Spirituality is much wider than any particular religion , and in the larger ideas of it that are now coming on us even the greatest religion becomes no more than a broad sect or branch of the one universal religion, by which we shall understand in the future man's seeking for the eternal , the divine, the greater self , the source of unity and his attempt to arrive at some equation, some increasing approximation of the values of human life with the eternal and the divine values.

Sri Aurobindo inAll my life I've beenworking on the workevery canvas a sentence or paragraph of it. Each picture is onlyan approximation of what I want.

Robert MotherwellI agree that our methods of control are unlikely to be sufficiently delicate or sufficiently powerful to maintain continuous full employment. I should be quite content with a reasonable approximation to it, and in practice I should probably relax my expansionist measures a little before technical full employment had actually been reached.

Keynes (of Tilton),John Maynard, 1st BaronI do not underrate the yearning for mechanical and formal tests. They are possible and useful in zones upon the legal sphere. The pain of choosing is the pain of marking off such zones from others. It is a pain we must endure, for uniformity of method will carry us upon the rocks. The curse of this fluidity, of an ever shifting approximation, is one the law must bear, or other curses yet more dreadful will be invited in exchange.

benjamin n. cardozoThe art of the theater is action. It is the study of commitment. The word is an act. To SAY the word in such a way as to make it heard and understood by all in the theater is a commitment — it is the highest art to see a human being out on a stage speaking to a thousand of his or her peers saying, 'These words which I am speaking are the TRUTH — they are not an approximation of any kind. They are the God's truth, and I support them with my life,' which is what the actor does on stage.

david mametI think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.

john von neumannNow I want to begin to fulfill a certain obligation by stating that there was one person, no longer here, who had something to say, and who said it, but whom no one believed or really understood. Forgotten. For reasons that will become apparent I'd prefer that he remain forgotten, but there's no choice other than to reopen his case.I don't know his whole story. No one ever will, except Phædrus himself, and he can no longer speak. But from his writings and from what others have said and from fragments of my own recall it should be possible to piece together some kind of approximation of what he was talking about.

robert m. pirsigLet us suppose that we have set the problem of finding a solution to the equation This is a problem for which the Babylonians around 1700 BC found the excellent approximation ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen the problem which caused the existentialist crisis in ancient Greek mathematics. The exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!

Philip J. Davis and Reuben Hersh,An artist cannot be partially sincere any more than art can be an approximation of beauty.

andrei tarkovskyEach piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected. ... The test of all knowledge is experiment. Experiment is the sole judge of scientific “truth”.

richard feynman“To stamp becoming with the character of being that is the supreme will to power.” (WM 617) This suggests that becoming only is if it is grounded in being as being: “That everything recurs is the closest approximation of a world of becoming to one of being.”

Martin HeideggerMr. Darwin's hypothesis is not, so far as I am aware, inconsistent with any known biological fact; on the contrary, if admitted, the facts of Development, of Comparative Anatomy, of Geographical Distribution, and of Palaeontology, become connected together, and exhibit a meaning such as they never possessed before; and I, for one, am fully convinced that if not precisely true, that hypothesis is as near an approximation to the truth as, for example, the Copernican hypothesis was to the true theory of the planetary motions.

thomas henry huxleyEach such answer to the great question, invariably asserted by the followers of its propounder, if not by himself, to be complete and final, remains in high authority and esteem, it may be for one century, or it may be for twenty: but, as invariably, Time proves each reply to have been a mere approximation to the truth tolerable chiefly on account of the ignorance of those by whom it was accepted, and wholly intolerable when tested by the larger knowledge of their successors.

thomas henry huxleyWe need tremendous energy to bring about a psychological change in ourselves as human beings, because we have lived far too long in a world of make-belief, in a world of brutality, violence, despair, anxiety. To live humanly, sanely, one has to change. To bring about a change within oneself and therefore within society, one needs this radical energy, for the individual is not different from society the society is the individual and the individual is the society. And to bring about a necessary radical, essential change in the structure of society which is corrupt, which is immoral there must be change in the human heart and mind. To bring about that change you need great energy and that energy is denied or perverted, or twisted, when you act according to a concept; which is what we do in our daily life. The concept is based on past history, or on some conclusion, so it is not action at all, it is an approximation to a formula. So one asks if there is an action which is not based on an idea, on a conclusion formed by dead things which have been.

jiddu krishnamurtiWho is, in the classical conception, the subject that comprehends the ontological condition of truth and untruth? It is the master of pure contemplation (theoria), and the master of a practice guided by theoria, i.e., the philosopher-statesman. To be sure, the truth which he knows and expounds is potentially accessible to everyone. Led by the philosopher, the slave in Plato’s Meno is capable of grasping the truth of a geometrical axiom, i.e., a truth beyond change and corruption. But since truth is a state of Being as well as of thought, and since the latter is the expression and manifestation of the former, access to truth remains mere potentiality as long as it is not living in and with the truth. And this mode of existence is closed to the slave and to anyone who has to spend his life procuring the necessities of life. Consequently, if men no longer had to spend their lives in the realm of necessity, truth and a true human existence would be in a strict and real sense universal. Philosophy envisages the equality of man but, at the same time, it submits to the factual denial of equality. For in the given reality, procurement of the necessities is the life-long job of the majority, and the necessities have to be procured and served so that truth (which is freedom from material necessities) can be. Here, the historical barrier arrests and distorts the quest for truth; the societal division of labor obtains the dignity of an ontological condition. If truth presupposes freedom from toil, and if this freedom is, in the social reality, the prerogative of a minority, then the reality allows such a truth only in approximation and for a privileged group. This state of affairs contradicts the universal character of truth, which defines and “prescribes” not only a theoretical goal, but the best life of man qua man, with respect to the essence of man. For philosophy, the contradiction is insoluble, or else it does not appear as a contradiction because it is the structure of the slave or serf society which this philosophy does not transcend. Thus it leaves history behind, unmastered, and elevates truth safely above the historical reality. There, truth is reserved intact, not as an achievement of heaven or in heaven, but as an achievement of thought intact because its very notion expresses the insight that those who devote their lives to earning a living are incapable of living a human existence.

herbert marcuseThere is a noticeable general difference between the sciences and mathematics on the one hand, and the humanities and social sciences on the other. It's a first approximation, but one that is real. In the former, the factors of integrity tend to dominate more over the factors of ideology. It's not that scientists are more honest people. It's just that nature is a harsh taskmaster. You can lie or distort the story of the French Revolution as long as you like, and nothing will happen. Propose a false theory in chemistry , and it'll be refuted tomorrow.

Noam Chomsky (1992) inSpirituality is much wider than any particular religion , and in the larger ideas of it that are now coming on us even the greatest religion becomes no more than a broad sect or branch of the one universal religion, by which we shall understand in the future man's seeking for the eternal , the divine, the greater self , the source of unity and his attempt to arrive at some equation, some increasing approximation of the values of human life with the eternal and the divine values.

Sri Aurobindo inIn the book on the Measurement of the Circle , Archimedes proves first that the area of a circle is equal to that of a right triangle having the length of the circumference for its base, and the radius for its altitude. In this he assumes that there exists a straight line equal in length to the circumference -- an assumption objected to by some ancient critics, on the ground that it is not evident that a straight line can equal a curved one. The finding of such a line was the next problem. He first finds an upper limit to the ratio of the circumference to the diameter, or <pi symbol>. To do this, he starts with an equilateral triangle of which the base is a tangent and the vertex is the centre of the circle. By successively bisecting the angle at the centre, by comparing ratios, and by taking the irrational square roots always a little too small, he finally arrived at the conclusion that ? < 3 1/7. Next he finds a lower limit by inscribing in the circle regular polygons of 6, 12, 24, 48, 96 sides, finding for each successive polygon its perimeter, which is, of course, always less than the circumference. Thus he finally concludes that "the circumference of a circle exceeds three times its diameter by a part which is less than 1/7 but more than 10/71 of the diameter." This approximation is exact enough for most purposes.

p. 41 (The Greeks)In geometry the forte of the Egyptians lay in making constructions and determining areas. The area of an isosceles triangle, of which the sides measure 10 ruths and the base 4 ruths , was erroneously given as 20 square ruths , or half the product of the base by one side. The area of an isosceles trapezoid is found, similarly by multiplying half the sum of the parallel sides by one of the non-parallel sides. The area of a circle is found by deducting from the diameter 1/2 of its length and squaring the remainder. Here ? is taken=(16/9) 2 =3.1604..., a very fair approximation. The papyrus explains also such problems as these, To mark out in the field a right triangle whose sides are 10 and 4 units; or a trapezoid whose parallel sides are 6 and 4, and the non-parallel sides each 20 units.

p. 11 (The Egyptians)The societal division of labor obtains the dignity of an ontological condition. If truth presupposes freedom from toil, and if this freedom is, in the social reality, the prerogative of a minority, then the reality allows such a truth only in approximation and for a privileged group.

Herbert Marcuse (1964),To a good approximation, all species are insects.

Robert May, quoted in Richard Dawkins,In geometry his greatest achievement was an accurate value of ?. His rule is stated as: dn^2+(2a-d)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.

In, p.245 (Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures)His value of ? is a very close approximation to the modern value and the most accurate among those of the ancients. There are reasons to believe that he devised a particular method for finding this value. It is shown with sufficient grounds that he himself used it, and several later Indian mathematicians and even the Arabs adopted it. The conjecture that Aryabhata's value of ? is of Greek origin is critically examined and is found to be without foundation. He discovered this value independently and also realised that ? is an irrational number. He had the Indian background, no doubt, but excelled all his predecessors in evaluating ?. Thus the credit of discovering this exact value of ? may be ascribed to the celebrated mathematician, Aryabhata I.

P Jha, Aryabhata I and the value of ?, Math. Ed. (Siwan) 16 (3) (1982), 54-59, quoted in: J J O'Connor and E F Robertson— Aryabhata is also known as Aryabhata I to distinguish him from the later mathematician of the same name who lived about 400 years later.

The principle of bounded rationality [is] the capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problems whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality.

Herbert A. Simon, (1947).A poor relation is the most irrelevant thing in nature, a piece of impertinent correspondence, an odious approximation, a haunting conscience, a preposterous shadow, lengthening in the noon-tide of our prosperity. He is known by his knock.

Charles Lamb (1838)The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problems whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality.

Herbert Simon (1957)The differences between minds might be... like the differences between languages, or styles of music or art inexhaustible in the limit, but approachable to any degree of approximation you like. But the difference between having a mind and not having a mind at all being something with its own subjective point of view and being something that is all outside and no inside, like a rock or a discarded sliver of fingernail is apparently an all-or-nothing difference.

Daniel C. Dennett, ibid.,It is probably dangerous to use this theory of information in ?elds for which it was not designed, but I think the danger will not keep people from using it. In psychology, at least in the psychology of communication, it seems to ?t with a fair approximation. When it occurs that the learnability of material is roughly proportional to the information content calculated | by the theory, I think it looks interesting. There may have to be modi?cations, of course. For example, I think that the human receiver of information gets more out of a message that is encoded into a broad vocabulary (an extensive set of symbols) and presented at a slow pace, than from a message, equal in information content, that is encoded into a restricted set of symbols and presented at a faster pace. Nevertheless, the elementary parts of the theory appear to be very useful. I say it may be dangerous to use them, but I don’t think the danger will scare us off.

j. c. r. lickliderExperience is, for me, the highest authority. The touchstone of validity is my own experience. No other person's ideas, and none of my own ideas, are as authoritative as my experience. It is to experience that I must return again and again, to discover a closer approximation to truth as it is in the process of becoming in me. Neither the Bible nor the prophets -- neither Freud nor research -- neither the revelations of God nor man -- can take precedence over my own direct experience. My experience is not authoritative because it is infallible. It is the basis of authority because it can always be checked in new primary ways. In this way its frequent error or fallibility is always open to correction.

carl rogers