...[T]he natural history of the rat is tragically similar to that of man ... some of the more obvious qualities in which rats resemble men — ferocity, omnivorousness, and adaptability to all climates ... the irresponsible fecundity with which both species breed at all seasons of the year with a heedlessness of consequences, which subjects them to wholesale disaster on the inevitable, occasional failure of the food supply.... [G]radually, these two have spread across the earth, keeping pace with each other and unable to destroy each other, though continually hostile. They have wandered from East to West, driven by their physical needs, and — unlike any other species of living things — have made war upon their own kind. The gradual, relentless, progressive extermination of the black rat by the brown has no parallel in nature so close as that of the similar extermination of one race of man by another...

[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. … On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller’s works on geology, or read Mr. Lewes's “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!

[W.H.R.] Rivers is the Rider Haggard of anthropology; I shall be the Conrad.
[Drawing parallel with popular novelists.]

Question: Account for the delicate shades of colour sometimes seen on the inside of an oyster shell. State and explain the appearance presented when a beam of light falls upon a sheet of glass on which very fine equi-distant parallel lines have been scratched very close to one another.
Answer: The delicate shades are due to putrefaction; the colours always show best when the oyster has been a bad one. Hence they are considered a defect and are called chromatic aberration.
The scratches on the glass will arrange themselves in rings round the light, as any one may see at night in a tram car.

Question: If you walk on a dry path between two walls a few feet apart, you hear a musical note or “ring” at each footstep. Whence comes this?
Answer: This is similar to phosphorescent paint. Once any sound gets between two parallel reflectors or walls, it bounds from one to the other and never stops for a long time. Hence it is persistent, and when you walk between the walls you hear the sounds made by those who walked there before you. By following a muffin man down the passage within a short time you can hear most distinctly a musical note, or, as it is more properly termed in the question, a “ring” at every (other) step.

Copernicus and Lobatchewsky were both of Slavic origin. Each of them has brought about a revolution in scientific ideas so great that it can only be compared with that wrought by the other. And the reason of the transcendent importance of these two changes is that they are changes in the conception of the Cosmos. … Now the enormous effect of the Copernican system, and of the astronomical discoveries that have followed it, is … the change effected by Copernicus in the idea of the universe. But there was left another to be made. For the laws of space and motion…. So, you see, there is a real parallel between the work of Copernicus and … the work of Lobatchewsky.

Criticism of first principles which Aristotle and Ptolemy and Galen underwent waited longer in Euclid’s case than in theirs, it came for him at last. What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobatchewsky to Euclid. There is, indeed, a somewhat instructive parallel between … Copernicus and Lobatchewsky.

Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.
Having himself spent a lifetime unsuccessfully trying to prove Euclid’s postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.

Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there.
Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.

England was nothing, compared to continental nations until she had become commercial … until about the middle of the last century, when a number of ingenious and inventive men, without apparent relation to each other, arose in various parts of the kingdom, succeeded in giving an immense impulse to all the branches of the national industry; the result of which has been a harvest of wealth and prosperity, perhaps without a parallel in the history of the world.

Evolution is an integration of matter and concomitant dissipation of motion during which the matter passes from an indefinite incoherent homogeneity to a definite coherent heterogeneity, and during which the retained motion undergoes a parallel transformation.

Exper. I. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed a small looking-glass without the window-shutter, in such a position as to reflect the sun's light, in a direction nearly horizontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall or on other cards held at different distances. Besides the fringes of colour on each side of the shadow, the shadow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card and inflected, or rather diffracted, into the shadow. For, a little screen being placed a few inches from the card, so as to receive either edge of the shadow on its margin, all the fringes which had before been observed in the shadow on the wall, immediately disappeared, although the light inflected on the other side was allowed to retain its course, and although this light must have undergone any modification that the proximity of the other edge of the slip of card might have been capable of occasioning... Nor was it for want of a sufficient intensity of light that one of the two portions was incapable of producing the fringes alone; for when they were both uninterrupted, the lines appeared, even if the intensity was reduced to one-tenth or one-twentieth.

Finally in a large population, divided and subdivided into partially isolated local races of small size, there is a continually shifting differentiation among the latter (intensified by local differences in selection but occurring under uniform and static conditions) which inevitably brings about an indefinitely continuing, irreversible, adaptive, and much more rapid evolution of the species. Complete isolation in this case, and more slowly in the preceding, originates new species differing for the most part in nonadaptive parallel orthogenetic lines, in accordance with the conditions. It is suggested, in conclusion, that the differing statistical situations to be expected among natural species are adequate to account for the different sorts of evolutionary processes which have been described, and that, in particular, conditions in nature are often such as to bring about the state of poise among opposing tendencies on which an indefinitely continuing evolutionary process depends.

For God’s sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.
Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.

I consider the differences between man and animals in propensities, feelings, and intellectual faculties, to be the result of the same cause as that which we assign for the variations in other functions, viz. difference of organization; and that the superiority of man in rational endowments is not greater than the more exquisite, complicated, and perfectly developed structure of his brain, and particularly of his ample cerebral hemispheres, to which the rest of the animal kingdom offers no parallel, nor even any near approximation, is sufficient to account for.

If you were plowing a field, which would you rather use? Two strong oxen or 1024 chickens?
[Comparing the power of supercomputers versus parallel computing.]

In 1905, a physicist measuring the thermal conductivity of copper would have faced, unknowingly, a very small systematic error due to the heating of his equipment and sample by the absorption of cosmic rays, then unknown to physics. In early 1946, an opinion poller, studying Japanese opinion as to who won the war, would have faced a very small systematic error due to the neglect of the 17 Japanese holdouts, who were discovered later north of Saipan. These cases are entirely parallel. Social, biological and physical scientists all need to remember that they have the same problems, the main difference being the decimal place in which they appear.

In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain.

It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through feedback. Both of them have sensory receptors as one stage in their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended aetion, is reported back to the central regulatory apparatus.

It is well-known that both rude and civilized peoples are capable of showing unspeakable, and as it is erroneously termed, inhuman cruelty towards each other. These acts of cruelty, murder and rapine are often the result of the inexorable logic of national characteristics, and are unhappily truly human, since nothing like them can be traced in the animal world. It would, for instance, be a grave mistake to compare a tiger with the bloodthirsty exectioner of the Reign of Terror, since the former only satisfies his natural appetite in preying on other mammals. The atrocities of the trials for witchcraft, the indiscriminate slaughter committed by the negroes on the coast of Guinea, the sacrifice of human victims made by the Khonds, the dismemberment of living men by the Battas, find no parallel in the habits of animals in their savage state. And such a comparision is, above all, impossible in the case of anthropoids, which display no hostility towards men or other animals unless they are first attacked. In this respect the anthropid ape stands on a higher plane than many men.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]

Men are noisy, narrow-band devices, but their nervous systems have very many parallel and simultaneously active channels. Relative to men, computing machines are very fast and very accurate, but they are constrained to perform only one or a few elementary operations at a time. Men are flexible, capable of “programming themselves contingently” on the basis of newly received information. Computing machines are single-minded, constrained by their “pre-programming.”

More than the diamond Koh-i-noor, which glitters among their crown jewels, they prize the dull pebble which is wiser than a man, whose poles turn themselves to the poles of the world, and whose axis is parallel to the axis of the world. Now, their toys are steam and galvanism.

Once I dipt into the future far as human eye could see,
And I saw the Chief Forecaster, dead as any one can be-
Dead and damned and shut in Hades as a liar from his birth,
With a record of unreason seldom paralleled on earth.
While I looked he reared him solemnly, that incandescent youth,
From the coals that he’s preferred to the advantages of truth.
He cast his eyes about him and above him; then he wrote
On a slab of thin asbestos what I venture here to quote-
For I read it in the rose-light of the everlasting glow:
Cloudy; variable winds, with local showers; cooler; snow.

Once regarded as the herald of enlightenment in all spheres of knowledge, science is now increasingly seen as a strictly instrumental system of control. Its use as a means of social manipulation and its role in restricting human freedom now parallel in every detail its use as a means of natural manipulation.

Sheppey hath long been noted for producing large quantities of Sheep (whence probably its name is derived) as well as Corn; and exhibits to the Curious Naturalist a most desirable Spot, by affording many rare Plants, and more especially in the of its Northern Cliffs, so great a Quantity and Variety of Fossils, both native and extraneous are scarcely to be paralleled. These Cliffs length about six miles; Minster, Shurland and Warden are the Manors to which they appertain, the more elevated parts whereof reach about thirds of their extension, and are at the very highest of them not less than fifty yards perpendicular height above the Beach and Shore.

Some of the men stood talking in this room, and at the right of the door a little knot had formed round a small table, the center of which was the mathematics student, who was eagerly talking. He had made the assertion that one could draw through a given point more than one parallel to a straight line; Frau Hagenström had cried out that this was impossible, and he had gone on to prove it so conclusively that his hearers were constrained to behave as though they understood.

Suppose you were given a watch, a tube to sight with and a string, and then asked to determine the distance to the nearest star. Or you were asked the chemical composition, pressure or temperature of the Sun. A hundred or more years ago, these questions seemed impossible. Now astronomers are answering them all the time, and they believe their answers. Why? Because there are many parallel ways and tests, and they all give the same answers.

The human understanding is of its own nature prone to suppose the existence of more order and regularity in the world than it finds. And though there be many things in nature which are singular and unmatched, yet it devises for them parallels and conjugates and relatives which do not exist. Hence the fiction that all celestial bodies move in perfect circles, spirals and dragons being (except in name) utterly rejected.

The morphological characteristics of plant and animal species form the chief subject of the descriptive natural sciences and are the criteria for their classification. But not until recently has it been recognized that in living organisms, as in the realm of crystals, chemical differences parallel the variation in structure.

The rise of the ecologist almost exactly parallels the decline of the naturalist.

The X-ray spectrometer opened up a new world. It proved to be a far more powerful method of analysing crystal structure…. One could examine the various faces of a crystal in succession, and by noting the angles at which and the intensity with which they reflected the X-rays, one could deduce the way in which the atoms were arranged in sheets parallel to these faces. The intersections of these sheets pinned down the positions of the atoms in space.… It was like discovering an alluvial gold field with nuggets lying around waiting to be picked up.… It was a glorious time when we worked far into every night with new worlds unfolding before us in the silent laboratory.

Then one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.

There is no absurdity in theology so great that you cannot parallel it by a greater absurdity in Nature.

Those who suggest that the “dark ages” were a time of violence and superstition would do well to remember the appalling cruelties of our own time, truly without parallel in past ages, as well as the fact that the witch-hunts were not strictly speaking a medieval phenomenon but belong rather to the so-called Renaissance.

Though the parallel is not complete, it is safe to say that science will never touch them unaided by its practical applications. Its wonders may be catalogued for purposes of education, they may be illustrated by arresting experiments, by numbers and magnitudes which startle or fatigue the imagination but they will form no familiar portion of the intellectual furniture of ordinary men unless they be connected, however remotely, with the conduct of ordinary life.

Till the fifteenth century little progress appears to have been made in the science or practice of music; but since that era it has advanced with marvelous rapidity, its progress being curiously parallel with that of mathematics, inasmuch as great musical geniuses appeared suddenly among different nations, equal in their possession of this special faculty to any that have since arisen. As with the mathematical so with the musical faculty it is impossible to trace any connection between its possession and survival in the struggle for existence.

We [may] answer the question: “Why is snow white?” by saying, “For the same reason that soap-suds or whipped eggs are white”—in other words, instead of giving the reason for a fact, we give another example of the same fact. This offering a similar instance, instead of a reason, has often been criticised as one of the forms of logical depravity in men. But manifestly it is not a perverse act of thought, but only an incomplete one. Furnishing parallel cases is the necessary first step towards abstracting the reason imbedded in them all.

We can trace the development of a nervous system, and correlate with it the parallel phenomena of sensation and thought. We see with undoubting certainty that they go hand in hand. But we try to soar in a vacuum the moment we seek to comprehend the connexion between them … Man the object is separated by an impassable gulf from man the subject.

We come finally, however, to the relation of the ideal theory to real world, or “real” probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: “If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician”. In practice he is apt to say: “try this; if it works that will justify it”. But now he is not merely philosophizing; he is committing the characteristic fallacy. Inductive experience that the system works is not evidence.

We may conclude, that the flux and reflux of the ocean have produced all the mountains, valleys, and other inequalities on the surface of the earth; that currents of the sea have scooped out the valleys, elevated the hills, and bestowed on them their corresponding directions; that that same waters of the ocean, by transporting and depositing earth, &c., have given rise to the parallel strata; that the waters from the heavens gradually destroy the effects of the sea, by continually diminishing the height of the mountains, filling up the valleys, and choking the mouths of rivers; and, by reducing every thing to its former level, they will, in time, restore the earth to the sea, which, by its natural operations, will again create new continents, interspersed with mountains and valleys, every way similar to those we inhabit.

We see only the simple motion of descent, since that other circular one common to the Earth, the tower, and ourselves remains imperceptible. There remains perceptible to us only that of the stone, which is not shared by us; and, because of this, sense shows it as by a straight line, always parallel to the tower, which is built upright and perpendicular upon the terrestrial surface.

When we make the photon meet a tourmaline crystal, we are subjecting it to an observation. We are observing whether it is polarised parallel or perpendicular to the optic axis. The effect of making the observation is to force the photon entirely into the state of perpendicular polarisation. It has to make a sudden jump from being partly in each of these two states to being entirely in one or other of them. Which of the two states it will jump into cannot be predicted, but is governed only by probability laws. If it jumps into the perpendicular state it passes through the crystal and appears on the other side preserving this state of polarisation.

While no one can ascribe a single weather event to climate change with any degree of scientific certainty, higher maximum temperatures are one of the most predictable impacts of accelerated global warming, and the parallels—between global climate change and global terrorism—are becoming increasingly obvious.

Whoever wishes to acquire a deep acquaintance with Nature must observe that there are analogies which connect whole branches of science in a parallel manner, and enable us to infer of one class of phenomena what we know of another. It has thus happened on several occasions that the discovery of an unsuspected analogy between two branches of knowledge has been the starting point for a rapid course of discovery.

Why are you so sure parallel lines exist?
Believe nothing, merely because you have been told it, or because it is traditional, or because you have imagined it.