“Receptively it [the work as human action] is limited by the limitations of the perceiving eye. The limitation of the eye is its inability to see even a small surface equally sharp at all points. The eye must "graze" over the surface, grasping sharply portion after portion, to convey them to the brain which collects and stores the impressions.”

I.13 Productive | Receptive, p. 33
1921 - 1930, Pedagogical Sketch Book, (1925)

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Paul Klee104

German Swiss painter 1879–1940

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“That which has no limitations, has no form. The limitations of two conterminous bodies are interchangeably the surface of each. All the surfaces of a body are not parts of that body.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

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“We have, over the centuries, devised a management structure for running things, whether firms or whole countries. This structure depends absolutely on the limitations of the human hand, eye, and brain. The discoveries of management cybernetics, coupled with the techniques of operational research and with the new technology of automation, make possible a new way of running things which is not so limited. Yet we insist on retaining the original structures and automating them. In so doing, we enshrine in steel, glass, and semiconductors those very limitations of hand, eye, and brain that the computer was invented precisely to transcend.”

Anthony Stafford Beer (1926–2002) British theorist, consultant, and professor

Source: Management Science (1968), Chapter 7, Automation and Such, p. 177.

“Strain your brain more than your eye… You can copy a thing to a certain limit. Then you must use intellect.”

Thomas Eakins (1844–1916) American painter

Advice to his art students; quoted in Lloyd Goodrich, Thomas Eakins (1933).

“Riemann has shewn that as there are different kinds of lines and surfaces, so there are different kinds of space of three dimensions; and that we can only find out by experience to which of these kinds the space in which we live belongs. In particular, the axioms of plane geometry are true within the limits of experiment on the surface of a sheet of paper, and yet we know that the sheet is really covered with a number of small ridges and furrows, upon which (the total curvature not being zero) these axioms are not true. Similarly, he says although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space.”

William Kingdon Clifford On the Space-Theory of Matter

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On the Space-Theory of Matter (read Feb 21, 1870)

“To cope with this difficulty [of limited capacity], even a mechanical recognition system must have some way to select portions of the incoming information for detailed analysis.”

Ulric Neisser (1928–2012) American psychologist

Source: Cognitive Psychology, 1967, p. 94

“The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.”

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“Don’t believe what your eyes are telling you. All they show is limitation. Look with your understanding.”

Richard Bach book Jonathan Livingston Seagull

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“The flaw must lie in our methods of description, in languages, in social networks of meaning, in moral structures, and in philosophies and religions — all of which convey implicit limits where no limits exist.”

Frank Herbert (1920–1986) American writer

Dune Genesis (1980)
Context: No matter how finely you subdivide time and space, each tiny division contains infinity.
But this could imply that you can cut across linear time, open it like a ripe fruit, and see consequential connections. You could be prescient, predict accurately. Predestination and paradox once more.
The flaw must lie in our methods of description, in languages, in social networks of meaning, in moral structures, and in philosophies and religions — all of which convey implicit limits where no limits exist. Paul Muad'Dib, after all, says this time after time throughout Dune.

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit. It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Introductory Chapter, pp.9-10
The Differential and Integral Calculus (1836)

“Never acknowledge the limitations of man. Smash all boundaries! Deny whatever your eyes see. Die every moment, but say: "Death does not exist."”

Nikos Kazantzakis book The Saviors of God

The Saviors of God (1923)

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