Let us calculate the motion of bodies, but also consult the plans of the Intelligence that makes them move. It seems that the ancient philosophers made the first attempts at this sort of science, in looking for metaphysical relationships between numbers and material bodies. When they said that God occupies himself with geometry, they surely meant that He unites in that science the works of His power with the perspectives of His wisdom. From the all too few ancient geometers who undertook such studies, we have little that is intelligible or well-founded. The perfection which geometry has acquired since their time puts us in a better position to succeed, and may more than compensate for the advantages that those great minds had over us.
Pierre Louis MaupertuisRelated topics
consult few geometry great intelligence looking mean move position power science sort wisdom worksRelated quotes
The classic instrument to measure drawn angles and to draw angles of a given measure is the protractor - essentially half a circular ring, subdivided by ray segments into 180 degrees. For reasons I was unable to find out, this instrument has recently been superseded by an isosceles right triangle - called geo-triangle, solid, transparant, made of plastic - with an angular division radiating from the midpoint of the hypotenuse to the other sides. Well, inside the triangle half a circle with the midpoint of the hypotenuse as its centre is indicated, and from the position of the degree numbers it becomes clear that it is the semicircle that really matters. One is inclined to say "an outrageously misleading instrument"...
Hans Freudenthal
I wasn't aware of Chargaff's rules when he said them, but the effect on me was quite electric because I realized immediately that if you had this sort of scheme that John Griffith was proposing, of adenine being paired with thymine, and guanine being paired with cytosine, then you should get Chargaff's rules. I was very excited, but I didn't actually tell Chargaff because it was something I was doing with John Griffith.... This was very exciting, and we thought "ah ha!" and we realized - I mean what anyone who is familiar with the history of science ought to realize - that when you have one-to-one ratios, it means things go to together. And how on Earth no one pointed out this simple fact in those years, I don't know.
Francis Crick
Traditionally, economic analysis treats the economic system as one of the givens. The term "design" in the title is meant to stress that the structure of the economic system is to be regarded as an unknown. An unknown in what problem? Typically that of finding a system that would be, in a sense to be specified, superior to the existing one. The idea of searching for a better system is at least as ancient as Plato's Republic, but it is only recently that tools have become available for a systematic, analytical approach to such search procedures. This new approach refuses to accept the institutional status quo of a particular time and place as the only legitimate object of interest and yet recognizes constraints that disqualify naive Utopias.
Leonid Hurwicz
It is one of the most beautiful characteristics of Theosophy that it gives back to people in a more rational form everything which was really useful and helpful to them in the religions which they have outgrown... in this teaching as to the immortality of the soul and the life after death, Theosophy...does not put forward these great truths merely on the authority of some sacred book of long ago; in speaking of these subjects it is not dealing with pious opinions, or metaphysical speculations, but with solid, definite facts, as real and as close to us as the air we breathe or the houses we live in - facts of which many among us have constant experience - facts among which lies the daily work of some of our students, as will presently be seen.
Charles Webster Leadbeater
1. The human mind is so constructed that it must see every perception in a time-relation-in an order-and every perception of an object in a space-relation-as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.
Nicholas Murray Butler