When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. ... Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone. And even if it had been reached by pure thought, how could anyone have proceeded to the dimension 4/3? To bring this topic to life it was necessary for the Antaeus of Mathematics to be compelled to touch his Mother Earth, if only for one fleeting moment.
Benoît MandelbrotRelated topics
anyone call complexity concept dimension distinctive earth end hide homogeneity mathematics might moment mother natural necessary order property pure seek tail thought topic touch yesterday todayRelated quotes
The best educators are the ones that inspire their students. That inspiration comes from a passion that teachers have for the subject they're teaching. Most commonly, that person spent their lives studying that subject, and they bring an infectious enthusiasm to the audience. I think many people have that enthusiasm, but they are prevented from being teachers because they didn't go through the teacher mill. Now you have teachers who have been through the teacher mill, yet they have no capacity to inspire anyone at all. It's the inspired student that continues to learn on their own. That's what separates the real achievers in the world from those who pedal along, finishing assignments.
Neil deGrasse Tyson
Centuries ago, sailors on long voyages used to leave a pair of pigs on every deserted island. Or they'd leave a pair of goats. Either way, on any future visit, the island would be a source of meat. These islands, they were pristine. These were home to breeds of birds with no natural predators. Breeds of birds that lived nowhere else on earth. The plants there, without enemies they evolved without thorns or poisons. Without predators and enemies, these islands, they were paradise. The sailors, the next time they visited these islands, the only things still there would be herds of goats or pigs. .... Does this remind you of anything Maybe the ol' Adam and Eve story .... You ever wonder when God's coming back with a lot of barbecue sauce.
Chuck Palahniuk
Isaac Newton's Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.
Nick Land
With the assistance of mathematics, I can see a property of the ninety-nine dimensional surfaces hidden from the naked eye. If an increase in the price of fertilizer alone always increases the amount the firm buys of caviar, from that fact alone I can predict the answer to the following experiment which I have never seen performed and upon which I have no observations: an increase in the price of caviar alone will increase the amount the firm buys of fertilizer. In thermodynamics such reciprocity or integrability conditions are known as Maxwell Conditions; in economics they are known as Hotelling conditions in honor of Harold Hotelling's 1932 work.
Paul Samuelson
An Asian peasant who labors through all of his waking hours, with tools created in Biblical times-a South American aborigine who is devoured by piranha in a jungle stream-an African who is bitten by the tsetse fly-an Arab whose teeth are green with decay in his mouth-these do live with their 'natural environment,' but are scarcely able to appreciate its beauty. Try to tell a Chinese mother, whose child is dying of cholera: 'Should one do everything one can? Of course not.' Try to tell a Russian housewife, who trudges miles on foot in sub-zero weather in order to spend hours standing in line at a state store dispensing food rations, that America is defiled by shopping centers, expressways and family cars.
Ayn Rand