Carroll and TennielThrough the Looking-Glass


Never swallow anything whole. We live perforce by half-truths and get along fairly well as long as we do not mistake them for whole-truths, but when we do so mistake them, they raise the devil with us.
Alfred North Whitehead, Dialogues of Alfred North Whitehead

If you ‘understand’ something in only one way, then you scarcely understand it at all—because when you get stuck, you’ll have nowhere to go. But if you represent something in several ways, then when you get frustrated enough, you can switch among different points of view, until you find one that works for you!
Marvin Minsky, The Emotion Machine

To have a great idea, have a lot of them.
— Thomas Edison

Results? Why, man, I have gotten lots of results! If I find 10,000 ways something won't work, I haven't failed. I am not discouraged, because every wrong attempt discarded is often a step forward.
— Thomas Edison

The pages of the history of science record thousands of instances of similar discoveries having been made by scientists working independently of one another. Sometimes the discoveries are simultaneous or almost so; sometimes a scientist will make anew a discovery which, unknown to him, somebody else had made years before. Such occurrences suggest that discoveries become virtually inevitable when prerequisite kinds of knowledge and tools accumulate in man's cultural store and when the attention of an appreciable number of investigators becomes focussed on a problem, by emerging social needs, by developments internal to the science, or by both.
Robert Merton, Resistance to the Systematic Study of Multiple Discoveries in Science

Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself — and you are the easiest person to fool. So you have to be very careful about that. After you've not fooled yourself, it's easy not to fool other scientists. You just have to be honest in a conventional way after that.
Richard Feynman, Caltech commencement address, 1974

Religion is a culture of faith; science is a culture of doubt.
Richard Feynman

It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
Richard Feynman

Not only is the universe stranger than we imagine, it is stranger than we can imagine.
Arthur Stanley Eddington

One may say the eternal mystery of the world is its comprehensibility.
Albert Einstein

One thing I have learned in a long life: All our science, measured against reality, is primitive and childlike — and yet it is the most precious thing we have.
Albert Einstein

It seems safe to say that significant discovery, really creative thinking, does not occur with regard to problems about which the thinker is lukewarm.
Mary Henle

Art is uniquely well designed as a Darwinian system for producing new variations. It is not well designed to generate useful ideas. ... Art offers a system of "unnatural" variation. ... Art may produce results not directly useful except in terms of mattering to other humans, but in a species as highly social as ours this itself makes a difference. ... If art is "unnatural" variation, science is "unnatural" selection. ... It tests ideas not against human preferences but against a resistant world, and its methods of testing, by logic, observation, and experiment, encourage us to reject ideas that seem self-evident and apparently repeatedly confirmed by tradition.
Brian Boyd, On the Origin of Stories

Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you.
Edsger W. Dijkstra

Computer science is no more about computers than astronomy is about telescopes.
Edsger W. Dijkstra

Analogy and Metaphor

The metaphor is perhaps one of man's most fruitful potentialities. Its efficacy verges on magic, and it seems a tool for creation which God forgot inside one of His creatures when He made him. All our other faculties keep us within the realm of the real, of what is already there. The most we can do is to combine things or to break them up. The metaphor alone furnishes an escape; between the real things, it lets emerge imaginary reefs, a crop of floating islands. A strange thing, indeed, the existence in man of this mental activity which substitutes one thing for another — from an urge not so much to get at the first as to get rid of the second.
José Ortega y Gasset

We have repeatedly seen how analogies and mappings give rise to secondary meanings that ride on the backs of primary meanings. We have seen that even primary meanings depend on unspoken mappings, and so in the end, we have seen that all meaning is mapping-mediated, which is to say, all meaning comes from analogies.
Douglas Hofstadter, I am a Strange Loop, 2007

I've managed to convince myself that analogy is really at the core of thinking — not just for myself, but for other people, too. I'm trying to put forth a vision of thought that involves — if you don't want to say "analogy-making" you can say "stripping away irrelevancies to get at the gist of things." I feel I've discovered something essential about what thinking is, and I'm on a crusade to make it clear to everybody.
Douglas Hofstadter, Wired 3.11, 1995

One should not think of analogy-making as a special variety of reasoning (as in the dull and uninspiring phrase "analogical reasoning and problem-solving," a long-standing cliché in the cognitive-science world), for that is to do analogy a terrible disservice. After all, reasoning and problem-solving have (at least I dearly hope!) been at long last recognized as lying far indeed from the core of human thought. If analogy were merely a special variety of something that in itself lies way out on the peripheries, then it would be but an itty-bitty blip in the broad blue sky of cognition. To me, however, analogy is anything but a bitty blip — rather, it's the very blue that fills the whole sky of cognition — analogy is everything, or very nearly so, in my view.
Douglas Hofstadter, Analogy as the Core of Cognition, 2001

My thesis is this: what makes humans smart is (1) our exceptional ability to learn by analogy, (2) the possession of symbol systems such as language and mathematics, and (3) a relation of mutual causation between them whereby our analogical prowess is multiplied by the possession of relational language.
Dedre Gentner, Why We're So Smart, 2003

Our conceptual networks are intricately structured by analogical and metaphorical mappings, which play a key role in the synchronic construction of meaning and in its diachronic evolution. Parts of such mappings are so entrenched in everyday thought and language that we do not consciously notice them; other parts strike us as novel and creative. The term metaphor is often applied to the latter, highlighting the literary and poetic aspects of the phenomenon. But the general cognitive principles at work are the same, and they play a key role in thought and language at all levels.
Gilles Fauconnier, Mappings in Thought and Language, 1997

Intelligence is the capacity of the brain to predict the future by analogy to the past.
Jeff Hawkins, On Intelligence, 2004

Still, I think that metaphor really is a key to explaining thought and language. The human mind comes equipped with an ability to penetrate the cladding of sensory appearance and discern the abstract construction underneath — not always on demand, and not infallibly, but often enough and insightfully enough to shape the human condition. Our powers of analogy allow us to apply ancient neural structures to newfound subject matter, to discover hidden laws and systems in nature, and not least, to amplify the expressive power of language itself.
Steven Pinker, The Stuff of Thought, 2007

The ability to consider differences between differences is important because it lies at the heart of our abilities to solve new problems. This is because these "second-order-differences" are what we use to remind ourselves of other problems we already know how to solve. Sometimes this is called "reasoning by analogy" and is considered to be an exotic or unusual way to solve problems. But in my view, it's our most ordinary way of doing things.
Marvin Minsky, The Society of Mind, 1988

What, then, is a metaphor? It might be easy to agree on functional definitions like "A metaphor is that which allows us to replace one kind of thought with another." But when we ask for a structural definition of "metaphor," we find no unity, only an endless variety of processes and strategies. Some are simple, as when we make an analogy by stripping away so many details that two different objects seem the same. But other forms of metaphor are as complex as can be. In the end there is little to gain by cloaking them all under the same name "metaphor," because there isn't any boundary between metaphorical thought and ordinary thought. No two things or mental states ever are identical, so every psychological process must employ one means or another to induce the illusion of sameness. Every thought is to some degree a metaphor.
Marvin Minsky, The Society of Mind, 1988

Logical Thinking: The popular but unsound theory that much of human reasoning proceeds in accord with clear-cut rules that lead to foolproof conclusions. In my view, we employ logical reasoning only in special forms of adult thought, which are used mainly to summarize what has already been discovered. Most of our ordinary mental work — that is, our commonsense reasoning — is based more on "thinking by analogy" — that is, applying to our present circumstances our representations of seemingly similar previous experiences.
Marvin Minsky, The Society of Mind, 1988

How do we ever understand anything? Almost always, I think, by using one or another kind of analogy — that is, by representing each new thing as though it resembles something we already know. Whenever a new thing's internal workings are too strange or complicated to deal with directly, we represent whatever parts of it we can in terms of more familiar signs. This way, we make each novelty seem similar to some more ordinary thing. It really is a great discovery, the use of signals, symbols, words, and names. They let our minds transform the strange into the commonplace.
Marvin Minsky, The Society of Mind, 1988

Logical and analogical reasoning are sometimes viewed as mutually exclusive alternatives, but formal logic is actually a highly constrained and stylized method of using analogies. Before any subject can be formalized to the stage where logic can be applied to it, analogies must be used to derive an abstract representation from a mass of irrelevant detail. After the formalization is complete, every logical step — of deduction, induction, or abduction — involves the application of some version of analogy.
John Sowa and Arun Majumdar, Analogical Reasoning, 2003

We never map mathematics to reality. We map a simplified system to a more complicated one, using the language of mathematics. Think of a computer simulation to predict the solar cycle. It’s a map from one system (the computer) to another system (the sun). If you do a calculation on a sheet of paper and produce some numbers that you later match with measurements, you’re likewise mapping one system (your brain) to another (your measurement), not some mathematical world to a real one. Mathematics is just a language that you use, a procedure that adds rigor and has proved useful.
Sabine Hossenfelder, What are you, really?, 2012

Nothing unknown can ever become known except through its analogy with other things known.
Charles Sanders Peirce, Logic, Considered as Semeiotic, 1902

Let us speak of metaphor. The most fascinating property of language is its capacity to make metaphors. But what an understatement! For metaphor is not a mere extra trick of language, as it is so often slighted in the old schoolbooks on composition; it is the very constitutive ground of language. I am using metaphor here in its most general sense: the use of a term for one thing to describe another because of some kind of similarity between them or between their relations to other things.
Julian Jaynes, The Origin of Consciousness in the Breakdown of the Bicameral Mind, 1976

The concepts of science are all of this kind, abstract concepts generated by concrete metaphors. In physics, we have force, acceleration (to increase one's steps), inertia (originally an indolent person), impedance, resistance, fields, and now charm. In physiology, the metaphier of a machine has been at the very center of discovery. We understand the brain by metaphors to everything from batteries and telegraphy to computers and holograms. Medical practice is sometimes dictated by metaphor. In the eighteenth century, the heart in fever was like a boiling pot, and so bloodletting was prescribed to reduce its fuel. And even today, a great deal of medicine is based upon the military metaphor of defense of the body against attacks of this or that. The very concept of law in Greek derives from nomos, the word for the foundations of a building. To be liable, or bound in law, comes form the Latin ligare, meaning to bind with cord. In early times, language and its referents climbed up from the concrete to the abstract on the steps of metaphors, even, we may say, created the abstract on the bases of metaphors.
Julian Jaynes, The Origin of Consciousness in the Breakdown of the Bicameral Mind, 1976

It is important to see that we don't just talk about arguments in terms of war. We can actually win or lose arguments. We see the person we are arguing with as an opponent. We attack his positions and we defend our own. We gain and lose ground. ... Imagine a culture where an argument is viewed as a dance, the participants are seen as performers, and the goal is to perform in a balanced and aesthetically pleasing way. In such a culture, people would view arguments differently, experience them differently, carry them out differently, and talk about them differently.
George Lakoff and Mark Johnson, Metaphors We Live By, 1980

Artificial Intelligence

The survival of man depends on the early construction of an ultra-intelligent machine.
Irving John Good, Speculations Concerning the First Ultraintelligent Machine, 1963

Problems cannot be solved by the level of awareness that created them.
Albert Einstein

The question of whether Machines Can Think... is about as relevant as the question of whether Submarines Can Swim.
Edsger W. Dijkstra


When others are doing something like you are, let that activity go because that means you don’t have to do it! If they are stealing your ideas, ripping off your moves, knocking off your style, and they are doing it well, thank them. You’ve just learned that that assignment is something you don’t need to do because someone else can do it. This is scary because you are giving up things you do well, and you might think that after surrendering all the good stuff, there won’t be anything excellent left for you. Trust me, there is more to you than that. But it will take all your life to find it. All, as in all your days. And all, as in all your ceaseless effort. Your greatest job is shedding what you don’t have to do.
Kevin Kelly, What You Don't Have To Do


People say that life is the thing, but I prefer reading.
Logan Pearsall Smith

Reading, after a certain age, diverts the mind too much from its creative pursuits. Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein

I have claimed that Escape is one of the main functions of fairy-stories, and since I do not disapprove of them, it is plain that I do not accept the tone of scorn or pity with which 'Escape' is now so often used. Why should a man be scorned if, finding himself in prison, he tries to get out and go home? Or if he cannot do so, he thinks and talks about other topics than jailers and prison-walls?
John Ronald Reuel Tolkien


I have come to the conclusion that my subjective account of my motivation is largely mythical on almost all occasions. I don't know why I do things.
J.B.S. Haldane

To construct oneself, to know oneself — are these two distinct acts or not?
Paul Valéry


Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.
Samuel Beckett

The perfect is the enemy of the good.

The road to wisdom? — Well, it's plain
and simple to express:
and err
and err again
but less
and less
and less.
Piet Hein


Ethical axioms are found and tested not very differently from the axioms of science. Truth is what stands the test of experience.
Albert Einstein

I have never looked upon ease and happiness as ends in themselves — such an ethical basis I call more proper for a herd of swine. The ideals which have lighted me on my way and time after time given me new courage to face life cheerfully, have been Truth, Goodness, and Beauty. Without the sense of fellowship with men of like mind, of preoccupation with the objective, the eternally unattainable in the field of art and scientific research, life would have seemed to me empty. The ordinary objects of human endeavor — property, outward success, luxury — have always seemed to me contemptible.
Albert Einstein

We are what we repeatedly do. Excellence, then, is not an act, but a habit.
Will Durant, interpreting Aristotle's Nicomachean Ethics


I shall call it cosmic religious feeling. It is very difficult to elucidate this feeling to anyone who is entirely without it, especially as there is no anthropomorphic conception of God corresponding to it. The individual feels the futility of human desires and aims and the sublimity and marvelous order which reveal themselves both in nature and in the world of thought. Individual existence impresses him as a sort of prison and he wants to experience the universe as a single significant whole. The beginnings of cosmic religious feeling already appear at an early stage of development, e.g., in many of the Psalms of David and in some of the Prophets. Buddhism, as we have learned especially from the wonderful writings of Schopenhauer, contains a much stronger element of this. The religious geniuses of all ages have been distinguished by this kind of religious feeling, which knows no dogma and no God conceived in man's image; so that there can be no church whose central teachings are based on it.
Albert Einstein, Ideas and Opinions

Joy and happiness are born of concentration. When you are having a cup of tea, the value of that experience depends on your concentration. You have to drink the tea with 100 percent of your being. The true pleasure is experienced in the concentration. When you walk and you are 100 percent concentrated, the joy you get from the steps you are taking is much greater than the joy you would get without concentration. You have to invest 100 percent of your body and mind in the act of walking.
Thich Nhat Hanh, You Are Here

Concentration is the practice of happiness. There is no happiness without concentration.
Thich Nhat Hanh, You Are Here

We are in the habit of identifying ourselves with our bodies. The idea that we are this body is deeply entrenched in us. But we are not just this body; we are much more than that. The idea that "This body is me and I am this body" is an idea we must get rid of. If we do not, we will suffer a great deal. We are life, and life is far vaster than this body, this concept, this mind.
Thich Nhat Hanh, You Are Here

A human being is a part of the whole, called by us "Universe", a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest — a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security.
Albert Einstein

Suffering is a big word in Buddhist thought. It is a key term and it should be thoroughly understood. The Pali word is 'dukkha', and it does not just mean the agony of the body. It means the deep, subtle sense of unsatisfactoriness which is a part of every mental treadmill.
Henepola Gunaratana, Mindfulness In Plain English


The process of preparing programs for a digital computer is especially attractive, not only because it can be economically and scientifically rewarding, but also because it can be an aesthetic experience much like composing poetry or music.
Donald Knuth

Computer science is no more about computers than astronomy is about telescopes.
Edsger W. Dijkstra


The inhabitants of each successive period in the world's history have beaten their predecessors in the race for life, and are, insofar, higher in the scale of nature; and this may account for that vague yet ill-defined sentiment, felt by many palaeontologists, that organisation on the whole has progressed.
Charles Darwin, On the Origin of Species By Means of Natural Selection, Chapter 10

As all the living forms of life are the lineal descendants of those which lived long before the Silurian epoch, we may feel certain that the ordinary succession by generation has never once been broken, and that no cataclysm has desolated the whole world. Hence we may look with some confidence to a secure future of equally inappreciable length. And as natural selection works solely by and for the good of each being, all corporeal and mental endowments will tend to progress towards perfection.
Charles Darwin, On the Origin of Species By Means of Natural Selection, Chapter 14