Interesting Quotes (153 quotes)
...after my first feeling of revulsion had passed, I spent three of the most entertaining and instructive weeks of my life studying the fascinating molds which appeared one by one on the slowly disintegrating mass of horse-dung. Microscopic molds are both very beautiful and absorbingly interesting. The rapid growth of their spores, the way they live on each other, the manner in which the different forms come and go, is so amazing and varied that I believe a man could spend his life and not exhaust the forms or problems contained in one plate of manure.
...the remark attributed to Mrs. [Agatha] Christie that 'the older you get, the more interesting you become to an archaeologist,' was the creation of some pundit whose neck Mrs. Christie would be glad to wring if he would care to identify himself—she neither made the remark nor does she consider it particularly complimentary or amusing.
[About a conference on Systematic Biology] Many interesting statements were made that apply directly to the work of taxonomists. In some cases the interest lay in the value of the suggestion and sometimes in the obvious need for rebuttal.
[Among the books he chooses, a statesman] ought to read interesting books on history and government, and books of science and philosophy; and really good books on these subjects are as enthralling as any fiction ever written in prose or verse.
[In my home workshop,] generally I’m mending things, which is interesting because you learn a lot about why they broke.
[O]ne might ask why, in a galaxy of a few hundred billion stars, the aliens are so intent on coming to Earth at all. It would be as if every vertebrate in North America somehow felt drawn to a particular house in Peoria, Illinois. Are we really that interesting?
[The Book of Genesis is] [p]rofoundly interesting and indeed pathetic to me are those attempts of the opening mind of man to appease its hunger for a Cause. But the Book of Genesis has no voice in scientific questions. It is a poem, not a scientific treatise. In the former aspect it is for ever beautiful; in the latter it has been, and it will continue to be, purely obstructive and hurtful.'
Replying to G. H. Hardy’s suggestion that the number of a taxi (1729) was “dull”: No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 1³ + 12³ and 9³ + 10³.
Ron Hutcheson, a Knight-Ridder reporter: [Mr. President, what are your] personal views [about the theory of] intelligent design?
President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”
Hutcheson: Both sides ought to be properly taught?
President: Yes ... so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we've got to give these groups—...
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]
President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”
Hutcheson: Both sides ought to be properly taught?
President: Yes ... so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we've got to give these groups—...
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]
A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical quantities of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
A living speck—the merest dab of life—capable of pleasure and pain, is far more interesting to me than all the immensities of mere matter.
A lot of people ask, “Do you think humans are parasites?” It’s an interesting idea and one worth thinking about. People casually refer to humanity as a virus spreading across the earth. In fact, we do look like some strange kind of bio-film spreading across the landscape. A good metaphor? If the biosphere is our host, we do use it up for our own benefit. We do manipulate it. We alter the flows and fluxes of elements like carbon and nitrogen to benefit ourselves—often at the expense of the biosphere as a whole. If you look at how coral reefs or tropical forests are faring these days, you’ll notice that our host is not doing that well right now. Parasites are very sophisticated; parasites are highly evolved; parasites are very successful, as reflected in their diversity. Humans are not very good parasites. Successful parasites do a very good job of balancing—using up their hosts and keeping them alive. It’s all a question of tuning the adaptation to your particular host. In our case, we have only one host, so we have to be particularly careful.
A scientifically unimportant discovery is one which, however true and however interesting for other reasons, has no consequences for a system of theory with which scientists in that field are concerned.
A very interesting set of compounds that were waiting for the right disease.
[Commenting on AZT and similar drugs he had synthesized.]
[Commenting on AZT and similar drugs he had synthesized.]
About eight days ago I discovered that sulfur in burning, far from losing weight, on the contrary, gains it; it is the same with phosphorus; this increase of weight arises from a prodigious quantity of air that is fixed during combustion and combines with the vapors. This discovery, which I have established by experiments, that I regard as decisive, has led me to think that what is observed in the combustion of sulfur and phosphorus may well take place in the case of all substances that gain in weight by combustion and calcination; and I am persuaded that the increase in weight of metallic calxes is due to the same cause... This discovery seems to me one of the most interesting that has been made since Stahl and since it is difficult not to disclose something inadvertently in conversation with friends that could lead to the truth I have thought it necessary to make the present deposit to the Secretary of the Academy to await the time I make my experiments public.
Abraham Maslow, felt … [an] instinctive revolt against the “atmosphere” of Freudian psychology, with its emphasis on sickness and neurosis, and decided that he might obtain some equally interesting results if he studied extremely healthy people.
All interesting issues in natural history are questions of relative frequency, not single examples. Everything happens once amidst the richness of nature. But when an unanticipated phenomenon occurs again and again–finally turning into an expectation–then theories are overturned.
Any scientist of any age who wants to make important discoveries must study important problems. Dull or piffling problems yield dull or piffling answers. It is not not enough that a problem should be “interesting.” … The problem must be such that it matters what the answer is—whether to science generally or to mankind.
As few subjects are more interesting to society, so few have been more frequently written upon than the education of youth.
As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.
At age 36.
At age 36.
Astronomy teaches the correct use of the sun and the planets. These may be put on a frame of little sticks and turned round. This causes the tides. Those at the ends of the sticks are enormously far away. From time to time a diligent searching of the sticks reveals new planets. The orbit of the planet is the distance the stick goes round in going round. Astronomy is intensely interesting; it should be done at night, in a high tower at Spitzbergen. This is to avoid the astronomy being interrupted. A really good astronomer can tell when a comet is coming too near him by the warning buzz of the revolving sticks.
At Arcueil ... I dined in distinguished company... There was a lot of very interesting discussion. It is these gatherings which are the joy of life.
Biological disciplines tend to guide research into certain channels. One consequence is that disciplines are apt to become parochial, or at least to develop blind spots, for example, to treat some questions as “interesting” and to dismiss others as “uninteresting.” As a consequence, readily accessible but unworked areas of genuine biological interest often lie in plain sight but untouched within one discipline while being heavily worked in another. For example, historically insect physiologists have paid relatively little attention to the behavioral and physiological control of body temperature and its energetic and ecological consequences, whereas many students of the comparative physiology of terrestrial vertebrates have been virtually fixated on that topic. For the past 10 years, several of my students and I have exploited this situation by taking the standard questions and techniques from comparative vertebrate physiology and applying them to insects. It is surprising that this pattern of innovation is not more deliberately employed.
Biology has at least 50 more interesting years.
Bradley is one of the few basketball players who have ever been appreciatively cheered by a disinterested away-from-home crowd while warming up. This curious event occurred last March, just before Princeton eliminated the Virginia Military Institute, the year’s Southern Conference champion, from the NCAA championships. The game was played in Philadelphia and was the last of a tripleheader. The people there were worn out, because most of them were emotionally committed to either Villanova or Temple-two local teams that had just been involved in enervating battles with Providence and Connecticut, respectively, scrambling for a chance at the rest of the country. A group of Princeton players shooting basketballs miscellaneously in preparation for still another game hardly promised to be a high point of the evening, but Bradley, whose routine in the warmup time is a gradual crescendo of activity, is more interesting to watch before a game than most players are in play. In Philadelphia that night, what he did was, for him, anything but unusual. As he does before all games, he began by shooting set shots close to the basket, gradually moving back until he was shooting long sets from 20 feet out, and nearly all of them dropped into the net with an almost mechanical rhythm of accuracy. Then he began a series of expandingly difficult jump shots, and one jumper after another went cleanly through the basket with so few exceptions that the crowd began to murmur. Then he started to perform whirling reverse moves before another cadence of almost steadily accurate jump shots, and the murmur increased. Then he began to sweep hook shots into the air. He moved in a semicircle around the court. First with his right hand, then with his left, he tried seven of these long, graceful shots-the most difficult ones in the orthodoxy of basketball-and ambidextrously made them all. The game had not even begun, but the presumably unimpressible Philadelphians were applauding like an audience at an opera.
But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.
Butterflies are very interesting. Here these things are little grubs for a while. And then they go into a little coffin. There they are in a sarcophagus, and then they come out and dance with the angels.
Computer science … jobs should be way more interesting than even going to Wall Street or being a lawyer--or, I can argue, than anything but perhaps biology, and there it’s just a tie.
Diamond, for all its great beauty, is not nearly as interesting as the hexagonal plane of graphite. It is not nearly as interesting because we live in a three-dimensional space, and in diamond each atom is surrounded in all three directions in space by a full coordination. Consequently, it is very difficult for an atom inside the diamond lattice to be confronted with anything else in this 3D world because all directions are already taken up.
Difficulties [in defining mathematics with full generality, yet simplicity] are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting. Nowhere is intellectual beauty so deeply felt and fastidiously appreciated.
Ethnologists regard man as the primitive element of tribes, races, and peoples. The anthropologist looks at him as a member of the fauna of the globe, belonging to a zoölogical classification, and subject to the same laws as the rest of the animal kingdom. To study him from the last point of view only would be to lose sight of some of his most interesting and practical relations; but to be confined to the ethnologist’s views is to set aside the scientific rule which requires us to proceed from the simple to the compound, from the known to the unknown, from the material and organic fact to the functional phenomenon.
Every physical fact, every expression of nature, every feature of the earth, the work of any and all of those agents which make the face of the world what it is, and as we see it, is interesting and instructive. Until we get hold of a group of physical facts, we do not know what practical bearings they may have, though right-minded men know that they contain many precious jewels, which science, or the expert hand of philosophy will not fail top bring out, polished, and bright, and beautifully adapted to man's purposes.
Failure is so much more interesting because you learn from it. That’s what we should be teaching children at school, that being successful the first time, there’s nothing in it. There’s no interest, you learn nothing actually.
First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
For a stone, when it is examined, will be found a mountain in miniature. The fineness of Nature’s work is so great, that, into a single block, a foot or two in diameter, she can compress as many changes of form and structure, on a small scale, as she needs for her mountains on a large one; and, taking moss for forests, and grains of crystal for crags, the surface of a stone, in by far the plurality of instances, is more interesting than the surface of an ordinary hill; more fantastic in form and incomparably richer in colour—the last quality being, in fact, so noble in most stones of good birth (that is to say, fallen from the crystalline mountain ranges).
For my part, I must say that science to me generally ceases to be interesting as it becomes useful.
For the evolution of science by societies the main requisite is the perfect freedom of communication between each member and anyone of the others who may act as a reagent.
The gaseous condition is exemplified in the soiree, where the members rush about confusedly, and the only communication is during a collision, which in some instances may be prolonged by button-holing.
The opposite condition, the crystalline, is shown in the lecture, where the members sit in rows, while science flows in an uninterrupted stream from a source which we take as the origin. This is radiation of science. Conduction takes place along the series of members seated round a dinner table, and fixed there for several hours, with flowers in the middle to prevent any cross currents.
The condition most favourable to life is an intermediate plastic or colloidal condition, where the order of business is (1) Greetings and confused talk; (2) A short communication from one who has something to say and to show; (3) Remarks on the communication addressed to the Chair, introducing matters irrelevant to the communication but interesting to the members; (4) This lets each member see who is interested in his special hobby, and who is likely to help him; and leads to (5) Confused conversation and examination of objects on the table.
I have not indicated how this programme is to be combined with eating.
The gaseous condition is exemplified in the soiree, where the members rush about confusedly, and the only communication is during a collision, which in some instances may be prolonged by button-holing.
The opposite condition, the crystalline, is shown in the lecture, where the members sit in rows, while science flows in an uninterrupted stream from a source which we take as the origin. This is radiation of science. Conduction takes place along the series of members seated round a dinner table, and fixed there for several hours, with flowers in the middle to prevent any cross currents.
The condition most favourable to life is an intermediate plastic or colloidal condition, where the order of business is (1) Greetings and confused talk; (2) A short communication from one who has something to say and to show; (3) Remarks on the communication addressed to the Chair, introducing matters irrelevant to the communication but interesting to the members; (4) This lets each member see who is interested in his special hobby, and who is likely to help him; and leads to (5) Confused conversation and examination of objects on the table.
I have not indicated how this programme is to be combined with eating.
For the past 10 years I have had the interesting experience of observing the development of Parkinson's syndrome on myself. As a matter of fact, this condition does not come under my special medical interests or I would have had it solved long ago. … The condition has its compensations: one is not yanked from interesting work to go to the jungles of Burma ... one avoids all kinds of deadly committee meetings, etc.
Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.
He who is only a traveler learns things at second-hand and by the halves, and is poor authority. We are most interested when science reports what those men already know practically or instinctively, for that alone is a true humanity.
Hemoglobin is one of the most interesting chemical substances in the world—to me it is the most interesting of all.
His [Marvin Minsky’s] basic interest seemed to be in the workings of the human mind and in making machine models of the mind. Indeed, about that time he and a friend made one of the first electronic machines that could actually teach itself to do something interesting. It monitored electronic “rats” that learned to run mazes. It was being financed by the Navy. On one notable occasion, I remember descending to the basement of Memorial Hall, while Minsky worked on it. It had an illuminated display panel that enabled one to follow the progress of the “rats.” Near the machine was a hamster in a cage. When the machine blinked, the hamster would run around its cage happily. Minsky, with his characteristic elfin grin, remarked that on a previous day the Navy contract officer had been down to see the machine. Noting the man’s interest in the hamster, Minsky had told him laconically, “The next one we build will look like a bird.”
Human behaviour reveals uniformities which constitute natural laws. If these uniformities did not exist, then there would be neither social science nor political economy, and even the study of history would largely be useless. In effect, if the future actions of men having nothing in common with their past actions, our knowledge of them, although possibly satisfying our curiosity by way of an interesting story, would be entirely useless to us as a guide in life.
I am not a lover of lawns; … the least interesting adjuncts of the country-house. … Rather would I see daisies in their thousands, ground ivy, hawkweed, and even the hated plantain with tall stems, and dandelions with splendid flowers and fairy down, than the too-well-tended lawn.
I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
I believe as a matter of faith that the extension of space travel to the limits of the solar system will probably be accomplished in several decades, perhaps before the end of the century. Pluto is 4000 million miles from the sun. The required minimum launching velocity is about 10 miles per second and the transit time is 46 years. Thus we would have to make the velocity considerably higher to make the trip interesting to man. Travel to the stars is dependent on radically new discoveries in science and technology. The nearest star is 25 million million miles way and requires a travel time of more than four years at the speed of light. Prof. Dr. Ing. E. Sanger has speculated that velocities comparable with the speed of light might be attained in the next century, but such extrapolation of current technology is probably not very reliable.
I believe that the human mind, or even the mind of a cat, is more interesting in its complexity than an entire galaxy if it is devoid of life.
I can live with doubt and uncertainty. I think it’s much more interesting to live not knowing than to have answers which might be wrong.
I can no more explain why I like “natural history” than why I like California canned peaches; nor why I do not care for that enormous brand of natural history which deals with invertebrates any more than why I do not care for brandied peaches. All I can say is that almost as soon as I began to read at all I began to like to read about the natural history of beasts and birds and the more formidable or interesting reptiles and fishes.
I can’t think of any definition of the words mathematician or scientist that would apply to me. I think of myself as a journalist who knows just enough about mathematics to be able to take low-level math and make it clear and interesting to nonmathematicians. Let me say that I think not knowing too much about a subject is an asset for a journalist, not a liability. The great secret of my column is that I know so little about mathematics that I have to work hard to understand the subject myself. Maybe I can explain things more clearly than a professional mathematician can.
I can’t work well under the conditions at Bell Labs. Walter [Brattain] and I are looking at a few questions relating to point-contact transistors, but [William] Shockley keeps all the interesting problems for himself.
I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
I decided that life rationally considered seemed pointless and futile, but it is still interesting in a variety of ways, including the study of science. So why not carry on, following the path of scientific hedonism? Besides, I did not have the courage for the more rational procedure of suicide.
I have often thought that an interesting essay might be written on the influence of race on the selection of mathematical methods. methods. The Semitic races had a special genius for arithmetic
and algebra, but as far as I know have never produced a single geometrician of any eminence. The Greeks on the other hand adopted a geometrical procedure wherever it was possible, and they even treated arithmetic as a branch of geometry by means of the device of representing numbers by lines.
I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.
I remember being with my grandmother and mother and my uncle came in and asked what I wanted to be when grew up. I said ‘A doctor,’ which took him aback. He was expecting me to say ‘nurse’ or ‘actress.’ And my mother and grandmother laughed like, ‘Kids say the darndest things.’ I grew up in a time when women were not expected to do anything interesting.
I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”
I think there will always be something interesting left to be discovered.
I was introduced to Mr. Davy, who has rooms adjoining mine (in the Royal Institution); he is a very agreeable and intelligent young man, and we have interesting conversation in an evening; the principal failing in his character as a philosopher is that he does not smoke.
I was suffering from a sharp attack of intermittent fever, and every day during the cold and succeeding hot fits had to lie down for several hours, during which time I had nothing to do but to think over any subjects then particularly interesting me. One day something brought to my recollection Malthus's 'Principles of Population', which I had read about twelve years before. I thought of his clear exposition of 'the positive checks to increase'—disease, accidents, war, and famine—which keep down the population of savage races to so much lower an average than that of more civilized peoples. It then occurred to me that these causes or their equivalents are continually acting in the case of animals also; and as animals usually breed much more rapidly than does mankind, the destruction every year from these causes must be enormous in order to keep down the numbers of each species, since they evidently do not increase regularly from year to year, as otherwise the world would long ago have been densely crowded with those that breed most quickly. Vaguely thinking over the enormous and constant destruction which this implied, it occurred to me to ask the question, Why do some die and some live? The answer was clearly, that on the whole the best fitted live. From the effects of disease the most healthy escaped; from enemies, the strongest, swiftest, or the most cunning; from famine, the best hunters or those with the best digestion; and so on. Then it suddenly flashed upon me that this self-acting process would necessarily improve the race, because in every generation the inferior would inevitably be killed off and the superior would remain—that is, the fittest would survive.
[The phrase 'survival of the fittest,' suggested by the writings of Thomas Robert Malthus, was expressed in those words by Herbert Spencer in 1865. Wallace saw the term in correspondence from Charles Darwin the following year, 1866. However, Wallace did not publish anything on his use of the expression until very much later, and his recollection is likely flawed.]
[The phrase 'survival of the fittest,' suggested by the writings of Thomas Robert Malthus, was expressed in those words by Herbert Spencer in 1865. Wallace saw the term in correspondence from Charles Darwin the following year, 1866. However, Wallace did not publish anything on his use of the expression until very much later, and his recollection is likely flawed.]
I worked for many years in almost total obscurity doing what I thought was interesting.
I would like to start by emphasizing the importance of surfaces. It is at a surface where many of our most interesting and useful phenomena occur. We live for example on the surface of a planet. It is at a surface where the catalysis of chemical reactions occur. It is essentially at a surface of a plant that sunlight is converted to a sugar. In electronics, most if not all active circuit elements involve non-equilibrium phenomena occurring at surfaces. Much of biology is concerned with reactions at a surface.
I’ve never consciously tried to keep myself out of anything I write, and I’ve always talked clearly when people interview me. I don’t think my life is too interesting. It’s lived mainly inside my brain.
If we range through the whole territory of nature, and endeavour to extract from each department the rich stores of knowledge and pleasure they respectively contain, we shall not find a more refined or purer source of amusement, or a more interesting and unfailing subject for recreation, than that which the observation and examination of the structure, affinities, and habits of plants and vegetables, afford.
In mathematics, … and in natural philosophy since mathematics was applied to it, we see the noblest instance of the force of the human mind, and of the sublime heights to which it may rise by cultivation. An acquaintance with such sciences naturally leads us to think well of our faculties, and to indulge sanguine expectations concerning the improvement of other parts of knowledge. To this I may add, that, as mathematical and physical truths are perfectly uninteresting in their consequences, the understanding readily yields its assent to the evidence which is presented to it; and in this way may be expected to acquire the habit of trusting to its own conclusions, which will contribute to fortify it against the weaknesses of scepticism, in the more interesting inquiries after moral truth in which it may afterwards engage.
In physics we have dealt hitherto only with periodic crystals. To a humble physicist’s mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master.
In science the primary duty of ideas is to be useful and interesting even more than to be “true.”
In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.
In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than twenty formulae extracted from our minds.
Isn’t it interesting that the same people who laugh at science fiction listen to weather forecasts and economists
It [analysis] lacks at this point such plan and unity that it is really amazing that it can be studied by so many people. The worst is that it has not at all been treated with rigor. There are only a few propositions in higher analysis that have been demonstrated with complete rigor. Everywhere one finds the unfortunate manner of reasoning from the particular to the general, and it is very unusual that with such a method one finds, in spite of everything, only a few of what many be called paradoxes. It is really very interesting to seek the reason.
In my opinion that arises from the fact that the functions with which analysis has until now been occupied can, for the most part, be expressed by means of powers. As soon as others appear, something that, it is true, does not often happen, this no longer works and from false conclusions there flow a mass of incorrect propositions.
In my opinion that arises from the fact that the functions with which analysis has until now been occupied can, for the most part, be expressed by means of powers. As soon as others appear, something that, it is true, does not often happen, this no longer works and from false conclusions there flow a mass of incorrect propositions.
It is distinctly proved, by this series of observations, that the reflex function exists in the medulla independently of the brain; in the medulla oblongata independently of the medulla spinalis; and in the spinal marrow of the anterior extremities, of the posterior extremities, and of the tail, independently of that of each other of these parts, respectively. There is still a more interesting and satisfactory mode of performing the experiment: it is to divide the spinal marrow between the nerves of the superior and inferior extremities. We have then two modes of animal life : the first being the assemblage of the voluntary and respiratory powers with those of the reflex function and irritability; the second, the two latter powers only: the first are those which obtain in the perfect animal, the second those which animate the foetus. The phenomena are precisely what might have been anticipated. If the spinal marrow be now destroyed, the irritability alone remains,—all the other phenomena having ceased.
It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms.
It is interesting to note how many fundamental terms which the social sciences are trying to adopt from physics have as a matter of historical fact originated in the social field. Take, for instance, the notion of cause. The Greek aitia or the Latin causa was originally a purely legal term. It was taken over into physics, developed there, and in the 18th century brought back as a foreign-born kind for the adoration of the social sciences. The same is true of the concept of law of nature. Originally a strict anthropomorphic conception, it was gradually depersonalized or dehumanized in the natural sciences and then taken over by the social sciences in an effort to eliminate final causes or purposes from the study of human affairs. It is therefore not anomalous to find similar transformations in the history of such fundamental concepts of statistics as average and probability. The concept of average was developed in the Rhodian laws as to the distribution of losses in maritime risks. After astronomers began to use it in correcting their observations, it spread to other physical sciences; and the prestige which it thus acquired has given it vogue in the social field. The term probability, as its etymology indicates, originates in practical and legal considerations of probing and proving.
It is interesting to observe the result of habit in the peculiar shape and size of the giraffe (Camelo-pardalis): this animal, the largest of the mammals, is known to live in the interior of Africa in places where the soil is nearly always arid and barren, so that it is obliged to browse on the leaves on the trees and to make constant efforts to reach them. From this habit long maintained in all its race, it has resulted that the animal's fore-legs have become longer than its hind legs, and that its neck is lengthened to such a degree that the giraffe, without standing up on its hind legs, attains a height of six metres (nearly 20 feet).
It is interesting to transport one’s self back to the times when Astronomy began; to observe how discoveries were connected together, how errors have got mixed up with truth, have delayed the knowledge of it, and retarded its progress; and, after having followed the various epochs and traversed every climate, finally to contemplate the edifice founded on the labours of successive centuries and of various nations.
It is more important that a proposition be interesting than it be true. … But of course a true proposition is more apt to be interesting than a false one.
It is most interesting to observe into how small a field the whole of the mysteries of nature thus ultimately resolve themselves. The inorganic has one final comprehensive law, GRAVITATION. The organic, the other great department of mundane things, rests in like manner on one law, and that is,—DEVELOPMENT. Nor may even these be after all twain, but only branches of one still more comprehensive law, the expression of that unity which man's wit can scarcely separate from Deity itself.
It is the function of notions in science to be useful, to be interesting, to be verifiable and to acquire value from anyone of these qualities. Scientific notions have little to gain as science from being forced into relation with that formidable abstraction, “general truth.”
It seems to me that every phenomenon, every fact, itself is the really interesting object. Whoever explains it, or connects it with other events, usually only amuses himself or makes sport of us, as, for instance, the naturalist or historian. But a single action or event is interesting, not because it is explainable, but because it is true.
It would be interesting to inquire how many times essential advances in science have first been made possible by the fact that the boundaries of special disciplines were not respected… Trespassing is one of the most successful techniques in science.
It’s important to always bear in mind that life occurs in historical time. Everyone in every culture lives in some sort of historical time, though it might not be perceived in the same way an outside observer sees it. It’s an interesting question, “When is now?” “Now” can be drawn from some point like this hour, this day, this month, this lifetime, or this generation. “Now” can also have occurred centuries ago; things like unfair treaties, the Trail of Tears, and the Black Hawk War, for instance, remain part of the “Now” from which many Native Americans view their place in time today. Human beings respond today to people and events that actually occurred hundreds or even thousands of years ago. Ethnohistorians have played a major role in showing how now is a social concept of time, and that time is part of all social life. I can only hope that their work will further the understanding that the study of social life is a study of change over time.
Just think of the differences today. A young person gets interested in chemistry and is given a chemical set. But it doesn't contain potassium cyanide. It doesn't even contain copper sulfate or anything else interesting because all the interesting chemicals are considered dangerous substances. Therefore, these budding young chemists don't get a chance to do anything engrossing with their chemistry sets. As I look back, I think it is pretty remarkable that Mr. Ziegler, this friend of the family, would have so easily turned over one-third of an ounce of potassium cyanide to me, an eleven-year-old boy.
LEAD, n. A heavy blue-gray metal much used ... as a counterpoise to an argument of such weight that it turns the scale of debate the wrong way. An interesting fact in the chemistry of international controversy is that at the point of contact of two patriotisms lead is precipitated in great quantities.
[Referring to bullets.]
[Referring to bullets.]
Let the young know they will never find a more interesting, more instructive book than the patient himself.
Little Birds are writing
Interesting books.
To be read by cooks:
Read, I say, not roasted—
Letterpress, when toasted,
Loses its good looks.
Interesting books.
To be read by cooks:
Read, I say, not roasted—
Letterpress, when toasted,
Loses its good looks.
Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.
Medical statistics are like a bikini bathing suit: what they reveal is interesting; what they conceal is vital.
Men have been talking now for a week at the post office about the age of the great elm, as a matter interesting but impossible to be determined. The very choppers and travelers have stood upon its prostrate trunk and speculated upon its age, as if it were a profound mystery. I stooped and read its years to them (127 at nine and a half feet), but they heard me as the wind that once sighed through its branches. They still surmised that it might be two hundred years old, but they never stooped to read the inscription. Truly they love darkness rather than light. One said it was probably one hundred and fifty, for he had heard somebody say that for fifty years the elm grew, for fifty it stood still, and for fifty it was dying. (Wonder what portion of his career he stood still!) Truly all men are not men of science. They dwell within an integument of prejudice thicker than the bark of the cork-tree, but it is valuable chiefly to stop bottles with. Tied to their buoyant prejudices, they keep themselves afloat when honest swimmers sink.
Men will gather knowledge no matter what the consequences. Science will go on whether we are pessimistic or optimistic, as I am. More interesting discoveries than we can imagine will be made, and I am awaiting them, full of curiosity and enthusiasm.
Microbiology is usually regarded as having no relevance to the feelings and aspirations of the man of flesh and bone. Yet, never in my professional life do I find myself far removed from the man of flesh and bone. It is not only because microbes are ubiquitous in our environment, and therefore must be studied for the sake of human welfare. More interesting, and far more important in the long run, is the fact that microbes exhibit profound resemblances to man. They resemble him in their physical makeup, in their properties, in their responses to various stimuli; they also display associations with other living things which have perplexing and illuminating analogies with human societies.
My attitude was: “Just look at all the interesting atoms in that region of the periodic table; certainly the reason that carbon dominates chemistry is our own ignorance.”
Nature. As the word is now commonly used it excludes nature's most interesting productions—the works of man. Nature is usually taken to mean mountains, rivers, clouds and undomesticated animals and plants. I am not indifferent to this half of nature, but it interests me much less than the other half.
Nothing in the whole system of nature is isolated or unimportant. The fall of a leaf and the motion of a planet are governed by the same laws. … It is in the study of objects considered trivial and unworthy of notice by the casual observer that genius finds the most important and interesting phenomena. It was in the investigation of the varying colors of the soap-bubble that Newton detected the remarkable fact of the fits of easy reflection and easy refraction presented by a ray of light in its passage through space, and upon which he established the fundamental principle of the present generalization of the undulatory theory of light. … The microscopic organization of animals and plants is replete with the highest instruction; and, surely, in the language of one of the fathers of modern physical science, “nothing can be unworthy of being investigated by man which was thought worthy of being created by GOD.”
Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.
Nothing is more interesting to the true theorist than a fact which directly contradicts a theory generally accepted up to that time, for this is his particular work.
Now I must take you to a very interesting part of our subject—to the relation between the combustion of a candle and that living kind of combustion which goes on within us. In every one of us there is a living process of combustion going on very similar to that of a candle, and I must try to make that plain to you. For it is not merely true in a poetical sense—the relation of the life of man to a taper; and if you will follow, I think I can make this clear.
Observation is simple, indefatigable, industrious, upright, without any preconceived opinion. Experiment is artificial, impatient, busy, digressive; passionate, unreliable. We see every day one experiment after another, the second outweighing the impression gained from the first, both, often enough, carried out by men who are neither much distinguished for their spirit, nor for carrying with them the truth of personality and self denial. Nothing is easier than to make a series of so-called interesting experiments. Nature can only in some way be forced, and in her distress, she will give her suffering answer. Nothing is more difficult than to explain it, nothing is more difficult than a valid physiological experiment. We consider as the first task of current physiology to point at it and comprehend it.
Obviously we biologists should fit our methods to our materials. An interesting response to this challenge has been employed particularly by persons who have entered biology from the physical sciences or who are distressed by the variability in biology; they focus their research on inbred strains of genetically homogeneous laboratory animals from which, to the maximum extent possible, variability has been eliminated. These biologists have changed the nature of the biological system to fit their methods. Such a bold and forthright solution is admirable, but it is not for me. Before I became a professional biologist, I was a boy naturalist, and I prefer a contrasting approach; to change the method to fit the system. This approach requires that one employ procedures which allow direct scientific utilization of the successful long-term evolutionary experiments which are documented by the fascinating diversity and variability of the species of animals which occupy the earth. This is easy to say and hard to do.
Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels.
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.
One of the great triumphs of 20th Century astrophysics, was tracing the elements of your body, of all the elements around us, to the actions of stars—that crucible in the centers of stars that cooked basic elements into heavier elements, light elements into heavy elements. (I say “cooked”—I mean thermonuclear fusion.) The heat brings them together, gets you bigger atoms, that then do other interesting chemical things, fleshing out the contents of the Periodic Table.
One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
One of the most important choices any researcher makes is picking a significant topic to study. If you choose the right problem, you get important results that transform our perception of the underlying structure of the universe. If you don’t choose the right problem, you may work very hard but only get an interesting result.
One of the most interesting parts is the detective element. Archaeology is like a jigsaw puzzle, except that you can't cheat and look at the box, and not all the pieces are there.
One striking peculiarity of mathematics is its unlimited power of evolving examples and problems. A student may read a book of Euclid, or a few chapters of Algebra, and within that limited range of knowledge it is possible to set him exercises as real and as interesting as the propositions themselves which he has studied; deductions which might have pleased the Greek geometers, and algebraic propositions which Pascal and Fermat would not have disdained to investigate.
Ours is the commencement of a flying age, and I am happy to have popped into existence at a period so interesting.
Perhaps I am just a hopeless rationalist, but isn’t fascination as comforting as solace? Isn’t nature immeasurably more interesting for its complexities and its lack of conformity to our hopes? Isn’t curiosity as wondrously and fundamentally human as compassion?
Plasma seems to have the kinds of properties one would like for life. It’s somewhat like liquid water—unpredictable and thus able to behave in an enormously complex fashion. It could probably carry as much information as DNA does. It has at least the potential for organizing itself in interesting ways.
Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics.
Questions of personal priority, however interesting they may be to the persons concerned, sink into insignificance in the prospect of any gain of deeper insight into the secrets of nature.
Reality may avoid the obligation to be interesting, but ... hypotheses may not.
Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns, there are things we know we know.
We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. ... And each year, we discover a few more of those unknown unknowns.
We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. ... And each year, we discover a few more of those unknown unknowns.
Run the tape again, and let the tiny twig of Homo sapiens expire in Africa. Other hominids may have stood on the threshold of what we know as human possibilities, but many sensible scenarios would never generate our level of mentality. Run the tape again, and this time Neanderthal perishes in Europe and Homo erectus in Asia (as they did in our world). The sole surviving human stock, Homo erectus in Africa, stumbles along for a while, even prospers, but does not speciate and therefore remains stable. A mutated virus then wipes Homo erectus out, or a change in climate reconverts Africa into inhospitable forest. One little twig on the mammalian branch, a lineage with interesting possibilities that were never realized, joins the vast majority of species in extinction. So what? Most possibilities are never realized, and who will ever know the difference? Arguments of this form lead me to the conclusion that biology's most profound insight into human nature, status, and potential lies in the simple phrase, the embodiment of contingency: Homo sapiens is an entity, not a tendency.
Suppose [an] imaginary physicist, the student of Niels Bohr, is shown an experiment in which a virus particle enters a bacterial cell and 20 minutes later the bacterial cell is lysed and 100 virus particles are liberated. He will say: “How come, one particle has become 100 particles of the same kind in 20 minutes? That is very interesting. Let us find out how it happens! How does the particle get in to the bacterium? How does it multiply? Does it multiply like a bacterium, growing and dividing, or does it multiply by an entirely different mechanism ? Does it have to be inside the bacterium to do this multiplying, or can we squash the bacterium and have the multiplication go on as before? Is this multiplying a trick of organic chemistry which the organic chemists have not yet discovered ? Let us find out. This is so simple a phenomenon that the answers cannot be hard to find. In a few months we will know. All we have to do is to study how conditions will influence the multiplication. We will do a few experiments at different temperatures, in different media, with different viruses, and we will know. Perhaps we may have to break into the bacteria at intermediate stages between infection and lysis. Anyhow, the experiments only take a few hours each, so the whole problem can not take long to solve.”
[Eight years later] he has not got anywhere in solving the problem he set out to solve. But [he may say to you] “Well, I made a slight mistake. I could not do it in a few months. Perhaps it will take a few decades, and perhaps it will take the help of a few dozen other people. But listen to what I have found, perhaps you will be interested to join me.”
[Eight years later] he has not got anywhere in solving the problem he set out to solve. But [he may say to you] “Well, I made a slight mistake. I could not do it in a few months. Perhaps it will take a few decades, and perhaps it will take the help of a few dozen other people. But listen to what I have found, perhaps you will be interested to join me.”
Sylvester’s writings are flowery and eloquent. He was able to make the dullest subject bright, fresh and interesting. His enthusiasm is evident in every line. He would get quite close up to his subject, so that everything else looked small in comparison, and for the time would think and make others think that the world contained no finer matter for contemplation. His handwriting was bad, and a trouble to his printers. His papers were finished with difficulty. No sooner was the manuscript in the editor’s hands than alterations, corrections, ameliorations and generalizations would suggest themselves to his mind, and every post would carry further directions to the editors and printers.
Take the rose—most people think it very beautiful: I don’t care for it at all. I prefer the cactus, for the simple reason that it has a more interesting personality. It has wonderfully adapted itself to its surroundings! It is the best illustration of the theory of evolution in plant life.
Teachers need to be more inspirational. But it’s also up to engineering to make itself more interesting.
The Babylonian and Assyrian civilizations have perished; Hammurabi, Sargon and Nebuchadnezzar are empty names; yet Babylonian mathematics is still interesting, and the Babylonian scale of 60 is still used in Astronomy.
The degree of exactness of the intuition of space may be different in different individuals, perhaps even in different races. It would seem as if a strong naive space-intuition were an attribute pre-eminently of the Teutonic race, while the critical, purely logical sense is more fully developed in the Latin and Hebrew races. A full investigation of this subject, somewhat on the lines suggested by Francis Gallon in his researches on heredity, might be interesting.
The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.
The flight was extremely normal ... for the first 36 seconds then after that got very interesting.
About the Apollo 12 launch, during which two electrical discharges almost ended the mission.
About the Apollo 12 launch, during which two electrical discharges almost ended the mission.
The future is too interesting and dangerous to be entrusted to any predictable, reliable agency. We need all the fallibility we can get. Most of all, we need to preserve the absolute unpredictability and total improbability of our connected minds. That way we can keep open all the options, as we have in the past.
The general knowledge of our author [Leonhard Euler] was more extensive than could well be expected, in one who had pursued, with such unremitting ardor, mathematics and astronomy as his favorite studies. He had made a very considerable progress in medical, botanical, and chemical science. What was still more extraordinary, he was an excellent scholar, and possessed in a high degree what is generally called erudition. He had attentively read the most eminent writers of ancient Rome; the civil and literary history of all ages and all nations was familiar to him; and foreigners, who were only acquainted with his works, were astonished to find in the conversation of a man, whose long life seemed solely occupied in mathematical and physical researches and discoveries, such an extensive acquaintance with the most interesting branches of literature. In this respect, no doubt, he was much indebted to an uncommon memory, which seemed to retain every idea that was conveyed to it, either from reading or from meditation.
The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.
The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.
The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube for three. Two men cooperating with two different pieces of apparatus, say a special furnace and a pyrometer or a hydraulic press and new chemical substances, are more powerful than their arithmetical sum. These facts doubtless assist as assets of a research laboratory.
The nature of light is a subject of no material importance to the concerns of life or to the practice of the arts, but it is in many other respects extremely interesting.
The question of questions for mankind—the problem which underlies all others, and is more deeply interesting than any other—is the ascertainment of the place which Man occupies in nature and of his relations to the universe of things.
The traveler was active; he went strenuously in search of people, of adventure, of experience. The tourist is passive; he expects interesting things to happen to him. He goes “sight-seeing.”
The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject. … The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty. It would probably be a good thing also to give a preference to those branches of mathematics that have an interesting group of transformations underlying them, since transformations play an important role in modern physical theory, both relativity and quantum theory seeming to show that transformations are of more fundamental importance than equations.
The whole subject of the X rays is opening out wonderfully, Bragg has of course got in ahead of us, and so the credit all belongs to him, but that does not make it less interesting. We find that an X ray bulb with a platinum target gives out a sharp line spectrum of five wavelengths which the crystal separates out as if it were a diffraction grating. In this way one can get pure monochromatic X rays. Tomorrow we search for the spectra of other elements. There is here a whole new branch of spectroscopy, which is sure to tell one much about the nature of an atom.
The world probably being of much greater antiquity than physical science has thought to be possible, it is interesting and harmless to speculate whether man has shared with the world its more remote history. … Some of the beliefs and legends which have come down to us from antiquity are so universal and deep-rooted that we have are accustomed to consider them almost as old as the race itself. One is tempted to inquire how far the unsuspected aptness of some of these beliefs and sayings to the point of view so recently disclosed is the result of mere chance or coincidence, and how far it may be evidence of a wholly unknown and unsuspected ancient civilization of which all other relic has disappeared.
There are all kinds of interesting questions that come from a knowledge of science, which only adds to the excitement and mystery and awe of a flower.
There is a reward structure in science that is very interesting: Our highest honors go to those who disprove the findings of the most revered among us. So Einstein is revered not just because he made so many fundamental contributions to science, but because he found an imperfection in the fundamental contribution of Isaac Newton.
There is another approach to the extraterrestrial hypothesis of UFO origins. This assessment depends on a large number of factors about which we know little, and a few about which we know literally nothing. I want to make some crude numerical estimate of the probability that we are frequently visited by extraterrestrial beings.
Now, there is a range of hypotheses that can be examined in such a way. Let me give a simple example: Consider the Santa Claus hypothesis, which maintains that, in a period of eight hours or so on December 24-25 of each year, an outsized elf visits one hundred million homes in the United States. This is an interesting and widely discussed hypothesis. Some strong emotions ride on it, and it is argued that at least it does no harm.
We can do some calculations. Suppose that the elf in question spends one second per house. This isn't quite the usual picture—“Ho, Ho, Ho,” and so on—but imagine that he is terribly efficient and very speedy; that would explain why nobody ever sees him very much-only one second per house, after all. With a hundred million houses he has to spend three years just filling stockings. I have assumed he spends no time at all in going from house to house. Even with relativistic reindeer, the time spent in a hundred million houses is three years and not eight hours. This is an example of hypothesis-testing independent of reindeer propulsion mechanisms or debates on the origins of elves. We examine the hypothesis itself, making very straightforward assumptions, and derive a result inconsistent with the hypothesis by many orders of magnitude. We would then suggest that the hypothesis is untenable.
We can make a similar examination, but with greater uncertainty, of the extraterrestrial hypothesis that holds that a wide range of UFOs viewed on the planet Earth are space vehicles from planets of other stars.
Now, there is a range of hypotheses that can be examined in such a way. Let me give a simple example: Consider the Santa Claus hypothesis, which maintains that, in a period of eight hours or so on December 24-25 of each year, an outsized elf visits one hundred million homes in the United States. This is an interesting and widely discussed hypothesis. Some strong emotions ride on it, and it is argued that at least it does no harm.
We can do some calculations. Suppose that the elf in question spends one second per house. This isn't quite the usual picture—“Ho, Ho, Ho,” and so on—but imagine that he is terribly efficient and very speedy; that would explain why nobody ever sees him very much-only one second per house, after all. With a hundred million houses he has to spend three years just filling stockings. I have assumed he spends no time at all in going from house to house. Even with relativistic reindeer, the time spent in a hundred million houses is three years and not eight hours. This is an example of hypothesis-testing independent of reindeer propulsion mechanisms or debates on the origins of elves. We examine the hypothesis itself, making very straightforward assumptions, and derive a result inconsistent with the hypothesis by many orders of magnitude. We would then suggest that the hypothesis is untenable.
We can make a similar examination, but with greater uncertainty, of the extraterrestrial hypothesis that holds that a wide range of UFOs viewed on the planet Earth are space vehicles from planets of other stars.
There is certainly no absolute standard of beauty. That precisely is what makes its pursuit so interesting.
Through the naturalist’s eyes, a sparrow can be as interesting as a bird of paradise, the behaviour of a mouse as interesting as that of a tiger, and a humble lizard as fascinating as a crocodile. … Our planet is beautifully intricate, brimming over with enigmas to be solved and riddles to be unravelled.
To day we made the grand experiment of burning the diamond and certainly the phenomena presented were extremely beautiful and interesting… The Duke’s burning glass was the instrument used to apply heat to the diamond. It consists of two double convex lenses … The instrument was placed in an upper room of the museum and having arranged it at the window the diamond was placed in the focus and anxiously watched. The heat was thus continued for 3/4 of an hour (it being necessary to cool the globe at times) and during that time it was thought that the diamond was slowly diminishing and becoming opaque … On a sudden Sir H Davy observed the diamond to burn visibly, and when removed from the focus it was found to be in a state of active and rapid combustion. The diamond glowed brilliantly with a scarlet light, inclining to purple and, when placed in the dark, continued to burn for about four minutes. After cooling the glass heat was again applied to the diamond and it burned again though not for nearly so long as before. This was repeated twice more and soon after the diamond became all consumed. This phenomenon of actual and vivid combustion, which has never been observed before, was attributed by Sir H Davy to be the free access of air; it became more dull as carbonic acid gas formed and did not last so long.
To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
Von Neumann gave me an interesting idea: that you don’t have to be responsible for the world that you’re in. So I have developed a very powerful sense of social irresponsibility as a result of Von Neumann’s advice. It’s made me a very happy man ever since.
We have one of his [Newton’s] college memorandum-books, which is highly interesting. The following are some of the entries: “Drills, gravers, a hone, a hammer, and a mandril, 5s.;” “a magnet, 16s.;” “compasses, 2s.;” “glass bubbles, 4s.;” “at the tavern several other times, £1;” “spent on my cousin, 12s.;” “on other acquaintances, 10s.;” “Philosophical Intelligences, 9s. 6d.;” “lost at cards twice, 15s.;” “at the tavern twice, 3s. 6d.;” “to three prisms, £3;” “four ounces of putty, 1s. 4d.;” “Bacon’s Miscellanies, 1s. 6d.;” “a bible binding, 3s.;” “for oranges to my sister, 4s. 2d.;” “for aquafortis, sublimate, oyle pink, fine silver, antimony, vinegar, spirit of wine, white lead, salt of tartar, £2;” “Theatrum chemicum, £1 8s.”
We hence acquire this sublime and interesting idea; that all the calcareous mountains in the world, and all the strata of clay, coal, marl, sand, and iron, which are incumbent on them, are MONUMENTS OF THE PAST FELICITY OF ORGANIZED NATURE!
We’ll get to the details of what’s around here, but it looks like a collection of just about every variety of shape - angularity, granularity, about every variety of rock. The colors - well, there doesn’t appear to be too much of a general color at all; however, it looks as though some of the rocks and boulders [are] going to have some interesting colors to them. Over.
When I was in college studying science, I found the experience fundamentally unsatisfying. I was continually oppressed by the feeling that my only role was to “shut up and learn.” I felt there was nothing I could say to my instructors that they would find interesting. … As I sat in the science lecture hall, I was utterly silent. That’s not a good state to be in when you are 19 years old.
When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.
When we no longer look at an organic being as a savage looks at a ship, as something wholly beyond his comprehension; when we regard every production of nature as one which has had a long history; when we contemplate every complex structure and instinct as the summing up of many contrivances, each useful to the possessor, in the same way as any great mechanical invention is the summing up of the labour, the experience, the reason, and even the blunders of numerous workmen; when we thus view each organic being, how far more interesting, I speak from experience, does the study of natural history become!
With time, I attempt to develop hypotheses that are more risky. I agree with [Karl] Popper that scientists need to be interested in risky hypotheses because risky hypotheses advance science by producing interesting thoughts and potential falsifications of theories (of course, personally, we always strive for verification—we love our theories after all; but we should be ready to falsify them as well.
Without consciousness the mind-body problem would be much less interesting. With consciousness it seems hopeless.
Without some kind of God, man is not even very interesting.
You can't really discover the most interesting conflicts and problems in a subject until you've tried to write about them. At that point, one discovers discontinuities in the data, perhaps, or in one's own thinking; then the act of writing forces you to work harder to resolve these contradictions.