Infinite Quotes - page 33
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
Part of the charm of synthetic organic chemistry derives from the vastness of the intellectual landscape along several dimensions. First, there is the almost infinite variety and number of possible target structures that lurk in the darkness waiting to be made. Then, there is the vast body of organic reactions that serve to transform one substance into another, now so large in number as to be beyond credibility to a non-chemist. There is the staggering range of reagents, reaction conditions, catalysts, elements, and techniques that must be mobilized in order to tame these reactions for synthetic purposes. Finally, it seems that new information is being added to that landscape at a rate that exceeds the ability of a normal person to keep up with it. In such a troubled setting any author, or group of authors, must be regarded as heroic if through their efforts, the task of the synthetic chemist is eased.
Elias James Corey
There is a construct in computer programming called 'the infinite loop' which enables a computer to do what no other physical machine can do - to operate in perpetuity without tiring. In the same way it doesn't know exhaustion, it doesn't know when it's wrong and it can keep doing the wrong thing over and over without tiring.
John Maeda
It is now known that the truth or falsity of the continuum hypothesis and other related conjectures cannot be determined by set theory as we know it today. This state of affairs regarding a classical and presumably well-posed problem must certainly appear rather unsatisfactory to the average mathematician. One is tempted to look more closely and perhaps more critically at the foundations of mathematics. Although our present "Cantorian" mathematics is highly successful in its treatment of abstractions, one must not overlook the fact that from the very beginning the use of infinite processes was regarded with suspicion by many people.
Paul Cohen
![We don't know why we are here and . . . our role in the universe, and the thought of an infinite universe. It's something the human mind can't really grasp. [And] it's statistically impossible that there's not life on other planets. (Joel Kinnaman)](https://cdn.quotesdtb.com/img/quotes_images_webp/58/joel-kinnaman-grasp-human-588558.webp)
In every country and every human breast there is a natural desire to find a stable equilibrium - something that does not change. We cannot find it in nature, for all the universe is nothing but an infinite mass of changes. But to infer from that that nothing unchanging exists is to fall into the error of the Southern school of Buddhists and the Chârvâkas, which latter believe that all is matter and nothing mind, that all religion is a cheat, and morality and goodness, useless superstitions.
Charvaka
We see that each surface is really a pair of surfaces, so that, where they appear to merge, there are really four surfaces. Continuing this process for another circuit, we see that there are really eight surfaces etc and we finally conclude that there is an infinite complex of surfaces, each extremely close to one or the other of two merging surfaces.
Edward Norton Lorenz
Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small.
Morris Kline
Though Wallis was advanced for his times and accepted negative numbers, he thought they were larger than infinity but not less than zero. In his Arithmetica Infinitorum (1655), he argued that since the ratio a/0, when a is positive, is infinite, then, when the denominator is changed to a negative number, as in a/b with b negative, the ratio must be greater than infinity.
Morris Kline
The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. ...Simplicius.
Morris Kline
In the field of non-Euclidean geometry, Riemann... began by calling attention to a distinction that seems obvious once it is pointed out: the distinction between an unbounded straight line and an infinite line. The distinction between unboundedness and infiniteness is readily illustrated. A circle is an unbounded figure in that it never comes to an end, and yet it is of finite length. On the other hand, the usual Euclidean concept of a straight line is also unbounded in that it never reaches an end but is of infinite length.
...he proposed to replace the infiniteness of the Euclidean straight line by the condition that it is merely unbounded. He also proposed to adopt a new parallel axiom... In brief, there are no parallel lines. This ... had been tried... in conjunction with the infiniteness of the straight line and had led to contradictions. However... Riemann found that he could construct another consistent non-Euclidean geometry.
Morris Kline
Then there is the final possibility, my favorite.
-Yes?
-The final possibility is that I'm God.
-You're God?
-Just a theory, but the data are provocative. I mean, look at me. Faceless, shapeless, holey, undifferentiated, Jewish, inscrutable...and a hermaphrodite to boot. Years ago, I told you sponges cannot be fatally dismembered, for each part quickly becomes the whole. To wit, I am both immortal and infinite.
-You're God? You're God herself? You?
-The data are provocative.
-God is a sponge? A sponge? There's not much comfort in that.
-Agreed.
-Sponges can't help us.
-Neither can God, as far as I can tell. I'd be happy to see some contrary data.
James K. Morrow
The disproportion between our capabilities and our shared situations would be merely ironic or tragic if we were unable to diminish it. By doing so, we change, to our benefit, the quality of our relation to our cognitive and social assumptions. As a result, we also alter, to our advantage, the quality of our relations to one another. We put more of the infinite us into the finite worlds in which we live.
Roberto Mangabeira Unger
