Benjamin Franklin

Quotes of Benjamin Franklin :

Wise men don't need advice. Fools won't take it.

The proof of gold is fire...

Admiration is the daughter of ignorance.

Words may show a man's wit but actions his meaning.

The absent are never without fault. Nor the present without excuse.

Quotations by Galileo Galilei

Quotations by Galileo Galilei

You cannot teach a man anything; you can only help him find it within himself.

Doubt is the father of invention.

[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

Opere Il Saggiatore p. 171.

Measure what is measurable, and make measurable what is not so.
Quoted in I Gordonand and S Sorkin, The Armchair Science Reader (New York 1959).
And who can doubt that it will lead to the worst disorders when minds created free by God are compelled to submit slavishly to an outside will? When we are told to deny our senses and subject them to the whim of others? When people devoid of whatsoever competence are made judges over experts and are granted authority to treat them as they please? These are the novelties which are apt to bring about the ruin of commonwealths and the subversion of the state.

[On the margin of his own copy of Dialogue on the Great World Systems].
Quoted in J R Newman, The World of Mathematics (New York 1956)

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.
Quoted in Arago, Eulogy of Galileo (1874)
Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position -- eventually, I say, at such a time as it might be proved that the earth moves and the sun stands still.
Dialogue
Epur si muove
And yet it does move.
[Apocryphal words to himself after making his abjuration of heliocentricity.]
I wish, my dear Kepler, that we could have a good laugh together at the extraordinary stupidity of the mob. What do you think of the foremost philosophers of this University? In spite of my oft-repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope.
[Through which the satellites of Jupiter were visible -- seen first in January 1610]
Opera
I mentally conceive of some movable projected on a horizontal plane all impediments being put aside. Now it is evident ... that the equable motion on this plane would be perpetual if the plane were of infinite extent; but if we assume it to be ended, and [situated] on high, the movable ... , driven to the end of the plane and going on further, adds on to its previous equable and indelible motion that downward tendency which it has from its own heaviness. Thus there emerges a certain motion, compounded from equable horizontal and from naturally accelerated downward [motion], which I call projection.
Two New Sciences 1638
Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
Two New Sciences 1638
Among the great men who have philosophized about [the action of the tides], the one who surprised me most is Kepler. He was a person of independent genius, [but he] became interested in the action of the moon on the water, and in other occult phenomena, and similar childishness.
It is very pious to say and prudent to affirm that the holy Bible can never speak untruth -- whenever its true meaning is understood. But I believe nobody will deny that it is often very abstruse, and may say things which are quite different from what its bare words signify.
Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
Quoted in E Maor, To infinity and beyond (Princeton 1991)
To excite in us tastes, odors, and sounds I believe that nothing is required in external bodies except shapes, numbers, and slow or rapid movements. ... if ears, tongues, and noses were removed, shapes and numbers and motions would remain, but not odors or tastes or sounds.
The Divine intellect indeed knows infinitely more propositions [than we can ever know]. But with regard to those few which the human intellect does understand, I believe that its knowledge equals the Divine in objective certainty.
Dialogue on the Great World Systems
The laws of Nature are written in the language of mathematics ... the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.
Quoted in M Kline, Mathematical thought from ancient to modern times
[The difficulties in the study of the infinite arise because] we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this ... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
Two New Sciences 1638
I do not feel obliged to believe that the same God who endowed us with sense, reason, and intellect intended us to forgo their use.
Quoted in Des MacHale, Wisdom (London, 2002).
I have never met a man so ignorant that I couldn't learn something from him.
All truths are easy to understand once they are discovered; the point is to discover them. Top of Form 1
Bottom of Form 1

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Quotations by Albert Einstein

Quotations by Albert Einstein

But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.

Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions.

All these primary impulses, not easily described in words, are the springs of man's actions.

We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race.

One must not attempt to justify them, but rather to sense their nature simply and clearly.

(During a lecture)
This has been done elegantly by Minkowski; but chalk is cheaper than grey matter, and we will do it as it comes.
[Attributed by Pólya.]
Quoted in J E Littlewood, A Mathematician's Miscellany, 1953.

Everything should be made as simple as possible, but not simpler.
Reader's Digest. Oct. 1977.

I don't believe in mathematics.
Quoted in Carl Seelig. Albert Einstein.

Imagination is more important than knowledge.
On Science.

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.
What I Believe.

The bitter and the sweet come from the outside, the hard from within, from one's own efforts.
Out of My Later Years.

Gott würfelt nicht.

Common sense is the collection of prejudices acquired by age eighteen.
Quoted in E T Bell Mathematics, Queen and Servant of the Sciences. 1952.

God does not care about our mathematical difficulties. He integrates empirically.
Quoted in L Infeld Quest, 1942.

How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?

(About Newton)
Nature to him was an open book, whose letters he could read without effort.
Quoted in G Simmons Calculus Gems (New York 1992).

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.
Quoted in J R Newman, The World of Mathematics (New York 1956).

What is this frog and mouse battle among the mathematicians?
[i.e. Brouwer vs. Hilbert]
Quoted in H Eves Mathematical Circles Squared (Boston 1972).

Raffiniert ist der Herr Gott, aber boshaft ist er nicht.
God is subtle, but he is not malicious.
Inscribed in Fine Hall, Princeton University.

Nature hides her secrets because of her essential loftiness, but not by means of ruse.

The human mind has first to construct forms, independently, before we can find them in things.

Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
Quoted in P A Schilpp, Albert Einstein, Philosopher-Scientist (Evanston 1949).

Do not worry about your difficulties in mathematics, I assure you that mine are greater.

The truth of a theory is in your mind, not in your eyes.
Quoted in H Eves Mathematical Circles Squared (Boston 1972).

These thoughts did not come in any verbal formulation. I rarely think in words at all. A thought comes, and I may try to express it in words afterward.
Quoted in H Eves Mathematical Circles Adieu (Boston 1977).

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 resta 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.
Quoted in H Eves Mathematical Circles Adieu (Boston 1977).

The world needs heroes and it's better they be harmless men like me than villains like Hitler.
Quoted in H Eves Return to Mathematical Circles (Boston 1988).

It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiousity of inquiry.
Quoted in H Eves Return to Mathematical Circles (Boston 1988).

Everything that is really great and inspiring is created by the individual who can labor in freedom.
Quoted in H Eves Return to Mathematical Circles (Boston 1988).

The search for truth is more precious than its possession.
The American Mathematical Monthly 100 (3).

If my theory of relativity is proven successful, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.
Address at the Sorbonne, Paris.

We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.
"Space-Time." Encyclopaedia Britannica, 14th ed.

Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
The Evolution of Physics.

Science without religion is lame; religion without science is blind.
Reader's Digest, Nov. 1973.

(To a student)
Dear Miss --
I have read about sixteen pages of your manuscript ... I suffered exactly the same treatment at the hands of my teachers who disliked me for my independence and passed over me when they wanted assistants ... keep your manuscript for your sons and daughters, in order that they may derive consolation from it and not give a damn for what their teachers tell them or think of them. ... There is too much education altogether.
The World as I See It, (New York, 1949), 21-22.

(Written in old age)
I have never belonged wholeheartedly to a country, a state, nor to a circle of friends, nor even to my own family.
When I was still a rather precocious young man, I already realized most vividly the futility of the hopes and aspirations that most men pursue throughout their lives.
Well-being and happiness never appeared to me as an absolute aim. I am even inclined to compare such moral aims to the ambitions of a pig.
Quoted in C P Snow, Variety of Men, (Harmondsworth 1969) 77.

The relativity principle in connection with the basic Maxwellian equations demands that the mass should be a direct measure of the energy contained in a body; light transfers mass. With radium there should be a noticeable diminution of mass. The idea is amusing and enticing; but whether the Almighty is laughing at it and is leading me up the garden path -- that I cannot know.

When I am judging a theory, I ask myself whether, if I were God, I would have arranged the world in such a way.

Great spirits have always encountered violent opposition from mediocre minds.

.. common sense is nothing more than a deposit of prejudices laid down in the mind before you reach eighteen.
Quoted in E T Bell, Mathematics: Queen and Servant of Science

Thus the partial differential equation entered theoretical physics as a handmaid, but has gradually become mistress.
The World as I See It

But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed.
Quoted in H R Pagels, The Cosmic Code

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, withut mathematics, they could not attain.
Quoted in E T Bell Men of Mathematics

One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
Sidelights on Relativity

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.
Sidelights on Relativity

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?
Sidelights on Relativity

Mathematics are well and good but nature keeps dragging us around by the nose.
Quoted in A P French, Einstein: a Centenary Volume

Education is that which remains when one has forgotten everything learned in school.
Ideas and opinions (New York, 1954).

A hundred times every day I remind myself that my inner and outer life depend on the labours of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received.
Quoted in Des MacHale, Wisdom (London, 2002).

Before God we are all equally wise - equally foolish.
Quoted in Des MacHale, Wisdom (London, 2002).

Each of us visits that Earth involuntarily and without an invitation. For me, it is enough to wonder at its secrets.
Quoted in Des MacHale, Wisdom (London, 2002).

If at first the idea is not absurd, then there is no hope for it.
Quoted in Des MacHale, Wisdom (London, 2002).

It is my contention that killing under the cloak of war is nothing but an act of murder.
Quoted in Des MacHale, Wisdom (London, 2002).

My religion consists of a humble admiration of the illimitable superior spirit who reveals himself in the slightest details we are able to perceive with our frail and feeble minds.
Quoted in Des MacHale, Wisdom (London, 2002).

Reading after a certain time 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.
Quoted in Des MacHale, Wisdom (London, 2002).
[EFR: For a modern view replace reading by watching television.]

Sometimes one pays most for things one gets for nothing.
Quoted in Des MacHale, Wisdom (London, 2002).

The most incomprehensible fact about the universe is that it is comprehensible.
Quoted in Des MacHale, Wisdom (London, 2002).

The world we have made, as a result of the level of thinking we have done thus far, creates problems we cannot solve at the same level of thinking at which we created them.
Quoted in Des MacHale, Wisdom (London, 2002).

There are two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.
Quoted in Des MacHale, Wisdom (London, 2002).

JOC/EFR February 2006


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Mark Twain's Quote's

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