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.

As knowledge advances, science ceases to scoff at religion; and religion ceases to frown on science. The hour of mockery by the one, and of reproof by the other, is passing away. Henceforth, they will dwell together in unity and goodwill. They will mutually illustrate the wisdom, power, and grace of God. Science will adorn and enrich religion; and religion will ennoble and sanctify science.

Evolution is the conviction that organisms developed their current forms by an extended history of continual transformation, and that ties of genealogy bind all living things into one nexus. Panselectionism is a denial of history, for perfection covers the tracks of time. A perfect wing may have evolved to its current state, but it may have been created just as we find it. We simply cannot tell if perfection be our only evidence. As Darwin himself understood so well, the primary proofs of evolution are oddities and imperfections that must record pathways of historical descent–the panda’s thumb and the flamingo’s smile of my book titles (chosen to illustrate this paramount principle of history).

I am sure the daisies and buttercups have as little use for the science of Geometry as I, in spite of the fact that they so beautifully illustrate its principles.

In the real changes which animals undergo during their embryonic growth, in those external transformations as well as in those structural modifications within the body, we have a natural scale to measure the degree or the gradation of those full grown animals which corresponds in their external form and in their structure, to those various degrees in the metamorphoses of animals, as illustrated by embryonic changes, a real foundation for zoological classification.

Learning obscures as well as illustrates; it heaps up chaff when there is no more wheat.

More than any other the practitioner of medicine may illustrate … that we are here not to get all we can out of life for ourselves, but to try to make the lives of others happier.

The “grand old Book of God still stands”, and this grand old earth, the more its leaves are turned over and pondered, the more it will sustain, enlighten and illustrate the Sacred word.

The emancipation of logic from the yoke of Aristotle very much resembles the emancipation of geometry from the bondage of Euclid; and, by its subsequent growth and diversification, logic, less abundantly perhaps but not less certainly than geometry, has illustrated the blessings of freedom.

The Jewish scriptures admirably illustrate the development from the religion of fear to moral religion, a development continued in the New Testament. The religions of all civilized peoples, especially the peoples of the Orient, are primarily moral religions. The development from a religion of fear to moral religion is a great step in peoples’ lives. And yet, that primitive religions are based entirely on fear and the religions of civilized peoples purely on morality is a prejudice against which we must be on our guard. The truth is that all religions are a varying blend of both types, with this differentiation: that on the higher levels of social life the religion of morality predominates.

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals.

The visible figures by which principles are illustrated should, so far as possible, have no accessories. They should be magnitudes pure and simple, so that the thought of the pupil may not be distracted, and that he may know what features of the thing represented he is to pay attention to.

There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.

To illustrate the apparent contrast between statistics and truth … may I quote a remark I once overheard: “There are three kinds of lies: white lies, which are justifiable; common lies—these have no justification; and statistics.” Our meaning is similar when we say: “Anything can be proved by figures”; or, modifying a well-known quotation from Goethe, with numbers “all men may contend their charming systems to defend.”