... every step of the upward way is strewn with wreckage of body, mind, and morals.

…the Form or true definition of heat … is in few words as follows: Heat is a motion; expansive, restrained, and acting in its strife upon the smaller particles of bodies. But the expansion is thus modified; while it expands all ways, it has at the same time an inclination upward. And the struggle in the particles is modified also; it is not sluggish, but hurried and with violence.

[The Elements] are mutually bound together, the lighter being restrained by the heavier, so that they cannot fly off; while, on the contrary, from the lighter tending upwards, the heavier are so suspended, that they cannot fall down. Thus, by an equal tendency in an opposite direction, each of them remains in its appropriate place, bound together by the never-ceasing revolution of the world.

1122 … Thereafter there were many sailors on the sea and on inland water who said that they had seen a great and extensive fire near the ground in the northeast which continuously increased in width as it mounted to the sky. And the heavens opened into four parts and fought against it as if determined to put it out, and the fire stopped rising upwards. They saw that fire at the first streak of dawn, and it lasted until full daylight: this happened on 7 December.

A great ball of fire about a mile in diameter, changing colors as it kept shooting upward, from deep purple to orange, expanding, growing bigger, rising as it was expanding, an elemental force freed from its bonds after being chained for billions of years.
On the first atomic explosion in New Mexico, 16 Jul 1945.

Describing laughter: The sound is produced by a deep inspiration followed by short, interrupted, spasmodic contractions of the chest, and especially the diaphragm... the mouth is open more or less widely, with the corners drawn much backwards, as well as a little upwards; and the upper lip is somewhat raised.

Digital clocks … lack the friendly spatial relationships that exist between the hands and the numerals on an analog clock. There’s a psychological component: to me, the first half of any hour, as the minute hand falls from 12 to 6, passes a lot more quickly than the second half, when it has to struggle upward, fighting gravity all the way.

For any two portions of fire, small or great, will exhibit the same ratio of solid to void; but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size.

For it is obvious to everybody, I think, that this study [of astronomy] compels the soul to look upward and leads it away from things here to higher things.

His genius now began to mount upwards apace & shine out with more strength, & as he told me himself, he excelled particularly in making verses... In everything he undertook he discovered an application equal to the pregnancy of his parts & exceeded the most sanguine expectations his master had conceived of him.
[About Newton's recollection of being a schoolboy at Grantham, written by Conduitt about 65 years after that time.]

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

I finally saw that the blood, forced by the action of the left ventricle into the arteries, was distributed to the body at large, and its several parts, in the same manner as it is sent through the lungs, impelled by the right ventricle into the pulmonary artery, and that it then passed through the veins and along the vena cava, and so round to the left ventricle in the manner already indicated. Which motion we may be allowed to call circular, in the same way as Aristotle says that the air and the rain emulate the circular motion of the superior bodies; for the moist earth, warmed by the sun, evaporates; the vapours drawn upwards are condensed, and descending in the form of rain, moisten the earth again; and by this arrangement are generations of living things produced.

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain … But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.

I searched along the changing edge
Where, sky-pierced now the cloud had broken.
I saw no bird, no blade of wing,
No song was spoken.
I stood, my eyes turned upward still
And drank the air and breathed the light.
Then, like a hawk upon the wind,
I climbed the sky, I made the flight.

I shall never forget the sight. The vessel of crystallization was three quarters full of slightly muddy water—that is, dilute water-glass—and from the sandy bottom there strove upwards a grotesque little landscape of variously colored growths: a confused vegetation of blue, green, and brown shoots which reminded one of algae, mushrooms, attached polyps, also moss, then mussels, fruit pods, little trees or twigs from trees, here, and there of limbs. It was the most remarkable sight I ever saw, and remarkable not so much for its profoundly melancholy nature. For when Father Leverkühn asked us what we thought of it and we timidly answered him that they might be plants: “No,” he replied, “they are not, they only act that way. But do not think the less of them. Precisely because they do, because they try as hard as they can, they are worthy of all respect.”
It turned out that these growths were entirely unorganic in their origin; they existed by virtue of chemicals from the apothecary's shop.

If [science] tends to thicken the crust of ice on which, as it were, we are skating, it is all right. If it tries to find, or professes to have found, the solid ground at the bottom of the water it is all wrong. Our business is with the thickening of this crust by extending our knowledge downward from above, as ice gets thicker while the frost lasts; we should not try to freeze upwards from the bottom.

In ancient days two aviators procured to themselves wings. Daedalus flew safely through the middle air and was duly honored on his landing. Icarus soared upwards to the sun till the wax melted which bound his wings and his flight ended in fiasco. In weighing their achievements, there is something to be said for Icarus. The classical authorities tell us that he was only “doing a stunt,” but I prefer to think of him as the man who brought to light a serious constructional defect in the flying machines of his day.

In the benzene nucleus we have been given a soil out of which we can see with surprise the already-known realm of organic chemistry multiply, not once or twice but three, four, five or six times just like an equivalent number of trees. What an amount of work had suddenly become necessary, and how quickly were busy hands found to carry it out! First the eye moves up the six stems opening out from the tremendous benzene trunk. But already the branches of the neighbouring stems have become intertwined, and a canopy of leaves has developed which becomes more spacious as the giant soars upwards into the air. The top of the tree rises into the clouds where the eye cannot yet follow it. And to what an extent is this wonderful benzene tree thronged with blossoms! Everywhere in the sea of leaves one can spy the slender hydroxyl bud: hardly rarer is the forked blossom [Gabelblüte] which we call the amine group, the most frequent is the beautiful cross-shaped blossom we call the methyl group. And inside this embellishment of blossoms, what a richness of fruit, some of them shining in a wonderful blaze of color, others giving off an overwhelming fragrance.

In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the old Oolitic Silurian Period, must a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have their streets joined together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

It is an error to imagine that evolution signifies a constant tendency to increased perfection. That process undoubtedly involves a constant remodeling of the organism in adaptation to new conditions; but it depends on the nature of those conditions whether the direction of the modifications effected shall be upward or downward.

It is suitable to the magnificent harmony of the universe that the species of creatures should, by gentle degrees, ascend upward from us toward His perfection, as we see them gradually descend from us downward.

Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilometers per second. That is to say, an object fired vertically upward from the surface of the star with a velocity of less than 1,000 kilometers per second would be dragged back by the gravitational field of the star and would return to the surface, whereas an object with a velocity greater than that would escape to infinity.
When the star had exhausted its nuclear fuel, there would be nothing to maintain the outward pressure, and the star would begin to collapse because of its own gravity. As the star shrank, the gravitational field at the surface would become stronger and the escape velocity would increase. By the time the radius had got down to 10 kilometers the escape velocity would have increased to 100,000 kilometers per second, the velocity of light. After that time any light emitted from the star would not be able to escape to infinity but would be dragged back by the gravitational field. According to the special theory of relativity nothing can travel faster than light, so that if light cannot escape, nothing else can either. The result would be a black hole: a region of space-time from which it is not possible to escape to infinity.

Life spirals laboriously upward to higher and even higher levels, paying for every step.

Man has risen, not fallen. He can choose to develop his capacities as the highest animal and to try to rise still farther, or he can choose otherwise. The choice is his responsibility, and his alone. There is no automatism that will carry him upward without choice or effort and there is no trend solely in the right direction. Evolution has no purpose; man must supply this for himself. The means to gaining right ends involve both organic evolution and human evolution, but human choice as to what are the right ends must be based on human evolution.

May we not assure ourselves that whatever woman’s thought and study shall embrace will thereby receive a new inspiration, that she will save science from materialism, and art from a gross realism; that the ‘eternal womanly shall lead upward and onward’?

Most variables can show either an upward or downward trend, depending on the base year chosen.

Nature gropes and blunders and performs the crudest acts. There is no steady advance upward. There is no design.

Only the individual can think, and thereby create new values for society–nay, even set up new moral standards to which the life of the community conforms. Without creative, independently thinking and judging personalities the upward development of society is as unthinkable as the development of the individual personality without the nourishing soil of the community.

Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.

Space isn’t remote at all. It’s only an hour’s drive away if your car could go straight upwards.

That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.

The development of the Vertebrate proceeds from an axis upward, in two layers, which coalesce at the edges, and also downward, in two layers, which likewise coalesce at the edges. Thus two main tubes are formed, one above the other. During the formation of these, the embryo separates into strata, so that the two main tubes are composed of subordinate tubes which enclose each other as fundamental organs, and are capable of developing into all the organs.

The earth was covered by a huge ice sheet which buried the Siberian mammoths, and reached just as far south as did the phenomenon of erratic boulders. This ice sheet filled all the irregularities of the surface of Europe before the uplift of the Alps, the Baltic Sea, all the lakes of Northern Germany and Switzerland. It extended beyond the shorelines of the Mediterranean and of the Atlantic Ocean, and even covered completely North America and Asiatic Russia. When the Alps were uplifted, the ice sheet was pushed upwards like the other rocks, and the debris, broken loose from all the cracks generated by the uplift, fell over its surface and, without becoming rounded (since they underwent no friction), moved down the slope of the ice sheet.

The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.

The growth curves of the famous Hopkins' rats are familiar to anyone who has ever opened a textbook of physiology. One recalls the proud ascendant curve of the milk-fed group which suddenly turns downwards as the milk supplement is removed, and the waning curve of the other group taking its sudden milk-assisted upward spring, until it passes its fellow now abruptly on the decline. 'Feeding experiments illustrating the importance of accessory factors in normal dietaries', Jour. Physiol., 1912, xliv, 425, ranks aesthetically beside the best stories of H. G. Wells.

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.

The last few meters up to the summit no longer seem so hard. On reaching the top, I sit down and let my legs dangle into space. I don’t have to climb anymore. I pull my camera from my rucksack and, in my down mittens, fumble a long time with the batteries before I have it working properly. Then I film Peter. Now, after the hours of torment, which indeed I didn’t recognize as torment, now, when the monotonous motion of plodding upwards is at an end, and I have nothing more to do than breathe, a great peace floods my whole being. I breathe like someone who has run the race of his life and knows that he may now rest forever. I keep looking all around, because the first time I didn’t see anything of the panorama I had expected from Everest, neither indeed did I notice how the wind was continually chasing snow across the summit. In my state of spiritual abstraction, I no longer belong to myself and to my eyesight. I am nothing more than a single, narrow, gasping lung, floating over the mists and the summits.

The mystery of creation is not within the range of [Nature’s] legitimate territory; [Nature] says nothing, but she points upwards.

The world is desperately imperfect. Even if a quarter of the working people were engrossed in new thoughts and inventions and lived off the others, humanity would still gain tremendously thanks to the constant stream of inventions and intellectual work emerging from this horde of people striving upward.

We find it hard to picture to ourselves the state of mind of a man of older days who firmly believed that the Earth was the centre of the Universe, and that all the heavenly bodies revolved around it. He could feel beneath his feet the writhings of the damned amid the flames; very likely he had seen with his own eyes and smelt with his own nostrils the sulphurous fumes of Hell escaping from some fissure in the rocks. Looking upwards, he beheld ... the incorruptible firmament, wherein the stars hung like so many lamps.

We find ourselves, in consequence of the progress of physical science, at the pinnacle of one ascent of civilisation, taking the first step upwards out on to the lowest plane of the next. Above us still rises indefinitely the ascent of physical power—far beyond the dreams of mortals in any previous system of philosophy.

We receive it as a fact, that some minds are so constituted as absolutely to require for their nurture the severe logic of the abstract sciences; that rigorous sequence of ideas which leads from the premises to the conclusion, by a path, arduous and narrow, it may be, and which the youthful reason may find it hard to mount, but where it cannot stray; and on which, if it move at all, it must move onward and upward… . Even for intellects of a different character, whose natural aptitude is for moral evidence and those relations of ideas which are perceived and appreciated by taste, the study of the exact sciences may be recommended as the best protection against the errors into which they are most likely to fall. Although the study of language is in many respects no mean exercise in logic, yet it must be admitted that an eminently practical mind is hardly to be formed without mathematical training.

We shall find everywhere, that the several Species are linked together, and differ but in almost insensible degrees. And when we consider the infinite Power and Wisdom of the Maker, we have reason to think, that it is suitable to the magnificent Harmony of the Universe, and the great Design and infinite Goodness of the Architect, that the Species of Creatures should also, by gentle degrees, ascend upward from us toward his infinite Perfection, as we see they gradually descend from us downwards.

When we think how narrow and devious this path of nature is, how dimly we can trace it, for all our lamps of science, and how from the darkness which girds it round great and terrible possibilities loom ever shadowly upwards, it is a bold and a confident man who will put a limit to the strange by-oaths into which the human spirit may wander.