Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion, one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
The words 'theory' and 'practice' are of Greek origin; they carry our thoughts back to the ancient philosophers by whom they were contrived, and by whom they were also contrasted and placed in opposition, as denoting two mutually conflicting and mutually inconsistent ideas. ... [this fallacy] based on a double system of natural laws retarded for centuries the development of physical science, notably mechanics.
The most remarkable discovery made by scientists is science itself. The discovery must be compared in importance with the invention of cave-painting and of writing. Like these earlier human creations, science is an attempt to control our surroundings by entering into them and understanding them from inside. And like them, science has surely made a critical step in human development which cannot be reversed. We cannot conceive a future society without science.
Hinduism has made marvelous discoveries in things of religion, of the spirit, of the soul. We have no eye for these great and fine discoveries. We are dazzled by the material progress that Western science has made. Ancient India has survived because Hinduism was not developed along material but spiritual lines.
In stark contrast with the views of the Greek philosophers and with those of the rest of western intellectuals to the present day, Chinese Taoist thought always defended individual liberty and laissez-faire while attacking the systematic and coercive use of violence typical of government.
The most remarkable discovery ever made by scientists is science itself. The discovery must be compared in importance with the invention of cave-painting and of writing.
Science is based on the possibility of objectivity, on the possibility of different people checking out for themselves the observations made by others. Without that possibility, there is no empirical principle capable of deciding between different arguments and theories.
...the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.
The medicines of today are based upon thousands of years of knowledge accumulated from folklore, serendipity and scientific discovery. The new medicines of tomorrow will be based on the discoveries that are being made now, arising from basic research in laboratories around the world.
It [ non-Euclidean geometry ] would be ranked among the most famous achievements of the entire [nineteenth] century, but up to 1860 the interest was rather slight.
It drove me mad not being able to know more about Pink Floyd when I was a little kid. But that's the great thing - there was this mystery behind it, and we couldn't find out enough. It made your mind work, it made you seek after it or try to interpret it. It made you envision or imagine what they were doing.
Discoveries are always accidental; and the great use of science is by investigating the nature of the effects produced by any process or contrivance, and of the causes by which they are brought about, to explain the operation and determine the precise value of every new invention. This fixes as it were the latitude and longitude of each discovery, and enables us to place it in that part of the map of human knowledge which it ought to occupy. It likewise enables us to use it in taking bearings and distances, and in shaping our course when we go in search of new discoveries.
Gregorian chant, Romanesque architecture, the Iliad , the invention of geometry were not, for the people through whom they were brought into being and made available to us, occasions for the manifestation of personality.
We are constantly being astonished these days at the amazing discoveries in the field of violence. But I maintain that far more undreamt of and seemingly impossible discoveries will be made in the field of nonviolence.