“Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small.”

—  Morris Kline

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 176

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by…" by Morris Kline?
Morris Kline photo
Morris Kline42
American mathematician 1908–1992

Related quotes

“The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 57
Context: The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces."

Georg Cantor photo

“The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

"Mitteilungen" (1887-8)

Joanne Harris photo

“The process of giving is without limits.”

Joanne Harris book Chocolat

Source: Chocolat

Noam Chomsky photo

“Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied. Even the interpretation and use of words involves a process of free creation.”

Noam Chomsky (1928) american linguist, philosopher and activist

Tarik Gunersel photo

“The process of creative discovery is endless. That’s why “holiness” tends to limit mental vitality and progress by freezing a given work (a life guide) in time, no matter how interpretations differ and even change over the years.”

Tarik Gunersel (1953) Turkish actor

"A Conversation with Tarık Günersel -by Dawn Kotapish “ in World Literature Today (Jan-Feb 2011).
Other

Victor Hugo photo

“The infinite exists. It is there. If the infinite had nothewould be its limit; it would not be the infinite; in other words, it would not be. But it is. Then it has aThisof the infinite is God.”

Victor Hugo book Les Misérables

Source: Les Misérables

Mwanandeke Kindembo photo

“In the process of finding the true 'I' you have to become formless and infinite as the Supreme One. Become one with the universe.”

Mwanandeke Kindembo (1996) Congolese author

David Bohm photo

“Dialogue is really aimed at going into the whole thought process and changing the way the thought process occurs collectively. We haven't really paid much attention to thought as a process. we have engaged in thoughts, but we have only paid attention to the content, not to the process.”

David Bohm (1917–1992) American theoretical physicist

"On Dialogue"
Context: Dialogue is really aimed at going into the whole thought process and changing the way the thought process occurs collectively. We haven't really paid much attention to thought as a process. we have engaged in thoughts, but we have only paid attention to the content, not to the process. Why does thought require attention? Every thinking requires attention, really. If we ran machines withinout paying attention to them, they would break down. Our thought, too, is a process, and it requires attention, otherwise its going to go wrong.

Jacques Ellul photo

“Images produce an intellectual process different from the ancient one or the one developed by classical education. It goes without saying that this process is not completely new; of course, since sight existed, and since people themselves chose their images, they also thought by means of images and entered into this kind of thinking. But this was limited and not frequent, because images were not dominant. The new factor in our day comes from the effect of visual reproduction’s triumph over all else, which involves us in the domination of one form of thought. This supremacy is new, even though we are not dealing with a completely new form of thought.”

Jacques Ellul (1912–1994) French sociologist, technology critic, and Christian anarchist

J. Hanks, trans. (1985), p. 210
The Humiliation of the Word (1981)

Jacques Ellul photo

“A person who thinks by images becomes less and less capable of thinking by reasoning, and vice versa. The intellectual process based on images is contradictory to the intellectual process of reasoning that is related to the word. There are two different ways of dealing with an object. They involve not only different approaches, but even more important, opposing mental attitudes. This is not a matter of complementary processes, such as analysis and synthesis or logic and dialectic. These processes lack any qualitative common denominator.”

Jacques Ellul (1912–1994) French sociologist, technology critic, and Christian anarchist

J. Hanks, trans. (1985), p. 214
The Humiliation of the Word (1981)

Related topics