Approximation Quotes - page 2

Another feature to which I will allude is that the new constitution provides that cabinet ministers and heads of departments may have the privilege of seats upon the floor of the Senate and House of Representatives and may have the right to participate in the debates and discussions upon the various subjects of administration. I should have preferred that this provision should have gone further, and required the President to select his constitutional advisers from the Senate and House of Representatives. That would have conformed entirely to the practice in the British Parliament, which, in my judgment, is one of the wisest provisions in the British constitution. It is the only feature that saves that government. It is that which gives it stability in its facility to change its administration. Ours, as it is, is a great approximation to the right principle. (Alexander H. Stephens)

The administrator is more like the engineer who constructs a power plant, that is, he is concerned with the realization of conscious human purposes by the conscious use of human beings and materials. It is true that the mere student of administration may be just an observer, but he does not merely observe natural, unconscious, and automatic operations. He observes the formulation of human purposes, consciously and deliberately and operations designed to effect given results. And he sees calculations of results in advance realized later in practice with a high degree of approximation. The degree of approximation between advance calculations and results is not often, if ever, as exact as in the case of a hydro-electric plant, but it is constantly exact enough for practical purposes.

Charles A. Beard

We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in part, an experimental science. If it were experimental it would be only approximative and provisional. And what rough approximation! ...The object of geometry is the study of a particular 'group'; but the general group concept pre-exists... in our minds. It is imposed on us, not as form of our sense, but as form of our understanding. Only, from among all the possible groups, that must be chosen... will be... the standard to which we shall refer natural phenomena. Experience guides us in this choice without forcing it upon us; it tells us not which is the truest geometry, but which is the most convenient. Notice that I have been able to describe the fantastic worlds... imagined without ceasing to employ the language of ordinary geometry.

Henri Poincaré

When you write a computer program you've got to not just list things out and sort of take an algorithm and translate it into a set of instructions. But when there's a bug - and all programs have bugs - you've got to debug it. You've got to go in, change it, and then re-execute ... and you iterate. And that iteration is really a very, very good approximation of learning.

Nicholas Negroponte

The first approximation in this future that we're looking at is that everyone will be physically well off. They will have a great abundance in material goods, and I think that will soften some of the conflicts we see now.

Ralph Merkle

We are looking at a future where to a first approximation, everyone is wealthy.

Ralph Merkle

In the "static" universe expansion is impossible, the "empty" universe does expand. Therefore we may be tempted to consider the empty universe as the most likely approximation; and we can proceed to compute the radius of curvature of the universe, supposing it to be of the empty type, from the observed rate of expansion.

Willem de Sitter

Matter is actually distributed very unevenly... conglomerated into stars and galactic systems. The average density is the density that we should get if all... could be evaporated into atoms of hydrogen, or protons, and... distributed evenly over the whole of space. ...three or four protons in every cubic foot. ...a million million times less than that of the most perfect vacuum that we can produce... The universe thus consists mostly of emptiness... consider a universe without any matter at all, an empty universe, as a good approximation. But we may also take as our first approximation a universe containing... three or four protons per cubic foot. The local deviations from the average, caused by the conglomeration of matter into stars and stellar systems, are then disregarded in the grand scale model, and are only taken into account when we come to study details.

Willem de Sitter

Is the density anywhere near that corresponding to the static universe, or is it so small that we can consider the empty universe as a good approximation?

Willem de Sitter

To a rough approximation, and setting aside vertebrate chauvinism, it can be said that essentially all organisms are insects.

Robert M. May

Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity. In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction. The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogolyubov's. (Yoichiro Nambu)

A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.

Roger Shepard

Personally, I don't see old economics and behavioural economics as opposed. It is useful to assume people are rational as a good approximation to their long term behaviour, but it would be unwise not to think how in practice their behaviour may deviate from that simplifying assumption.

Evan Davis

It's a pretty widely-accepted notion that the atmosphere is a ridiculously complex system, and the best we can do with our models is a rough approximation.

Jamais Cascio

It seems that truth is progressive approximation in which the relative fraction of our spontaneously tolerated residual error constantly diminishes.

Buckminster Fuller

General relativity has changed our understanding of space and time. ...The spacetime of general relativity ...is likely to be just a classical approximation that loses its meaning in the quantum theory, for the same reason the trajectory of a particle does.

Carlo Rovelli

The writer of the above lines (E. W. Bovill), a supposed European authority on the Western Sudan, then goes on to say that silent trade or dumb barter was a feature of the Western Sudan's gold trade throughout all the centuries until modern times. Actually, the only thing dumb about the trade is what he writes about it. The story of dumb barter for gold in West Africa is repeated in several accounts, starting with ancient Greek scripts. It is clearly a rough approximation of the first attempts at exchange of a people coming into contact with strangers, and it was not a permanent procedure.

Walter Rodney

Like books you will never have the chance to read, there are languages you do not know, and you're not going to get a chance to learn, so you'll never really know what was written, only the approximation.

James Salter

The result of the struggle between the thought and the ability to express it, between dream and reality, is seldom more than a compromise or an approximation.

M. C. Escher

I 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.

John von Neumann

Each 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 Huxley)

All exact science is dominated by the idea of approximation.

Bertrand Russell

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. Pirsig

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

Anyone who wants to look at sunlight naturally wipes his eye clear first, in order to make, at any rate, some approximation to the purity of that on which he looks; and a person wishing to see a city or country goes to the place in order to do so.

Athanasius of Alexandria

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