Stanford University Alumni

"I swear to abide by the constitution and laws of the Belgian people, to maintain national independence and the integrity of the land."

"Tom Van Grieken: It is completely normal to invite a party that has won the elections. I was pleased with the invitation … I am not going to say it is unnatural. This is natural. What happened over the past 40 years was not democratic."

"Laurette Onkelinx: Why did the king have to receive the Vlaams Belang? This is a racist and violent party and I think that the message given by the king is damaging."

"Princess Marie-Esméralda of Belgium: I am accused of attacking my family and especially the person of the king. That was clearly never my intention, I know how complex and delicate the situation in Belgium is. I know that the king cannot act politically without the permission of the government. I also know how passionate my cousin is about history, but also sensitive to the aspirations and feelings of his fellow citizens. We live in a crucial moment. The opportunity for inter-community dialogue must be seized."

"I begin my reign with the desire to put myself at the service of all Belgians. I will work for it in perfect agreement with the government and in accordance with the constitution."

"The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so also can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular."

"By the time I was a student in high school I was reading the classic Men of Mathematics by E. T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself p times where p is a prime."

"He was admired for his science fiction and his Men of Mathematics. I was shocked when, just a few years later, Walter Pitts told me the latter was nothing but a string of Hollywood scenarios; my own subsequent study of the sources has shown me that Pitts was right, and I now find the contents of that still popular book to be little more than rehashes enlivened by nasty gossip and banal or indecent fancy."

"The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future; and should analysis ever appear to be without or blemish, its perfection might only be that of death."

"[[History of logarithms|[L]ogarithms]] are one of the most disorderly battlegrounds in mathematical history. ... Disputes like this and the other over the calculus have made more than one man of science envy his successors of ten thousand years hence, to whom Newton and Leibniz, Napier and Bürgi, and scores of lesser contestants for individual fame will be semimythical figures as indistinct as Pythagoras."

"Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics."

"Science makes no pretension to eternal truth or absolute truth; some of its rivals do. That science is in some respects inhuman may be the secret of its success in alleviating human misery and mitigating human stupidity."

"Some, of my unmathematical friends have incautiously urged me to include a note about the origin of modern calculating machines. This is the proper place to do so, as the Queen of queens has enslaved a few of these infernal things to do some of her more repulsive drudgery. What I shall say about these marvelous aids to the feeble human intelligence will be little indeed, for two reasons: I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly."

"Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos."

"Some of his deepest discoveries were reasoned out verbally with very few if any symbols, and those for the most part mere abbreviations of words. Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust on him should try to get on without it for a week."

"Fashion as king is sometimes a very stupid ruler. As was observed a little way back, the kernel of Plücker's theory of geometric dimensionality is that the dimensionality of a given space is not an absolute constant, but depends upon the elements, accepted as irreducible, in terms of which the space is described."

"The so-called obvious was repeatedly scrutinized from every angle and was frequently found to be not obvious but false. "Obvious" is the most dangerous word in mathematics."

"Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about."

"Objections... inspired Kronecker and others to attack Weierstrass' "sequential" definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth — whatever that may be, if anything — precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals."

"Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness."

"Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid's notorious oversights drove this lesson home."

"The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry."

"If you use a Macintosh or an iPhone, which honestly I would not recommend, you would be using code that I wrote more than 25 years ago."

"Corporate governance is concerned with holding the balance between economic and social goals and between individual and communal goals. The governance framework is there to encourage the efficient use of resources and equally to require accountability for the stewardship of those resources. The aim is to align as nearly as possible the interests of individuals, corporations and society."

"The key books about object-oriented graphical modeling languages appeared between 1988 and 1992. Leading figures included Grady Booch [Booch,OOAD]; Peter Coad [Coad, OOA], [Coad, OOD]; Ivar Jacobson (Objectory) [Jacobson, OOSE]; Jim Odell [Odell]; Jim Rumbaugh (OMT) [Rumbaugh, insights], [Rumbaugh, OMT]; Sally Shlaer and Steve Mellor [Shlaer and Mellor, data], [Shlaer and Mellor, states] ; and Rebecca Wirfs-Brock (Responsibility Driven Design) [Wirfs-Brock]."

"While a small domain (consisting of fifty or fewer objects) can generally be analyzed as a unit, large domains must be partitioned to make the analysis a manageable task. To make such a partitioning, we take advantage of the fact that objects on an information model tend to fall into clusters: groups of objects that are interconnected with one another by many relationships. By contrast, relatively few relationships connect objects in different clusters. When partitioning a domain, we divide the information model so that the clusters remain intact... Each section of the information model then becomes a separate subsystem. Note that when the information model is partitioned into subsystems, each object is assigned to exactly one subsystem."

"An object in OOA represents a single typical but unspecified instance of something in the real world - any airplane, I don't care which one, as long as it is typical. The object-oriented analyst distinguishes this concept from that of a specified instance: Airplane number N2713A, Air Force One, or The Spirit of St. Louis, for example."

"Non-local influences do not diminish with distance. They are as potent at a million miles as at a millimeter. Non-local influences act instantaneously. The speed of their transmission is not limited by the velocity of light. A non-local interaction links up one location with another without crossing space, without decay, and without delay. A non-local interaction is, in short, unmediated, unmitigated, and immediate."

"Bell himself managed to devise such a proof which rejects all models of reality possessing the property of "locality". This proof has since become known as Bells theorem. It asserts that no local model of reality can underlie the quantum facts. Bell's theorem says that reality must be non-local."

"The gist of Bell's theorem is this: no local model of reality can explain the results of a particular experiment."

"No local reality can explain the type of world we live in."

"Physicists continue to debate whether Bell's theorem is airtight or not. However, the real question is not whether Bell can prove beyond doubt that reality is non-local, but whether the world is in fact no-local."

"A universe that displays local phenomena but upon a non-local reality is the only sort of world consistent with known facts and Bell's proof."

"The simplicity of Bell's proof opens it to everyone, not just physicists and mathematicians."

"Physicists cannot explain atoms to their children, not because we are ignorant but because we know too much."

"The entire visible universe, what Bishop Berkley called "the mighty frame of the world," rests ultimately on a strange quantum kind of being no more substantial than a promise."

"Legendary King Midas never knew the feel of silk or a human hand after everything he touched turned to gold. Humans are stuck in a similar Midas-like predicament: we can't directly experience the true texture of reality because everything we touch turns to matter."

"Strictly speaking, there are no "measurements" in the world, only correlations."

"If a friend in Texas seals a silver coin in one envelope and a gold coin in another and mails the envelopes to Tokyo and London, the instant you open you envelope in Japan you know the contents of my envelope in England. But opening your letter causes no physical change in England (faster-than-light or otherwise) but merely involves a change in your knowledge concerning something happening far away and outside your control."

"The quantum world is objective but objectless."

"The quantum world is not made up of objects."

"The pragmatist regards any theory as a mere mathematical machine for generating numbers which he then compares with experiment. A pragmatist is concerned with results, not reality. The pragmatist refuses on principle to speculate about deep reality, such a concept being meaningless from his point of view. Pragmatism is an intelectually safe but ultimately sterile philosophy."

"So minuscule is the scale of quantum events compared to the actions of everyday life that it's a wonder humans ever found out about the quantum world at all."

"Most everywhere, most of the time, the world dwells in an unmeasured state."

"Physicists, for all their odd notions, are basically a conservative lot."

"Though today's quantum theory shows no sign of weakness, someday it may collapse."

"Quantum physics emerged from the Stone Age with an embarrassment of riches - three quantum theories, each claiming to explain the world. As it turned out, all three were right."

"One of the best-kept secrets of science is that physicists have lost their grip on reality."

"Although mathematics originates in the human mind, its remarkable effectiveness in explaining the world does not extend to the mind itself. Psychology has proved unusually resistant to the mathematization that works so well in physics."

"One of the curious features of modern physics is that in spite of its overwhelming success in explaining a vast range of physical phenomena from quark to quasar, it fails to give us a single metaphor for how the universe really works."