Escher Quotes

Only those who attempt the absurd...will achieve the impossible. I think ...I think it's in my basement...Let me go upstairs and check.

Meaning lies as much in the mind of the reader as in the Haiku.

The truth is that even big collections of ordinary books distort space, as can readily be proved by anyone who has been around a really old-fashioned secondhand bookshop, one that looks as though they were designed by M. Escher on a bad day and has more stairways than storeys and those rows of shelves which end in little doors that are surely too small for a full-sized human to enter. The relevant equation is: Knowledge = power = energy = matter = mass; a good bookshop is just a genteel Black Hole that knows how to read.

Are you really sure that a floor can't also be a ceiling?

I don't use drugs, my dreams are frightening enough.

Sometimes it seems as though each new step towards AI, rather than producing something which everyone agrees is real intelligence, merely reveals what real intelligence is not.

Or are "being" and "having" thoroughly inaccurate verbs in the twisted skein of desire, where having someone's body to touch and being that someone we're longing to touch are one and the same, just opposite banks on a river that passes from us to them, back to us and over to them again in this perpetual circuit where the chambers of the heart, like the trapdoors of desire, and the wormholes of time, and the false-bottomed drawer we call identity share a beguiling logic according to which the shortest distance between real life and the life unlived, between who we are and what we want, is a twisted staircase designed with the impish cruelty of M. C. Escher.

We adore chaos because we love to produce order.

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

How gullible are you? Is your gullibility located in some "gullibility center" in your brain? Could a neurosurgeon reach in and perform some delicate operation to lower your gullibility, otherwise leaving you alone? If you believe this, you are pretty gullible, and should perhaps consider such an operation.

This idea that there is generality in the specific is of far-reaching importance.

[...] provability is a weaker notion than truth

I wish my wish would not be granted!

For now, what is important is not finding the answer, but looking for it.

What I give form to in daylight is only one per cent of what I have seen in darkness.

Tonight feels like a board game co-designed by M. C. Escher on a bender and Stephen King in a fever.

He who wonders discovers that this in itself is wonderful.

What is an "I", and why are such things found (at least so far) only in association with, as poet Russell Edson once wonderfully phrased it, "teetering bulbs of dread and dream" -- that is, only in association with certain kinds of gooey lumps encased in hard protective shells mounted atop mobile pedestals that roam the world on pairs of slightly fuzzy, jointed stilts?

So let us then try to climb the mountain, not by stepping on what is below us, but to pull us up at what is above us, for my part at the stars; amen.

I enjoy acronyms. Recursive Acronyms Crablike "RACRECIR" Especially Create Infinite Regress

My work is a game, a very serious game.

But finally I realized that to me, Godel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to construct the central object, and came up with this book.

Since, as is well know, God helps those who help themselves, presumably the Devil helps all those, and only those, who don't help themselves. Does the Devil help himself?

It now becomes clear that consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.

At moments of great enthusiasm it seems to me that no one in the world has ever made something this beautiful and important.

Hands, are the most honest part of the human body, they cannot lie as laughing eyes and the mouth can.

Did I want to be like him? Did I want to be him? Or did I just want to have him? Or are “being” and “having” thoroughly inaccurate verbs in the twisted skein of desire, where having someone’s body to touch and being that someone we’re longing to touch are one and the same, just opposite banks on a river that passes from us to them, back to us and over to them again in this perpetual circuit where the chambers of the heart, like the trapdoors of desire, and the wormholes of time, and the false-bottomed drawer we call identity share a beguiling logic according to which the shortest distance between real life and the life unlived, between who we are and what we want, is a twisted staircase designed with the impish cruelty of M. C. Escher.

My mind is more like a roller coaster inside a labyrinth buried in an M. C. Escher painting that is riding on another roller coaster.

To paraphrase Descartes again: "I think; therefore I have no access to the level where I sum.

A computer program can modify itself but it cannot violate its own instructions — it can at best change some parts of itself by *obeying* its own instructions.

[...] intelligent people only have a certain amount of time (measured in subjective time spent thinking about religion) to become atheists. After a certain point, if you're smart, have spent time thinking about and defending your religion, and still haven't escaped the grip of Dark Side Epistemology, the inside of your mind ends up as an Escher painting.

We do not know space. We do not see it, we do not hear it, we do not feel it. We are standing in the middle of it, we ourselves are part of it, but we know nothing about it.

Now what is "music"–a sequence of vibrations in the air, or a succession of emotional responses in the brain?

Did I want to be like him? Did I want to be him? Or did I just want to have him? Or are "being" and "having" thoroughly inaccurate verbs in the twisted skein of desire, where having someone's body to touch and being that someone we're longing to touch are one and the same, just opposite banks on a river that passes from us to them, back to us and over to them again in this perpetual circuit where the chambers of the heart, like the trapdoors of desire, and the wormholes of time, and the false-bottomed drawer we call identity share a beguiling logic according to which the shortest distance between real life and the life unlived, between who we are and what we want, is a twisted staircase designed with the impish cruelty of M.C. Escher.

Something, somewhere, somewhen, must have happened differently... PETUNIA EVANS married Michael Verres, a Professor of Biochemistry at Oxford. HARRY JAMES POTTER-EVANS-VERRES grew up in a house filled to the brim with books. He once bit a math teacher who didn't know what a logarithm was. He's read Godel, Escher, Bach and Judgment Under Uncertainty: Heuristics and Biases and volume one of The Feynman Lectures on Physics. And despite what everyone who's met him seems to fear, he doesn't want to become the next Dark Lord. He was raised better than that. He wants to discover the laws of magic and become a god. HERMIONE GRANGER is doing better than him in every class except broomstick riding. DRACO MALFOY is exactly what you would expect an eleven-year-old boy to be like if Darth Vader were his doting father. PROFESSOR QUIRRELL is living his lifelong dream of teaching Defense Against the Dark Arts, or as he prefers to call his class, Battle Magic. His students are all wondering what's going to go wrong with the Defense Professor this time. DUMBLEDORE is either insane, or playing some vastly deeper game which involved setting fire to a chicken. DEPUTY HEADMISTRESS MINERVA MCGONAGALL needs to go off somewhere private and scream for a while. Presenting: HARRY POTTER AND THE METHODS OF RATIONALITY You ain't guessin' where this one's going.

I personally cannot imagine that consciousness will be fully understood without reference to Godelian loops or level-crossing feedback loops.

Why is some music so much deeper and more beautiful than other music? It is because form, in music, is expressive–expressive to some strange subconscious regions of our minds. The sounds of music do not refer to serfs or city-states, but they do trigger clouds of emotion in our innermost selves; in that sense musical meaning IS dependent on intangible links from symbols to things in the world–those 'things', in this case, being secret software structures in our minds.

Perhaps the greatest contradiction in our lives, the hardest to handle, is the knowledge 'There was a time when I was not alive, and there will come a time when I am not alive.' On one level, when you 'step out of yourself' and see yourself as 'just another human being', it makes complete sense. But on another level, perhaps a deeper level, personal nonexistence makes no sense at all. All that we know is embedded inside our minds, and for all that to be absent from the universe is not comprehensible. This is a basic undeniable problem of life...

What does it matter if two brains are isomorphic, or quasi-isomorphic, or not isomorphic at all? The answer is that we have an intuitive sense that, although other people differ from us in important ways, they are still 'the same' as we are in some deep and important ways. It would be instructive to be able to pinpoint what this invariant core of human intelligence is, and then to be able to describe the kinds of 'embellishments' which can be added to it, making each one of us a unique embodiment of this abstract and mysterious quality called 'intelligence.

And speaking of Escher, it’s worth recording this for posterity: the artists were right, literally right, all along. Beneath what we used to call ‘reality’ there was always an Escheresque, a Boschian, a Munchian fact—a scuttling Guernicopia of horrors just waiting to be discovered once the civilizational rock was finally overturned.

It sometimes feels as if I had shouted a deeply cherished message out into an empty chasm and nobody heard me.

It’s a staircase in a house built by the construction firm of Escher and Sons.

Only those who attempt the absurd will achieve the impossible. —M. C. ESCHER

People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds -more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, “There are 17 languages in India, and 462 dialects.” There is something strange about the precise statements like that, when the concepts “language” and “dialect” are themselves fuzzy.

untrue. The truth is that even big collections of ordinary books distort space, as can readily be proved by anyone who has been around a really old-fashioned secondhand bookshop, one of those that look as though they were designed by M. Escher on a bad day and has more staircases than storys and those rows of shelves which end in little doors that are surely too small for a full-sized human to enter. The

There exist formal systems whose negative space (set of non-theorems) is not the positive space (set of theorems) of any formal system.

The perception of an isomorphism between two known structures is a significant advance in knowledge-and I claim that it is such perceptions of isomorphism which create meanings in the minds of people.

I can't help but recall, at this point, a horribly elitist but very droll remark by one of my favorite writers, the American "critic of the seven arts", James Huneker, in his scintillating biography of Frédéric Chopin, on the subject of Chopin's étude Op. 25, No. 11 in A minor, which for me, and for Huneker, is one of the most stirring and most sublime pieces of music ever written: “Small-souled men, no matter how agile their fingers, should avoid it.” "Small-souled men"?! Whew! Does that phrase ever run against the grain of American democracy! And yet, leaving aside its offensive, archaic sexism (a crime I, too, commit in GEB, to my great regret), I would suggest that it is only because we all tacitly do believe in something like Hueneker's' shocking distinction that most of us are willing to eat animals of one sort or another, to smash flies, swat mosquitos, fight bacteria with antibiotics, and so forth. We generally concur that "men" such as a cow, a turkey, a frog, and a fish all possess some spark of consciousness, some kind of primitive "soul" but by God, it's a good deal smaller than ours is — and that, no more and no less, is why we "men" feel that we have the perfect right to extinguish the dim lights in the heads of these fractionally-souled beasts and to gobble down their once warm and wiggling, now chilled and stilled protoplasm with limitless gusto, and not feel a trace of guilt while doing so.

If words were nuts and bolts, people could make any bolt fit into any nut: they'd just squish the one into the other, as in some surrealistic painting where everything goes soft. Language, in human hands, becomes almost like a fluid, despite the coarse grain of its components.

TRANSCENDING Escher got it right. Men step down and yet rise up, the hand is drawn by the hand it draws, and a woman is poised on her very own shoulders. Without you and me this universe is simple, run with the regularity of a prison. Galaxies spin along stipulated arcs, stars collapse at the specified hour, crows u-turn south and monkeys rut on schedule. But we, whom the cosmos shaped for a billion years to fit this place, we know it failed. For we can reshape, reach an arm through the bars and, Escher-like, pull ourselves out. And while whales feeding on mackerel are confined forever in the sea, we climb the waves, look down from clouds. —From Look Down from Clouds (Marvin Levine, 1997)

She knew for a fact that being left-handed automatically made you special. Marie Curie, Albert Einstein, Linus Pauling, and Albert Schweitzer were all left-handed. Of course, no believable scientific theory could rest on such a small group of people. When Lindsay probed further, however, more proof emerged. Michelangelo, Leonardo da Vinci, M.C. Escher, Mark Twain, Hans Christian Andersen, Lewis Carrol, H.G. Wells, Eudora Welty, and Jessamyn West- all lefties. The lack of women in her research had initially bothered her until she mentioned it to Allegra. "Chalk that up to male chauvinism," she said. "Lots of left-handed women were geniuses. Janis Joplin was. All it means is that the macho-man researchers didn't bother asking.

It folded back on itself like something that M. C. Escher, had he been given to hard nights on the town, which it is no part of this narrative’s purpose to suggest was the case, though it is sometimes hard, looking at his pictures, particularly the one with all the awkward steps, not to wonder, might have dreamed up after having been on one, for the little chandeliers which should have been hanging inside were on the outside pointing up.

Trying to navigate the halls of Hogwarts was like... probably not quite as bad as wandering around inside an Escher painting, that was the sort of thing you said for rhetorical effect rather than for its being true. A short time later, Harry was thinking that in fact an Escher painting would have both pluses and minuses compared to Hogwarts. Minuses: No consistent gravitational orientation. Pluses: At least the stairs wouldn't move around WHILE YOU WERE STILL ON THEM.

From the advertisement, his eyes moved up the skywalk, the zigzagging metal bridge that connected various locations in the neighborhood to the Banda train station. Behind the metal grid, men moved back and forth. Tommy Sir's eyes grew tired. He felt that up there, on that seemingly never-ending bridge, shadowy figures were moving toward obscure destinations, possibly only to return to their point of origin, like in an architectural sketch of infinity by M.C. Escher. Hell is a choice, made daily and by millions, and breathing slowly and watching this aerial cage, Tommy Sir saw Mumbai, minute by minute, unbecome and become hell.

Consistent or inconsistent, no one is exempt from the mystery of the self. Probably we are all inconsistent. The world is just too complicated for a person to be able to afford the luxury of reconciling all of his beliefs with each other. Tension and confusion are important in a world where many decisions must be made quickly. Miguel de Unamuno once said, 'If a person never contradicts himself, it must be that he says nothing.' I would say that we all are in the same boast as the Zen master who, after contradicting himself several times in a row, said to the confused Doko, 'I cannot understand myself.'.

an open-plan multilayered interior like something M. C. Escher might have come up with after bingeing on too many copies of Architectural Digest,

M.C. Escher called. He wanted to sell me some upside-down stairs. I said I already have a few, and then I got him to buy an upwalking slinky.

M. C. Escher

Therefore Godel's theorem had an electrifying effect upon logicians, mathematicians, and philosophers interested in the foundations of mathematics, for it showed that no fixed system, no matter how complicated could represent the complexity of the whole numbers: 0,1,2,3,.....

When he did think—when his brain began the slow chugging of rusty gears—the only thoughts that came were unspeakable things like, what’s the worst age a child can die? Worse yet was—after hours spent staring at the ceiling until it became a real-life Escher print with fans on the floor, useless windowsills, and dresser drawers that spilled underwear when opened—worse yet was when his mind found answers to those questions. Two-years-old isn’t so bad, he mused. They barely had a life. Twenty? At least they got to experience life! But fourteen... fourteen was the worst.

There is something in such laws that takes the breath away. They are not discoveries or inventions of the human mind, but exist independently of us. In a moment of clarity, one can at most discover that they are there and take them into account. Long before there were people on the earth, crystals were already growing in the earth's crust. On one day or another, a human being first came across such a sparkling morsel of regularity lying on the ground or hit one with his stone tool and it broke off and fell at his feet, and he picked it up and regarded it in his open hand, and he was amazed.

«It is impossible for the inhabitants of different worlds to walk or sit or stand on the same floor, because they have differing conceptions of what is horizontal and what is vertical. Yet they may well share the use of the same staircase. On the top staircase illustrated here, two people are moving side by side and in the same direction, and yet one of them is going downstairs and the other upstairs. Contact between them is out of the question because they live in different worlds and therefore can have no knowledge of each other's existence.»

Historically, people have been naive about what qualities, if mechanized, would undeniably constitute intelligence. Is intelligence an ability to integrate functions symbolically? If so, then AI already exists, since symbolic integration routines outdo the best people in most cases. If intelligence involves learning, creativity, emotional responses, a sense of beauty, a sense of self, then there is a long road ahead, and it may be that these will only be realized when we have totally duplicated a living brain.

I click to buy it and I’m furious to discover that it’s not available in Ireland and they won’t post it from abroad and the only place that sells it is Harrods and it’s impossible for me to go to Harrods because it’s like being trapped in an Escher painting.

(1) Blurting may be considered as the reciprocal substitution of semiotic material (dubbing) for a semiotic dialogical product in a dynamic reflexion. The human-written sentences are numbers (1) to 3; they were drawn from the contemporary journal Art-Language and are -- as far as I can tell-- completely serious efforts among literate and sane people to communicate something to each other.

There can be conceptual skeletons on several different levels of abstraction. For instance, the "isomorphism" between Bongard problems 70 and 71, already pointed out, involves higher-level conceptual skeleton than that needed to solve either problem in isolation.

No matter how cleverly we disguise our anxieties they bear witness to the imperfect nature of the human heart. To be is to become. To become is not to be. We are a work-in-progress, incomplete, imperfect, unrealised, and by virtue of temporal actions, temporary - a verb more than a noun, an inner quest and an outward odyssey framed by metaphors, like Escher's "Print Gallery"; we make the endless journey round the pictures, retracing our steps in forgetfulness, avoiding but mindful of the space where there are no pictures, where there is no gallery, where there is nothing at all. And like flies in a fly bottle, trapped by a failure of vision, we go round and round and round the moebius loop of a print gallery of our own making, a picture inside a picture inside a picture, forever.

For the burglar, every building is infinite, endlessly weaving back into itself through meshed gears made of fire escapes and secondary stairways, window frames and screened-in porches, pet doors and ventilation shafts, everything interpenetrating, everything mixed together in a fantastic knot. Rooms and halls coil together like dragons inside of dragons or snakes eating their own tails, rooms opening onto every other room in the city. For the burglar, doors are everywhere. Where we see locks and alarms, they see M. C. Escher.

I want to find happiness in the tiniest of things - a minute moss plant, 2 cm across, on a rock - and I want to try to do what I've been wanting to do for so long, that is, to copy these infinitesimally small things as precisely as possible and to be aware of their size.

Consistent or inconsistent, no one is exempt from the mystery of the self. Probably we are all inconsistent. Te world is just too complicated for a person to be able to afford the luxury of reconciling all of his beliefs with each other. Tension and confusion are important in a world where many decisions must be made quickly. Miguel de Unamuno once said, 'If a person never contradicts himself, it must be that he says nothing.' I would say that we all are in the same boast as the Zen master who, after contradicting himself several times in a row, said to the confused Doko, 'I cannot understand myself.

Computers are ridiculous. So is science in general. CHURCH_TURING Thesis, Theodore Rosak Version This view is prevalent among certain people who see in anything smacking of numbers or exactitude a threat to human values. It is too bad that they do not appreciate the depth and complexity and beauty involved in exploring abstract structures sch as the human mind, where, indeed, one comes in intimate contact with the ultimate questions of what to be human is.

the Godelian strange loop that arises in formal systems in mathematics (i.e., collections of rules for churning out an endless series of mathematical truths solely by mechanical symbol-shunting without any regard to meanings or ideas hidden in the shapes being manipulated) is a loop that allows such a system to "perceive itself", to talk about itself, to become "self-aware", and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self.

It was a hundred years later that Einstein gave a theory (general relativity) which said that the geometry of the universe is determined by its content of matter, so that no one geometry is intrinsic to space itself. Thus to the question, "Which geometry is true?" nature gives an ambiguous answer not only in mathematics, but also in physics

When you think about it, the cause-effect begins to resemble some mad logic-loop by the data artist Carolus or perhaps a print by Escher: the Shrike had come into existence because of the incantatory powers of my poem but the poem could not have existed without the threat/presence of the Shrike as muse. Perhaps I was a bit mad in those days. In

We have seen recursion in the grammars of languages, we have seen recursive geometrical trees, which grow upwards forever, and we have seen one way in which recursion enters the theory of solid state physics. Now we are going to see yet another way in which the whole world is built out of recursion. This has to do with the structure of elementary particles: electrons, protons, neutrons, and the tiny quanta of electromagnetic radiation called "photons". We are going to see that particles are - in a certain sense which can only be defined rigorously in relativistic quantum mechanics- nested inside each other in a way which can be described recursively, perhaps even by some sort of "grammar".

Depois de alguns anos estudando e fazendo experiências, cheguei a uma conclusão: Não sou eu que sou anti-social, são as pessoas.

An interpretation [of a formal system] will be meaningful to the extent that is accurately reflects some isomorphism to the real world.

Did I want to be like him? Did I want to be him? Or did I just want to have him? Or are "being" and "having" thoroughly inaccurate verbs in the twisted skein of desire, where having someone's body to touch and being that someone we're longing to touch are one and the same, just opposite banks on a river that passes from us to them, back to us and over to them again in this perpetual circuit where the chambers of the heart, like the trapdoors of desire, and the wormholes of time, and the false-bottomed drawer we call identity share a beguiling logic according to which the shortest distance between real life and the life unlived, between who we are and what we want, is a twisted staircase designes with the impish creulty of M.C. Escher.

When a system of "meaningless" symbols has patterns in it that accurately track, or mirror, various phenomena in the world, then that tracking or mirroring imbues the symbols with some degree of meaning-indeed, such tracking or mirroring is no less and no more than what meaning is. Depending on how complex and subtle and reliable the tracking is, different degrees of meaningfulness arise.

Now sophisticated operating systems carry out similar traffic-handling and level-switching operations with respect to users and their programs. It is virtually certain that there are somewhat parallel things which take place in the brain: handling of many stimuli at the same time; decisions of what should have priority over what and for how long; instantaneous "interrupts" caused by emergencies or other unexpected occurrences; and so on.

It is extremely interesting, then, to think about the meaning of the word ‘form’ as it applies to constructions of arbitrarily complex shapes. For instance, what is it that we respond to when we look at a painting and feel its beauty? Is if the ‘form’ of the lines and dots on our retina? Evidently it must be, for that is how it gets passed along to the analyzing mechanisms in our heads–but the complexity of the processing makes us feel that we are not merely looking at a two-dimensional surface; we are responding to some sort of inner meaning inside the picture, a multidimensional aspect trapped somehow inside those two dimensions. It is the word ‘meaning’ which is important here. Our minds contain interpreters which accept two-dimensional patterns and then ‘pull’ from them high-dimensional notions which are so complex that we cannot consciously describe them. The same can be said about how we respond to music, incidentally.

This was a tall order, and one could criticize it on the grounds that it was somewhat circular: how can you justify your methods of reasoning on the basis of those same methods of reasoning? It is like lifting yourself up by your own bootstraps.

I was peculiarly moved by the angelic life growing on the ground. I have no idea what sorts of flowers grow there in profusion -- I don’t know their names. But I was so moved that I sat down, trying to flatten as few grasses and plants as possible with my clumsy backside... This brought my head quite close to the silent, joyful, exuberant, celestial children of heaven. They are so humble, so quiet, and they do not mind if you observe them, if you think they are beautiful... Nor do they mind if you don’t look at all -- they just stand there together all by themselves in the huge stretch of woods and grow and bloom just the same, peacefully, joyfully, and silently. I am absolutely sure that they know nothing of the swinish and filthy behaviour of people in their dirty stinking houses -- they know only about heaven.

When the sea is calm, the landscape (seascape) seems simple and even monotonous, sometimes with a distant, sometimes with a close coastline, but usually with no land in sight at all. You feel 'free', not only free of care, but also free of the solidity of the earth's crust. It is a wonderful sensation, feeling the liquidity of the water under the ship. This salutary freedom is constantly present, on deck by day, in bed at nights. The movements of the ship vary from a gentle rocking to swinging and hurtling; you are never motionless while at sea. Then you start to observe and assimilate all these natural phenomena surrounding you: the infinite variety of the waves and the swell of the sea, and for the first time in ages you look again at the heavenly bodies, the sun, the moon and the stars, and you see the living creatures in and over the sea, the fish and the birds.

Or are "being" and "having" thoroughly inaccurate verbs in the twisted skein of desire, where having someone's body to touch and being that someone we're longing to touch are one and the same, just opposite banks on a river that passes from us to them, back to us and over to them again in this perpetual circuit where the chambers of desire, and the wormholes of time, and the false-bottomed drawer we call identity share a beguiling logic according to which the shortest distance between real life and the life unlived, between who we are and what we want, is a twisted staircase designed with impish cruelty of M. C. Escher.

Think of a dentist who has a list of patients, and for each patient, a list of teeth. It makes perfect sense (and plenty of money) to hold the patient fixed and vary his teeth-but it makes no sense at all to hold one tooth fixed and vary the patient. (Although sometimes it makes good sense to vary the dentist ... )

Believing is not to be reduced to thinking that such-and-such might be the case. It is not a weaker form of thinking, laced with doubt. Sometimes we speak like this: ‘I believe that the train leaves at 6:13', where ‘I believe that’ simply means that ‘I think (but am not certain) that’. Since the left hemisphere is concerned with what is certain, with knowledge of the facts, its version of belief is that it is just absence of certainty. If the facts were certain, according to its view, I should be able to say ‘I know that’ instead. This view of belief comes from the left hemisphere's disposition towards the world: interest in what is useful, therefore fixed and certain (the train timetable is no good if one can't rely on it). So belief is just a feeble form of knowing, as far as it is concerned. But belief in terms of the right hemisphere is different, because its disposition towards the world is different. The right hemisphere does not ‘know’ anything, in the sense of certain knowledge. For it, belief is a matter of care: it describes a relationship, where there is a calling and an answering, the root concept of ‘responsibility’. Thus if I say that ‘I believe in you’, it does not mean that I think that such-and-such things are the case about you, but can't be certain that I am right. It means that I stand in a certain sort of relation of care towards you, that entails me in certain kinds of ways of behaving (acting and being) towards you, and entails on you the responsibility of certain ways of acting and being as well. It is an acting ‘as if’ certain things were true about you that in the nature of things cannot be certain. It has the characteristic right-hemisphere qualities of being a betweenness: a reverberative, ‘re-sonant’, ‘respons-ible’ relationship, in which each party is altered by the other and by the relationship between the two, whereas the relationship of the believer to the believed in the left-hemisphere sense is inert, unidirectional, and centres on control rather than care. I think this is what Wittgenstein was trying to express when he wrote that ‘my’ attitude towards the other is an ‘attitude towards a soul. I am not of the opinion that he has a soul.’ An ‘opinion’ would be a weak form of knowledge: that is not what is meant by a belief, a disposition or an ‘attitude’. This helps illuminate belief in God. This is not reducible to a question of a factual answer to the question ‘does God exist?’, assuming for the moment that the expression ‘a factual answer’ has a meaning. It is having an attitude, holding a disposition towards the world, whereby that world, as it comes into being for me, is one in which God belongs. The belief alters the world, but also alters me. Is it true that God exists? Truth is a disposition, one of being true to someone or something. One cannot believe in nothing and thus avoid belief altogether, simply because one cannot have no disposition towards the world, that being in itself a disposition. Some people choose to believe in materialism; they act ‘as if’ such a philosophy were true. An answer to the question whether God exists could only come from my acting ‘as if’ God is, and in this way being true to God, and experiencing God (or not, as the case might be) as true to me. If I am a believer, I have to believe in God, and God, if he exists, has to believe in me. Rather like Escher's hands, the belief must arise reciprocally, not by a linear process of reasoning. This acting ‘as if’ is not a sort of cop-out, an admission that ‘really’ one does not believe what one pretends to believe. Quite the opposite: as Hans Vaihinger understood, all knowledge, particularly scientific knowledge, is no more than an acting ‘as if’ certain models were, for the time being, true. Truth and belief, once more, as in their etymology, are profoundly connected. It is only the left hemisphere that thinks there is certainty to be found anywhere.

Godel showed how a statement about any mathematical formal system (such as the assertion that Principia Mathematica is contradiction-free) can be translated into a mathematical statement inside number theory (the study of whole numbers). In other words, any metamathematical statement can be imported into mathematics, and in its new guise the statement simply asserts (as do all statements of number theory) that certain whole numbers have certain properties or relationships to each other. But on another level, it also has a vastly different meaning that, on its surface, seems as far removed from a statement of number theory as would be a sentence in a Dostoevsky novel.

O problema de eu não confiar em ninguém não é a pessoa ganhar ou não a minha confiânça, eu não confio em ninguém porque não confio na natureza humana mesmo. Somos seres individualistas que em caso de último recurso, trairia e enganaria até mesmo a pessoa que mais credibilidade em você tem. O ser humano é traiçoeiro e eu não confio em ninguém.

Did I want to be like him? Did I want to be him? Or did I just want to have him? Or are "being" and "having" thoroughly inaccurate verbs in the twisted skein of desire, where having someone's body to touch and being that someone we're longing to touch are one and the same, just opposite banks on a river that passes from us to them, back to us and over to them again in this perpetual circuit where the chambers of the heart, like the trapdoors of desire, and the wormholes of time, and the false-bottomed drawer we call identity share a beguiling logic according to which the shortest distance between real life and the life unlived, between who we are and what we want, is a twisted stair-case designed with the impish cruelty of M.C. Escher.

The amazing flexibility of our minds seems nearly irreconcilable with the notion that our brains must be made out of fixed-rule hardware, which cannot be reprogrammed. We cannot make our neurons fire faster or slower, we cannot rewire our brains, we cannot redesign the interior of a neuron, we cannot make [any] choices about the hardware—and yet, we can control how we think.

Пытаясь предусмотреть некоторые трудности будущих переводчиков, я, слово за словом, прошелся по книге с красной ручкой и отметил все каламбуры, и акростихи, все словесные перестановки, и переклички далеких отрывков текста: я объяснил трудноуловимые двойные (или тройные, или четверные, или пятерные) значения и указал отрывки, в которых форма отражает содержание; отметил те места книги, в которых сами особенности типографского набора передают важную информацию, посоветовал, какие затруднительные пассажи могут быть облегчены в переводе, а какие необходимо сохранить, и так далее. С этой кропотливой работой я провозился целый год, но делал ее с любовью; так или иначе, она была необходима, чтобы предотвратить катастрофу." Праздничное предисловие автора к русскому изданию книги «Гёдель, Эшер, Бах»

His house was certainly peculiar, and since this was the first thing that Fenchurch and Arthur had encountered it would help to know what it was like. It was like this: It was inside out. Actually inside out, to the extent that they had had to park on the carpet. All along what one would normally call the outer wall, which was decorated in a tasteful interior-designed pink, were bookshelves, also a couple of those odd three-legged tables with semicircular tops which stand in such a way as to suggest that someone just dropped the wall straight through them, and pictures which were clearly designed to soothe. Where it got really odd was the roof. It folded back on itself like something that M. C. Escher, had he been given to hard nights on the town, which it is no part of this narrative’s purpose to suggest was the case, though it is sometimes hard, looking at his pictures, particularly the one with all the awkward steps, not to wonder, might have dreamed up after having been on one, for the little chandeliers which should have been hanging inside were on the outside pointing up. Confusing. The sign above the front door said “Come Outside,” and so, nervously, they had. Inside, of course, was where the Outside was. Rough brickwork, nicely done pointing, guttering in good repair, a garden path, a couple of small trees, some rooms leading off. And the inner walls stretched down, folded curiously, and opened at the end as if, by an optical illusion which would have had M. C. Escher frowning and wondering how it was done, to enclose the Pacific Ocean itself. “Hello,” said John Watson, Wonko the Sane. Good, they thought to themselves, “hello” is something we can cope with. “Hello,” they said, and all, surprisingly, was smiles.

An amusing way to see the incorrectness of Lucas' argument is to translate it into a battle between men and women ... In his wanderings, Loocus the Thinker one day comes across an unknown object—a woman. Such a thing he has never seen before, and at first he is wondrous thrilled at her likeness to himself; but then, slightly scared of her as well, he cries to all the men about him, "Behold! I can look upon her face, which is something she cannot do—therefore women can never be like me!" And thus he proves man's superiority over women, much to his relief, and that of his male companions. Incidentally, the same argument proves that Loocus is superior to all other males, as well—but he doesn't point that out to them. The woman argues back: "Yes, you can see my face, which is something I can't do—but I can see your face, which is something you can't do! We're even." However, Loocus comes up with an unexpected counter: "I'm sorry, you're deluded if you think you can seemy face. What you women do is not the same as what we men do—it is, as I have already pointed out, of an inferior caliber, and does not deserve to be called by the same name. You may call it 'womanseeing'. Now the fact that you can 'womansee' my face is of no import, because the situation is not symmetric. You see?" "I woman-see," womanreplies the woman, and womanwalks away...

It is an inherent property of intelligence that it can jump out of the task which it is performing, and survey what it has done; it is always looking for, and often finding, patterns. Now I said that an intelligence canjump out of its task, but that does not mean that it always will. However, a little prompt- ing will often suffice. For example, a human being who is reading a book may grow sleepy. Instead of continuing to read until the book is finished, he is just as likely to put the book aside and turn off the light. He has stepped "out of the system" and yet it seems the most natural thing in the world to us. Or, suppose person A is watching television when person B comes in the room, and shows evident displeasure with the situation. Person A may think he understands the problem, and try to remedy it by exiting the present system (that television program), and flipping the chan- nel knob, looking for a better show. Person B may have a more radical concept of what it is to "exit the system"-namely to turn the television off! Of course, there are cases where only a rare individual will have the vision to perceive a system which governs many peoples' lives, a system which had never before even been recognized as a system; then such people often devote their lives to convincing other people that the system really is there, and that it ought to be exited from!

Just as science is permeated with 'conceptual revolution' on all levels at all times, so the thinking of individuals is shot through and through with creative and new acts. Computer programs today do not yet seem to produce many small creations. Most of what they do is quite 'mechanical' still. That just testifies to the fact that they are not close to simulating the way we think–but they are getting closer. Perhaps what differentiates highly creative ideas from ordinary ones is some combined sense of beauty, simplicity, and harmony.

If you listened to each voice on its own, you would find that it seemed to make sense all by itself. It could stand alone, and that is the sense in which I meant that it is independent. But you are quite right in pointing out that each of these individually meaningful lines fuses with the others in a highly nonrandom way, to make a graceful totality. The art of writing a beautiful fugue lies precisely in this ability, to manufacture several different lines, each one of which gives the illusion of having been written for its own beauty, and yet which when taken together form a whole, which does not feel forced in any way.

Something, somewhere, somewhen, must have happened differently… PETUNIA EVANS married Michael Verres, a Professor of Biochemistry at Oxford. HARRY JAMES POTTER-EVANS-VERRES grew up in a house filled to the brim with books. He once bit a math teacher who didn’t know what a logarithm was. He’s read Godel, Escher, Bach and Judgment Under Uncertainty: Heuristics and Biases and volume one of The Feynman Lectures on Physics. And despite what everyone who’s met him seems to fear, he doesn’t want to become the next Dark Lord. He was raised better than that. He wants to discover the laws of magic and become a god. HERMIONE GRANGER is doing better than him in every class except broomstick riding. DRACO MALFOY is exactly what you would expect an eleven-year-old boy to be like if Darth Vader were his doting father. PROFESSOR QUIRRELL is living his lifelong dream of teaching Defense Against the Dark Arts, or as he prefers to call his class, Battle Magic. His students are all wondering what’s going to go wrong with the Defense Professor this time. DUMBLEDORE is either insane, or playing some vastly deeper game which involved setting fire to a chicken. DEPUTY HEADMISTRESS MINERVA MCGONAGALL needs to go off somewhere private and scream for a while. Presenting: HARRY POTTER AND THE METHODS OF RATIONALITY You ain’t guessin’ where this one’s going.

When we’re talking about whether or not a story’s “time travel logic” makes sense, it is important to remember that every story builds its own framework for its own logic. In that sense, time travel is more of a fantasy-based story element than a science-based one. Time travel does not exist in the real world, and any broadly accepted rules for how it can and can’t work were derived from a bunch of “that guys” talking about time travel fiction. There is no “makes sense” in the universal sense – that is to say, criticizing a time travel story because its rules do not line up with rules in the real world is akin to dismissing the Harry Potter books because the conductive properties of wood could never sustain the energy required for spell casting. Approaching a time travel story with a dogmatic measuring stick in hand also denies the unique pleasure that the genre affords tinkerers. A good story’s internal logic is flawless, and everything in between its first and last word makes sense on its own terms. In that way, it presents the tinkerer with the literary equivalent of an Escher drawing. Internally, step by step, the logic of Escher’s staircase makes (or makes you believe it makes) nefariously perfect sense, and its dissonance with what we know to be possible is not something you have to “just accept and get over to enjoy it,” but is the very source of what’s enjoyable about it.

It was 1996, and the word “appropriation” never occurred to either of them. They were drawn to these references because they loved them, and they found them inspiring. They weren’t trying to steal from another culture, though that is probably what they did. Consider Mazer in a 2017 interview with Kotaku, celebrating the twentieth-anniversary Nintendo Switch port of the original Ichigo: kotaku: It is said that the original Ichigo is one of the most graphically beautiful low-budget games ever made, but its critics also accuse it of appropriation. How do you respond to that? mazer: I do not respond to that. kotaku: Okay…But would you make the same game if you were making it now? mazer: No, because I am a different person than I was then. kotaku: In terms of its obvious Japanese references, I mean. Ichigo looks like a character Yoshitomo Nara could have painted. The world design looks like Hokusai, except for the Undead level, which looks like Murakami. The soundtrack sounds like Toshiro Mayuzumi… mazer: I won’t apologize for the game Sadie and I made. [Long pause.] We had many references—Dickens, Shakespeare, Homer, the Bible, Philip Glass, Chuck Close, Escher. [Another long pause.] And what is the alternative to appropriation? kotaku: I don’t know. mazer: The alternative to appropriation is a world in which artists only reference their own cultures. kotaku: That’s an oversimplification of the issue. mazer: The alternative to appropriation is a world where white European people make art about white European people, with only white European references in it. Swap African or Asian or Latin or whatever culture you want for European. A world where everyone is blind and deaf to any culture or experience that is not their own. I hate that world, don’t you? I’m terrified of that world, and I don’t want to live in that world, and as a mixed-race person, I literally don’t exist in it. My dad, who I barely knew, was Jewish. My mom was an American-born Korean. I was raised by Korean immigrant grandparents in Koreatown, Los Angeles. And as any mixed-race person will tell you—to be half of two things is to be whole of nothing. And, by the way, I don’t own or have a particularly rich understanding of the references of Jewishness or Koreanness because I happen to be those things. But if Ichigo had been fucking Korean, it wouldn’t be a problem for you, I guess?