...for the animals, which we resemble and which would be our equals if we did not have reason, do not reflect upon the actions or the passions of their external or internal senses, and do not know what is color, odor or sound, or if there is any differences between these objects, to which they are moved rather than moving themselves there. This comes about by the force of the impression that the different objects make on their organs and on their senses, for they cannot discern if it is more appropriate to go and drink or eat or do something else, and they do not eat or drink or do anything else except when the presence of objects or the animal imagination [l'imagination brutalle], necessitates them and transports them to their objects, without their knowing what they do, whether good or bad; which would happen to us just as to them if we were destitute of reason, for they have no enlightenment except what they must have to take their nourishment and to serve us for the uses to which God has destined them.
[Arguing the uniqueness of man by regarding animals to be merely automatons.].

Ode to The Amoeba
Recall from Time's abysmal chasm
That piece of primal protoplasm
The First Amoeba, strangely splendid,
From whom we're all of us descended.
That First Amoeba, weirdly clever,
Exists today and shall forever,
Because he reproduced by fission;
He split himself, and each division
And subdivision deemed it fitting
To keep on splitting, splitting, splitting;
So, whatsoe'er their billions be,
All, all amoebas still are he.
Zoologists discern his features
In every sort of breathing creatures,
Since all of every living species,
No matter how their breed increases
Or how their ranks have been recruited,
From him alone were evoluted.
King Solomon, the Queen of Sheba
And Hoover sprang from that amoeba;
Columbus, Shakespeare, Darwin, Shelley
Derived from that same bit of jelly.
So famed is he and well-connected,
His statue ought to be erected,
For you and I and William Beebe
Are undeniably amoebae!

~~[Attributed, authorship undocumented]~~ Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.

A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one’s ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop these laws is based entirely on a fact, whose existence has hitherto been vaguely discerned rather than demonstrated. This fact is that in all minerals which belong to the same species, these little solids, which are the crystal elements and which I call their integrant molecules, have an invariable form, in which the faces lie in the direction of the natural fracture surfaces corresponding to the mechanical division of the crystals. Their angles and dimensions are derived from calculations combined with observation.

An eye critically nice will discern in every colour a tendency to some other colour, according as it is influenced by light, shade, depth or diluteness; nor is this the case only in the inherent colours of pigments, &c. but it is so also in the transient colours of the prism, &c. Hence blue in its depth inclines to purple; deep-yellow to orange, &c.; nor is it practicable to realize these colours to the satisfaction of the critical eye,-since perfect colours, like perfect geometrical figures, are pure ideals. My examples of colours are therefore quite as adequate to their office of illustrating and distinguishing, as the figure of an angle inclining to the acute or obtuse, instead of a perfect right angle, or middle form, would be in illustrating the conception of an angle in general.

And when with excellent Microscopes I discern in otherwise invisible Objects the Inimitable Subtlety of Nature’s Curious Workmanship; And when, in a word, by the help of Anatomicall Knives, and the light of Chymicall Furnaces, I study the Book of Nature, and consult the Glosses of Aristotle, Epicurus, Paracelsus, Harvey, Helmont, and other learn'd Expositors of that instructive Volumne; I find my self oftentimes reduc’d to exclaim with the Psalmist, How manifold are thy works, O Lord? In wisdom hast thou made them all.

As we discern a fine line between crank and genius, so also (and unfortunately) we must acknowledge an equally graded trajectory from crank to demagogue. When people learn no tools of judgment and merely follow their hopes, the seeds of political manipulation are sown.

Believing, as I do, in the continuity of nature, I cannot stop abruptly where our microscopes cease to be of use. Here the vision of the mind authoritatively supplements the vision of the eye. By a necessity engendered and justified by science I cross the boundary of the experimental evidence, and discern in that Matter which we, in our ignorance of its latent powers, and notwithstanding our professed reverence for its Creator, have hitherto covered with opprobrium, the promise and potency of all terrestrial Life.

Consider the very roots of our ability to discern truth. Above all (or perhaps I should say “underneath all”), common sense is what we depend on—that crazily elusive, ubiquitous faculty we all have to some degree or other. … If we apply common sense to itself over and over again, we wind up building a skyscraper. The ground floor of the structure is the ordinary common sense we all have, and the rules for building news floors are implicit in the ground floor itself. However, working it all out is a gigantic task, and the result is a structure that transcends mere common sense.

Do not … keep children to their studies by compulsion but by play. That will also better enable you to discern the natural capacities of each

During my stay in London I resided for a considerable time in Clapham Road in the neighbourhood of Clapham Common... One fine summer evening I was returning by the last bus 'outside' as usual, through the deserted streets of the city, which are at other times so full of life. I fell into a reverie (Träumerei), and 10, the atoms were gambolling before my eyes! Whenever, hitherto, these diminutive beings had appeared to me, they had always been in motion: but up to that time I had never been able to discern the nature of their motion. Now, however, I saw how, frequently, two smaller atoms united to form a pair: how the larger one embraced the two smaller ones: how still larger ones kept hold of three or even four of the smaller: whilst the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain, dragging the smaller ones after them but only at the ends of the chain. I saw what our past master, Kopp, my highly honoured teacher and friend has depicted with such charm in his Molekular-Welt: but I saw it long before him. The cry of the conductor 'Clapham Road', awakened me from my dreaming: but I spent part of the night in putting on paper at least sketches of these dream forms. This was the origin of the 'Structural Theory'.

Even the humblest creature has to know how to react to the difference between food and toxin if it's to survive. ... Life and some level of intelligent behavior—discerning and doing what's best for one's survival—appear to go hand in hand.

For the first time there was constructed with this machine [locomotive engine] a self-acting mechanism in which the interplay of forces took shape transparently enough to discern the connection between the heat generated and the motion produced. The great puzzle of the vital force was also immediately solved for the physiologist in that it became evident that it is more than a mere poetic comparison when one conceives of the coal as the food of the locomotive and the combustion as the basis for its life.

Fossil bones and footsteps and ruined homes are the solid facts of history, but the surest hints, the most enduring signs, lie in those miniscule genes. For a moment we protect them with our lives, then like relay runners with a baton, we pass them on to be carried by our descendents. There is a poetry in genetics which is more difficult to discern in broken bomes, and genes are the only unbroken living thread that weaves back and forth through all those boneyards.

He has something demoniacal in him, who can discern a law, or couple two facts.

He that believes, without having any Reason for believing, may be in love with his own Fancies; but neither seeks Truth as he ought, nor pays the Obedience due to his Maker, who would have him use those discerning Faculties he has given him, to keep him out of Mistake and Errour.

I confess, that after I began … to discern how useful mathematicks may be made to physicks, I have often wished that I had employed about the speculative part of geometry, and the cultivation of the specious Algebra I had been taught very young, a good part of that time and industry, that I had spent about surveying and fortification (of which I remember I once wrote an entire treatise) and other parts of practick mathematicks.

I took a good clear piece of Cork and with a Pen-knife sharpen'd as keen as a Razor, I cut a piece of it off, and thereby left the surface of it exceeding smooth, then examining it very diligently with a Microscope, me thought I could perceive it to appear a little porous; but I could not so plainly distinguish them, as to be sure that they were pores, much less what Figure they were of: But judging from the lightness and yielding quality of the Cork, that certainly the texture could not be so curious, but that possibly, if I could use some further diligence, I might find it to be discernable with a Microscope, I with the same sharp Penknife, cut off from the former smooth surface an exceeding thin piece of it with a deep plano-convex Glass, I could exceedingly plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular; yet it was not unlike a Honey-comb in these particulars.
First, in that it had a very little solid substance, in comparison of the empty cavity that was contain'd between, ... for the Interstitia or walls (as I may so call them) or partitions of those pores were neer as thin in proportion to their pores as those thin films of Wax in a Honey-comb (which enclose and constitute the sexangular cells) are to theirs.
Next, in that these pores, or cells, were not very deep, but constituted of a great many little Boxes, separated out of one continued long pore, by certain Diaphragms...
I no sooner discerned these (which were indeed the first microscopical pores I ever saw, and perhaps, that were ever seen, for I had not met with any Writer or Person, that had made any mention of them before this) but me thought I had with the discovery of them, presently hinted to me the true and intelligible reason of all the Phænomena of Cork.

If the juices of the body were more chymically examined, especially by a naturalist, that knows the ways of making fixed bodies volatile, and volatile fixed, and knows the power of the open air in promoting the former of those operations; it is not improbable, that both many things relating to the nature of the humours, and to the ways of sweetening, actuating, and otherwise altering them, may be detected, and the importance of such discoveries may be discerned.

In the preface to his great History of Europe, H. A. L. Fisher wrote: “Men wiser than and more learned than I have discerned in history a plot, a rhythm, a predetermined pattern. These harmonies are concealed from me. I can see only one emergency following upon another as wave follows upon wave …” It seems to me that the same is true of the much older [geological stratigraphical] history of Europe.

It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have “collected data” that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler.

Our failure to discern a universal good does not record any lack of insight or ingenuity, but merely demonstrates that nature contains no moral messages framed in human terms. Morality is a subject for philosophers, theologians, students of the humanities, indeed for all thinking people. The answers will not be read passively from nature; they do not, and cannot, arise from the data of science. The factual state of the world does not teach us how we, with our powers for good and evil, should alter or preserve it in the most ethical manner.

Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”

Science is the attempt to discern the order that underlies the chaos of nature; art is the attempt to discern the order that underlies the chaos of man.

Tapestries are made by many artisans working together. The contributions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics.

The discerning man who acknowledges his limitations is not far off perfection.

The inherent unpredictability of future scientific developments—the fact that no secure inference can be drawn from one state of science to another—has important implications for the issue of the limits of science. It means that present-day science cannot speak for future science: it is in principle impossible to make any secure inferences from the substance of science at one time about its substance at a significantly different time. The prospect of future scientific revolutions can never be precluded. We cannot say with unblinking confidence what sorts of resources and conceptions the science of the future will or will not use. Given that it is effectively impossible to predict the details of what future science will accomplish, it is no less impossible to predict in detail what future science will not accomplish. We can never confidently put this or that range of issues outside “the limits of science”, because we cannot discern the shape and substance of future science with sufficient clarity to be able to say with any assurance what it can and cannot do. Any attempt to set “limits” to science—any advance specification of what science can and cannot do by way of handling problems and solving questions—is destined to come to grief.

The intellect is a cleaver; it discerns and rifts its way into the secret of things.

The method of science depends on our attempts to describe the world with simple theories: theories that are complex may become untestable, even if they happen to be true. Science may be described as the art of systematic over-simplification—the art of discerning what we may with advantage omit.

The philosophy of mathematics still consists essentially in discerning the rational order of dependence of as many abstract truths as the sagacity of inventive minds has successfully and laboriously discovered, often by very roundabout means.

The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and we must descend from laws to consequences, by the deductive and synthetic way. We must gather and group appearances, until the scientific imagination discerns their hidden law, and unity arises from variety; and then from unity must reduce variety, and force the discovered law to utter its revelations of the future.

There are many arts and sciences of which a miner should not be ignorant. First there is Philosophy, that he may discern the origin, cause, and nature of subterranean things; for then he will be able to dig out the veins easily and advantageously, and to obtain more abundant results from his mining. Secondly there is Medicine, that he may be able to look after his diggers and other workman ... Thirdly follows astronomy, that he may know the divisions of the heavens and from them judge the directions of the veins. Fourthly, there is the science of Surveying that he may be able to estimate how deep a shaft should be sunk … Fifthly, his knowledge of Arithmetical Science should be such that he may calculate the cost to be incurred in the machinery and the working of the mine. Sixthly, his learning must comprise Architecture, that he himself may construct the various machines and timber work required underground … Next, he must have knowledge of Drawing, that he can draw plans of his machinery. Lastly, there is the Law, especially that dealing with metals, that he may claim his own rights, that he may undertake the duty of giving others his opinion on legal matters, that he may not take another man’s property and so make trouble for himself, and that he may fulfil his obligations to others according to the law.

Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.

To the scientist, nature is always and merely a 'phenomenon,' not in the sense of being defective in reality, but in the sense of being a spectacle presented to his intelligent observation; whereas the events of history are never mere phenomena, never mere spectacles for contemplation, but things which the historian looks, not at, but through, to discern the thought within them.

We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.