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Who said: “Dangerous... to take shelter under a tree, during a thunder-gust. It has been fatal to many, both men and beasts.”
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Home > Category Index for Science Quotations > Category Index H > Category: Height

Height Quotes (33 quotes)

… just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts—ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:—thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science.
In Lectures on Science, Philosophy and Art (1908), 26
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…with common water. Its substance reaches everywhere; it touches the past and prepares the future; it moves under the poles and wanders thinly in the heights of air. It can assume forms of exquisite perfection in a snowflake, or strip the living to a single shining bone cast up by the sea.
From essay 'The Flow of the River', collected in The Immense Journey: An Imaginative Naturalist Explores the Mysteries of Man and Nature (1957, 1959), 16.
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“In order to ascertain the height of the tree I must be in such a position that the top of the tree is exactly in a line with the top of a measuring-stick—or any straight object would do, such as an umbrella—which I shall secure in an upright position between my feet. Knowing then that the ratio that the height of the tree bears to the length of the measuring stick must equal the ratio that the distance from my eye to the base of the tree bears to my height, and knowing (or being able to find out) my height, the length of the measuring stick and the distance from my eye to the base of the tree, I can, therefore, calculate the height of the tree.”
“What is an umbrella?”
In Mr. Fortune’s Maggot (1927), 175.
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[Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone—a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.
In 'The Story of Mathematics at Harvard', Harvard Alumni Bulletin (3 Jan 1924), 26, 376. Cited by R. C. Archibald in 'Benjamin Peirce: V. Biographical Sketch', The American Mathematical Monthly (Jan 1925), 32, No. 1, 10.
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[On common water.] Its substance reaches everywhere; it touches the past and prepares the future; it moves under the poles and wanders thinly in the heights of air. It can assume forms of exquisite perfection in a snowflake, or strip the living to a single shining bone cast up by the sea.
From essay 'The Flow of the River', collected in The Immense Journey: An Imaginative Naturalist Explores the Mysteries of Man and Nature (1957, 1959), 16.
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[Introducing two perfectly ordinary performers of average stature to a circus audience.]
The Punkwat twins! Brentwood is the world's smallest giant, whilst his brother, Elwood, is the largest midget in the world. They baffle science!
As character Larson E. Whipsnade, circus ring-master, in movie, You Can't Cheat an Honest Man (1939). As transcribed in Simon Louvish, Man on the Flying Trapeze: The Life and Times of W. C. Fields (1999), 4.
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An inventor is an opportunist, one who takes occasion by the hand; who, having seen where some want exists, successfully applies the right means to attain the desired end. The means may be largely, or even wholly, something already known, or there may be a certain originality or discovery in the means employed. But in every case the inventor uses the work of others. If I may use a metaphor, I should liken him to the man who essays the conquest of some virgin alp. At the outset he uses the beaten track, and, as he progresses in the ascent, he uses the steps made by those who have preceded him, whenever they lead in the right direction; and it is only after the last footprints have died out that he takes ice-axe in hand and cuts the remaining steps, few or many, that lift him to the crowning height which is his goal.
In Kenneth Raydon Swan, Sir Joseph Swan (1946), 44.
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But come, hear my words, for truly learning causes the mind to grow. For as I said before in declaring the ends of my words … at one time there grew to be the one alone out of many, and at another time it separated so that there were many out of the one; fire and water and earth and boundless height of air, and baneful Strife apart from these, balancing each of them, and Love among them, their equal in length and breadth.
From The Fragments, Bk. 1, line 74. In Arthur Fairbanks (ed., trans.), Quotations from The First Philosophers of Greece (1898), 167-168.
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Courage is the price that
Life exacts for granting peace.
The soul that knows it not, knows no release
From little things:
Knows not the livid loneliness of fear,
Nor mountain heights where bitter joy can hear
The sound of wings.
From poem 'Courage' (1927), opening lines, included in magazine article by Marion Perkins, 'Who Is Amelia Earhart?', Survey (1 Jul 1928), 60. Quoted as epigraph, and cited in Mary S. Lovell, The Sound of Wings: The Life of Amelia Earhart (1989), ix.
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Developmental Biology, in capitals, is the wave of the future. The creeping reductionism of biochemistry and molecular biology has taken over the cell and heredity, and looks covetously toward the heights of development and evolution. Recent literature is last year. Ancient literature is a decade ago. The rest is history, doubtfully alive. There is no time and often no opportunity to find and study the work of experimental biologists of 50 or 100 years ago, yet that was a time when the world was fresh.
Developmental biology was a lowercase phrase that graduated about 1950 and had previously lived under the cloak of Experimental Zoology
In obituary by Charles R. Scriver, Biographical Memoirs of Fellows of the Royal Society (Nov 1999), 45, 33.
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During the eight days I spent in space, I realized that mankind needs height primarily to better know our long-suffering Earth, to see what cannot be seen close up. Not just to love her beauty, but also to ensure that we do not bring even the slightest harm to the natural world
In Jack Hassard and Julie Weisberg , Environmental Science on the Net: The Global Thinking Project (1999), 40.
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Form your life humanly, and you have done enough: but you will never reach the height of art and the depth of science without something divine.
Idea 68. In Friedrich Schlegel, translated by Ernst Behler and Roman Struc, Dialogue on Poetry and Literary Aphorisms (trans. 1968), 155.
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I have seen the sea lashed into fury and tossed into spray, and its grandeur moves the soul of the dullest man; but I remember that it is not the billows, but the calm level of the sea from which all heights and depths are measured.
Speech (5 Jun 1880) at the 7th Republican National Convention, Chicago to nominate John Sherman to be President. In John Tweedy, A History of the Republican National Conventions from 1856 to 1908 (1910), 191. The Convention subsequently nominated Garfield to run for President. He won the election, and was inaugurated on 4 Mar 1881.
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If we make a couple of discoveries here and there we need not believe things will go like this for ever. An acrobat can leap higher than a farm-hand, and one acrobat higher than another, yet the height no man can overleap is still very low. Just as we hit water when we dig in the earth, so we discover the incomprehensible sooner or later.
Aphorisms, trans. R. J. Hollingdale (1990), 92.
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In despair, I offer your readers their choice of the following definitions of entropy. My authorities are such books and journals as I have by me at the moment.
(a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius.
(b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait.
(c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne.
(d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson.
(e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid.
(f) Entropy is one of the factors of heat, temperature being the other.—Engineering.
I set up these bald statement as so many Aunt Sallys, for any one to shy at.
[Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]
In The Electrician (9 Jan 1903).
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It is, as Schrödinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 537.
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It then came into my mind what that most careful observer of natural phenomena [Amontons] had written about the correction of the barometer; for he had observed that the height of the column of mercury in the barometer was a little (though sensibly enough) altered by the varying temperature of the mercury. From this I gathered that a thermometer might be perhaps constructed with mercury.
From 'Experimenta circa gradum caloris liquorum nonnullorum ebullientium instituta', Philosophical Transactions (1724), 33, 1, as translated in William Francis Magie, A Source Book in Physics (1935), 131.
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Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure.
In Mathematics in Western Culture (1964), 408.
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Oh, I have slipped the surly bonds of earth
and danced the skies on laughter-silvered wings;
Sunward I’ve climbed, and joined the tumbling mirth
of sun-split clouds and done a hundred things
you have not dreamed of wheeled and soared and swung
high in the sunlit silence. Hovering there,
I’ve chased the shouting wind along, and flung
my eager craft through footless halls of air.
Up, up the long, delirious, burning blue
I’ve topped the windswept heights with easy grace
where never lark, or even eagle flew
and, while with silent, lifting mind I’ve trod
the high untrespassed sanctity of space,
put out my hand, and touched the face of God.
…...
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Our sun is one of 100 billion stars in our galaxy. Our galaxy is one of billions of galaxies populating the universe. It would be the height of presumption to think that we are the only living things in that enormous immensity.
…...
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People travel to wonder at the height of mountains, at the huge waves of the sea, at the long courses of rivers, at the vast compass of the ocean, at the circular motion of the stars; and they pass by themselves without wondering.
In Circulations: Webster's Quotations, Facts and Phrases, 1.
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Phenomena unfold on their own appropriate scales of space and time and may be invisible in our myopic world of dimensions assessed by comparison with human height and times metered by human lifespans. So much of accumulating importance at earthly scales ... is invisible by the measuring rod of a human life. So much that matters to particles in the microscopic world of molecules ... either averages out to stability at our scale or simply stands below our limits of perception.
…...
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Researchers, with science as their authority, will be able to cut [animals] up, alive, into small pieces, drop them from a great height to see if they are shattered by the fall, or deprive them of sleep for sixteen days and nights continuously for the purposes of an iniquitous monograph... Animal trust, undeserved faith, when at last will you turn away from us? Shall we never tire of deceiving, betraying, tormenting animals before they cease to trust us?
…...
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The Himalayas are the crowning achievement of the Indo-Australian plate. India in the Oligocene crashed head on into Tibet, hit so hard that it not only folded and buckled the plate boundaries but also plowed into the newly created Tibetan plateau and drove the Himalayas five and a half miles into the sky. The mountains are in some trouble. India has not stopped pushing them, and they are still going up. Their height and volume are already so great they are beginning to melt in their own self-generated radioactive heat. When the climbers in 1953 planted their flags on the highest mountain, they set them in snow over the skeletons of creatures that had lived in a warm clear ocean that India, moving north, blanked out. Possibly as much as 20,000 feet below the sea floor, the skeletal remains had turned into rock. This one fact is a treatise in itself on the movements of the surface of the earth.
If by some fiat, I had to restrict all this writing to one sentence; this is the one I would choose: the summit of Mount Everest is marine limestone.
Annals of the Former World
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The history of aëronautic adventure affords a curious illustration of the same [dip of the horizon] principle. The late Mr. Sadler, the celebrated aeronaut, ascended on one occasion in a balloon from Dublin, and was wafted across the Irish Channel, when, on his approach to the Welsh coast, the balloon descended nearly to the surface of the sea. By this time the sun was set, and the shades of evening began to close in. He threw out nearly all his ballast, and suddenly sprang upwards to a great height, and by so doing brought his horizon to dip below the sun, producing the whole phenomenon of a western sunrise. Subsequently descending in Wales, he of course witnessed a second sunset on the same evening.
This describes how a rapidly ascending balloonist can see more of a setting sun, from the top down, as the viewer gradually rises more and thus sees further, beyond the curvature of the earth. The sun gradually appears as if at sunrise. It is the reverse of the view of a ship sailing toward the horizon which disappears from its hull up to the tip of the mast. In Outlines of Astronomy (1849), 20. A similar description appeared earlier, in Astronomy (1833), 36, which also footnoted Herschel's comment that he had this anecdote from Dr. Lardner, who was present at the ascent
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The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …
Kurzer Grundriss eines Versuchs (1851), 44. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 158.
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The most remarkable thing was his [Clifford’s] great strength as compared with his weight, as shown in some exercises. At one time he could pull up on the bar with either hand, which is well known to be one of the greatest feats of strength. His nerve at dangerous heights was extraordinary. I am appalled now to think that he climbed up and sat on the cross bars of the weathercock on a church tower, and when by way of doing something worse I went up and hung by my toes to the bars he did the same.
Anonymous
Quoted from a letter by one of Clifford’s friends to F. Pollock, in Clifford’s Lectures and Essays (1901), Vol. 1, Introduction, 8.
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Theories cannot claim to be indestructible. They are only the plough which the ploughman uses to draw his furrow and which he has every right to discard for another one, of improved design, after the harvest. To be this ploughman, to see my labours result in the furtherance of scientific progress, was the height of my ambition, and now the Swedish Academy of Sciences has come, at this harvest, to add the most brilliant of crowns.
'The Method of Direct Hydrogenation by Catalysis', Nobel Lecture (11 Dec 1912). Noble Lectures in Chemistry 1901-1921 (1966), 230-1.
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To feed applied science by starving basic science is like economising on the foundations of a building so that it may be built higher. It is only a matter of time before the whole edifice crumbles.
In article, 'Lest the Edifice of Science Crumble', New Scientist (4 Sep 1986), 111, No. 1574, 16.
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Truth travels down from the heights of philosophy to the humblest walks of life, and up from the simplest perceptions of an awakened intellect to the discoveries which almost change the face of the world. At every stage of its progress it is genial, luminous, creative. When first struck out by some distinguished and fortunate genius, it may address itself only to a few minds of kindred power. It exists then only in the highest forms of science; it corrects former systems, and authorizes new generalizations. Discussion, controversy begins; more truth is elicited, more errors exploded, more doubts cleared up, more phenomena drawn into the circle, unexpected connexions of kindred sciences are traced, and in each step of the progress, the number rapidly grows of those who are prepared to comprehend and carry on some branches of the investigation,— till, in the lapse of time, every order of intellect has been kindled, from that of the sublime discoverer to the practical machinist; and every department of knowledge been enlarged, from the most abstruse and transcendental theory to the daily arts of life.
In An Address Delivered Before the Literary Societies of Amherst College (25 Aug 1835), 16-17.
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When I was a small boy [my father] used to sit me on his lap and read to me from the [Encyclopaedia] Britannica … say, about … the Tyrannosaurus rex, and it would say something like, “This dinosaur is twenty-five feet high and its head is six feet across.” My father would stop reading and say, “Now, let’s see what that means. That would mean that if he stood in our front yard, he would be tall enough to put his head through our window up here.” (We were on the second floor.) “But his head would be too wide to fit in the window.” Everything he read to me he would translate as best he could into some reality. …
In 'The Making of a Scientist', What Do You Care What Other People Think?": Further Adventures of a Curious Character (2001), 12-13. I learned from my father to translate: everything I read I try to figure out what it really means, what it’s really saying.
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When the Heavens were a little blue Arch, stuck with Stars, methought the Universe was too straight and close: I was almost stifled for want of Air: but now it is enlarged in height and breadth, and a thousand Vortex’s taken in. I begin to breathe with more freedom, and I think the Universe to be incomparably more magnificent than it was before.
In A Plurality of Worlds (1688), 126, as translated by Mr. Glanvill.
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You see, if the height of the mercury [barometer] column is less on the top of a mountain than at the foot of it (as I have many reasons for believing, although everyone who has so far written about it is of the contrary opinion), it follows that the weight of the air must be the sole cause of the phenomenon, and not that abhorrence of a vacuum, since it is obvious that at the foot of the mountain there is more air to have weight than at the summit, and we cannot possibly say that the air at the foot of the mountain has a greater aversion to empty space than at the top.
In letter to brother-in-law Perier (Nov 1647) as given in Daniel Webster Hering, Physics: the Science of the Forces of Nature (1922), 114. As also stated by Hering, Perier conducted an experiment on 19 Sep 1648 comparing readings on two barometers, one at the foot, and another at the top of 4,000-ft Puy-de-Dôme neighboring mountain.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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Sophie Germain
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Ernest Rutherford
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William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
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Winston Churchill
- 80 -
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Bible
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- 70 -
Samuel Morse
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Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
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Carolus Linnaeus
- 60 -
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Immanuel Kant
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Karl Popper
Paul Dirac
Avicenna
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William Shakespeare
- 50 -
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- 40 -
Pierre Fermat
Edward Wilson
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Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
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