Nor let yourself by usual habit follow this path bound by a random-moving eye, a ringing in the ear, and a tongue, decide but reckon the much-contested argument. - Parmenides

Let no one ignorant of geometry come under my roof. - inscription reportedly over Plato’s Academy door

Since, then, the now is a beginning and end of a time, and the point a beginning and end of a line; and since the beginning of anything is not continuous with its end, but they have an interval between them; it follows that neither nows nor points can be continuous with one another. – On Indivisible Lines, Pseudoaristotlean Treatise (I have my doubts, but it is an interesting quote, presaging Galileo)

For neither the definition of line, nor that of straight line, will apply to the indivisible line, since the latter is not between any terminal points, and does not possess a middle. – On Indivisible Lines, Pseudoaristotlean Treatise

Vain is the word of the philosopher which does not heal any suffering of man. For just as there is no profit in medicine if it does not expel the diseases of the body, so there is no profit in philosophy either if it does not expel the suffering of the mind. - Epicurus

Find the path, enter the path, travel the path, become the path. (Taoist saying)

To enter the spiritual path, you must begin to understand your own mental attitude and how your mind perceives things. If you’re all caught up in attachment to tiny atoms, your limited, craving mind will make it impossible for you to enjoy life’s pleasures. External energy is so incredibly limited that if you allow yourself to be bound by it, your mind itself will become just as limited. When your mind is narrow, small things easily agitate you. Make your mind an ocean. - Lama Thubten Yeshe

Yet although the Logos is common, most men live as if they had their own private understanding. – Heraclitus

This Logos holds always but humans always prove unable to understand it, both before hearing it and when they have first heard it. For though all things come to be in accordance with this Logos, humans are like the inexperienced when they experience such words and deeds as I set out, distinguishing each in accordance with its nature and saying how it is. But other people fail to notice what they do when awake, just as they forget what they do while asleep. – Heraclitus

The wise is to know how that all things are governed through all things - Heraclitus

All things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. – Richard Feynman

“Elementary” means that very little is required to know ahead of time in order to understand it, except to have an infinite amount of intelligence. - Richard Feynman in his Lost Lecture “The Motion of Planets around the Sun”

There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true. - Niels Bohr

I have diverse definitions for the straight line. The straight line is a curve, any part of which is similar to the whole, and it alone has this property, not only among curves but among sets.” – Gottfried Leibniz

I had a scheme, which I still use to-day when somebody is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem… As they’re telling me the conditions of the theorem, I construct something that fits all the conditions. You know, you have a set (one ball) – disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally, they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!” – Richard Feynman

We have life interacting with no-life all the time. – Ilya Prigogine

The random assumption is a way of throwing up one’s hands, a null hypothesis in the absence of any information. – Steven Strogatz

I have universally observed among all those who make a profession of portraying faces from life, that he who paints the best likeness is the worst of all composers of narrative painting. – Leonardo da Vinci

The Swineherd then gave orders to his men: “Bring in our best pig for a stranger’s dinner. A feast will do our hearts good, too; we know grief and pain, hard scrabbling with our swine, while the outsiders live on our labor.” – from Homer’s Odyssey, Robert Fitzgerald translation

Drawing what you actually see—that is, drawing the plastic bull that’s in front of you rather than the simplified, idealized image of a bull that’s in your head—is something that does not come naturally to most people, let alone children. At its root, my gift was not the ability to draw what I saw. Rather, it was the ability to look at what I had drawn thus far and understand what was wrong with it. – John Siracusa in “Hypercritical”

Knowing what’s wrong with something (or thinking that you do, which, for the purposes of this discussion, should be considered the same thing) does a fat lot of good if you lack the skills to correct it. – John Siracusa in “Hypercritical”

Would a musician feel flattered by the loud applause of an audience if he knew they were nearly all deaf, and that, to conceal their infirmity, they set to work to clap vigorously as soon as ever they saw one or two persons applauding? And what would he say if he got to know that those one or two persons had often taken bribes to secure the loudest applause for the poorest player! – Arthur Schopenhauer, from the Wisdom of Life

I am certain there is too much certainty in the world – Michael Crichton

We of the craft are all crazy. Some are affected by gaiety, others by melancholy, but all are more or less touched – Lord Byron

I don’t use drugs, my dreams are frightening enough – M. C. Escher

… all men, all women resemble each other: no love resists the effects of sane reflection. – the Marquis de Sade

Your mind is your religion. – Lama Thubten Yeshe

All that has a form is an illusive existence. When it is perceived that all form is
no−form, the Tathagata is recognized. – Buddha, in The Diamond Sutra (Tathagata means one who has thus gone and one who has thus come, and a reference to Buddha when referring to himself)

Meditation in the midst of activity is a thousand times superior to meditation in stillness – Hakuin Ekaku

No pleasure is bad per se: but the causes of some pleasures produce stresses many times greater than the pleasures.  Epicurus

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. – Albert Einstein

There is no exquisite beauty without some strangeness in the proportion – Edgar Allan Poe (who credits Francis Bacon)

The pleasure of imitation, as the ancients knew, is one of the most innate in the human spirit; but here we not only enjoy a perfect imitation, we also enjoy the conviction that imitation has reached its apex and afterwards reality will always be inferior to it – Umberto Eco

The beauty of the Internet is that it connects people. The value is in the other people. If we start to believe that the Internet itself is an entity that has something to say, we’re devaluing those people and making ourselves into idiots. – Jaron Lanier

Cantor is overwhelmed by amazement at his own findings, and slips from German to French to exclaim that “to see is not to believe” (“je le vois, mai je ne le crois pas”) And, as if on cue, mathematics seeks to avoid being misled by the graven images of monsters. … The wide and uncritical acceptance of this view has become destructive. In particular, in the theory of fractals, “to see is to believe” - Benoit Mandelbrot

Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry. - Charles S. Peirce

The seeker after truth is not one who studies the writings of the ancients and following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them.  - Abu Ali al-Hasan-ibn al-Haytham

The duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make an enemy of all that he reads, and applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examinations of it, so that he may avoid falling into either prejudice or leniency. - Abu Ali al-Hasan-ibn al-Haytham

…beware of mathematicians (astrologers) and all those who make empty prophesies. - Aurelius Augustinus, Bishop of Hippo

Divine determination depends on the life of a man, and not his life upon the determination. - St. Theophan the Recluse

So I say to you –
This is how to contemplate our conditioned existence in this fleeting world:

Like a tiny drop of dew, or a bubble floating in a stream;
Like a flash of lightning in a summer cloud,
Or a flickering lamp, an illusion, a phantom, or a dream.

Buddha, in The Diamond Sutra

–
From Alice in Wonderland (Charles Dodgson)

“To begin with,” said the Cat, “a dog’s not mad. You grant that?”

“I suppose so,” said Alice.

“Well, then,” the Cat went on, “you see, a dog growls when it’s angry, and wags its tail when it’s pleased. Now I growl when I’m pleased, and wag my tail when I’m angry. Therefore I’m mad.”

“I call it purring, not growling,” said Alice.

“Call it what you like,” said the Cat.

Advertisement