Computation 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
Computation, storage, and communications capacity are in the hands of practically every connected person - and these are the basic physical capital means necessary for producing information, knowledge and culture, in the hands of something like 600 million to a billion people around the planet.
Yochai Benkler
Fermat died with the belief that he had found a long-sought-for law of prime numbers in the formula 2^{2^n} + 1 = a prime, but he admitted that he was unable to prove it rigorously. The law is not true, as was pointed out by Euler in the example 2^{2^5} + 1 = 4,294,967,297 = 6,700,417 times 641. The American lightning calculator Zerah Colburn, when a boy, readily found the factors but was unable to explain the method by which he made his marvellous mental computation.
Florian Cajori
The speed and density of computation have been doubling every three years (at the beginning of the twentieth century) to one year (at the end of the twentieth century), regardless of the type of hardware used. ...Despite many decades of progress since the first calculating equipment was used in the 1890 census, it was not until the mid-1960s that this phenomenon was even noticed.
Ray Kurzweil
The greatness of an estate, in bulk and territory, doth fall under measure; and the greatness of finances and revenue, doth fall under computation. The population may appear by musters; and the number and greatness of cities and towns by cards and maps. But yet there is not any thing amongst civil affairs more subject to error, than the right valuation and true judgment concerning the power and forces of an estate.
Francis Bacon
Does life in some way make use of the potentiality for vast quantum superpositions, as would be required for serious quantum computation? How important are the quantum aspects of DNA molecules? Are cellular microtubules performing some essential quantum roles? Are the subtleties of quantum field theory important to biology? Shall we gain needed insights from the study of quantum toy models? Do we really need to move forward to radical new theories of physical reality, as I myself believe, before the more subtle issues of biology - most importantly conscious mentality - can be understood in physical terms? How relevant, indeed, is our present lack of understanding of physics at the quantum/classical boundary? Or is consciousness really "no big deal,” as has sometimes been expressed?
It would be too optimistic to expect to find definitive answers to all these questions, at our present state of knowledge, but there is much scope for healthy debate...
Roger Penrose
The speed and density of computation have been doubling every three years (at the beginning of the twentieth century) to one year (at the end of the twentieth century), regardless of the type of hardware used. ...Despite many decades of progress since the first calculating equipment was used in the 1890 census, it was not until the mid-1960s that this phenomenon was even noticed (although Alan Turing had an inkling of it in 1950).
Ray Kurzweil
