To make these digital technologies work, we have to cooperate with them, just as astronauts had to do with their equipment. We have to care for them. We patiently wait for them to boot-up. We keep them in cool environments so that they do not overheat. We feed them electricity, sometimes in carefully regulated doses to keep the batteries charged. We present ourselves to them in ways they can recognize, accept, and respond to whether that it through a keyboard or stylized gestures. We keep them charged up. We keep updating the app software. We discipline ourselves to work with the devices. (No one calls them machines, though that is what they are.)
Because of his famous philosophical writings ("Cogito ergo sum") heis considered, along with Aristotle, to be one of themost influential thinkers in history.
an excellent approximationto the sine function, are known only from the writings ofBhaskara I, who wrote: "Aryabhata isthe master who, after reaching the furthest shores and plumbing the inmostdepths of the sea of ultimate knowledge of mathematics, kinematicsand spherics, handed over the three sciences to the learned world."
No one person gets unique credit for the invention of thedecimal system but Brahmagupta's textbook was very influential, and is sometimes consideredthe first textbook "to treat zero as a number in its own right."It also treated negative numbers.
Today I did have a look at the Web of Knowledge and found a few more recent sources, but none that claimed or seemed to be definitive, all of which cited these three as foundation texts on the subject.
In a logic that neither Mr Spock nor I understand, the left luggage office at a Heathrow terminal was on an upper floor. Cheaper floor space, I suppose. Leaving and later collecting luggage meant getting it to that floor. On one trip the lift to that office was out of order both when I left the luggage and later when I went to collect it, so it had to be man(me)handled up and later down the stairs. No explanation, no apology, no discount on the fee for the extra trouble. Just the usual snarl when I mentioned this fact to the attendant who had no doubt heard it all before, and it bounced off.
For Ptolemy and other geocentrists, the "fixed" starswere just lights on a sphere , but afterthe Copernican Revolution the fixed stars were understood to beimmensely far away; this made it possible to imagine that they werethemselves suns, perhaps with planets of their own.
"His position gave him access to documents of the Portuguese Empire in Asia and Africa and to the military and colonial officials that staffed it; he used this knowledge to produce his brilliantly written Decadas da Asia (1552â53, 1563), a stirring narrative of the building of the Portuguese Empire." - Columbia Encyclopedia, 6th Edition.
The illustrations are much more than just costume plates, for they show people (mostly peasants, but also city dwellers, clergymen, soldiers and others) engaged in a wide variety of activities (selling goods, going to church, courting, etc.), though always in their best clothes.
Chang's book gives methods of arithmetic (including cube roots)and algebra,uses the decimal system (though zero was represented as just a space,rather than a discrete symbol),proves the Pythagorean Theorem,and includes a clever geometric proof that the perimeter ofa right triangle times the radius of its inscribingcircle equals the area of its circumscribing rectangle.
(He seems to have been a much better mathematicianthan Chang, but just as Newton might have gotten nowhere without Kepler,Vieta, Huygens, Fermat, Wallis, Cavalieri, etc., so Liu Hui mighthave achieved little had Chang not preserved the ancientChinese learnings.)Among Liu's achievementsare an emphasis on generalizations and proofs,incorporation of negative numbers into arithmetic,an early recognition of the notions of infinitesimals and limits,the Gaussian elimination method of solvingsimultaneous linear equations,calculations of solid volumes (including the use of Cavalieri's Principle),anticipation of Horner's Method,and a new method to calculate square roots.
For those who missed the first act, Irving Kristol, William’s father, was a prime and proud architect of the Neo-Conservative movement. Its motto was ‘No more Mr Nice Guy’ and its practice was ‘Anything Goes,’ just ask Karl Rove.
He advanced a rudimentary arithmetic and algebraic notation, allowedrational-number solutions to his problems rather than just integers,and was aware of results like the Brahmagupta-Fibonacci Identity;for these reasons he is often called the "Father of Algebra."His work, however, may seem quite limited to a modern eye:his methods were not generalized, he knew nothingof negative numbers, and, though he often dealt with quadraticequations, never seems to have commented on their second solution.
Aristotle used to be regarding politics and ethics as two related but very separate field of study because ethics examines the good concerning an individual, while politics is about examining the good of the city-state....