Boole Quotes

We are such small, stupid things. For most of my life I thought of nature as the stupid thing: Blind, animal, destructive. We, the humans, were clean and smart and in control: we had wrestled the rest of the world into submission, battered it down, pinned it to a glass slide and the pages of The Bool of Shhh.

Bool! The end.

That's what I love about reading: one tiny thing will interest you in a book, and that tiny thing will lead you onto another bool, and another bit there will lead you onto a third book. It's geometrically progressive-all with no end in sight, and for no other reason than sheer enjoyment.

Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s 'The Mathematical Analysis of Logic'.

There is a common ground upon which all sincere votaries of truth may meet, exchanging with each other the language of Flamsteed's appeal to Newton, "The works of the Eternal Providence will be better understood through your labors and mine.

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.

Abracadabra! Bool! The end!

Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to give rest had no tendency to prove them.

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.

Then Daddy is saying it's over, the blood-bool is over and Scott can take care of his brother. His father tells him he's brave, one brave little sumbitch, his father says he loves him and in that moment of victory Scott doesn't even mind the blood on the floor, he loves his father too, he loves his crazy blood-bool Daddy for letting it be over this time even though he knows, even at three he knows that next time will come.

Vellum” is another name for skin—at one point, philosophy was bound up in the stuff. I reached down to pick up James’s first edition of Samuel Clarke’s A Demonstration of the Being and Attributes of God, published in 1705, and gently fingered its cold white surface as if it were a sacred relic. The term “philosophical corpus” had never made sense until now. I turned the book over. Tenderly. It was a little body: skin wrapped around something beautiful and inexplicable. Putting it under my arm, I turned to the back corners of the library. Tucked away on one of the back shelves was Josiah Royce’s library: Descartes, Spinoza, Fichte, Mill, Dilthey, Lotze, Tarde, Boole. These books were filled with marginalia. I took a quick look at one of Royce’s jottings—something written in Greek about God and strife—but then grabbed the books that I could carry. I would think about marginalia later. This wasn’t just any set of books. It was the bridge between European and American philosophy. That afternoon at dusk I had the unshakable sense that I was missing the most important part of West Wind, and over the course of three years I saw that this premonition was more correct than I could have known. Instead

That language is an instrument of human reason and not merely a medium for the expression of thought, is a truth generally admitted. -George Boole The way I feel about music is that there is no right and wrong. Only true and false. -Fiona Apple

Fortunately classical algebra of logic [i.e. Boole and so on] has its merits quite apart from the question of its applicability to mathematics. Not only as a formal image of the technique of common-sensical thinking has it reached a high degree of perfection, but also in itself, as an edifice of thought, it is a thing of exceptional harmony and beauty. Indeed, its successor, the sumptuous symbolic logic of the twentieth century which at present is continually raising the most captivating problems and making the most surprising and penetrating discoveries, likewise is for a great part cultivated for its own sake.

Booleans are named after George Boole, an English mathematician who invented Boolean logic. You’ll

Conectores logicos�. Tablas de verdad.Tecnicas �de demostracion�. � Algebras de Boole. Camacho Introd. a la Matem

Modern mathematics contains much more than that, of course. It includes set theory, for example, created by Georg Cantor in 1874, and “foundations,” which another George, the Englishman George Boole, split off from classical logic in 1854, and in which the logical underpinnings of all mathematical ideas are studied. The traditional categories have also been enlarged to include big new topics—geometry to include topology, algebra to take in game theory, and so on. Even before the early nineteenth century there was considerable seepage from one area into another. Trigonometry, for example, (the word was first used in 1595) contains elements of both geometry and algebra. Descartes had in fact arithmetized and algebraized a large part of geometry in the seventeenth century, though pure-geometric demonstrations in the style of Euclid were still popular—and still are— for their clarity, elegance, and ingenuity.

Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.

We never knew Jim's surname but to us, as youngsters, he was "Jim Bool the Fool". It may not have been respectful but Jim Bool was the most outrageous liar you could ever meet. If it was test cricket time Jim would tell, in all seriousness, of how he played for Australia, of the centuries he had made and he wickets he had taken. In the football season he would describe the days when he had captained Melbourne. He had won King's Prizes for rifle shooting, the gun championship at Monte Carlo and when Melbourne Cup time came around we were treated to a vivid account of how he had won the Cup in his jockeying days.

I notice that when all a man’s information is confined to the field in which he is working, the work is never as good as it ought to be. A man has to get perspective, and he can get it from bools or from people-preferably from both.

Diablo Space Time Set Code Abstract : Sacred Globe Inna Whorl Turn Ring > BubbleSort = Off = BindMetaQuadSwitch = Bool BindSΦRT(SΦRT{FindHashSet({BindMetaQuadSwitch() = On;})});

When I was a digital system designer in the 1960s, I didn’t worry very much about minimization. If a simplification was obvious, then of course I used it. But I didn’t try to do anything “clever.” In college, minimization was a big deal, and textbook writers generally made minimization a central topic. In real life, however, the fact is that right up until the project is actually accepted, shipped, and paid for by the client, designers are ever alert for changes, that is, memos (called engineering change orders) from the client saying something like “we didn’t really mean what we originally asked for in paragraph 19 on page 73, but instead we now want …” To make such changes on a machine that is already 80% wired on the production floor meant that you’d better have some spare logic gates in your design (typically, 10% of the nominal design). Minimization was actually counterproductive, something I didn’t learn until I actually designed for a paycheck and not for homework points.

Another completely different way that the contacts of a relay could fail was if dirt or an insect got trapped in the spacing between contacts. If a fly or a moth, for example, happened to be sitting on the make contact when the coil was energized, then it could be squashed and, after its smashed little body dried, the contacts would be covered with a very disgusting but quite effective insulator. To clean up such a disabled relay was called debugging, a term that has survived in the vocabulary of modern computer users trying to fix their faulty programs. This is not a joke—I heard it as a quite serious story in a lecture at the Naval Postgraduate School in 1982 from a legend in computer science, Rear Admiral Grace Hopper (1906–1992), a Yale PhD mathematician who worked during the Second World War with Harvard’s five ton, 800 cubic foot Mark I relay computer, which when operating was described as sounding like a “roomful of ladies knitting.” To debug such a machine must have been an “interesting” job for someone;

Exercise 7.10: The sort.Interface type can be adapted to other uses. Write a function IsPalindrome(s sort.Interface) bool that reports whether the sequence s is a palindrome, in other words, reversing the sequence would not change it. Assume that the elements at indices i and j are equal if !s.Less(i, j) && !s.Less(j, i).

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his folley with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply (without expressing the limitation) that it is of men only under certain circumstances and conditions that we speak, as of civilized men, or of men in the vigour of life, or of men under some other condition or relation. Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse.

There he recognized that he could combine telephone call-routing technology with Boole’s logic system to encode and transmit any type of information electronically. It was the fundamental insight on which computers rely. “It just happened that no one else was familiar with both those fields at the same time,

Truthy values: In Python, this includes non-zero numbers, non-empty sequences (lists, tuples, strings), and non-empty containers (dictionaries, sets) (Sequences and containers will be discussed in Chapter 6: Python’s Data Structures.). Additionally, objects with a __bool__() method returning True or a __len__() method returning a non-zero value are considered truthy