Conjecture Quotes - page 2
Rapidly going over what I could recall of Jim Bursley's information about pathological curves confirmed the conjecture. The snowball curve, derived from an equilateral triangle, is a perimeter of infinite length enclosing a finite area. The angles or points of the perimeter are uncountable. An equilateral triangle projected integrally in the third dimension is a triangular pyramid of equal surfaces. The three-dimensional snowflake derived from this pyramid--hence its diamantine appearance--is a finite volume enclosed in a surface of infinite area. The convolutions of such a surface, to be gathered around its defined content extrude a number of discrete angles or points beyond all possibility of computation. The pressure on each point is infinitesimal, unmeasurably small; the total external pressure exerted on any part of the surface is an aggregate of infinitesimal values, itself infinitesimal.
William Grey Walter
If we find, when we read again one of our classics-say Virgil for instance-that we like it better than ever, the experience may suggest an even more pleasing conjecture. Psychologists tell us that fullness of life is the goal of everything that lives, that the impulse towards completeness, towards ripeness and self-realization, is the most compelling of all motives. These discoveries in old books of new beauties and aspects of interest may persuade us, therefore, that we are not only still ourselves, but more ourselves than ever: that our spirit has not only persisted in its being, but has become more lucid in the process.
Logan Pearsall Smith
Only someone who (like the Intuitionist) denies that the concepts and axioms of classical set theory have any meaning could be satisfied with such a solution, not someone who believes them to describe some well-determined reality. For in reality Cantor's conjecture must be either true or false, and its undecidability from the axioms as known today can only mean that these axioms do not contain a complete description of reality.
Kurt Gödel
The agnostic does not simply say, "l do not know." He goes another step, and he says, with great emphasis, that you do not know. He insists that you are trading on the ignorance of others, and on the fear of others. He is not satisfied with saying that you do not know, -- he demonstrates that you do not know, and he drives you from the field of fact -- he drives you from the realm of reason -- he drives you from the light, into the darkness of conjecture -- into the world of dreams and shadows, and he compels you to say, at last, that your faith has no foundation in fact.
Robert G. Ingersoll
Even in physics, there is no infallible procedure for generating reliable knowledge. The calm order and perfection of well-established theories, accredited by innumerable items of evidence from a thousand different hands, eyes and brains, is not characteristic of the front-line of research, where controversy, conjecture, contradiction and confusion are rife. The physics of undergraduate text-books is 90% true; the contents of the primary research journals of physics is 90% false. The scientific system is as much involved in distilling the former out of the latter as it is in creating and transferring more and more bits of data and items of 'information'.
John Ziman
This place is the Devil, or at least his principal residence, they call it the University, but any other appellation would have suited it much better, for study is the last pursuit of the society the Master eats, drinks, and sleeps, the Fellows drink, dispute and pun, the employments of the undergraduates you will probably conjecture without my description.
Lord Byron
The present industrial era brought with it a new governing class, as every considerable change in human environment must bring with it a governing class to give it expression. Perhaps, for lack of a recognized name, I may describe this class as the industrial capitalistic class, composed in the main of administrators and bankers. I conjecture that this class attained its acme of popularity and power, at least in America, toward the close of the third quarter of the nineteenth century. Almost at the opening of the present century a progressively rigorous opposition found for its mouthpiece the President of the Union himself. If Mr. Roosevelt became, what his adversaries are pleased to call, an agitator, his agitation had a cause which is as deserving of study as is the path of a cyclone.
Brooks Adams
SF means Supreme Fascist - this would show that God is bad. I don't claim that this is correct, or that God exists, but it is just sort of half a joke. ... As a joke I said, "What is the purpose of Life?" "Proof and conjecture, and keep the SF's score low."
Now, the game with the SF is defined as follows:
If you do something bad the SF gets at least two points.
If you don't do something good which you could have done, the SF gets at least one point.
And if nothing - if you are okay, then no one gets any point.
And the aim is to keep the SF's score low.
Paul Erdős
Let us here return to the sublime conjecture of Franklin, that "mind will one day become omnipotent over matter.” If over all other matter, why not over the matter of our own bodies? If over matter at ever so great a distance, why not over matter which, however ignorant we may be of the tie that connects it with the thinking principle, we always carry about with us, and which is in all cases the medium of communication between that principle and the external universe? In a word, why may not man be one day immortal?
The different cases in which thought modifies the external universe are obvious to all. It is modified by our voluntary thoughts or design. We desire to stretch out our hand, and it is stretched out. We perform a thousand operations of the same species every day, and their familiarity annihilates the wonder. They are not in themselves less wonderful than any of those modifications which we are least accustomed to conceive. - Mind modifies body involuntarily.
William Godwin