positive of camp life, opportunities which really did exist.”

Or, as others have said, “lean into the sharp points”. There is value in fully experiencing the difficult things in life, rather than running away from them.

Not everyone gave up, however:

“We who lived in concentration camps can remember the men who walked through the huts comforting others, giving away their last piece of bread. They may have been few in number, but they offer sufficient proof that everything can be taken from a man but one thing: the last of the human freedoms – to choose one’s attitude in any given set of circumstances, to choose one’s own way.”

That insight forms the foundation of Stephen Covey’s hugely successful book, The Seven Habits of Highly Effective People.

We can find meaning in suffering by changing the way we look at it:

“Once, an elderly general practitioner consulted me because of his severe depression. He could not overcome the loss of his wife who had died two years before and whom he had loved above all else. Now, how could I help him? What should I tell him? Well, I refrained from telling him anything but instead confronted him with the question, “What would have happened, Doctor, if you had died first, and your wife would have had to survive you?” “Oh,” he said, “for her this would have been terrible; how she would have suffered!” Whereupon I replied, “You see, Doctor, such a suffering has been spared her, and it was you who have spared her this suffering – to be sure, at the price that now you have to survive and mourn her.” He said no word but shook my hand and calmly left my office.”

In addition, we cannot be sure that a given situation is good or bad. Frankl recounts an instance when a transport of sick inmates to a “rest camp” was being organised. His name was on the list, supposedly because a few doctors were needed too. Despite the stated purpose of the transport, all the inmates believed it was actually destined for the gas chambers. However, when given the opportunity to have his name removed from the list, Frankl refused, an earlier incident having convinced him that it was better to let fate take its course.

“The next morning I departed with the transport. This time it was not a ruse. We were not heading for the gas chambers, and we actually did go to a rest camp. Those who had pitied me remained in a camp where famine was to rage even more fiercely than in our new camp.

Months later, after liberation, I met a friend from the old camp. He related to me how he, as camp policeman, had searched for a piece of human flesh that was missing from a pile of corpses. He confiscated it from a pot in which he found it cooking. Cannibalism had broken out. I had left just in time.”

The transitoriness of life should not deter us from searching for meaning:

“The only really transitory aspects of life are the potentialities; but as soon as they are actualised… they are are saved and delivered into the past, wherein they are rescued and preserved”

It’s for this reason that we should not envy the young:

“What reasons has he to envy a young person? For the possibilities that a young person has, the future which is in store for him? “No, thank you,” he will think. “Instead of possibilities, I have realities in my past, not only the reality of work done and of love loved, but of sufferings bravely suffered. These sufferings are even the things of which I am most proud, though these are things which cannot inspire envy.”

Man’s Search For Meaning is an incredible story of survival and an invaluable guide to dealing with the difficult times in our own lives.


Pale Blue Dot

Cassini-saturn-ear_2624749kPhoto of the Earth from Saturn, taken by the Cassini spacecraft on 19 July 2013

"From this distant vantage point, the Earth might not seem of any particular interest. But for us, it's different. Consider again that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there.... 

Think of the rivers of blood spilled by all those generals and emperors so that in glory and triumph they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner. How frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds. Our posturings, our imagined self-importance, the delusion that we have some privileged position in the universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark."

Carl Sagan


Nascence

Like a mountain on the horizon, fixed, immovable, the one constant in life is death.

To some, it seems inconceivably distant. To others, labouring in its foothills, its shadow looms large. But one day, we will all make our way to its summit and look back on our life. If we are dissatisfied with the path we took to get there, by then it will be too late to change it.

In The Seven Habits of Highly Effective People, Stephen Covey urges us to “begin with the end in mind”. It’s with that end in mind that I begin this blog.

Much of our written communication today is superficial. A tweet or a Facebook status update are too short to convey anything but the most perfunctory of thoughts. Occasionally they may offer a brief moment of interest or entertainment. Most of the time they are entirely disposable.

This blog is a place for me to write in more depth. To reflect upon my thoughts, experiences, insights and learnings in order to put them into a wider context and help me think more clearly about my life.

My posts are likely to be infrequent. I don’t want to write about ephemera, and I don’t expect weightier topics to present themselves often. Moreover, writing longer, more thoughtful pieces is time-consuming and time is not something I have in abundance any more.

Death is the landmark towards which every life flows, where we all come together in a final confluence before being extinguished. Better to chart our path there than being swept along on the tide.