“The strongest use of the symbol is to be found in its magical power of doubling the actual universe, and placing by its side an ideal universe, its exact counterpart, with which it can be compared and contrasted, and, by means of curiously connecting fibres, form with it an organic whole, from which modern analysis has developed her surpassing geometry.”

— Benjamin Peirce

On the Uses and Transformations of Linear Algebra (1875)

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Benjamin Peirce24

American mathematician 1809–1880

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“In the struggle of mankind with the elements, its aim is dominion over nature. Dominion is a relationship of the organizer to the organized. Step by step, mankind acquires control over and conquers nature; this means that step by step it organizes the universe; it organizes the universe for Itself and in its own interests. Such is the meaning and content of the age-long labour of mankind.
Nature resists elementally and blindly with the terrible strength of its dark, chaotic, but innumerable and Infinite army of elements. In order to conquer it, mankind must organize itself into a mighty army. Unconsciously, it has been doing this for centuries by forming working collective, ranging from the small primitive communes of the primordial epoch to the contemporary cooperation of hundreds of millions of people.
If mankind had to organize the universe only with the forces and means given to it by nature, it would not have any advantage over the other living creatures which also fight for survival against the rest of nature. In its labour mankind uses tools, which it takes from the same external nature. This forms the basis of its victories; it is this which long ago provided and continues to provide mankind with a growing superiority over the strongest and most terrible giants of elemental life and which distinguishes it from the rest of nature's kingdom.”

Alexander Bogdanov (1873–1928) Physician, philosopher, writer

Source: Essays in tektology, 1980, p. 1-2.

“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.

“Even the modern word "concept" means "a grasping together," implying that the mind itself, in its act of knowing, functions like the intervening hand (in contrast to its ancient counterpart, “idea,” “that which can be beheld,” which implies that the mind functions like the receiving eye). And modern science rejects, as meaningless or useless, questions that cannot be answered by the application of method. Science becomes not the representation and demonstration of truth, but an art: the art of finding the truth—or, rather, that portion of truth that lends itself to be artfully found.”

Leon R. Kass (1939) American academic

Source: The Problem of Technology (1993), p. 8

“In terms of composition the new plasticism is dualistic. Through the exact reconstruction of cosmic relations it is a direct expression of the universal; by its rhythm, by the material reality of its plastic form, it expresses the artist's individual subjectivity. It thus unfolds before us a whole world of universal beauty without thereby renouncing the human element.”

Piet Mondrian (1872–1944) Peintre Néerlandais

1910's, Natural Reality and Abstract Reality', 1919

“As the nature of the universal has given to every rational being all the powers that it has, so we have received from it this power also. For as the universal nature converts and fixes in its predestined place everything which stands in the way and opposes it, and makes such things a part of itself, so also the rational animal is able to make every hindrance its own material, and to use it for such purpose as it may have designed.”

Marcus Aurelius book Meditations

VIII, 35
Meditations (c. 121–180 AD), Book VIII

“That the universe has organized its own self-awareness – is for me powerful evidence that there is 'something going on' behind it all. The impression of design is overwhelming. Science may explain all the processes whereby the universe evolves its own destiny, but that still leaves room for there to be a meaning behind existence.”

Paul Davies (1946) British physicist

Source: The Cosmic Blueprint: New Discoveries In Nature's Creative Ability To Order Universe (1988), Ch. 14: 'Is There a Blueprint?', p. 203

“The modern scientific counterpart to belief in God is the belief in the universe as an organism: this disgusts me. This is to make what is quite rare and extremely derivative, the organic, which we perceive only on the surface of the earth, into something essential, universal, and eternal! This is still an anthropomorphizing of nature!”

Friedrich Nietzsche (1844–1900) German philosopher, poet, composer, cultural critic, and classical philologist

KSA 9,11 [201]

“The experience and ideas of contemporary science lead us to the only integral, the only monistic understanding of the universe. It appears before us as an in nitely unfolding fabric of all types of forms and levels of organization, from the unknown elements of ether to human collectives and star systems. All these forms, in their interlacement and mutual struggle, in their constant changes, create the universal organizational process, in nitely split in its parts, but continuous and unbroken in its whole.”

Alexander Bogdanov (1873–1928) Physician, philosopher, writer

Source: Essays in tektology, 1980, p. 6

“Compatibility, not incompatibility, is the issue. For pc set 'analysis' is incompatible with nothing, as the fact of its universal potential applicability already testifies. It begins not with observation of musical particularities but with a universe of possibilities. The comparison of any musical entity with such a universe yields an inexhaustible quarry of 'true facts' but no criterion of relevence. As long as not such criterion has been established…the endless stream of ostensible relations stemming from the pc survey can persuade us for a while that analysis is being accomplished. But in fact it is only a tabulation that can just as well be carried on in the presense of analysis as in its absence (hence the universal 'compatibility'). Nor is it really so innocuous as I may be making it seem, since in its anodyne effect (one never comes back from the fishing expedition empty-handed, there is always 'something to say' some 'finding' to report) it can deflect attention away from the task at hand, which is to formulate analytical methods, not concoct a universal solvent.”

Richard Taruskin (1945) American writer

Taruskin, Richard. "Reply to van den Toorn", p. 57.

“The last decades of scientific development have led us to the recognition of a new universal law of all natural phenomena, which, from its extraordinarily extended range, and from the connection which it constitutes between natural phenomena of all kinds, even of the remotest times and the most distant places, is especially fitted to give us an idea of what I have described as the character of the natural sciences, which I have chosen as the subject of this lecture.”

Hermann von Helmholtz (1821–1894) physicist and physiologist

"On the Conservation of Force" (1862), p. 279
Popular Lectures on Scientific Subjects (1881)

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