A TRUE TEACHER is "one whose actual lessons may be forgotten, but whose LIVING ENTHUSIASM is a quickening, animating and inspiring power.
Pagels, Heinz R.
Paige, Satchel Leroy
Don't look back. Something may be gaining on you.
- The common ground of high ENERGY PHYSICISTS and RELATIVISTIC COSMOLOGISTS is the EARLY UNIVERSE, a region of energy and momentum, time and space for which they have the LEAST CONFIDENCE that they know what is going on. Yet such circumstance is what creates the INTELLECTUAL CHALLENGE.
- We have already entered the era of POST-ACCELERATOR-PHYSICS for which the entire HISTORY of the UNIVERSE becomes the PROVING GROUND for FUNDAMENTAL PHYSICS.
He who knows nothing, LOVES nothing. He who can do nothing, understands nothing. He who understands nothing is worthless. But he who understands also LOVES, notices, sees . . . The more knowledge is inherent in a thing, the greater the LOVE . . . Anyone who imagines that all fruits ripen at the same time as the strawberries knows nothing about grapes.
HOPE is not the lucky gift of circumstance or disposition, but a VIRTUE like FAITH and LOVE, to be practiced whether or not we find it easy or even natural, because it is NECESSARY to our survival as human beings.
Park, David Allen
- If I do not BELIEVE as you BELIEVE, it PROVES that you do not BELIEVE as I BELIEVE, and this is all that it PROVES.
- Great part of that order which reigns among mankind is not the effect of GOVERNMENT. It had its origins in the PRINCIPLES of SOCIETY and the NATURAL CONSTITUTION of MEN. It existed prior to government, and would exist of the formality of GOVERNMENT were abolished. The MUTUAL DEPENDENCE and RECIPROCAL INTEREST which man has upon man, and all parts of a civilized community upon one another, create that great chain of connection which hold it together תתת In fine, SOCIETY performs for itself almost everything which is ascribed to GOVERNMENT.
- HUMAN NATURE is not of itself vicious.
Four be the things I'd been better without: LOVE, curiosity, freckles, and doubt.
WORK expands so as to fill the TIME for its COMPLETION. General recognition of this fact is shown in the proverbial phrase: 'It is the
BUSIEST man who has TIME to SPARE.'
When we speak of the LIMITS of the UNIVERSE we imply the LIMITS of KNOWLEDGE. Temporary LIMITS to be sure, but nevertheless LIMITS. In probing the UNIVERSE man probes his BRAIN. The nature of his boldest and 'maddest' THEORIES is determined by his way of thinking. That is why the secrets of the cosmos and the microworld excite and attract me. They are a mirror which reflects our CAPABILITY for KNOWLEDGE. And man is born for KNOWLEDGE. This is the meaning and the purpose of CIVILIZATION which is why man will never stop looking into the mirror of the UNIVERSE.
Pasachoff, Jay M.
- The EQUATIONS of THEORETICAL PHYSICS consist of MATHEMATICAL SYMBOLS written on paper. These symbols have perfectly precise mathematical meanings. They are also supposed to have something to do with our EXPERIENCE of NATURE; if these were not the case, the equations would remain as PURE MATHEMATICS. The mathematical and physical DEFINITIONS of the SYMBOLS have nothing to do with each other; they are logically entirely INDEPENDENT. MATHEMATICAL DEFINITIONS are CONVENTIONAL in nature; PHYSICAL DEFINITIONS assume the truth of PHYSICAL HYPOTHESES. I have made this point above in talking about time. To give but two other
well-known examples, the DEFINITION of the term 'solar system' supposes that the sun and planets form a system of objects and not a collection of little lights in the sky; the SCIENTIFIC DEFINITION of temperature assumes the truth of the second law of thermodynamics. The EQUATIONS of the SPECIAL THEORY of RELATIVITY were more or less known before Einstein to Fitzgerald, Lorentz, and Poincaré; Schrödinger wrote down the profound and essentially correct EQUATIONS of QUANTUM MECHANICS that bears his name with almost no idea of its PHYSICAL SIGNIFICANCE. There are people, of whom I am one, who solve the EQUATIONS of GENERAL RELATIVITY in their work, but sometimes do not have a perfectly clear idea what the solutions mean.
- . . . To say that REAL TIME does or does not take place is a statement without consequences. In fact, we are not anywhere in TIME and do not go anywhere in TIME; TIME is a DIMENSION of EXPERIENCE like SPACE, but the BEHAVIOUR of MATTER with RESPECT to that DIMENSION is so DIFFERENT from what it is with RESPECT to the DIMENSIONS of SPACE that almost no valid argument by analogy is possible.
Twinkle, twinkle, PULSING STAR
Newest puzzle from afar.
Beeping on and on you sing -
Are you saying anything?
Twinkle, twinkle more, PULSAR,
How I wonder what you are.
If GEOMETRY is to be regarded as a science born of DIRECT and EXACT observation of NATURE, a science that seeks by purely inductive means to win from IMMEDIATELY observed simple phenomena the LAWS of complicated phenomena, then one is indeed compelled to reject many a traditional idea; but if we do so, the material to be worked up will be brought back to its proper domain and the ground for a whole series of controversies will be eliminated. No matter how many sorts of speculation may still be associated with GEOMETRY, its fruitful application in the NATURAL SCIENCES and in practical life rests upon the fact that its concepts originally correspond to EMPIRICAL OBJECTS. As long as one limits himself from first to last to this EMPIRICAL CORE, GEOMETRY retains the character of a NATURAL SCIENCE, distinguished from the other parts of science by the fact that it needs to derive very few of its concepts and laws IMMEDIATELY from EXPERIENCE.
Pasternak, Boris Leonidovich
Everything that HAPPENS in the world takes place not only on the EARTH that buries its dead, but also in some OTHER DIMENSION which some call KINGDOM of GOD.
- People are usually more CONVINCED by REASONS they discovered themselves than by those found by others.
- EDUCATION produces NATURAL INTUITIONS, and natural intuitions are erased by education.
- If all men knew what each said of the other, there would not be four FRIENDS in the world.
- Le coeur a ses raisons, que la Raison connoit pas.
The HEART has its REASONS, which REASON does not know.
- Since we cannot KNOW all that is to be known of EVERYTHING, we ought to know a LITTLE about EVERYTHING.
- He [man] is ignorant in his life's first age, but he never ceases to learn as he goes forward, for he has the advantage not only of his own
experience but also of his predecessors', because he always keeps in his memory the KNOWLEDGE he has once acquired, and that of the ancients is always at hand in the books they have left. And since he keeps his KNOWLEDGE, he can also easily increase it, so that men today are in a certain sense in the same condition in which those ancient philosophers would be if they could have prolonged their old age until now, adding to the KNOWLEDGE they had what their studies might have won for them by the grace of so many centuries. Hence it is that by a special prerogative not only does man advance from day to day in the sciences, but all men together make a continual progress as the universe grows old, because the same thing happens in the succession of men as in the different ages of an individual man. So that the whole series of men during the course of so many centuries should be considered as one self-same man, always in existence and continually learning.
- KNOWLEDGE of MAN'S true nature, of his true good, of true virtue and of true religion are inseparable one from another.
- What a chimera, then is MAN! What a novelty! What a monster, what a chaos, what a contradiction, what a prodigy! Judge all things, feeble worms of the earth, depository of truth, a sink of uncertainty, and error, the pride and refuse of the UNIVERSE.
- MAN is but a REED, the weakest in NATURE; but he is a THINKING REED. It does not take the whole UNIVERSE in arms to crush him. A vapour, or a drop of water is enough to kill him. But if the UNIVERSE were to crush him, MAN would still be nobler than his killer. For he knows that he is dying and that the UNIVERSE has the advantage over him; the UNIVERSE KNOWS nothing of this.
- Our whole DIGNITY consists, therefore, in THOUGHT. By thought we must raise ourselves, not by SPACE or TIME, which we have no means of filling. Let us endeavour, then, to think well; this is the beginning of MORALITY.
- It is dangerous to show MAN too clearly how much he resembles the beast without at the same time showing his greatness. It is also
dangerous to allow too clear a vision of his greatness without his baseness. It is even more dangerous to leave him in ignorance of both.
But it is very profitable to show him both.
- The HAPPY have no need for MIRACLES.
- All men's MISERIES derive from not being able to sit QUIET in a room ALONE.
- SCIENTIFIC KNOWLEDGE will not make up for the lack of MORALS in time of AFFLICTION.
- The PERFECTION of NATURE shows that she is the IMAGE of GOD; her DEFECTS show that she is only his IMAGE.
- NOBLE DEEDS that are CONCEALED are most ESTEEMED.
- L'OPINION est la REINE du MONDE.
OPINION is the QUEEN of the WORLD.
- Do you wish men to speak well of you? Then speak never well of yourself.
- Two extravagances: to exclude REASON, to admit only REASON.
- It is not from SPACE that I must seek my dignity, but from the government of my THOUGHT. I shall have no more if I possess worlds. By
SPACE the Universe encompasses and swallows me up like an atom; by THOUGHT I COMPREHEND the world.
- We know the TRUTH not only by REASON, but also by the HEART.
- Nous ne cherchons jamais les choses, mais la recherche des choses.
We never look for the TRUTH of things but for the VANITY of KNOWLEDGE.
- It is far better to know something about everything than to know all about one thing. UNIVERSALITY is the best.
All ART constantly aspires to the condition of MUSIC.
There are questions which come to every man in FEELINGS of WASTELANDS and LONELINESS beyond the HEALING of KNOWN COMPANIONS. For these he has sung a sad song in the day and night and written stories of slaughter and agony. For want of answers his mind has splintered and he has wandered off into the ecstasy of madness. He has sought answers in the arguments of wind and wisdom of opium. Many have stifled the voices, drowning them in HURRY and NOISE. Many have listened unwillingly, and turned away as soon as they could. Some listen again and again, until the yearning unknown is itself known and familiar: the quandaries become remembered faces without names, and the mysteries, silent companions. To them the unanswerables are no longer pools of terrible drowning. These become the depth and body of the sea, the lifting presence beneath the keels of their vessels. They make of the mysteries a song and a story; they are taught the ways of acceptance and peace. Having known the wonder and been welded into it, they are secure and unconquerable.
- L'universe est un ensemble dissymé trique et je suis persuadé quela vie, telle qu'elle se manifeste à nous, est fonction de la dissemé trie de l'univers ou de consequences qu'elle entraine. L'UNIVERSE EST DISSEMÉTRIQUES.
- The Greeks have given us one of the most beautiful words of our language, the word 'ENTHUSIASM' - a GOD WITHIN. The GRANDEUR of the acts of men is measured by the INSPIRATION from which they spring. HAPPY is he who bears a GOD WITHIN.
LI>There are NOT two DIFFERENT KINDS of SCIENCE; there is science and there are APPLICATIONS of science. The two types constantly interplay, and one type cannot progress far without contact with the other.
- Take interest, I beseech you, in those sacred institutions which we designate under the expressive name of LABORATORIES. Demand that they be multiplied and adorned; they are the TEMPLES of WEALTH and of the FUTURE. There is it that humanity grows, becomes stronger and better. There it learns to read in the WORKS of NATURE, symbols of PROGRESS and of UNIVERSAL HARMONY, whereas the works of mankind are too often those of FANATICISM and DESTRUCTION.
- LIFE, as manifested to us, is a function of the ASYMMETRY of the UNIVERSE and of the consequences of this fact. The UNIVERSE is
ASYMMETRICAL; for, if the whole of the bodies which compose the SOLAR SYSTEM moving with their individual movements were placed before a glass, the image in the glass would not be superposed upon the reality. Even the movement of solar light is ASYMMETRICAL . . . TERRESTRIAL MAGNETISM, the opposition which exists between the north and the south poles in a magnet and between positive and negative electricity, are but resultants of ASYMMETRICAL ACTIONS and MOVEMENTS . . . LIFE is dominated by ASYMMETRICAL actions. I can even imagine that all living species are primordially, in their structure, in their external forms, functions of COSMIC ASYMMETRY.
- CHANCE favours the MIND that is PREPARED.
- Nothing is more SATISFYING for the MIND than to be able to follow a DISCOVERY from its very origin up to its LATEST DEVELOPMENTS.
- The immediate principles of LIVING BODIES would be, to a degree, indestructible of all the organisms created by GOD, the smallest and apparently most useless, were to be suppressed. And because the return to the atmosphere and to the mineral kingdom of everything which had ceased to live would be suddenly suspended, LIFE would become IMPOSSIBLE.
- SCIENCE belongs to no ONE COUNTRY.
- Soyez à vous même un adversaire vigilant et tenace, songez toujsours à vous prendre en faute.
Be always for yourself a vigilant and tenacious opponent, be always aware of your MISTAKES.
- FAITH is the substance of things hoped for, the evidence of things not seen.
- My own behaviour baffles me. For I find myself not doing what I really want to do but doing what I really loathe.
Pauling, Linus Carl
SCIENCE is the search for TRUTH - it is not a game in which one tries to BEAT his opponent, to do HARM to others. We need to have the SPIRIT of SCIENCE in INTERNATIONAL AFFAIRS, to make the conduct of international affairs the effort to find the right solution, the just solution of INTERNATIONAL PROBLEMS, not the effort by each nation to get the better of other nations, to do harm to them when it is possible.
Perhaps we are now in the process of building a CULTURE that will have IMMORTALITY on EARTH and in HEAVEN.
Pavlov, Ivan Petrrovich
However perfect the wing of a bird, it would never raise the bird aloft without the support provided by the AIR. FACTS are the air of scientists, without them you cannot fly. Without them your THEORIES are FUTILE EFFORTS.
It is necessary to point out the important role of methodological reflection in the HUMANITIES. This is partly due to the character of the object of investigation of the humanities; it is the result of human activities as signs with a descriptive and expressive function. The necessity and relative priority of methodological reflection is the greater since the language of the humanities is the common language, with all its INADEQUACIES. RESEARCH findings of any SCIENCE have or can have important SOCIO-CULTURAL CONSEQUENCES. Comprehensively existing sciences are the proper place for the analysis and judgement of these consequences, for they are a meeting-point of communication between the representatives of different disciplines.
- The THEORETICAL DETERMINATION of the FINE STRUCTURE CONSTANT is certainly the most important of the UNSOLVED problems of modern physics. We believe that any regression to the ideas of classical physics (as, for instance, to the use of the classical field concept) cannot bring us nearer to the goal. To reach it, we shall, presumably, have to pay with further revolutionary changes of the FUNDAMENTAL CONCEPTS of physics with still further digression from the CONCEPTS of the classical theories.
- What GOD hath put ASUNDER No man shall EVER JOIN.
- Since the seventeenth century the activities of the HUMAN SPIRIT have been strictly classified in separate compartments. But in my view the attempt to eliminate such distinction by a combination of RATIONAL UNDERSTANDING and the MYSTICAL EXPERIENCE of UNITY obeys the explicit or implicit imperative of our own contemporary age. Can the 'new modesty', along with a fresh recognition of an INNER WAY to SALVATION, exert as strong an influence on the coming centuries as the spirit of overweening pride, now revealed to have been disastrous?.
- In contrast to the purely empirical conception according to which natural laws can with virtual certainty be derived from the material of experience alone, many physicists have recently emphasized anew the fact that INTUITION and the DIRECTION of ATTENTION play a considerable role in the development of CONCEPTS and IDEAS, generally for transcending more experience, that are necessary for the erection of a system of NATURAL LAWS (that is, a scientific theory).
- I don't MIND your THINKING slowly; I mind you PUBLISHING FASTER than you THINK.
- SOMMERFELD . . . preferred . . . a DIRECT INTERPRETATION, as independent of MODELS as possible, of the laws of spectra in terms of INTEGRAL NUMBERS, following as KEPLER once did in his investigation of the planetary system, an inner feeling of harmony.
- What GOD hath put asunder, no man shall ever join.
Peale, Norman Vincent
GIVE all you've got to LIFE and it will give its greatest gifts to you.
Pearce, Joseph Chilton
- The whole motley confusion of acts, omissions, regrets and hopes which is the LIFE of each one of us find in DEATH not meaning or explanation, but an end.
- REALITY is a STAIRCASE going neither up nor down, we don't move, today is today, always is today.
- SOLITUDE is the profoundest fact of the human condition. MAN is the only being who knows he is ALONE.
- Man's MIND MIRRORS a UNIVERSE which mirrors man's mind.
- There is no world 'out there' available to dispassionate observation. OBJECTIVITY in relation to REALITY is a NATIVE DELUSION on our part . . . a universal common knowledge is denied. There appears to be no world-mind from which we may get cues, no secret wavelengths for our perceptors.
Peirce, Charles Sanders
- The second strand to my stay therefore is unexpected. It is not that the study of the PARANORMAL has moved closer to SCIENCE, but the best and most innovative of science has clearly taken a very large step toward a view of the universe which finds nothing at all outrageous on the idea that MINDS can communicate with MATTER or that minds can affect matter or minds affect minds.
- Finally I should declare my own attitude to the PARANORMAL. Having finished my investigation, my attitude is this. A scientist would have to be either massively ignorant or a confirmed bigot to deny the evidence that the human mind can make connection with SPACE, TIME and MATTER in ways which have nothing to do with the ordinary senses. Further, he cannot deny that these connections are compatible with current thinking in PHYSICS and may in the future become accepted as a part of an EXTENDED SCIENCE, in which the description of 'PARANORMAL' no longer applies and can be replaced by 'NORMAL'. Here is an account of my own investigation.
Penfield, Wilder Graves
- Our whole past experience is continually in our CONSCIOUSNESS, though most of it sunk to a GREAT DEPTH of DIMNESS. I think of CONSCIOUSNESS as a BOTTOMLESS LAKE, whose waters seem transparent, yet into which we can see but a little way.
- CONSIDER what EFFECTS that might CONCEIVABLY have PRACTICAL BEARINGS you CONCEIVE the objects of your CONCEPTION to have. Then, your conception of those EFFECTS is the WHOLE of your conception of the object.
- The HUMAN BRAIN is not a PREVIOUSLY PROGRAMMED CALCULATOR. It is a LIVING, GROWING, CHANGING organ. It can even carry out its own REPAIRS to some extent. But it is subject to an INEXORABLE EVOLUTION of its functional attitudes. No one can alter the time schedule of the human brain, not even a psychiatrist, or an educator. The built-in biological clock tells the passage of learning aptitudes and the teacher's opportunity.
- TEACHERS and PARENTS must always share responsibility for the EDUCATION of each new generation. This includes the CONDITIONING of each CHILD'S BRAIN. How and when it is conditioned, prepares the man for great achievement or limits him to mediocrity. A NEUROPHYSIOLOGIST can only suggest that the human brain is capable of far more than is demanded of it today. Adjust the time and the manner of TEACHING to the APTITUDES of the GROWING, CHANGING master-organ. Then, double your demands and your reasonable expectations.
- Mind, brain, and BODY make the MAN, and the man is capable of so much! Capable of comprehension of the universe, dedication to the good of others, planned research, happiness, despair, and eventually, perhaps, even an understanding of himself. He can hardly be subdivided. Certainly, mind and brain carry on their functions normally as a unit.
The neurologist's initial undertaking should be to try to explain the behaviour of this being on the basis of neuronal mechanisms alone. - this biped who falls on his knees to pray to his god and rises to his feet to lead an army, or to write a poem, or to dig a ditch, or to thrill to the beauty of the sunrise, or to laugh at the absurdities of this world!
Although only a few may originate a policy, we are all able to judge it.
François Jacob in 'The possible and the actual' (Washington UP) raises some of the basic problems of our existence, such as the way the genetic information that is laid down in a LINEAR script specifies the growth and development of an organism. We do not know how this happens, but Jacob argues that the unity of life at the molecular level conveys at least one important message. If the molecules that make up a chimpanzee are practically identical to those that make a man, then the difference between the two species must lie in the way these molecules are organized. NATURE ACTS like a CHILD with a LEGO set who uses the same components to build a helicopter, a crane or a carousel. Nature BUILDS VARIETY from STANDARD COMPONENTS, but it GENERATES new VARIETY without a plan, by RANDOMTRIAL. If the new assembly fails, NATURE discards it. If it works, NATURE allows it to propagate. Jacob compares this process to TINKERING (bricolage), making new gadgets from old bits and pieces that happen to be around. I enjoyed Jacob's book because it bears witness to an outstanding erudite and original mind that does not look back to past accomplishments, but forward to the great problems awaiting solutions. Ivan Turgenev wrote to Leo Tolstoy 'People who tie themselves to systems cannot encompass the whole truth, but try to catch it by the tail . . . truth is like a lizard: it leaves its tail in your fingers and runs away, knowing that it will grow a new one quickly.' By contrast, Jacob's arguments spring freshly from his penetrating powers of reasoning rather than from any preconceived framework of ideas. Jacob touches on profound truths lightly and humorously; and he leaves his readers to ponder on them.
BIFURCATION decreases ENTROPY
Peter I , Velikii Alekseevich
NECESSITY drove away SLOTH and forced me to WORK night and day.
Peter, Lawrence J.
- My own view is that ULTIMATELY PHYSICAL LAWS should find their most natural expression in terms of essentially COMBINATORIAL PRINCIPLES, that is to say, in terms of FINITE PROCESSES such as counting or other basically simple manipulative procedures. Thus, in accordance with such a view, should emerge some form of DISCRETE or COMBINATORIAL SPACE-TIME.
- COMPLEX GEOMETRY is a remarkably rich, elegant and powerful area of mathematics. A great deal of intricate structure can be subsumed into logically simple concepts. For example, even the flat tangent space of a 2-complex-dimensional manifold reveals, upon examination, our now familiar friend, the system of CLIFFORD PARALLELS on . And this, in its turn, has direct relevance to TWISTOR theory, to the structure of spinning massless particles and to the architecture of QUANTUM MECHANICS. Clearly there is much yet to be REVEALED in such interplay as this between mathematics and PHYSICS, or between the construction of the MIND and the WORKS of NATURE.
- COMPLEX NUMBERS are . . . a very important constituent of the STRUCTURE of PHYSICAL LAWS. The TWISTOR theory carries this further in suggesting that complex numbers may also be very basically involved in defining the nature of SPACETIME itself.
- If SPACETIME is considered from the point of view of its CONFORMAL STRUCTURE ONLY, POINTS AT INFINITY can be treated on the same basis as FINITE POINTS.
- I do not believe that a real understanding of the nature of ELEMENTARY PARTICLES can ever be achieved without a simultaneous deeper understanding of the nature of SPACETIME itself. But if we are concerned with a level of phenomena for which such an understanding is NOT necessary - and this will cover almost all of present-day physics - then the SMOOTH MANIFOLD picture presents an (unreasonably !) excellent framework for the discussion of phenomena.
- Under normal circumstances, GENERAL RELATIVITY can, for practical purposes, remain remarkably apart - almost aloof - from the rest of physics. At a SPACE-TIME SINGULARITY, the very reverse must surely be the case!
- The PHYSICAL theory of general RELATIVITY could not have been evolved were it not for the work of many generalizations of MATHEMATICIANS (in particular, Cart Friedrich Gauss and Bernhard Riemann) who were able to free GEOMETRY from its earlier imprisonment in EUCLIDEAN rigidity. But this debt to pure geometry that relativity has owed has now been amply repaid. For many of the ideas of the modern subject of DIFFERENTIAL GEOMETRY received their initial stimulus from concepts arising from Einstein's GENERAL RELATIVITY.
Thus we have, in the physics of relativity and in the mathematics of differential geometry, a supreme example which illustrates how PHYSICS and MATHEMATICS enrich one another. Here we can begin to see something of that profound interplay between the WORKINGS of the NATURAL World and the LAWS and SENSITIVITY of THOUGHT - an interplay which, as knowledge and understanding increase, must surely ultimately reveal a yet deeper interdependence of the on upon the other.
- It is sometimes said that if NAKED SINGULARITIES do occur, then this would be DISASTROUS for PHYSICS. I do not share this view. We already have the example of the big-bang SINGULARITY in the remote past, which seems not to be avoidable. The 'DISASTER' to physics occurred right at the beginning. Surely the presence if NAKED SINGULARITIES arising occasionally in collapse under much more 'controlled' circumstances would be the very reverse of a DISASTER. The effects of such Singular occurrences would be open to OBSERVATION now. Theories of SINGULARITIES would be open to OBSERVATIONAL TEST. The initial mystery of creation, therefore, would no longer be able to hide in the obscurity afforded by its supposed UNIQUENESS.
- The most important single lesson of relativity theory is, perhaps, that space and time are NOT concepts that can be considered independently of one another, but must be combined together to give a FOUR-DIMENSIONAL picture of phenomena: the description in terms of SPACETIME. Dynamics then becomes an aspect of GEOMETRY.
- It is thus very tempting to believe that a link between SPACETIME CURVATURE and QUANTUM PROCESSES may be supplied by the use of TWISTORS. Then, roughly speaking, it is the CONTINUAL SLIGHT 'SHIFTING' of the interpretations of the quantum (TWISTOR) operators which results in the CURVATURE of SPACETIME.
REF: MATHEMATICS is an exciting, dynamic field that continues to generate provocative ideas and novel concepts. Some notions quickly find their way into applications; others rest on their intrinsic beauty; still others occupy a modest place in the growing structure of mathematics itself.
The man who makes no MISTAKES does not usually make anything.
Phelps, William Lyon
The FEAR of LIFE is the favourite disease of the 20 th Century.
NUMBER is the bond of the eternal continuance of things.
- In a HIERARCHY every employee tends to RISE to his level of INCOMPETENCE.
- HUMILITY is the embarrassment you feel when you tell people how WONDERFUL you are.
Sir, I bear a rhyme excelling 3.14159
In mystic form and magic spelling 265358
Celestial sprites elucidate 8979
All my own striving can't relate. 323846
Que j'aime à faire apprendre 3.14159
Un nombre utile aux sages 26535
Immortal Archimè de artiste ingenieur 8979
Qui de ton jugement peut priser la valeur 32384626
Pour moi ton problème 4338
A les pareils avantages!. 1379
Pico della Mirandola, Giovanni
- I am only a PUBLIC ENTERTAINER who has understood HIS TIME.
- A PAINTER PAINTS to UNLOAD himself of FEELINGS and VISIONS.
- I do not SEEK, I FIND.
Apart from the KNOWN and the UNKNOWN, what else if there?
Pisarev, Dmitry Ivanovich
- We may more easily love GOD than comprehend Him or speak of Him.
- PHILOSOPHY seeks the truth, theology finds it, RELIGION possesses it.
Unlimited POWER is apt to corrupt the minds of those who possess it.
Pius XII, Eugenio Pacelli
True SCIENCE to an ever-increasing degree discovers God as though God were waiting behind each door opened by SCIENCE.
- Intellectual MEDIOCRITY is always distinguished by passive CONSERVATISM, whose inertness bluntly resists the assault of new ideas.
- It is not knowledge that ennobles, but LOVE and STRIVING for the TRUTH. This love and striving awakens when one begins to acquire knowledge. He who escapes the effect of this feeling will not be ennobled by university learning, extensive information, or a diploma.
- The ideal aim before the mind of the PHYSICIST is to understand the external world of reality.
- SCIENCE . . . means unresting endeavour and continually progressing development toward an aim which the poetic INTUITION may apprehend but which the INTELLECT can never fully grasp.
- SCIENCE cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of nature and therefore part of the mystery we are trying to solve.
Plekhanov, Georgi Valentinovich
The question of the relationship of ART to social life has always played a very important part in all literature that has reached a certain level of development. More often than not the question has been resolved in two ways which are directly contradictory to each other.
- ARITHMETIC has a very great and compelling effect, elevating the soul to reason about abstract numbers, and if visible or tangible objects are obtruding upon the argument, refusing to be satisfied.
- ASTRONOMY compels the soul to look UPWARDS and leads us from this world to another.
- Everything that DECEIVES may be said to enchant.
- Avoid compulsion and let your children's lessons take the form of PLAY. This will also help you to see what they are naturally fitted for. . . .
- Let no one un-acquainted with GEOMETRY enter here.
- The knowledge at which GEOMETRY aims is the knowledge of the eternal.
- GEOMETRY draws the soul towards truth.
- Copying the round shape of the UNIVERSE, they confined the two divine revolutions in a spherical body - the HEAD, as we now call it - which is the divinest part of us and lord over all the rest.
- When men speak ill of thee, live so as nobody may believe them.
- The man who neglects EDUCATION, walks lame to the end of his life.
Some have said and still say: Man is not made for the Sabbath, but the Sabbath for man. Society is not made for the artist, but the artist for society. Art must promote the development of human consciousness and the improvement of the social order.
Others decisively reject this viewpoint. In their opinion, art is an end in itself, and to turn it into a means of achieving some other end, however noble, is to lower the dignity of art.
Pliny, The Elder
It is precisely in its SMALLEST and simplest STRUCTURES that nature shows itself most perfect and accomplished.
Poincaré, Jules Henri
- KNOWING demands the organ fitted to the object.
- MANKIND is poised midway between the gods and the beasts.
LAPLACE'S view that ALL matters of our experience can ultimately be explained in terms of physics and chemistry prevails today in science and beyond science. It is the current scientific view of the universe. I hold this view to be false and believe that its baneful influence has caused the cultural and civil destruction of vast regions of Europe and has spread confusion through all countries spared the revolutions of the twentieth century.
Man's CULTURE is the most complex meaningful body in the universe and hence for a man to know even his own share of it amounts to a participation by his whole person. It determines his conceptual and emotional framework. However original and daring a great man's thinking
may be, it remains rooted in the framework that first shaped his mind.
If all men were exterminated, this would not affect the laws of inanimate nature. But the production of MACHINES would stop, and not until men arose again could machines be formed once more. Some animals can produce tools, but only men can construct machines; machines are human
artifacts, made of inanimate material.
An ART which has fallen into disuse for the period of a generation is altogether lost. There are hundreds of examples of this to which the process of mechanization is continually adding new ones. These losses are usually irretrievable. It is pathetic to watch the endless efforts - equipped with microscopy and chemistry, with mathematics and electronics - to reproduce a single violin of the kind the half-literate STRADIVARIUS turned out as a matter of routine more than two hundred years ago.
Poonpimai, Princess Diskul
Man thinks he has only body and the intellectual power, whereas he has his body as a sort of a frame or a puppet, intellectual power as an engine and the HEART or CONSCIENCE as the real human character. It is the third or the lack of it that contributes to the beneficial or the malevolent force . . . Our immediate problem is whether or how much man can still be HUMAN.
- SCIENCE is FACTS; just as houses are made of stones, so is science made of facts; but a pile of stone is not a house and a collection of facts is not necessarily science.
- AETHETICS SENSIBILITY plays the part of the delicate sieve.
- The SCIENTIST does not study NATURE because it is useful to do so. He studies it because he takes pleasure in it; and he takes pleasure in it because it is BEAUTIFUL. If nature were not beautiful, it would not be worth knowing and life would not be worth living.
- Does the HARMONY which human intelligence thinks it discovers in nature exist apart from such intelligence? Assuredly NO. A reality completely independent of the spirit that conceives it, sees it or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us. What we call 'objective reality' is, strictly speaking, that which is common to several thinking beings and might be common to all; this common part, we shall see, can only be the harmony expressed by mathematical laws.
- Now, what are the mathematical entities to which we attribute this character of BEAUTY and ELEGANCE, which are capable of developing in us a kind of aesthetic emotion? Those whose elements are harmoniously arranged so that the mind can, without effort, take in the whole without neglecting the details. This harmony is at once a satisfaction to our aesthetic requirements, and an assistance to the mind which it supports and guides. At the same time, by setting before our eyes a well-ordered whole, it gives us a presentiment of a mathematical law. Now, as I have said above,
the only mathematical facts worthy of retaining our attention and capable of being useful are those which can make us acquainted with a mathematical law. Accordingly we arrive at the following conclusion. The useful combinations are precisely the most beautiful, I mean those that can most charm that special sensibility that all mathematicians know, but which laymen are so ignorant of that they are often tempted to smile at it.
- What, in fact, is mathematical DISCOVERY? It does not consist in making new combinations with mathematical entities that are already known. That can be done by any one, and the combinations that could be so formed would be infinite in number, and the greater part of them would be absolutely devoid of interest. Discovery consists precisely in not constructing useless combinations, but in constructing that they are useful, which are an infinitely small minority. DISCOVERY is discernment, selection.
- There is a HIERARCHY of FACTS; some have no reach; they teach us nothing but themselves. The scientist who has ascertained them has learned nothing but a FACT, and has not become more capable of foreseeing new FACTS. Such FACTS, it seems, come once, but are not destined to reappear. There are, on the other hand, FACTS OF GREAT YIELD; each of them teaches us a new LAW. And since a CHOICE must be made, it is to these that the scientist should devote himself.
- The axioms of GEOMETRY therefore are neither a priori judgments nor experimental facts. They are CONVENTIONS; our choice among all possible conventions is guided by experimental facts; but it remains free and is limited only by the necessity of avoiding all contradictions.
- Un homme qui y consacrerait son existence arriverait peut-ê:tre a se peindre la quatriême DIMENSION.
- Would it be believable that the LOGICIANS always proceeded from the GENERAL to the particular, as the rules of FORMAL LOGIC seemed to prescribe? By this way they would never have been able to extend the frontiers of science; scientific conquests are only made by GENERALIZATION.
- If ARITHMETIC had remained free from all admixture of GEOMETRY, it would have known only the whole number; it is to adapt itself to the needs of GEOMETRY that it invented anything else.
- When mathematical science becomes RIGOROUS it assumes an ARTIFICIAL character that cannot be overlooked. IT FORGETS ABOUT its HISTORIC ORIGIN: it shows how problems can be solved but not how and why they are posed. This shows that LOGIC does NOT suffice; the science of proofs is not the whole of science, INTUITION is assigned a complementary part, I would say, as COUNTERPART or ANTIDOTE of logic.
- MATHEMATICS is the art of giving some name to different things.
- MATHEMATICIANS do not deal in objects, but in RELATIONS between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in FORM only.
- La PHYSIQUE ne nous donne pas seulement l'occasion de resoudre des
PROBLÊMES ....., elle nous fait presentir la SOLUTION.
- The problem is not what is the ANSWER, the problem is in what is the QUESTION.
- . . . without mathematical INFINITY, there would be no science at all, because there would be nothing general.
- THOUGHT is the lightening between two infinities of blackness. But it is the lightening which matters.
- The SCIENTIST does not study nature because it is useful. The studies it because he DELIGHTS in it, and he delights in it because it is BEAUTIFUL.
Popper, Karl R.
- A DISPUTANT no more cares for the TRUTH than the sportsman for the HARE.
- TRUE DISPUTANTS are like true SPORTSMEN; their whole delight is in the pursuit.
- Ask for what end the heavenly bodies shine,
Earth for whose use? PRIDE answers,` 'Tis for MINE:
For me kind nature wakes her genial power,
Suckles each herb, and spreads out every flower:
Annual for me. The grape, the rose, renew,
The juice nectareous, and the bahury dew;
For me, the mine a thousand treasures brings;
For me, health gushes from a thousand springs;
Sea roll to waft me, suns to light me rise;
My footstool earth, my canopy the skies.
- ALL ARE BUT PARTS OF ONE STUPENDOUS WHOLE,
Whose body nature is, and GOD the soul;
That, changed through all, and yet in all the same;
Great in the earth, as in the ethereal frame;
Warms in he sun, refreshes in the breeze,
Glows in the stars, and blossoms in the trees,
Lives through all life, extends through all extent,
Spreads undivided, operates unspent;
Breathes in our soul, informs our mortal part,
As full, as perfect, in a hair as heart;
As full, as perfect, in vile man that mourns,
As the rapt seraph that adores and burns;
To him no high, no low, no great, no small;
He fills, he bounds, connects, and equals all.
- HAPPY the man, whose wish and care
A few paternal acres bound,
Content to breathe his native air,
In his own ground.
- An HONEST man is the noblest work of GOD.
- HOPE springs eternal in the human breast:
Man NEVER is, but always to be blest:
The soul, UNEASY and confined from home,
Rests and expatiates in a life to come.
- It is just as easy to HOPE as it is to DESPAIR.
- Charms strike the sight, but MERIT wins the SOUL.
- All NATURE is but art, unknown to thee;
All chance, direction, which thou canst not see;
All discord, harmony not understood;
All partial evil, universal good:
And, spite of pride, in erring reason's spite,
One truth is clear, WHATEVER IS, IS RIGHT.
- Nature and Nature's laws lay hid in night;
God said, Let NEWTON BE! - And all was light.
- The PEOPLE'S voice is odd,
It is, and it is not, the voice of GOD.
- What will a child learn sooner than a SONG?
- Thus let me live, unseen, UNKNOWN,
Thus unlamented let me die,
Steal from the world, and not a stone
Tell where I lie.
Porter, Katherine Anne
- The way in which KNOWLEDGE progresses, and especially our scientific KNOWLEDGE, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by CONJECTURES. These conjectures are controlled by criticism; that is, by attempted refutations
which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable' (in the sense of probability calculus). Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us understand the difficulties of the problem which we are trying to solve. This is how we become better acquainted with our problem and able to proposes more mature solutions: the very refutation of a theory - that is, of any serious tentative solution of our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason for despair of reason. And since we can never know for certain, there can be no authority here for any claim to authority, for conceit
over our knowledge, or for smugness . . .
- There is no HISTORY of mankind, there are only many HISTORIES of all kinds of aspects of human life. And one of these is the HISTORY of political power. This is elevated into the HISTORY of the WORLD.
- But METAPHYSICAL HYPOTHESES are important for science in at least two ways. First of all, in order to have a general picture of the world we need metaphysical hypotheses. Secondly, in the actual preparation of our research, we are guided by what is called 'METAPHYSICAL RESEARCH PROGRAMMES.
- It was first in animals and children, but later also in adults, that I observed the immensely powerful NEED for REGULARITY - the need which makes them seek for regularities.
- In the open society I stressed that the initial method, though it will use tests whenever possible, and preferably practical tests, can be generalized into what I described as the critical or rational attitude. I agreed that one of the best senses of 'reason' and 'reasonableness' was OPENNESS TO CRITICISM - readiness to be criticized, and eagerness to criticize oneself; and I tried to argue that this initial attitude of reasonableness can be extended as far as possible. I suggested that the demand that we extend the critical attitude as far as possible might be called 'CRITICAL RATIONALISM', a suggestion which was later endowed by Adrienne Koch and by Hans Albert.
Implicit in this attitude is the realization that we SHOULD ALWAYS have to live in an IMPERFECT SOCIETY. This is so not because even very good people are very imperfect; nor is it because, obviously, we often make mistakes because we do not know enough. Even more important than either of these reasons is the fact that THERE ALWAYS EXIST IRRESOLVABLE CLASHES of VALUES: there are many moral problems which are insoluble because moral principles may conflict.
There can be no HUMAN SOCIETY WITHOUT CONFLICT: such a society would be a society not of friends but of ants. Even if it were attainable, there are human values of the greatest importance which would be destroyed by its attainment, and which therefore should prevent us from attempting to bring it about. On the other hand, we certainly ought to bring about a reduction of conflict. So already we have here an example of a CLASH of VALUES or PRINCIPLES. This example also shows that CLASHES of VALUES and PRINCIPLES may be VALUABLE, and indeed essential for an open society.
- Our belief in any particular NATURAL LAW cannot have a safer basis than our unsuccessful critical ATTEMPTS to REFUTE it.
LOVE must be learned
and learned again and again
there is no END to it.
Great LITERATURE is simply LANGUAGE charged with MEANING to the utmost possible degree.
People are either escapists or BUDDHISTS in this world.
All POLITICS stands in need of spiritualisation in the sense of MORALISATION, that is to say, permeation with the principles of TRUTH, SINCERITY, DISINTERESTEDNESS and HUMANITARIANISM.
In every case of AGING can be corrected, we might all be methuselahs, living 1,000 years or more.
We are the first generation of mankind to realise the transcendental, cosmic truth: In the entire universe, the only place where human life can exist in its natural form is the surface of the planet EARTH.
- To LOVE someone, even in the usual human manner, is to get a brief, dim glimpse of something within that person which is tremendous, awe-inspiring and eternal. In our ignorance, we think that this 'something' is unique. He or she, we say, is like nobody else. That is because our perception of the reality is clouded and obscured by the external manifestations - the character and individual qualities of the person we love - and by the way in which our ego-sense reacts to them.
Nevertheless, this weak flash of perception is a VALID SPIRITUAL EXPERIENCE and it should encourage us to purify our minds and make them fit for that infinitely greater kind of LOVE which always avails us. This love is not restless or transient, like our human love. It is secure and eternal and calm. It is absolutely free from desire, because lover and beloved have become one.
- FAITH is often used by agnostics as a term of abuse. That is to say, it is taken to refer to the blind credulity which accepts all kinds of dogmas and creeds without questioning repeating parrot-like what it has been taught, and closing its ear to doubt and reason. Such FAITH should certainly be attacked. It is compounded of laziness, obstinacy, ignorance and fear. Because it is rigid and unyielding it can quite easily be shaken and altogether destroyed. But this is not the true faith- the
faith which is recommended by Patanjali. True faith is provisional, flexible, undogmatic, open to doubt and reason. True faith is not like a picture frame, a permanently limited area of acceptance. It is like a plant which keeps on throwing forth shoots and growth.
When a PATTERN is set up in time by the activation of an ARCHETYPE, however, the crucial factor does not seem to be an EXTERNAL agency of any kind but rather an ORDERING PRINCIPLE that is inherent in the fact that a PATTERN is being formed.
Man is the measure of all things, of things that are that they are, and of things that they are not that they are not.
Happiness is beneficial for the body, but it is grief that develops the powers of the mind.
- Due to the overproduction of truth we are actually losing ground in the more fundamental aspects of science. Our preoccupation with trivial research and shallow truths make the public disinterested in scientific questions understandable. Unintegrated KNOWLEDGE is boring for the non-specialist. What matters is insight. It is not enough to have knowledge, the knowledge has to become an INNER EXPERIENCE with each of us, it has to become part of our culture. We have an enormous amount of scientific data but we have not yet found simple words for great ideas.
- SCIENCE, TECHNOLOGY, ART and RELIGION have their origin in the creative center of the psyche. Science assumes that there is order in nature; scientific theories try to relate the order of external objective reality to the order of a transpersonal inner reality.
Depth psychology describes the introspectively recognizable form of psychic orderedness by archetypes. Myths are well-known expressions of archetypes, they were not invented but experienced. Science is the myth of modern man.
- The legendary image of a SCIENTIST as a humble searcher for truth is more and more replaced by the image of a scientist as a well-paid brilliant expert, speaking an unintelligible professional jargon, highly competent in a narrowly defined domain but arrogantly extending his competence into fields in which he knows nothing, and neglecting the fact that science is only a small subdivision of human knowledge.
Johannes Kepler (1571 - 1630), who asked: 'God, whom I can almost touch with my hands when observing the universe, do I find him also in myself?' was probably a humble searcher for truth. The modern expert, fascinated in creating 'neutron bombs destroying only life, not property' cannot be said to be searching for truth about nature. Know-how has replaced WISDOM which is certainly a factor contributing to the revulsion from SCIENCE.
I know that I am mortal and the creation of a day,
But when I contemplate the intricate circling spirals of the stars,
No longer do my feet touch earth, but beside Zeus himself
I take my fill of the immortal nectar of the gods.
Pushkin, Alexander Sergeevich
FAIRY TALES, though often untrue,
Teach good lads a thing or two.
Puttkamer, von Jesco
Exhibiting that there are no limits to humanity's future in the universe could revive faith in the idea of PROGRESS.
LIFE resembles the olympic games; a few men strain their muscles to carry off a prize; other bring trinkets to sell to the crowd for a profit; and some there are who seek no further advantage than to look at the show and see how and why everything is done. They are SPECTATORS of other men's LIVES in order better to judge and manage their own.
Quintilian, Marcus Fabius
Men, even when alone, lighten their labors by SONG, however rude it may be.