Afford Quotes (17 quotes)
Again and again in reading even his [William Thomson] most abstract writings one is struck by the tenacity with which physical ideas control in him the mathematical form in which he expressed them. An instance of this is afforded by … an example of a mathematical result that is, in his own words, “not instantly obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result.”
Even today I still get letters from young students here and there who say, Why are you people trying to program intelligence? Why don’t you try to find a way to build a nervous system that will just spontaneously create it? Finally I decided that this was either a bad idea or else it would take thousands or millions of neurons to make it work and I couldn’t afford to try to build a machine like that.
He should avail himself of their resources in such ways as to advance the expression of the spirit in the life of mankind. He should use them so as to afford to every human being the greatest possible opportunity for developing and expressing his distinctively human capacity as an instrument of the spirit, as a centre of sensitive and intelligent awareness of the objective universe, as a centre of love of all lovely things, and of creative action for the spirit.
I can certainly wish for new, large, and properly constructed instruments, and enough of them, but to state where and by what means they are to be procured, this I cannot do. Tycho Brahe has given Mastlin an instrument of metal as a present, which would be very useful if Mastlin could afford the cost of transporting it from the Baltic, and if he could hope that it would travel such a long way undamaged… . One can really ask for nothing better for the observation of the sun than an opening in a tower and a protected place underneath.
I find out what the world needs, then I proceed to invent. My main purpose in life is to make money so that I can afford to go on creating more inventions.
If a patient is poor he is committed to a public hospital as a 'psychotic.' If he can afford a sanitarium, the diagnosis is 'neurasthenia.' If he is wealthy enough to be in his own home under the constant watch of nurses and physicians, he is simply 'an indisposed eccentric.'
It sometimes strikes me that the whole of science is a piece of impudence; that nature can afford to ignore our impertinent interference. If our monkey mischief should ever reach the point of blowing up the earth by decomposing an atom, and even annihilated the sun himself, I cannot really suppose that the universe would turn a hair.
Man cannot afford to be a naturalist, to look at Nature directly, but only with the side of his eye. He must look through and beyond her, to look at her is fatal as to look at the head of Medusa. It turns the man of science to stone. I feel that I am dissipated by so many observations. I should be the magnet in the midst of all this dust and filings.
Science can be the basis of an objective criticism of political power because it claims no power itself. Politics can afford the independence of science because science does not attempt to dictate its purposes.
The moral faculties are generally and justly esteemed as of higher value than the intellectual powers. But we should bear in mind that the activity of the mind in vividly recalling past impressions is one of the fundamental though secondary bases of conscience. This affords the strongest argument for educating and stimulating in all possible ways the intellectual faculties of every human being.
The objects which astronomy discloses afford subjects of sublime contemplation, and tend to elevate the soul above vicious passions and groveling pursuits.
There are pessimists who hold that such a state of affairs is necessarily inherent in human nature; it is those who propound such views that are the enemies of true religion, for they imply thereby that religious teachings are utopian ideals and unsuited to afford guidance in human affairs. The study of the social patterns in certain so-called primitive cultures, however, seems to have made it sufficiently evident that such a defeatist view is wholly unwarranted.
Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.
We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
We cannot see how the evidence afforded by the unquestioned progressive development of organised existence—crowned as it has been by the recent creation of the earth's greatest wonder, MAN, can be set aside, or its seemingly necessary result withheld for a moment. When Mr. Lyell finds, as a witty friend lately reported that there had been found, a silver-spoon in grauwacke, or a locomotive engine in mica-schist, then, but not sooner, shall we enrol ourselves disciples of the Cyclical Theory of Geological formations.
[Receiving a university scholarship] was fundamentally important to me, to be able to afford going to school, and I still believe so strongly in the value of public education and state-funded universities.
[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.