William Ellery Channing quote: “Error is discipline through which we advance.”

“I believe that through discipline, though not through discipline alone, we can achieve serenity, and a certain small but precious measure of the freedom from the accidents of incarnation, and charity, and that detachment which preserves the world which it renounces.”

Robert Oppenheimer (1904–1967) American theoretical physicist and professor of physics

Letter to his brother Frank (12 March 1932), published in Robert Oppenheimer : Letters and Recollections (1995) edited by Alice Kimball Smith, p. 155
Context: I believe that through discipline, though not through discipline alone, we can achieve serenity, and a certain small but precious measure of the freedom from the accidents of incarnation, and charity, and that detachment which preserves the world which it renounces. I believe that through discipline we can learn to preserve what is essential to our happiness in more and more adverse circumstances, and to abandon with simplicity what would else have seemed to us indispensable; that we come a little to see the world without the gross distortion of personal desire, and in seeing it so, accept more easily our earthly privation and its earthly horror — But because I believe that the reward of discipline is greater than its immediate objective, I would not have you think that discipline without objective is possible: in its nature discipline involves the subjection of the soul to some perhaps minor end; and that end must be real, if the discipline is not to be factitious. Therefore I think that all things which evoke discipline: study, and our duties to men and to the commonwealth, war, and personal hardship, and even the need for subsistence, ought to be greeted by us with profound gratitude, for only through them can we attain to the least detachment; and only so can we know peace.

“As knowledge advances and scientific disciplines change, so do the disciplines impinging on them.”

Eric R. Kandel (1929) American neuropsychiatrist

Psychiatry, Psychoanalysis, and the New Biology of Mind (2008)

“Peace is a path of hope, a path on which one advances through dialogue, reconciliation and conversion.”

Pope Francis (1936) 266th Pope of the Catholic Church

On New Year, Pope Wishes the Faithful a 2020 of Peace, Voice of America, (1 January 2020)
2020s, 2020

“Through discipline comes freedom.”

Aristotle (-384–-321 BC) Classical Greek philosopher, student of Plato and founder of Western philosophy

“Discipline is not revenge. The nation can only be built through commitment, discipline and elimination of corruption.”

Mahinda Rajapaksa (1945) Prime Minister of Sri Lanka

Quoted in The Hindu, "Rajapaksa promises peace and prosperity at Independence Day speech" http://www.thehindu.com/news/international/article100524.ece, February 4, 2010.

“The advancement of education and the advancement of society are absolutely synonymous. The causes of conflict can be eliminated only through the advancement of both.”

Newton Lee American computer scientist

Google It: Total Information Awareness, 2016

“When I speak of reason or rationalism, all I mean is the conviction that we can learn through criticism of our mistakes and errors, especially through criticism by others, and eventually also through self-criticism.”

Karl Popper (1902–1994) Austrian-British philosopher of science

"On Freedom" in All Life is Problem Solving (1999)
Context: When I speak of reason or rationalism, all I mean is the conviction that we can learn through criticism of our mistakes and errors, especially through criticism by others, and eventually also through self-criticism. A rationalist is simply someone for whom it is more important to learn than to be proved right; someone who is willing to learn from others — not by simply taking over another's opinions, but by gladly allowing others to criticize his ideas and by gladly criticizing the ideas of others. The emphasis here is on the idea of criticism or, to be more precise, critical discussion. The genuine rationalist does not think that he or anyone else is in possession of the truth; nor does he think that mere criticism as such helps us achieve new ideas. But he does think that, in the sphere of ideas, only critical discussion can help us sort the wheat from the chaff. He is well aware that acceptance or rejection of an idea is never a purely rational matter; but he thinks that only critical discussion can give us the maturity to see an idea from more and more sides and to make a correct judgement of it.

“He [the devil] always sends errors into the world in pairs—pairs of opposites. And he always encourages us to spend a lot of time thinking which is the worse. You see why, of course? He relies on your extra dislike of the one error to draw you gradually into the opposite one. But do not let us be fooled. We have to keep our eyes on the goal and go straight through between both errors. We have no other concern than that with either of them.”

Clive Staples Lewis book Mere Christianity

Book IV, chapter 6, "Two Notes"
Mere Christianity (1952)

“"Groping" and "muddling through" is usually described as a solution by trial and error…. a series of trials, each of which attempts to correct the error committed by the preceding and, on the whole, the errors diminished as we proceed and the successive trials come closer and closer to the desired final result…. we may wish a better characterization…"successive trials" or "successive corrections" or "successive approximations."… You use successive approximations when… looking for a word in the dictionary… A mathematician may apply the term… to a highly sophisticated procedure… to treat some very advanced problem… that he cannot treat otherwise. The term even applies to science as a whole; the scientific theories which succeed each other, each claiming a better explanation… may appear as successive approximations to the truth.
Therefore, the teacher should not discourage his students from using trial and error—on the contrary, he should encourage the intelligent use of the fundamental method of successive approximations. Yet he should convincingly show that for… many… situations, straightforward algebra is more efficient than successive approximations.”

George Pólya (1887–1985) Hungarian mathematician

George Pólya, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1962)

“Ninety per cent of all the mathematics we know has been discovered (or invented), in the last hundred years… the advances made in each of some dozen directions are converging into one single discipline uniting algebra, topology and analysis.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“Error is discipline through which we advance.”

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