by: Albert Einstein, read in 2009
16 "...knowledge and justice are ranked above wealth and power by a large section of the human race. My experience teaches me that this idealistic outlook is particularly prevalent in America, which is decribed as a singularly materialistic country."
18 "The prestige of government has undoubtedly been lowered considerably by the Prohibition law. For nothing is more destructive of respect for the government and the law of the land than passing laws which cannot be enforced. It is an open secret that the dangerous increase of crime in this country is closely connected with this."
29 "...everybody must live in fear of being eliminated from the economic cycle. In this way suffering for the want of everything. Furthermore, people living in different countries kill each other at irregular time intervals, so that also for this reason anyone who thinks about the future must live in fear and terror. This is due to the fact that the intelligence and character of the masses are incomparably lower than the intelligence and character of the few who produce something valuable for the community."
38 "The majority of the stupid is invincible and guaranteed for all time. The terror of their tyranny, however, is alleviated by their lack of consistency."
38 "Joy in looking and comprehending is nature's most beautiful gift."
39 "...there is also such a thing as a spirit of the times, an attitude of mind characteristic of a particular generation, which is passed on from individual to individual and gives its distinctive mark to a society. Each of us has to do his little bit toward transforming this spirit of the times."
39 "Let every man judge by himself, by what he has himself read, not by what others tell him."
44 "Those ideals and convictions which resulted from historical experience, from the craving for beauty and harmony, have been readily accepted in theory by man--and, at all times, have been trampled upon by the same people under the pressure of their animal instincts. A large part of history is therefore replete with the struggle for those human rights, an eternal struggle in which a final victory can never be won." I disagree. I think we can win the struggle and that in particular we have won the struggle for food.
50 "But the scientist is possessed by the sense of universal causation. The future, to him, is every whit as necessary and determined as the past. There is nothing divine about morality; it is a purely human affair. His religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection. This feeling is the guiding principle of his life and work, in so far as he succeeds in keeping himself from the shackles of selfish desire. It is beyond question closely akin to that which has possessed the religious geniuses of all ages." Develop and explain each of these points in the context of PC.
98 "I am inclined to the view that the state can only be of real use to industry as a limiting and regulative force."
109 "Political leaders or governments owe their position partly to force and partly to popular election. They cannot be regarded as representative of the best elements, morally or intellectually, in their respective nations."
123 The need for a world policeman
128 "The bombing of civilian centers was initiated by the Germans and adopted by the Japanese. To it the Allies responded in kind--as it turned out, with greater effectiveness--and they were morally justified in doing so."
195 "When thought is too greatly dominated by ... generalizations, misinterpretations of specific sequences of cause and effect readily occur, doing injustice to the actual multiplicity of events. Abandonment of generalization, on the other hand, means to relinquish understanding altogether."
195 "In political life I see two opposed tendencies at work, locked in constant struggle with each other. The first, optimistic trend proceeds from the belief that the free unfolding of the productive forces of individuals and groups essentially leads to a satisfactory state of society. It recognizes the need for a central power, placed above groups and individuals, but concedes to such power only organizational and regulatory functions. The second, pessimistic trend assumes that free interplay of individuals and groups leads to the destruction of society; it thus seeks to base society exclusively upon authority, blind obedience, and coercion. Actually this trend is pessimistic only to a limited extent; for it is optimistic in regard to those who are, and desire to be, the bearers of power and authority. The adherents of this second trend are the enemies of the free groups and of education for independent thought. They are, moreover, the carriers of political anti-Semitism.
"Here in America all pay lip service to the first, optimistic, tendency. Nevertheless, the second group is strongly represented. It appears on the scene everywhere, though for the most part it hides its true nature. Its aim is political and spiritual dominion over the people by a minority, by the circuitous route of control over the means of production."
220 "I believe with Schopenhauer that one of the strongest motives that leads men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one's own ever shifting desires. A finely tempered nature longs to escape from personal life into the world of objective perception and thought; this desire may be compared with the townsman's irresistible longing to escape from his noisy, cramped surroundings into the silence of high mountains, where the eye ranges freely through the still, pure air and fondly traces out the restful contours apparently built for eternity." You got it, Albert.
220 "Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world, he then tries to some extent to substitute this cosmos of his for the world of experience, and thus to overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own fashion. Each makes this cosmos and its construction the pivot of his emotional life, in order to find in this way the peace and security which he cannot find in the narrow whirlpool of personal experience."
228 "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?" Yes it is, according to Dr. Dick
228 "...as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
229 Axioms are implicit definitions
238 Visualizing a 4D Riemann sphere
241 "The influence of motion (relative to the coordinate system) on the form of bodies and on the motion of clocks, also the equivalence of energy and inert mass, follow from the interpretation of coordinates and time as products of measurement."
245 Formula for Coriolis force
255 "Denominational traditions I can only consider historically and psychologically; they have no other significance for me."
256 How Kepler figured out planetary orbits.
259 "...knowledge cannot spring from experience alone but only from the comparison of the inventions of the intellect with observed fact."
262 "...before Maxwell people conceived of physical reality--in so far as it is supposed to represent events in nature--as material points, whose changes consist exclusively of motions, which are subject to total differential equations. After Maxwell they conceived physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations."
263 "We shall then, I feel sure, have to return to the attempt to carry out the program which may be described properly as the Maxwellian--namely, the description of physical reality in terms of fields which satisfy partial differential equations without singularities."
268 The "great stumbling-block" to finding a unified field theory is continuous functions. Maybe my Practical Numbers could help get around it.
270 Meaning as cognitive value. It is the connection of concepts to experience.
277 The discoveries resulting from Special Relativity: "This method led to the discovery of the necessary connection between momentum and energy, between electric and magnetic field strength, electrostatic and electrodynamic forces, inert mass and energy; and the number of independent concepts and fundamental equations in physics was thereby reduced."
277 The general Riemannian metric.
283 "The whole of science is nothing more than a refinement of everyday thinking. It is for this reason that the critical thinking of the physicist cannot possibly be restricted to the examination of the concepts of his own specific field. He cannot proceed without considering critically a much more difficult problem, the problem of analyzing the nature of everyday thinking."
284 Einstein's description of Dr. Dick's sets "A", "B", and "C".
285 "The very fact that the totality of our sense experiences is such that by means of thinking ... it can be put in order, this fact is one which leaves us in awe, but which we shall never understand. One may say "the eternal mystery of the world is its comprehensibility." It is one of the great realizations of Immanual Kant that the postulation of a real external world would be senseless without this comprehensibility." Never say never! Dr. Dick has shown how to understand this awesome fact: it stems directly from consistency.
285 The "miracle" of comprehensibility.
314 Good summary of the development of modern physics.
315 "The sense-experiences are the given subject-matter. But the theory that shall interpret them is man-made."
316 "What we call physics comprises that group of natural sciences which base their concepts on measurements; and whose concepts and propositions lend themselves to mathematical formulation. Its realm is accordingly defined as that part of the sum total of our knowledge which is capable of being expressed in mathematical terms. With the progress of science, the realm of physics has so expanded that it seems to be limited only by the limitations of the method itself."
325 "On this point the quantum theory of today differs fundamentally from all previous theories of physics, mechanistic s well as field theories. Instead of a model description of actual space-time events, it gives the probability distributions for possible measurements as function of time."
326 Language and science
328 "Perfection of means and confusion of goals seem--in my opinion--to characterize our age."
332 "Why do we devise theories at all? The answer...is simply "because we enjoy "comprehending.""
334 "Once a theoretical idea has been acquired, one does well to hold fast to it until it leads to an untenable conclusion."
335 "It is fascinating to muse: Would Faraday have discovered the law of electromagnetic induction if he had received a regular college education?"
335 "Now a question arose: Since the field exists even in a vacuum, should one conceive of the field as a state of a "carrier," or should it rather be endowed with an independent existence not reducible to anything else? In other words, is there an "ether" which carries the field; the ether being considered in the undulatory state, for example, when it carries light waves?
"The question has a natural answer: Because one cannot dispense with the field concept, it is preferable not to introduce in addition a carrier with hypothetical properties."
336 "Maxwell's equations imply the "Lorentz group," but the Lorentz group does not imply Maxwell's equations. The Lorentz group may indeed be defined independently of Maxwell's equations as a group of linear transformations which leave a particular value of the velocity--the velocity of light-- invariant."
338 "What group of coordinate transformations can then be substituted for the group of Lorentz transformations? Mathematics suggests an answer which is based on the fundamental investigations of Gauss and Riemann: namely, that the appropriate substitute is the group of all continuous (analytical) transformations of the coordinates. Under these transformations the only thing that remains invariant is the fact that neighboring points have nearly the same coordinates; the coordinate system expresses only the topological order of the points in space (including its four-dimensional character). The equations expressing the laws of nature must be covariant with respect to all continuous transformations of the coordinates. This is the principle of general relativity." Could the corresponding group in my Practical Number system be used instead? It seems it would have the same topological significance and might lead to a more natural definition of "material point".
338 "The physical reality of space is represented by a field whose components are continuous functions of four independent variables--the coordinates of space and time. It is just this particular kind of dependence that expresses the spatial character of physical reality."
339 "...every theory is speculative. Where the basic concepts of a theory are comparatively "close to experience" (e.g. the concepts of force, pressure, mass), its speculative character is not so easily discernible. If. however, a theory is such as to require the application of complicated logical processes in order to reach conclusions from the premises that can be confronted with observation, everybody becomes conscious of the speculative nature of the theory. In such a case an almost irresistible feeling of aversion arises."
340 "...a theory has an important advantage if its basic concepts and fundamental hypotheses are "close to experience," and greater confidence in such a theory is certainly justified." Nothing is "closer to experience" than consciousness!
342 High level derivation of the field law differential equations.
342 "Evidently a complete relativistic field theory must be based on a field of more complex nature, that is, a generalization of the symmetrical tensor field."
343 "...the equations of gravitation are ten differential equations for the ten components of the symmetrical tensor g(ik).
343 Bianchi's identities
348 Einstein expresses his pessimism in 1950.
351 "cum grano salis" - with a grain of salt
352 Einstein's criticism of Kant's attempt to deny the objectivity of space.
352 "...a larger box can always be introduced to enclose the smaller one. In this way space appears as something unbounded." - Always?? >
©2009 Paul R. Martin, All rights reserved.