“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?”

[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.

[In childhood, to overcome fear, the] need took me back again and again to a sycamore tree rising from the earth at the edge of a ravine. It was a big, old tree that had grown out over the ravine, so that when you climbed it, you looked straight down fifty feet or more. Every time I climbed that tree, I forced myself to climb to the last possible safe limb and then look down. Every time I did it, I told myself I’d never do it again. But I kept going back because it scared me and I had to know I could overcome that.

The Redwoods

Here, sown by the Creator's hand,
In serried ranks, the Redwoods stand;
No other clime is honored so,
No other lands their glory know.

The greatest of Earth's living forms,
Tall conquerors that laugh at storms;
Their challenge still unanswered rings,
Through fifty centuries of kings.

The nations that with them were young,
Rich empires, with their forts far-flung,
Lie buried now—their splendor gone;
But these proud monarchs still live on.

So shall they live, when ends our day,
When our crude citadels decay;
For brief the years allotted man,
But infinite perennials' span.

This is their temple, vaulted high,
And here we pause with reverent eye,
With silent tongue and awe-struck soul;
For here we sense life's proper goal;

To be like these, straight, true and fine,
To make our world, like theirs, a shrine;
Sink down, oh traveler, on your knees,
God stands before you in these trees.

Toutes les fois que dans une équation finale on trouve deux quantités inconnues, on a un lieu, l'extrémité de l'une d’elles décrivant une ligne droite ou courbe. La ligne droite est simple et unique dans son genre; les espèces des courbes sont en nombre indéfini, cercle, parabole, hyperbole, ellipse, etc.
Whenever two unknown magnitudes appear in a final equation, we have a locus, the extremity of one of the unknown magnitudes describing a straight line or a curve. The straight line is simple and unique; the classes of curves are indefinitely many,—circle, parabola, hyperbola, ellipse, etc.

A bird maintains itself in the air by imperceptible balancing, when near to the mountains or lofty ocean crags; it does this by means of the curves of the winds which as they strike against these projections, being forced to preserve their first impetus bend their straight course towards the sky with divers revolutions, at the beginning of which the birds come to a stop with their wings open, receiving underneath themselves the continual buffetings of the reflex courses of the winds.

A drop from the nose of Fleming, who had a cold, fell onto an agar plate where large yellow colonies of a contaminant had grown, and lysosyme was discovered. He made this important discovery because when he saw that the colonies of the contaminant were fading, his mind went straight to the right cause of the phenomenon he was observing—that the drop from his nose contained a lytic substance. And also immediately, he thought that this substance might be present in many secretions and tissues of the body. And he found this was so—the substance was in tears, saliva, leucocytes, skin, fingernails, mother's milk—thus very widely distributed in amounts and also in plants.

A historical fact is rather like the flamingo that Alice in Wonderland tried to use as a croquet mallet. As soon as she got its neck nicely straightened out and was ready to hit the ball, it would turn and look at her with a puzzled expression, and any biographer knows that what is called a “fact” has a way of doing the same.

A mathematician thinks that two points are enough to define a straight line, while a physicist wants more data.

A mile and a half from town, I came to a grove of tall cocoanut trees, with clean, branchless stems reaching straight up sixty or seventy feet and topped with a spray of green foliage sheltering clusters of cocoanuts—not more picturesque than a forest of colossal ragged parasols, with bunches of magnified grapes under them, would be. I once heard a grouty northern invalid say that a cocoanut tree might be poetical, possibly it was; but it looked like a feather-duster struck by lightning. I think that describes it better than a picture—and yet, without any question, there is something fascinating about a cocoanut tree—and graceful, too.

A sentence should read as if its author, had he held a plow instead of a pen, could have drawn a furrow deep and straight to the end.

A small cabin stands in the Glacier Peak Wilderness, about a hundred yards off a trail that crosses the Cascade Range. In midsummer, the cabin looked strange in the forest. It was only twelve feet square, but it rose fully two stories and then had a high and steeply peaked roof. From the ridge of the roof, moreover, a ten-foot pole stuck straight up. Tied to the top of the pole was a shovel. To hikers shedding their backpacks at the door of the cabin on a cold summer evening—as the five of us did—it was somewhat unnerving to look up and think of people walking around in snow perhaps thirty-five feet above, hunting for that shovel, then digging their way down to the threshold.

A tree nowhere offers a straight line or a regular curve, but who doubts that root, trunk, boughs, and leaves embody geometry?

All that stuff I was taught about evolution, embryology, Big Bang theory, all that is lies straight from the pit of hell. It’s lies to try to keep me and all the folks who are taught that from understanding that they need a savior.
[Revealing his anti-science views, contrary to the qualifications needed to make important public policy on matters of science.]

Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.

But nature is remarkably obstinate against purely logical operations; she likes not schoolmasters nor scholastic procedures. As though she took a particular satisfaction in mocking at our intelligence, she very often shows us the phantom of an apparently general law, represented by scattered fragments, which are entirely inconsistent. Logic asks for the union of these fragments; the resolute dogmatist, therefore, does not hesitate to go straight on to supply, by logical conclusions, the fragments he wants, and to flatter himself that he has mastered nature by his victorious intelligence.

Can science ever be immune from experiments conceived out of prejudices and stereotypes, conscious or not? (Which is not to suggest that it cannot in discrete areas identify and locate verifiable phenomena in nature.) I await the study that says lesbians have a region of the hypothalamus that resembles straight men and I would not be surprised if, at this very moment, some scientist somewhere is studying brains of deceased Asians to see if they have an enlarged ‘math region’ of the brain.

Careful and correct use of language is a powerful aid to straight thinking, for putting into words precisely what we mean necessitates getting our own minds quite clear on what we mean.

Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.

Every body continues in its state of rest or uniform motion in a straight line, except in so far as it doesn’t. … The suggestion that the body really wanted to go straight but some mysterious agent made it go crooked is picturesque but unscientific.

Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.

Every cent we earn from Crocodile Hunter goes straight back into conservation. Every single cent.

Everything you’ve learned in school as “obvious” becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There’s not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines.

Four circles to the kissing come,
The smaller are the benter.
The bend is just the inverse of
The distance from the centre.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of squares of all four bends
Is half the square of their sum.

He [Robert Boyle] is very tall (about six foot high) and straight, very temperate, and vertuouse, and frugall: a batcheler; keepes a Coach; sojournes with his sister, the Lady Ranulagh. His greatest delight is Chymistrey. He has at his sister’s a noble laboratory, and severall servants (Prentices to him) to look to it. He is charitable to ingeniose men that are in want, and foreigne Chymists have had large proofe of his bountie, for he will not spare for cost to get any rare Secret.

He made an instrument to know If the moon shine at full or no;
That would, as soon as e’er she shone straight,
Whether ‘twere day or night demonstrate;
Tell what her d’ameter to an inch is,
And prove that she’s not made of green cheese.

Impressed force is the action exerted on a body to change its state either of resting or of moving uniformly straight forward.

Improvement makes straight road, but the crooked roads without improvement are roads of genius.

In all spheres of science, art, skill, and handicraft it is never doubted that, in order to master them, a considerable amount of trouble must be spent in learning and in being trained. As regards philosophy, on the contrary, there seems still an assumption prevalent that, though every one with eyes and fingers is not on that account in a position to make shoes if he only has leather and a last, yet everybody understands how to philosophize straight away, and pass judgment on philosophy, simply because he possesses the criterion for doing so in his natural reason.

In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.

In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite… Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a mathematical teaser, and yet its consequences lead straight to Goya’s Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.

Inherent force of matter is the power of resisting by which every body, so far as it is able, perseveres in its state either of resting or of moving uniformly straight forward.

It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.

It is difficult to conceive a grander mass of vegetation:—the straight shafts of the timber-trees shooting aloft, some naked and clean, with grey, pale, or brown bark; others literally clothed for yards with a continuous garment of epiphytes, one mass of blossoms, especially the white Orchids Caelogynes, which bloom in a profuse manner, whitening their trunks like snow. More bulky trunks were masses of interlacing climbers, Araliaceae, Leguminosae, Vines, and Menispermeae, Hydrangea, and Peppers, enclosing a hollow, once filled by the now strangled supporting tree, which has long ago decayed away. From the sides and summit of these, supple branches hung forth, either leafy or naked; the latter resembling cables flung from one tree to another, swinging in the breeze, their rocking motion increased by the weight of great bunches of ferns or Orchids, which were perched aloft in the loops. Perpetual moisture nourishes this dripping forest: and pendulous mosses and lichens are met with in profusion.

Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

Lawyers have to make a living and can only do so by inducing people to believe that a straight line is crooked. This accounts for their penchant for politics, where they can usually find everything crooked enough to delight their hearts.

Mathematics … certainly would never have come into existence if mankind had known from the beginning that in all nature there is no perfectly straight line, no true circle, no standard of measurement.

Medicinal discovery,
It moves in mighty leaps,
It leapt straight past the common cold
And gave it us for keeps.

Meton: With the straight ruler I set to work
To make the circle four-cornered.

Nature creates curved lines while humans create straight lines.

Nature, the parent of all things, designed the human backbone to be like a keel or foundation. It is because we have a backbone that we can walk upright and stand erect. But this was not the only purpose for which Nature provided it; here, as elsewhere, she displayed great skill in turning the construction of a single member to a variety of different uses.
It Provides a Path for the Spinal Marrow, Yet is Flexible.
Firstly, she bored a hole through the posterior region of the bodies of all the vertebrae, thus fashioning a suitable pathway for the spinal marrow which would descend through them.
Secondly, she did not make the backbone out of one single bone with no joints. Such a unified construction would have afforded greater stability and a safer seat for the spinal marrow since, not having joints, the column could not have suffered dislocations, displacements, or distortions. If the Creator of the world had paid such attention to resistance to injury and had subordinated the value and importance of all other aims in the fabric of parts of the body to this one, he would certainly have made a single backbone with no joints, as when someone constructing an animal of wood or stone forms the backbone of one single and continuous component. Even if man were destined only to bend and straighten his back, it would not have been appropriate to construct the whole from one single bone. And in fact, since it was necessary that man, by virtue of his backbone, be able to perform a great variety of movements, it was better that it be constructed from many bones, even though as a result of this it was rendered more liable to injury.

No force however great can stretch a cord however fine into an horizontal line which is accurately straight: there will always be a bending downward.

Numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

Our knowledge of stars and interstellar matter must be based primarily on the electromagnetic radiation which reaches us. Nature has thoughtfully provided us with a universe in which radiant energy of almost all wave lengths travels in straight lines over enormous distances with usually rather negligible absorption.

Peter Atkins, in his wonderful book Creation Revisited, uses a … personification when considering the refraction of a light beam, passing into a medium of higher refractive index which slows it down. The beam behaves as if trying to minimize the time taken to travel to an end point. Atkins imagines it as a lifeguard on a beach racing to rescue a drowning swimmer. Should he head straight for the swimmer? No, because he can run faster than he can swim and would be wise to increase the dry-land proportion of his travel time. Should he run to a point on the beach directly opposite his target, thereby minimizing his swimming time? Better, but still not the best. Calculation (if he had time to do it) would disclose to the lifeguard an optimum intermediate angle, yielding the ideal combination of fast running followed by inevitably slower swimming. Atkins concludes:
That is exactly the behaviour of light passing into a denser medium. But how does light know, apparently in advance, which is the briefest path? And, anyway, why should it care?
He develops these questions in a fascinating exposition, inspired by quantum theory.

Physics is imagination in a straight jacket.

Professor Brown: “Since this slide was made,” he opined, “My students have re-examined the errant points and I am happy to report that all fall close to the [straight] line.” Questioner: “Professor Brown, I am delighted that the points which fell off the line proved, on reinvestigation, to be in compliance. I wonder, however, if you have had your students reinvestigate all these points that previously fell on the line to find out how many no longer do so?”

Professor Cayley has since informed me that the theorem about whose origin I was in doubt, will be found in Schläfli’s De Eliminatione. This is not the first unconscious plagiarism I have been guilty of towards this eminent man whose friendship I am proud to claim. A more glaring case occurs in a note by me in the Comptes Rendus, on the twenty-seven straight lines of cubic surfaces, where I believe I have followed (like one walking in his sleep), down to the very nomenclature and notation, the substance of a portion of a paper inserted by Schlafli in the Mathematical Journal, which bears my name as one of the editors upon the face.

Progress has not followed a straight ascending line, but a spiral with rhythms of progress and retrogression, of evolution and dissolution.

Scientists are the easiest to fool. ... They think in straight, predictable, directable, and therefore misdirectable, lines. The only world they know is the one where everything has a logical explanation and things are what they appear to be. Children and conjurors—they terrify me. Scientists are no problem; against them I feel quite confident.

So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernoulli, Herapath, Joule, Kronig, Clausius, &c., have shewn that the relations between pressure, temperature and density in a perfect gas can be explained by supposing the particles move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure. (1860)

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.

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

That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

The Earth obey’d and straight
Op’ning her fertile womb, teem’d at a birth Innumerous living creatures, perfect forms,
Limb’d and full grown.

The longing to behold this pre-established harmony [of phenomena and theoretical principles] is the source of the inexhaustible patience and perseverance with which Planck has devoted himself ... The state of mind which enables a man to do work of this kind is akin to that of the religious worshiper or the lover; the daily effort comes from no deliberate intention or program, but straight from the heart.

The path isn’t a straight line; it’s a spiral. You continually come back to things you thought you understood and see deeper truths.

The phenomena in these exhausted tubes reveal to physical science a new world—a world where matter may exist in a fourth state, where the corpuscular theory of light may be true, and where light does not always move in straight lines, but where we can never enter, and with which we must be content to observe and experiment from the outside.

The progress of Science is generally regarded as a kind of clean, rational advance along a straight ascending line; in fact it has followed a zig-zag course, at times almost more bewildering than the evolution of political thought. The history of cosmic theories, in particular, may without exaggeration be called a history of collective obsessions and controlled schizophrenias; and the manner in which some of the most important individual discoveries were arrived at reminds one more of a sleepwalker’s performance than an electronic brain’s.

The publication of the Darwin and Wallace papers in 1858, and still more that of the 'Origin' in 1859, had the effect upon them of the flash of light, which to a man who has lost himself in a dark night, suddenly reveals a road which, whether it takes him straight home or not, certainly goes his way. That which we were looking for, and could not find, was a hypothesis respecting the origin of known organic forms, which assumed the operation of no causes but such as could be proved to be actually at work. We wanted, not to pin our faith to that or any other speculation, but to get hold of clear and definite conceptions which could be brought face to face with facts and have their validity tested. The 'Origin' provided us with the working hypothesis we sought.

The sun’s rays proceed from the sun along straight lines and are reflected from every polished object at equal angles, i.e. the reflected ray subtends, together with the line tangential to the polished object which is in the plane of the reflected ray, two equal angles. Hence it follows that the ray reflected from the spherical surface, together with the circumference of the circle which is in the plane of the ray, subtends two equal angles. From this it also follows that the reflected ray, together with the diameter of the circle, subtends two equal angles. And every ray which is reflected from a polished object to a point produces a certain heating at that point, so that if numerous rays are collected at one point, the heating at that point is multiplied: and if the number of rays increases, the effect of the heat increases accordingly.

The vast outpourings of publications by Professor Djerassi and his cohorts marks him as one of the most prolific scientific writers of our day... a plot of N, the papers published by Professor Djerassi in a given year, against T, the year (starting with 1945, T = 0) gives a good straight-line relationship. This line follows the equation N = 2.413T + 1.690 ... Assuming that the inevitable inflection point on the logistic curve is still some 10 years away, this equation predicts (a) a total of about 444 papers by the end of this year, (b) the average production of one paper per week or more every year beginning in 1966, and (c) the winning of the all-time productivity world championship in 10 years from now, in 1973. In that year Professor Djerassi should surpass the record of 995 items held by ...

Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it.

Time is awake when all things sleep.
Time stands straight when all things fall.
Time shuts in all and will not be shut.
Is, was, and shall be are Time’s children.
O Reason! be witness! be stable!

To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science. There is nothing for the investigator to do but go straight on, 'to explore up and down, inch by inch, with the taper his reason;' to follow the light wherever it may lead, even should it at times resemble a will-o'-the-wisp.
Referring to his interest in psychical (spiritual) research.

To work our railways, even to their present extent, there must be at least 5,000 locomotive engines; and supposing an engine with its tender to measure only 35 feet, it will be seen, that the whole number required to work our railway system would extend, in one straight line, over 30 miles, or the whole distance from London to Chatham.

We need people who can see straight ahead and deep into the problems. Those are the experts. But we also need peripheral vision and experts are generally not very good at providing peripheral vision.

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.

What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.

When first I applied my mind to Mathematics I read straight away most of what is usually given by the mathematical writers, and I paid special attention to Arithmetic and Geometry because they were said to be the simplest and so to speak the way to all the rest. But in neither case did I then meet with authors who fully satisfied me. I did indeed learn in their works many propositions about numbers which I found on calculation to be true. As to figures, they in a sense exhibited to my eyes a great number of truths and drew conclusions from certain consequences. But they did not seem to make it sufficiently plain to the mind itself why these things are so, and how they discovered them. Consequently I was not surprised that many people, even of talent and scholarship, should, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very outset from learning them. … But when I afterwards bethought myself how it could be that the earliest pioneers of Philosophy in bygone ages refused to admit to the study of wisdom any one who was not versed in Mathematics … I was confirmed in my suspicion that they had knowledge of a species of Mathematics very different from that which passes current in our time.

When I was eight, I played Little League. I was on first; I stole third; I went straight across. Earlier that week, I learned that the shortest distance between two points was a direct line. I took advantage of that knowledge.

When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.

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.

Why is geometry often described as “cold” and “dry?” One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line… Nature exhibits not simply a higher degree but an altogether different level of complexity.

You don't think progress goes in a straight line, do you? Do you recognize that it is an ascending, accelerating, maybe even exponential curve? It takes hell's own time to get started, but when it goes it goes like a bomb.