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We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer.
One of my colleagues likes to say that, mathematics is the - he thinks about the only subject that he knows in academia or in the real world where if two people disagree about something - if people are studying some mathematical object and there's supposed to be a proof and they disagree about whether this proof or not, the will go into a room, sit down and talk about it and fairly quickly or at the end of the day one of them will admit they're wrong.
I think that the scienti?c way of looking at the world, and the humanistic way of looking at the world are complementary. There are important differences which should be preserved, and in trying to do away with those differences we would lose something the same way as if we tried to make all religions one religion or all races one race. There is a cultural diversity that's very valuable, and it's valuable to have different ways of looking at the world.
There are many points in the history of an invention which the inventor himself is apt to overlook as trifling, but in which posterity never fail to take a deep interest. The progress of the human mind is never traced with such a lively interest as through the steps by which it perfects a great invention; and there is certainly no invention respecting which this minute information will be more eagerly sought after, than in the case of the steam-engine.
At this point in our global ecological crisis, the survival of humanity will require a fundamental shift in our attitude toward nature: from finding out how we can dominate and manipulate nature to how we can learn from her. In this brilliant and hopeful book, Jay Harman shows us how far the new field of Biomimicry has already progressed toward this goal. The Shark's Paintbrush makes for fascinating and joyful reading - much needed in these dark times.
Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.
When I began my career as a cosmologist some twenty years ago, I was a convinced atheist. I never in my wildest dreams imagined that one day I would be writing a book purporting to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them. I have been forced into these conclusions by the inexorable logic of my own special branch of physics.
A diverse ecosystem will also be resilient, because it contains many species with overlapping ecological functions that can partially replace one another. When a particular species is destroyed by a severe disturbance so that a link in the network is broken, a diverse community will be able to survive and reorganize itself... In other words, the more complex the network is, the more complex its pattern of interconnections, the more resilient it will be.
If I hold a twenty pound weight, I cannot detect a fly landing on it because the least detectable difference in the stimulus is half a pound. On the other hand, if i hold a feather, a fly landing on it makes a great difference. Obviously then, in order to be able to tell the differences in exertion one must first reduce the exertion. Finer and finer performance is possible only if the sensitivity, that is, the ability to feel the difference is improved.
In time, [a Martian] colony would grow to the point of being self- sustaining. When this stage was reached, humanity would have a precious insurance policy against catastrophe at home. During the next millennium there is a significant chance that civilization on Earth will be destroyed by an asteroid, a killer plague or a global war. A Martian colony could keep the flame of civilization and culture alive until Earth could be reverse-colonized from Mars.
It came to my mind that in the Yoga Sutras of Patanjali, in Indian spiritual literature, and in the Bhagavad Gita, and when I started reading about outstanding yogis and people of exceeding spiritual power such as Ramana Maharshi, or Yogananda, they all had the ability to do what we would call - I don't know what you would even call it - psychic phenomenon, magic, transform objects, be able to perceive the future, the past and the present simultaneously.
My soul is an entangled knot, Upon a liquid vortex wrought By Intellect in the Unseen residing, And thine doth like a convict sit, With marline-spike untwisting it, Only to find its knottiness abiding; Since all the tools for its untying In four-dimensional space are lying, Wherein they fancy intersperses Long avenues of universes, While Klein and Clifford fill the void With one finite, unbounded homoloid, And think the Infinite is now at last destroyed.
Pierre Curie voluntarily exposed his arm to the action of radium for several hours. This resulted in damage resembling a burn that developed progressively and required several months to heal. Henri Becquerel had by accident a similar burn as a result of carrying in his vest pocket a glass tube containing radium salt. He came to tell us of this evil effect of radium, exclaiming in a manner at once delighted and annoyed: "I love it, but I owe it a grudge."
A completed book exists in its entirety, although we humans read it in a time sequence from the beginning to the end. Just as an author does not write the first chapter, and then leave the others to write themselves, So God's creativity is not to seem as uniquely confined to, or even especially invested in, the event of the Big Bang. Rather his creativity has been seen as permeating equally all space and all time: his role as Creator and Sustainer merge.
My colleagues in elementary particle theory in many lands [and I] are driven by the usual insatiable curiosity of the scientist, and our work is a delightful game. I am frequently astonished that it so often results in correct predictions of experimental results. How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature?
Fall in love with some activity, and do it! Nobody ever figures out what life is all about, and it doesn't matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough. Work as hard and as much as you want to on the things you like to do the best. Don't think about what you want to be, but what you want to do. Keep up some kind of a minimum with other things so that society doesn't stop you from doing anything at all.
Alchemy and Kabbalah are later developments in my thinking. I think the primary interest has been the relationship of magic and mystery to logic and understanding. Those are the primary driving forces of my life. I have this ability, for some reason, to be able to hold both the Magical MysteryTour we're on in conjunction with the logical rigor of understanding theoretical physics, which makes me kind of a rare bird, because usually you're one or the other.
And who can doubt that it will lead to the worst disorders when minds created free by God are compelled to submit slavishly to an outside will? When we are told to deny our senses and subject them to the whim of others? When people devoid of whatsoever competence are made judges over experts and are granted authority to treat them as they please? These are the novelties which are apt to bring about the ruin of commonwealths and the subversion of the state.
When you are thinking something, you have the feeling that the thoughts do nothing except inform you the way things are and then you choose to do something and you do it. That's what people generally assume. But actually, the way you think determines the way you're going to do things. Then you don't notice a result comes back, or you don't see it as a result of what you've done, or even less do you see it as a result of how you were thinking. Is that clear?
This life of yours which you are living is not merely a piece of this entire existence, but in a certain sense the whole; only this whole is not so constituted that it can be surveyed in one single glance. This, as we know, is what the Brahmins express in that sacred, mystic formula which is yet really so simple and so clear; tat tvam asi, this is you. Or, again, in such words as "I am in the east and the west, I am above and below, I am this entire world."
It is my thesis that flying saucers are real and that they are space ships from another solar system. I think that they possibly are manned by intelligent observers who are members of a race that may have been investigating our Earth for centuries. I think that they possibly have been sent out to conduct systematic, long-range investigations, first of men, animals, vegetation, and more recently of atomic centers, armaments an centers of armament production.
Finally I got to carbon, and as you all know, in the case of carbon the reaction works out beautifully. One goes through six reactions, and at the end one comes back to carbon. In the process one has made four hydrogen atoms into one of helium. The theory, of course, was not made on the railway train from Washington to Ithaca ... It didn't take very long, it took about six weeks, but not even the Trans-Siberian railroad [has] taken that long for its journey.
If the 'Principle of Relativity' in an extreme sense establishes itself, it seems as if even Time would become discontinuous and be supplied in atoms, as money is doled out in pence or centimes instead of continuously;-in which case our customary existence will turn out to be no more really continuous than the events on a kinematograph screen;-while that great agent of continuity, the Ether of Space, will be relegated to the museum of historical curiosities.
It is the hope of those who work toward the breakout from planet Earth that the establishment of permanent, self-sustaining colonies of humans off-Earth will ... make human life forever unkillable, removing it from the endangered species list, where it now stands on a fragile Earth overarmed with nuclear weapons. Second, the opening of virtually unlimited new land areas in space will reduce territorial pressures and therefore diminish warfare on Earth itself.
Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.
'Conservation' (the conservation law) means this ... that there is a number, which you can calculate, at one moment-and as nature undergoes its multitude of changes, this number doesn't change. That is, if you calculate again, this quantity, it'll be the same as it was before. An example is the conservation of energy: there's a quantity that you can calculate according to a certain rule, and it comes out the same answer after, no matter what happens, happens.
In the history of physics, there have been three great revolutions in thought that first seemed absurd yet proved to be true. The first proposed that the earth, instead of being stationary, was moving around at a great and variable speed in a universe that is much bigger than it appears to our immediate perception. That proposal, I believe, was first made by Aristarchos two millenia ago ... Remarkably enough, the name Aristarchos in Greek means best beginning.
I think that the artificial-intelligence people are making a lot of noise recently, claiming that artificial intelligence is making huge progress and we're going to be outstripped by the machines. But, in my view, this whole field is based on a misconception. I think the brain is analog, whereas the machines are digital. They really are different. So I think that what the machines can do, of course, is wonderful, but it's not the same as what the brain can do.
Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
The incomplete knowledge of a system must be an essential part of every formulation in quantum theory. Quantum theoretical laws must be of a statistical kind. To give an example: we know that the radium atom emits alpha-radiation. Quantum theory can give us an indication of the probability that the alpha-particle will leave the nucleus in unit time, but it cannot predict at what precise point in time the emission will occur, for this is uncertain in principle.
In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other ... and if we admit this medium as an hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise.
Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
We have been forced to admit for the first time in history not only the possibility of the fact of the growth and decay of the elements of matter. With radium and with uranium we do not see anything but the decay. And yet, somewhere, somehow, it is almost certain that these elements must be continuously forming. They are probably being put together now in the laboratory of the stars. ... Can we ever learn to control the process. Why not? Only research can tell.
If we can avoid disaster for the next two centuries, our species should be safe as we spread into space. If we are the only intellegent beings in the galaxy we should make sure we survive and continue. . . . Our only chance of long-term survival is not to remain inward looking on planet Earth but to spread out into space. We have made remarkable progress in the last hundred years. But if we want to continue beyond the next hundred years, our future is in space.
The shell game that we play ... is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate.
Geneva has a long history of hosting international organizations, which is part of the reason why CERN is here. CERN has signed agreements with the ITU, WIPO and the WMO. At first sight, there may not seem to be much common ground between CERN and, say, the World Meteorological Organization, but scratch the surface, and you'll soon find a common thread. All of these organizations have a vocation to stimulate technological innovation, and together we're stronger.
I am very astonished that the scientific picture of the real world around me is deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity.
From what has been said it is also evident, that the Whiteness of the Sun's Light is compounded all the Colours wherewith the several sorts of Rays whereof that Light consists, when by their several Refrangibilities they are separated from one another, do tinge Paper or any other white Body whereon they fall. For those Colours ... are unchangeable, and whenever all those Rays with those their Colours are mix'd again, they reproduce the same white Light as before.
But in practical affairs, particularly in politics, men are needed who combine human experience and interest in human relations with a knowledge of science and technology. Moreover, they must be men of action and not contemplation. I have the impression that no method of education can produce people with all the qualities required. I am haunted by the idea that this break in human civilization, caused by the discovery of the scientific method, may be irreparable.
As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths. For Hypotheses are not to be regarded in experimental Philosophy.
Another problem of fragmentation is that thought divides itself from feeling and from the body. Thought is said to be the mind; we have the notion that it is something abstract or spiritual or immaterial. Then there is the body, which is very physical. And we have emotions, which are perhaps somewhere in between. The idea is that they are all different. That is, we think of them as different. And we experience them as different because we think of them as different.
Science has been effective at furthering our understanding of nature because the scientific ethos is based on three key principles: (1) follow the evidence wherever it leads; (2) if one has a theory, one needs to be willing to try to prove it wrong as much as one tries to prove that it is right; (3) the ultimate arbiter of truth is experiment, not the comfort one derives from one's a priori beliefs, nor the beauty or elegance one ascribes to one's theoretical models.
What historians will definitely wonder about in future centuries is how deeply flawed logic, obscured by shrewd and unrelenting propaganda, actually enabled a coalition of powerful special interests to convince nearly everyone in the world that CO2 from human industry was a dangerous, planet-destroying toxin. It will be remembered as the greatest mass delusion in the history of the world - that CO2, the life of plants, was considered for a time to be a deadly poison.
In this world, there are two times. There is mechanical time and there is body time." "They do not keep clocks in their houses. Instead, they listen to their heartbeats. They feel the rhythms of their moods and desires." "Then there are those who think their bodies don't exist. They live by mechanical time. They rise at seven o'clock in the morning. They eat their lunch at noon and their supper at six. They arrive at their appointments on time, precisely by the clock.
In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, "How many arbitrary parameters did you use for your calculations?" I thought for a moment about our cut-off procedures and said, "Four." He said, "I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." With that, the conversation was over.
Beauty means a lot of different things to a lot of different people. A lot of different ways in which things can be beautiful. But this really has a very specific meaning and which is more along the lines of elegance which is that we say an idea is beautiful or elegant in mathematics or physics if a very simple principle or a very simple idea, or simple set of ideas, turns out to be very powerful and leads to all sort of unexpected structure and unexpected predictions.
Scientists, therefore, are responsible for their research, not only intellectually but also morally. This responsibility has become an important issue in many of today's sciences, but especially so in physics, in which the results of quantum mechanics and relativity theory have opened up two very different paths for physicists to pursue. They may lead us - to put it in extreme terms - to the Buddha or to the Bomb, and it is up to each of us to decide which path to take.
In the Germany of the l920s, the Weimar Republic, both organismic biology and Gestalt psychology were part of a larger intellectual trend that saw itself as a protest movement against the increasing fragmentation and alienation of human nature. The entire Weimar culture was characterized by an antimechanistic outlook, a "hunger for wholeness". Organismic biology, Gestalt psychology, ecology, and, later on, general systems theory all grew out of this holistic zeitgeist.
So my antagonist said, "Is it impossible that there are flying saucers? Can you prove that it's impossible?" "No," I said, "I can't prove it's impossible. It's just very unlikely." At that he said, "You are very unscientific. If you can't prove it impossible then how can you say that it's unlikely?" But that is the way that is scientific. It is scientific only to say what is more likely and what less likely, and not to be proving all the time the possible and impossible.
In the last four days I have got the spectrum given by Tantalum, Chromium, Manganese, Iron, Nickel, Cobalt, and Copper and part of the Silver spectrum. The chief result is that all the elements give the same kind of spectrum, the result for any metal being quite easy to guess from the results for the others. This shows that the insides of all the atoms are very much alike, and from these results it will be possible to find out something of what the insides are made up of.