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April 10, 2026
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"From Adam Smith through John Maynard Keynes, economics had been mostly talk. At Harvard economics was talk. At MIT, Samuelson made it math."
"The engine driving the Kelly system is the "law of large numbers." In a 1713 treatise on probability, Swiss mathematician Jakob Bernoulli propounded a law that has been misunderstood by gamblers (and investors) ever since."
"The dealer now theorized that Thorp was memorizing the entire deck. He knew exactly which cards remained in the deck and bet accordingly. Thorp said it was impossible for any one to do that."
"The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy."
"By the mid-1930s, Moe Annenburg was AT&T's fifth largest customer."
"The assumption that anything true is knowable is the grandfather of paradoxes."
"Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy of science."
"At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox."
"The best paradoxes raise questions about what kinds of contradictions can occur—what species of impossibilities are possible."
"Are there any mythical beasts which aren't simple pastiches of nature? Centaurs, minotaurs, unicorns, griffons, chimeras, sphinxes, manticores, and the like don't speak well for the human imagination. None is as novel as a kangaroo or starfish."
"Simple rules can have complex consequences. This simple rule has such a wealth of implications that it is worth examining in detail. It is the far from self-evident guiding principle of reductionism and of most modern investigations into cosmic complexity. Reductionism will not be truly successful until physicists and cosmologists demonstrate that the large-scale phenomena of the world arise from fundamental physics alone. This lofty goal is still out of reach. There is uncertainty not only in how physics generates the structures of our world but also in what the truly fundamental rules of physics are."
"Regardless of the prophetic value of Dirac’s description [on interference] his was probably the first discussion... including a coherent beam of light. In other words, Dirac wrote the first chapter in laser optics."
"Another connection with Newton's pioneering work on spectra has been found by Duarte in modern quantum optics."
"After some algebra, a successive formula can be derived from Duarte's original equation."
"In 1994, Duarte first reported on solid-state dye laser oscillators."
"The sciences revolted under the guidance of several student activists, Frank Duarte in particular... we were fortunate that Duarte somehow established close links to the Federal Government, which was now the source of all funds."
"Ward was vocal in his denunciation of the trivia that filled up Senate agendas… suitably then, it was a close student associate of Ward’s, physics Ph. D. student Frank Duarte, who began to mobilize student opinion in favor of a change."
"One of Ward's few close friends at Macquarie is... Frank Duarte... the two make an odd couple - the restrained rather distant Englishman and the intense, earnest South American."
"From an interferometric perspective, there are no mysteries... and no paradoxes... in the physics of quantum entanglement."
"As noted previously Bell's theorem is completely disconnected from the physics leading to |\psi\rangle_+, |\psi\rangle_-, |\psi\rangle^+, and |\psi\rangle^- ."
"The most efficient and practical interpretation of quantum mechanics is... no interpretation at all."
"The EPR claim of an "all values" spread in the coordinate depends on an idealized absolute and exact measurement of p with \Delta p\ = 0. Since this is physically impossible, the claim of "no physical reality" can be negated."
"Personally, I find the concept of a "final theory," or a "theory of everything," rather limiting. The fun of discovery will most likely last as long as the human race continues."
"The two photons are entangled and according to local realism, their polarization planes should become independent... a typical EPR situation. Already in 1948, observations... agreed with quantum mechanics, not with local realism."
"The longer the cavity and the narrower the beam waist, the better the beam quality of the laser emission, or |\langle x | s \rangle|^2\ = \sum_{j=1}^\N\,\Psi(r_j)^2\ +2 \sum_{j=1}^\N\,\Psi(r_j)\bigg(\sum_{m=j+1}^\N\,\Psi(r_m)cos(\Omega_m-\Omega_j)\bigg)"
"Multiple-prism arrays were first introduced by Newton (1704) in his book Opticks. In that visionary volume Newton reported on arrays of nearly isosceles prisms in additive and compensating configurations to control the propagation path and the dispersion of light. Further, he also illustrated slight beam expansion in a single isosceles prism."
"The intimate relation between interference and diffraction has its origin in the interference equation itself."
"All the indistinguishable photons illuminate the array of N slits, or grating, simultaneously. If only one photon propagates, at any given time, then that individual photon illuminates the whole array of N slits simultaneously."
"The Dirac notation, though originally applied to the propagation of single particles, also applies to describing the propagation of ensembles of coherent, or indistinguishable, photons."
"Feynman uses Dirac's notation to describe the quantum mechanics of stimulated emission... he applies that physics to... dye molecules... In this regard, Feynman could have predicted the existence of the tunable laser."
"It's all done with gears. Also pinions, snails, arbors; pawls and ratchets; and cam followers; cables, levers, bell cranks, and pivots."
"I'm not a gambling person, but I've been around long enough and I know how to play it."
"I'm not a mathematician, but I've been hanging around with some of them long enough to know how the game is played."
"The absence of a golden rule for mattress flipping is a disappointment, but it does not pertend the demise of civilization. We can adapt; we can learn to live with it."
"In 1948 John Archibald Wheeler, in a telephone conversation with his student Richard Feynman, proposed the delightful hypothesis that there is just one electron in the universe."
"A big advantage of the serial-number approach to identity is that things stay the same even as they change."
"The integers, the rationals, and the irrationals, taken together, make up the continuum of real numbers. It's called a continuum because the numbers are packed together along the real number line with no empty spaces between them."
"By the way, the = notation was invented by Robert Recorde (1510-1558). He choose two parallel lines as a symbol of equality " because noe 2 thynges can be moare equalle.""
"The whirling gears of progress have put the gear makers out of work."
"I am reminded of those prodigies who spent years of their lives calculating digits of the decimal expansion of pi - a task that is now a mere warm-up exercise for computer software. I cannot help wandering which of my labors will appear equally quaint and pathetic to some future reader who ransacks libraries for old volumes like this one."
"How can we measure the effects if we can't even count the dead to the nearest million?"
"Empires come and go; so do ideologies and even religions, but war marches on through it all."
"A retired physicist reading the Encyclopedia Britannica can do just so much toward securing world peace."
"If saving human lives is the great desideratum, then there is more to be gained by the prevention of drowning, and auto wrecks than by the abolition of war."
"Compared with the elegant inventions of the theorists, nature's code seemed a bit of a kludge."
"After a few more centuries, perhaps the poorest billion will even be able to afford the $10.00 buffet."
"The condensation of all property in the hands of one individual is an economic catastrophe-something like the formation of a black hole in astrophysics. It's obviously bad news for the majority of the people, who are left penniless. But even if you happen to be the big winner, your victory may prove hollow. Although you have all the riches in the world, you can't buy a thing, because no one else has goods to sell."
"The fact that randomness requires a physical rather than a mathematical source is noted by almost everyone who writes on the subject, and yet the oddity of this situation is not much remarked."
"Fretting about a dearth of randomness seems like worrying that humanity might use up its last reserves of ignorance."
"The fact is, winding and dusting and fixing somebody else's clock is boring."