people-from-basel

"Mathematics"

"The remarkable principle of James Bernoulli consists exactly of this... namely, that the mean given by a series of trials falls near the number sought within limits so much the more narrow as the trials are more multiplied. All the properties which result from his learned researches constitute one of the most honourable monuments to his memory. But Bernoulli established his calculations on the hypothesis that the number sought was fixed and determined. ... It may happen that this quantity will experience small variations... But the principle of Bernoulli is still applicable to this case and has been demonstrated by M. Poisson by means of analysis. ...In the case before us the experiments should generally be very numerous: it is for this reason that M. Poisson has designated the extension of Bernoulli's principle as the law of great numbers."

"[T]he writings of the Bernoullis are not antiquated from loss of beauty, nor deserve neglect..."

"Notwithstanding the broad foundation for mechanics laid by Newton in his Principia, and notwithstanding the indefatigable labors of Clairaut, d'Alembert, the Bernoullis, and Euler, there was near the end of the eighteenth century no comprehensive treatise on the science. Its leading principles and methods were fairly well known, but scattered through many works, and presented from divers points of view. It remained for Lagrange to unite them into one harmonious system. Mechanics had not yet freed itself from the restrictions of geometry, though progress since Newton's time had been constantly toward analytical... methods. The emancipation came with Lagrange's Mécanique Analytique published one hundred and one years after the Principia."

"[H]e was soon seconded by two illustrious men, who adopted his method with such ardour, rendered it so completely their own, and made so many elegant applications of it that Leibnitz several times published in the journals, with a disinterestedness worthy of so great a man, that it was as much indebted to them as to himself. ...I am speaking of the two brothers James and John Bernoulli."

"We find an excellent tract by James Bernoulli concerning the elastic curve, isochronous curves, the path of mean direction in the course of a vessel, the inverse method of tangents, &c. On most of these subjects he had treated already; but here he has given them with additions, corrections, and improvements. His scientific discussions are interspersed with some historical circumstances, which will be read with pleasure. Here for the first time he repels the unjust and repeated attacks of his brother; and exhorts him to moderate his pretensions; to attach less importance to discoveries, which the instrument, with which they were both furnished, rendered easy; and to acknowledge, that, 'as quantities in geometry increase by degrees, so every man, furnished with the same instrument, would find by degrees the same results.' Very modest and remarkable expressions from the pen of one of the greatest geometricians, that ever lived. This memoir concluded with an invitation to mathematicians, to sum up a very general differential equation, of great use in analysis. The solution which James Bernoulli had found of this problem, as well as those which Leibnitz and John Bernoulli gave of it, were published in the Leipsic Transactions."

"[Newton] teaches us to take the fluxions, of any given order, of an equation with any given number of variable quantities, which belongs to the differential calculus: but he does not inform us, how to solve the inverse problem; that is to say, he has pointed out no means of resolving differential equations, either immediately, or by the separation of the indeterminate quantities, or by the reduction into series, &c. This theory however had already made very considerable progress in Germany, Holland, and France, as may be concluded from the problems of the catenarian, isochronous, and elastic curves, and particularly by the solution which James Bernoulli had given of the isoperimetrical problem."

"History of calculus"

"[P]robability as a measurable degree of certainty; necessity and chance; moral versus mathematical expectation; a priori an a posteriori probability; expectation of winning when players are divided according to dexterity; regard of all available arguments, their valuation, and their calculable evaluation; law of large numbers..."

"The art of measuring, as precisely as possible, probabilities of things, with the goal that we would be able always to choose or follow in our judgments and actions that course, which will have been determined to be better, more satisfactory, safer or more advantageous."

"Eadem mutata resurgo [Changed and yet the same, I rise again]"

"Elastic Curve is the name that James Bernoulli gave to the curve which is formed by an elastic blade, fixed horizontally by one of its extremities in a vertical plane, and loaded at the other extremity with a weight, which by its gravity bends the blade into a curve... This problem is resolved by James Bernoulli in the "Memoirs of the Acad. of Sciences for 1703;" and other solutions have been given by some of the most celebrated mathematicians of Europe..."

"In 1690... Jacob Bernoulli brought up the problem of the catenary in a memoir... in the '...Huygens' solution represents the past... a complex, though skillful, geometrical method. Leibniz, using his new [infinitesimal calculus] reaches a correct analytical formula...y/a = (b^\frac{x}{a} + b^\frac{-x}{a})/2 where a is [a] segment... and b... corresponds to... e... Johann Bernoulli ...supplied two correct constructions ...presents valid statistical arguments and... new and important... equations of equilibrium in differential form. ...In 1697-1698, Jacob Bernoulli was the first to derive the general equations that not only solved the problem, but also permitted the treatment of the more general theme of the equilibrium of a flexible rope, subject to any distribution of tangential (f_t) and normal (f_n) forces. Bernoulli's equations are...\frac{dT}{ds} + f_t = 0, \qquad \frac{T}{r} + f_n= 0where T is the tension, s the curvilinear abscissa, and r the radius of curvature."

"The term "induction" had been used by John Wallis in 1656, in his Arithmetica infinitorum; he used the induction known to natural science. In 1686 Jacob Bernoulli criticised him for using a process which was not binding logically and then advanced in place of it the proof from n to n + 1. This is one of the several origins of the process of mathematical induction."

"The tract in which Leibnitz deals with series appeared late in the seventeenth century and was among the first on the subject. ...the question of their convergence or divergence ...was in those days more or less ignored. ...It was not until the publication of Jacques Bernoulli's work on infinite series in 1713 that a clearer insight into the problem was gained. ...Bernoulli's work directed attention towards the necessity of establishing criteria of convergence. The evanescence of the general term, i.e., of the generating sequence, is certainly a necessary condition, but this is generally insufficient. Sufficient conditions have been established by d'Alembert and Maclauren, Cauchy, Abel, and many others. ...to recognized whether a series converges or diverges is even today rather difficult in some cases."

"The great invention... Descartes gave to the world, the analytical diagram, ...gives at a glance a graphical picture of the law governing a phenomenon, or of the correlation which exists between dependent events, or of the changes which a situation undergoes in the course of time. ...the invention of Descartes not only created the important discipline of analytic geometry, but it gave Newton, Leibnitz, Euler, and the Bernoullis that weapon for the lack of which Archimedes and later Fermat had to leave inarticulate their profound and far-reaching thoughts."

"The name is due to Jacques Bernoulli. The spiral has been called also the geometrical spiral, and the proportional spiral, but more commonly, because of the property observed by Descartes, the equiangular spiral. Bernoulli (and Collins at an earlier date) noted the analogous generation of the spiral and loxodrome ("loxodromica"), the spherical curve which cuts all meridians under a constant angle. ... During 1691-93 Jacques Bernoulli gave the following theorems among others: (a) Logarithmic spirals defined [by the polar equation \rho = ke^{c\theta} of a curve cutting radial vectors (drawn from a certain fixed point 0) under a constant angle \phi , where k is constant and c = cot\phi] for different values of k are equal and have the same asymptotic point; (b) the evolute of a logarithmic spiral is another equal logarithmic spiral having the same asymptotic point; (c) the pedal of a logarithmic spiral with respect to its pole is an equal logarithmic spiral (d) the caustics by reflection and refraction of a logarithmic spiral for rays emanating from the pole as a luminous point are equal logarithmic spirals. The discovery of such "perpetual renascence" of the spiral delighted Bernoulli. "Warmed with the enthusiasm of genius he desired, in imitation of Archimedes, to have the logarithmic spiral engraved on his tomb, and directed, in allusion to the sublime tenet of the resurrection of the body, this emphatic inscription to be affixed—Eadem mutata resurgo." The engraved spiral (very inaccurately executed) and inscription in accordance with Bernoulli's desire, may be seen to-day on his tomb in the cloister of the cathedral at Basel."

"The foundations of the new analysis were laid in the second half of the seventeenth century when Newton... and Leibnitz... founded the Differential and Integral Calculus, the ground having been to some extent prepared by the labours of Huyghens, Fermat, Wallis, and others. By this great invention of Newton and Leibnitz, and with the help of the brothers James Bernoulli... and John Bernoulli... the ideas and methods of the Mathematicians underwent a radical transformation which naturally had a profound effect upon our problem."

"It was in 1691, that the penetrating genius of James Bernoulli discovered the true nature of the catenarian curve. A similar investigation was soon produced by John Bernoulli, by Huygens, and by Leibnitz."

"The first investigation of any importance is that of the elastic line or elastica by James Bernoulli in 1705, in which the resistance of a bent rod is assumed to arise from the extension and contraction of its longitudinal filaments, and the equation of the curve assumed by the axis is formed. This equation practically involves the result that the resistance to bending is a couple proportional to the of the rod when bent, a result which was assumed by Euler in his later treatment of the problems of the elastica, and of the vibrations of thin rods."

"There is... [a] need to code cheaper and accessible programs in line with using sustainable methods to better the livelihood of mankind. To address this issue a theory is formulated based on the Euler-Bernoulli beam model. This model is applicable to thin elements which include plate and membrane elements. This paper illustrates a finite element theory to calculate the master stiffness of a curved plate. The master takes into account the stiffness, the geometry and the loading of the element. The of this is established from which the load which is unknown in the matrix is evaluated by the principle of bifurcation."

"I heard Edwin Fischer, who did not mean much to me. I heard another pianist in Berlin who had a big success and I thought he was awful — Mischa Levitzki. Just fingers, and you cannot listen only to fingers. There is a difference between artist and artisan. Levitzki was an artisan."

"In Switzerland, there’s now this semi-urbanism; architecture that’s neither good nor bad, neither urban nor rural, and yet well-connected to the public transport network; where there’s always something green, but never lush or a lot; where there’s always a bit of water in the form of a river, stream or a lake. As long as most people can live like that and it doesn’t suddenly become too dense and packed in the districts, and in the trams and suburban trains, it’s impossible to change it."

"The world is changing dramatically and architecture, and especially cities, need to move with these changes. What can we do to help as architects? Architecture as a way of thinking — as the title of our first exhibition in 1989 suggested — is more relevant than ever."

"Architecture and psychology suddenly become very close."

"Will the world enter a new phase of isolation, nationalization, ideologization? As a paradoxical counterplay to the onset of globalization? That would require new architecture or author architecture to degenerate into a kind of "parallel architecture," which it already is to a certain extent today."

"A city’s architecture is always a bit like a constructed, psychological version of its people."

"We’re still growing — slowly — but we’ve got a better handle on it now. We could take on even more projects, but we want to remain very selective. Switzerland is still a country that has good conditions for architects compared to most other countries we’re involved with — both in quality and quantity. Here, architects are even closer to the client and realization."

"Roger Federer will undoubtedly become the greatest tennis player to have graced the sport if he wins the French Open. It ends the discussion of where he fits in the history of the game. If it wasn't for [four-time champion Rafael] Nadal, he probably would have won a handful of these things. So nobody would underestimate where he deserves to fit in this game. He's extraordinarily talented and talk about grace on court; watching him play is something special to see and if he does it tomorrow, he'll know what an accomplishment it was."

"You guys are brutal. Absolutely brutal. The guy has only made two Grand Slam finals this year. I would love his bad year. I would love it."

"For me, in my prime, I felt unbeatable. In Roger's days, he's unbeatable. It's really hard to put one guy over the other. Having said that, I think Roger is dominating the game much more than I ever did. I think he's going to go on and pass 14 and win 16, 17, 18 majors. I think he's going to break all records."

"I had a taste of what the best is tonight and I think Roger has that extra gear. He has good volleys and he has this little backhand flick that honestly, I have never seen before... it’s something that I didn’t have. I am happy with my performance tonight. I hung in there right until the end."

"If he is playing very good, I have to play unbelievable. If not, it’s impossible, especially if he’s playing with good confidence. When he’s 100 percent, he’s playing in another league. It’s impossible to stop him. I fight. I fight. I fight. Nothing to say. Just congratulate him."

"In my opinion he's the best player ever. When you play tennis, playing Federer is kind of a dream because you can see he does everything you would love to do on the court."

"He's the most gifted player that I've ever seen in my life. I've seen a lot of people play. I've seen the (Rod) Lavers; I played against some of the great players—the Samprases, Beckers, Connors', Borgs, you name it. This guy could be the greatest of all time. That, to me, says it all."

"Roger is just the greatest player of all time. He is the most beautiful player I’ve ever seen and I don’t ever get tired of watching him. Rod Laver is my idol, Pete Sampras is the greatest grass court player ever, but Roger is just the greatest player of all. I think we can all appreciate how incredible he is even more lately, because he’s shown a bit more emotion on court and he’s become a father so he seems a bit more human, more relatable. That makes what he’s doing seem even more amazing."

"Federer is the best player in history, no other player has ever had such quality."

"Yes, I really hit with him when he was 15, during a tournament in Basel, and I knew then he would be good, but not this good. If he stays healthy, it will actually be a miracle if he doesn't win more Grand Slams than Pete [Sampras]. The way he picks his shots is unbelievable. He is fast, he has a great volley, a great serve, great backhand, great everything. If I was his coach, what can I tell him? He is a magician with a racket. Even when he is playing badly, which is rarely, he can still do things with his racket nobody else can do."

"Well, I think when I look at Roger, I mean, I'm a fan. I mean, I'm a fan of how he plays, what he's about, just the fact that I think he's a class—I don't know him personally, but seems like he's a class guy on and off the court. He's fun to watch. Just his athletic ability, what he's able to do on the run. I think he can and will break every tennis record out there."

"I don't see anyone with a big enough weapon to hurt him. They're just staying back and Roger is able to dictate well enough. You just have to serve well and attack him."

"I really consider myself top 5 player in the world, which doesn't mean that I am close to Roger."

"Oh, I would be honoured to even be compared to Roger. He has such an unbelievable talent, and is capable of anything. Roger could be the greatest tennis player of all time."

"Roger's got too many shots, too much talent in one body. It's hardly fair that one person can do all this—his backhands, his forehands, volleys, serving, his court position. The way he moves around the court, you feel like he's barely touching the ground. That's the sign of a great champion."

"The best way to beat him would be to hit him over the head with a racquet. Roger could win the Grand Slam if he keeps playing the way he is and, if he does that, it will equate to the two Grand Slams that I won because standards are much higher these days."

"He's the best I've ever played against. There's nowhere to go. There's nothing to do except hit fairways, hit greens and make putts. Every shot has that sort of urgency on it. I've played a lot of them [other players], so many years; there's a safety zone, there's a place to get to, there's something to focus on, there's a way. Anything you try to do, he potentially has an answer for and it's just a function of when he starts pulling the triggers necessary to get you to change to that decision."

"He hits that short chip, moves you forward, moves you back. He uses your pace against you. If you take pace off, so that he can't use your pace, he can step around and hurt you with the forehand. Just the amount of options he has to get around any particular stage of the match where maybe something's out of sync is—seems to be endless. His success out there is just a mere reflection of all the things that he can do."

"There's probably not a department in his game that couldn't be considered the best in that department. You watch him play Hewitt and everybody marvels at Hewitt's speed, as well as myself. And you start to realize, `Is it possible Federer even moves better?' Then you watch him play Andy [Roddick], and you go, `Andy has a big forehand. Is it possible Federer's forehand is the best in the game?' You watch him at the net, you watch him serve-volley somebody that doesn't return so well and you put him up there with the best in every department. You see him play from the ground against those that play from the ground for a living, and argue he does it better than anybody."

"He's a real person. He's not an enigma. Off the court he's not trying to be somebody. If you met him at McDonald's and you didn't know who he was, you would have no idea that he's one of the best athletes in the world."

"I think there's—he's the main guy and then there's probably four or five of us that are—I don't know. Maybe we need to do just a tag team effort or something, join forces, you know, like Power Rangers or something."

"[In the modern game], you're either a clay court specialist, a grass court specialist or a hard court specialist … or you're Roger Federer."