On Motion (1950-1999)

"Space and time are commonly regarded as the forms of existence of the real world, matter as its substance. A definite portion of matter occupies a definite part of space at a definite moment of time. It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship." (Hermann Weyl, "Space, Time, Matter", 1952)

"Mathematics, springing from the soil of basic human experience with numbers and data and space and motion, builds up a far-flung architectural structure composed of theorems which reveal insights into the reasons behind appearances and of concepts which relate totally disparate concrete ideas." (Saunders MacLane, "Of Course and Courses"The American Mathematical Monthly, Vol 61, No 3, 1954)

"The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analysing visible motions it has developed two ways of representing them by elementary processes; moving particles and waves. There is no other way of giving a pictorial description of motions - we have to apply it even in the region of atomic processes, where classical physics breaks down." (Max Born, "Atomic Physics", 1957)

"Mathematics is neither a description of nature nor an explanation of its operation; it is not concerned with physical motion or with the metaphysical generation of quantities. It is merely the symbolic logic of possible relations, and as such is concerned with neither approximate nor absolute truth, but only with hypothetical truth. That is, mathematics determines what conclusions will follow logically from given premises. The conjunction of mathematics and philosophy, or of mathematics and science is frequently of great service in suggesting new problems and points of view." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)

"While static stability is concerned with the tendency of a displaced body to return to equilibrium, dynamic stability is concerned with the resulting motion with time. If an object is disturbed from equilibrium, the time history of the resulting motion indicates the dynamic stability of the system. In general, the system will demonstrate positive dynamic stability if the amplitude of the motion decreases with time." (Hugh H Hurt, "Aerodynamics for Naval Aviators", 1960)

"Questions are the engines of intellect, the cerebral machines which convert energy to motion, and curiosity to controlled inquiry." (David H Fischer, "Historians’ Fallacies", 1970)

"The eye projects and focuses the inner image (idea) onto the physical world in the same manner that a motion picture camera transfers an image onto a screen. The mouth creates words. The ears create sound. The difficulty in understanding this principle is due to the fact that we’ve taken it for granted that the image and sound already exist for the senses to interpret. Actually the senses are the channels of creation by which idea is projected into material expression." (Jane Roberts,"The Seth Material", 1970)

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

"The classic example of chaos at work is in the weather. If you could measure the positions and motions of all the atoms in the air at once, you could predict the weather perfectly. But computer simulations show that tiny differences in starting conditions build up over about a week to give wildly different forecasts. So weather predicting will never be any good for forecasts more than a few days ahead, no matter how big (in terms of memory) and fast computers get to be in the future. The only computer that can simulate the weather is the weather; and the only computer that can simulate the Universe is the Universe." (John Gribbin, "The Little Book of Science", 1999)