Academics From Austria

"The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.—Mach, Ernst."

"The aim of research is the discovery of the equations which subsist between the elements of phenomena."

"Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it may seem, the strength of mathematics lies in the avoidance of all unnecessary thoughts, in the utmost economy of thought-operations. The symbols of order, which we call numbers, form already a system of wonderful simplicity and economy. When in the multiplication of a number with several digits we employ the multiplication table and thus make use of previously accomplished results rather than to repeat them each time, when by the use of tables of logarithms we avoid new numerical calculations by replacing them by others long since performed, when we employ determinants instead of carrying through from the beginning the solution of a system of equations, when we decompose new integral expressions into others that are familiar,—we see in all this but a faint reflection of the intellectual activity of a Lagrange or Cauchy, who with the keen discernment of a military commander marshalls a whole troop of completed operations in the execution of a new one."

"There was a loud echo of Hume in Mach’s work, as both emphasized the tangibility of all knowledge—ultimately, all knowledge is based in the senses. Mach also emphasized the internal nature of all knowledge, in that it is experienced in the mind. Finally, he emphasized the importance of quantitative and mathematical methods and models to understand sensory experience."

"Not bodies produce sensations, but element-complexes (sensation-complexes) constitute the bodies. When the physicist considers the bodies as the permanent reality, the `elements' as the transient appearance, he does not realise that all `bodies' are only mental symbols for element-complexes (sensation-complexes)"

"Nature consists of the elements given by the senses. Primitive man first takes out of them certain complexes of these elements that present themselves with a certain stability and are most important to him. The first and oldest words are names for "things". … The sensations are no "symbols of things". On the contrary the "thing" is a mental symbol for a sensation-complex of relative stability. Not the things, the bodies, but colours, sounds, pressures, times (what we usually call sensations) are the true elements of the world."

"I see the expression of... economy clearly in the gradual reduction of the statical laws of machines to a single one, viz. , the principle of virtual work: in the replacement of Kepler's laws by Newton's single law... and in the [subsequent] reduction, simplification and clarification of the laws of dynamics. I see clearly the biological-economical adaptation of ideas, which takes place by the principles of continuity (permanence) and of adequate definition and splits the concept 'heat' into the two concepts of 'temperature' and 'quantity of heat'; and I see how the concept 'quantity of heat' leads on to 'latent heat', and to the concepts of 'energy' and 'entropy'."

"Personally, people know themselves very poorly."

"In reality, the law always contains less than the fact itself, because it does not reproduce the fact as a whole but only in that aspect of it which is important for us, the rest being intentionally or from necessity omitted."

"The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not a logical process although such processes can be inserted as intermediary and auxiliary links. The principle effort that leads to the discovery of new knowledge is due to abstraction and imagination."

"There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathematical methods would take a lifetime."

"In the philosophy of Mach a world without matter is unthinkable. Matter in Mach's philosophy is not merely required as a test body to display properties of something already there ...it is an essential feature in causing those properties which it able to display, Inertia, for example, would not appear by the insertion of one test body in the world; in some way the presence of other matter is a necessary condition. It will be seen how welcome to such a philosophy is the theory that space and the inertial frame come into being with matter, and grow as it grows."

"I know of nothing more terrible than the poor creatures who have learned too much. Instead of the sound powerful judgement which would probably have grown up if they had learned nothing, their thoughts creep timidly and hypnotically after words, principles and formulae, constantly by the same paths. What they have acquired is a spider's web of thoughts too weak to furnish sure supports, but complicated enough to provide confusion."

"Although I think that life may be the result of an accident, I do not think that of consciousness. Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else."

"Conditions are admittedly such that we can always manage to make do in each concrete individual case without the two different aspects leading to different expectations as to the result of certain experiments. We cannot, however, manage to make do with such old, familiar, and seemingly indispensable terms as "real" or "only possible"; we are never in a position to say what really is or what really happens, but we can only say what will be observed in any concrete individual case. Will we have to be permanently satisfied with this...? On principle, yes. On principle, there is nothing new in the postulate that in the end exact science should aim at nothing more than the description of what can really be observed. The question is only whether from now on we shall have to refrain from tying description to a clear hypothesis about the real nature of the world. There are many who wish to pronounce such abdication even today. But I believe that this means making things a little too easy for oneself."

"If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts."

"\frac{\partial \psi}{\partial t} = -\frac{2 \pi i}{h} E \psi"

"No self is of itself alone. It has a long chain of intellectual ancestors. The "I" is chained to ancestry by many factors … This is not mere allegory, but an eternal memory."

"The stages of human development are to strive for: (1) Besitz [Possession] (2) Wissen [Knowledge] (3) Können [Ability] (4) Sein [Being]"

"When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or ψ-functions) have become entangled. [italics in the original]"

"For thousands of years men have striven and suffered and begotten and women have brought forth in pain. A hundred years ago, perhaps, another man sat on this spot; like you he gazed with awe and yearning in his heart at the dying light on the glaciers. Like you he was begotten of man and born of woman. He felt pain and brief joy as you do. Was he someone else? Was it not you yourself? What is this Self of yours? What was the necessary condition for making the thing conceived this time into you, just you and not someone else?"

"This life of yours which you are living is not merely apiece of this entire existence, but in a certain sense the whole; only this whole is not so constituted that it can be surveyed in one single glance. This, as we know, is what the Brahmins express in that sacred, mystic formula which is yet really so simple and so clear; tat tvam asi , this is you. Or, again, in such words as "I am in the east and the west, I am above and below, I am this entire world."

"But it is quite easy to express the solution in words, thus: the plurality that we perceive is only an appearance; it is not real. Vedantic philosophy, in which this is a fundamental dogma, has sought to clarify it by a number of analogies, one of the most attractive being the many-faceted crystal which, while showing hundreds of little pictures of what is in reality a single existent object, does not really multiply the object... 'You may suddenly come to see, in a flash, the profound rightness of the basic conviction of Vedanta: … knowledge, feeling and choice are essentially eternal and unchangeable and numerically one in all men, nay in all sentient beings.'"

"'If finally we look back at that idea of [Ernst] Mach [1838-1916], we shall realize that it comes as near to the orthodox dogma of the Upanishads as it could possibly do without stating it expressis verbis . The external world and consciousness are one and the same thing.'"

"Another way of expressing the peculiar situation is: the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts, even though they may be entirely separate and therefore virtually capable of being "best possibly known," i.e., of possessing, each of them, a representative of its own. The lack of knowledge is by no means due to the interaction being insufficiently known—at least not in the way that it could possibly be known more completely—it is due to the interaction itself. Attention has recently been called to the obvious but very disconcerting fact that even though we restrict the disentangling measurements to one system, the representative obtained for the other system is by no means independent of the particular choice of observations which we select for that purpose and which by the way are entirely arbitrary. It is rather discomforting that the theory should allow a system to be steered or piloted into one or the other type of state at the experimenter's mercy in spite of his having no access to it. [italics in the original]"

"Nirvana is a state of pure blissful knowledge... It has nothing to do with the individual. The ego or its separation is an illusion. Indeed in a certain sense two "I"'s are identical namely when one disregards all special contents — their Karma. The goal of man is to preserve his Karma and to develop it further... when man dies his Karma lives and creates for itself another carrier."

"God knows I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is."

"we never experiment with just one electron or atom or (small) molecule. In thought-experiments we sometimes assume that we do."

"I insist upon the view that 'all is waves'."

"So if we're going to ask... What is life? ...Erwin Schrödinger wrote a famous book on that theme ...Two famous ideas ...emerged ...one ...was ...that genes are a code-script, and that was the first time anybody had used the word "code-script" or really thought in terms of information, in biology. ...This was before DNA was discovered. He was a direct inspiration to Watson and Crick and many others. The second theme... was how life maintains its organization over time, and why don't we just fall to pieces as entropy would tend to suggest... He talked about life feeding on negative entropy, or "negentropy"... [H]e talked about continually sucking order... from its environment. ...[I]t's a wonderful book. ...[H]e said, "If I had been catering for physicists alone I should have let the discussion turn on free energy instead." ...In more modern terms he's saying something like life is the harnessing of chemical energy in such a way that the energy-harnessing device makes a copy of itself. ...[H]e's linking the two key themes of biology ...information and energy together."

"The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. In 1925, the world view of physics was a model of a great machine composed of separable interacting material particles. During the next few years, Schrodinger and Heisenberg and their followers created a universe based on super imposed inseparable waves of probability amplitudes. This new view would be entirely consistent with the Vedantic concept of All in One."

"Just a few months after de Broglie's suggestion, Schrödinger took the decisive step... by determining an equation that governs the shape and the evolution of probability waves, or as they became known, s. It was not long before Schrödinger's equation and the probabilistic interpretation were being used to make wonderfully accurate predictions. By 1927, therefore, classical innocence had been lost. Gone were the days of a whose individual constituents were set in motion at some moment in the past and obediently fulfilled their inescapable, uniquely determined destiny. According to quantum mechanics, the universe evolves according to a rigorous and precise mathematical formalism, but this framework determines only the probability that any particular function will happen—not which future actually ensues."

"I met him frequently in later life, and, of all the physicists that I met, I think Schrodinger was the one that I felt to be most closely similar to myself. I found myself getting into agreement with Schrodinger more readily than with anyone else. I believe the reason for this is that Schrodinger and I both had a very strong appreciation of mathematical beauty, and this appreciation of mathematical beauty dominated all our work. It was a sort of act of faith with us that any equations which describe fundamental laws of Nature must have great mathematical beauty in them. It was like a religion with us. It was a very profitable religion to hold, and can be considered as the basis of much of our success."

"You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality — if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality — reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation."

"[T]hose people who say "Life is baffling, we can't explain it," aren't necessarily saying we need or a miracle. They might just be saying "We need some new physics... or laws of life," if you like, and Schrödinger was open to that, he said "We must be prepared to find a new kind of physical law prevailing in it.""

"Like Schopenhauer, he accepted an hierarchical view of our understanding of the world, with philosophy above and physics below."

"Schrödinger, who was born in Vienna in 1887, was a fascinating man. I met him a few months before he died in 1961. All the inventors of the quantum theory, as it happened, were men of very broad culture, perhaps attributable in part to their European gymnasium educations, but even in this group Schrödinger stood out. He read very widely in a variety of languages, ancient and modern. He was a scientific polymath with a deep interest in Eastern religions. He was also a rather romantic figure who wrote poetry. I was told by that when Schrödinger appeared in 1939 at the Institute for Advanced Study in Dublin, where he had been offered sanctuary during the war, he did so with what Professor Frank referred to as two ‘‘wives.’’ (This was the least of it. Schrödinger had several mistresses, with whom he fathered at least two daughters.)"

"It is a poorly-kept secret that the grandfathers of quantum mechanics, Bohr, Oppenheimer, Heisenberg, Einstein, de Broglie, Jeans, but in particular Schrödinger were fascinated and inspired by Vedic cosmology."

"To my view the ‘statistical theory of time’ has an even stronger bearing on the philosophy of time than the theory of relativity. The latter, however revolutionary, leaves untouched the undirectional flow of time, which it presupposes, while the statistical theory constructs it from the order of events. This means a liberation from the tyranny of old Chronos. What we in our minds construct ourselves cannot, so I feel, have dictatorial power over our mind, neither the power of bringing it to the fore nor the power of annihilating it. But some of you, I am sure, will call this mysticism. So with all due acknowledgement to the fact that physical theory is at all times relative, in that it depends on certain basic assumptions, we may, or so I believe, assert that physical theory in its present stage strongly suggests the indestructibility of Mind by Time."

"Matter and energy seem granular in structure, and so does "life", but not so mind."

"If we were bees, ants, or Lacedaemonian warriors, to whom personal fear does not exist and cowardice is the most shameful thing in the world, warring would go on forever. But luckily we are only men — and cowards."

"There is obviously only one alternative, namely the unification of minds or consciousnesses. Their multiplicity is only apparent, in truth there is only one mind."

"Nature has no reverence towards life. Nature treats life as though it were the most valueless thing in the world.... Nature does not act by purposes."

"Seventy-five years ago Erwin Schrödinger published... What Is Life?... based on a series of lectures he gave in Dublin in 1943 during the height of World War II... [S]chrödinger was the... co-architect of one of the most difficult scientific theories that we know, quantum mechanics, but he was unable to wrap his head around the nature of life. He was baffled. He made some progress, but the key point he wanted to address was whether life can be explained by physics. ...[I]t's really important... to distinguish between known physics, what you find in the textbooks, and new physics."

"The only possible alternative is simply to keep to immediate experience that consciousness is a singular of which the plural is unknown; that there is only one thing and that what seems to be a plurality is merely a series of different aspects of this one thing, produced by a deception (the Indian MAJA); the same illusion is produced in a gallery of mirrors, and in the same way Gaurisankar and Mt Everest turned out to be the same peak seen from different valleys."

"From the early great Upanishads, the recognition ATHMAN = BRAHMAN (the personal self equals the omnipresent, all-comprehending eternal self) was in Indian thought considered, far from being blasphemous, to represent the quintessence of deepest insight into the happenings of the world. The striving of all the scholars of Vedanta was, after having learnt to pronounce with their lips, really to assimilate in their minds this grandest of all thoughts."

"He rejected traditional religious beliefs (Jewish, Christian, and Islamic) not on the basis of any reasoned argument, nor even with an expression of emotional antipathy, for he loved to use religious expressions and metaphors, but simply by saying that they are naive."

"The world is given to me only once, not one existing and one perceived. Subject and object are only one. The barrier between them cannot be said to have broken down as a result of recent experience in the physical sciences, for this barrier does not exist."

"The material world has only been constructed at the price of taking the self, that is, mind, out of it, removing it; mind is not part of it..."

"We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics. For that is just what is to be expected from the knowledge we have gained of the structure of living matter. We must also be prepared to find a new type of physical law prevailing in it. Or are we to term it a non-physical, not to say a super-physical, law?"