“A common monetary standard will be established, with the consent of the various governments, by which industrial transactions will be greatly facilitated. Three spheres made respectively of gold, silver, and platinum, and each weighing fifty grammes, would differ sufficiently in value for the purpose. The sphere should have a small flattened base, and on the great circle parallel to it the Positivist motto would be inscribed. At the pole would be the image of the immortal Charlemagne, the founder of the Western Republic, and round the image his name would be engraved, in its Latin form, Carolus; that name, respected as it is by all nations of Europe alike, would be the common appellation of the universal monetary standard.”

Source: A General View of Positivism (1848, 1856), p. 430

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Auguste Comte23

French philosopher 1798–1857

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“The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury.”

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“If the world as a whole returned to the gold standard there would be such fluctuations in the value of gold that it would very soon prove impractical.
Today an international gold standard could only mean that a few countries would maintain a real gold standard. The other countries would hang on to the system through a gold exchange standard — where the currency isn't really redeemable in gold but the government attempts to keep a fixed rate between its currency and gold.”

Friedrich Hayek (1899–1992) Austrian and British economist and Nobel Prize for Economics laureate

1980s and later, Interview in Silver & Gold Report (1980)

“A genius and an Apostle are qualitatively different, they are definitions which each belong in their own spheres: the sphere of immanence, and the sphere of transcendence.”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Source: 1840s, Two Ethical-Religious Minor Essays (1849), P. 90-91

“Proposition 1. Two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line drawn through the centres of the spheres is at right angles to each of the circles in which the surface of the cylinder, or of the cone, touches the spheres.”

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“It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. …the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection… analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". …If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels.”

Hans Reichenbach (1891–1953) American philosopher

The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.
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“That instrument(The Constitution) meant that its coordinate branches should be checks on each other. But the opinion which gives to the judges the right to decide what laws are constitutional and what not, not only for themselves in their own sphere of action but for the Legislature and Executive also in their spheres, would make the Judiciary a despotic branch.”

Thomas Jefferson (1743–1826) 3rd President of the United States of America

Letter to Abigail Adams about the Sedition Acts (1804) https://founders.archives.gov/documents/Jefferson/99-01-02-0348 <br class="br">1800s, First Presidential Administration (1801&ndash;1805) <br class="br">Context: You seem to think it devolved on the judges to decide on the validity of the sedition law. but nothing in the constitution has given them a right to decide for the executive, more than to the Executive to decide for them. Both magistracies are equally independant in the sphere of action assigned to them. The judges, believing the law constitutional, had a right to pass a sentence of fine and imprisonment; because that power was placed in their hands by the constitution. But the Executive, believing the law to be unconstitutional, was bound to remit the execution of it; because that power has been confided to him by the constitution That instrument(The Constitution) meant that its coordinate branches should be checks on each other. But the opinion which gives to the judges the right to decide what laws are constitutional and what not, not only for themselves in their own sphere of action but for the Legislature and Executive also in their spheres, would make the Judiciary a despotic branch.

“Class consciousness can be brought to the workers only from without, that is, only outside of the economic struggle, outside of the sphere of relations between workers and employers. The sphere from which alone it is possible to obtain this knowledge is the phere of relationships between all the various classes and strata and the state and the government-the sphere of the interrelations between all the various classes.”

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“Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place. Now in the present case, where we conceive the eye at an indefinite distance, this will be done by letting fall perpendiculars from each point of the circle on such a plane, which from the nature of the orthographic projection will form an ellipsis, whose greater axis will be equal to the diameter of that circle, and the lesser axis to the greater as the sine of the star's latitude to the radius, for this latter plane being perpendicular to a line drawn from the centre of the sphere through the star's true place, which line is inclined to the ecliptic in an angle equal to the star's latitude; the touching plane will be inclined to the plane of the ecliptic in an angle equal to the complement of the latitude. But it is a known proposition in the orthographic projection of the sphere, that any circle inclined to the plane of the projection, to which lines drawn from the eye, supposed at an infinite distance, are at right angles, is projected into an ellipsis, having its longer axis equal to its diameter, and its shorter to twice the cosine of the inclination to the plane of the projection, half the longer axis or diameter being the radius.
Such an ellipse will be formed in our present case…”

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“If a big country like the United States did return to the gold standard, it would start a great deflation. Most likely the government couldn't stick to it for long. They'd switch the policy to some halfway measure like a gold exchange standard.”

Friedrich Hayek (1899–1992) Austrian and British economist and Nobel Prize for Economics laureate

1980s and later, Interview in Silver & Gold Report (1980)

“A great deal of beauty is rapture. A circle is a necessity. Otherwise you would see no one. We each have our circle.”

Gertrude Stein (1874–1946) American art collector and experimental writer of novels, poetry and plays

"A Circular Play," from Last Operas and Plays (1949) [written in 1920]
Context: A beauty is not suddenly in a circle. It comes with rapture. A great deal of beauty is rapture. A circle is a necessity. Otherwise you would see no one. We each have our circle.

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Auguste Comte23

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