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CARTESIAN, adj. Relating to Descartes, a famous philosopher, author of the celebrated dictum, Cogito, ergo sum—whereby he was pleased to suppose he demonstrated the reality of human existence. The dictum might be improved, however, thus: Cogito ergo cogito sum—'I think that I think, therefore I think that I am;' as…
The mathematician Freeman Dyson, of the Institute for Advanced Study, offers a scheme in which the planet Jupiter is broken down piece by piece, transported to the distance of the Earth from the Sun, and reconstructed into a spherical shell – a swarm of individual fragments revolving about the Sun. The advantage of…
Fractal geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these…
Imagine, say, that you wanted to travel from New York to Madrid, two cities that are at almost the same latitude. If the earth were flat, the shortest route would be to head straight east. If you did that, you would arrive in Madrid after traveling 3,707 miles. But due to the earth's curvature, there is a path that on…
The young specialist in English Lit, having quoted me, went on to lecture me severely on the fact that in every century people have thought they understood the Universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern 'knowledge' is that it is wrong…
The sun's rays proceed from the sun along straight lines and are reflected from every polished object at equal angles, i.e. the reflected ray subtends, together with the line tangential to the polished object which is in the plane of the reflected ray, two equal angles. Hence it follows that the ray reflected from the…
There remains simple experience which, if taken as it comes, is called accident; if sought for, experiment. But this kind of experience is no better than a broom without its band, as the saying is — a mere groping, as of men in the dark, that feel all round them for the chance of finding their way, when they had much…
The similarity between different vertebrate embryos is indeed remarkable. Since the early 1800s, embryologists have been struck by the parallel between early development in various animal species and their evolutionary relationship, a resemblance conveniently abbreviated by the saying "ontogeny recapitulates…
One, two, three ragged files of Canada geese skim the treetops, preceded and followed by their honking chorus. I freeze in my tracks to watch them pass, heading south, feathers ruffled by the last warm breezes of the season. When their honks have faded into silence, I notice a chill in the air. The spinning planet has…
To ANYONE who has been in space and experienced its changelessness, the real excitement of space flight comes when it is time to land on a new planet. The ground speeds backward under you as you catch glimpses of land and water, of geometrical areas and lines that might represent fields and roads. You become aware of…
Mathematicians use the idea of proof to make a distinction between a 'conjecture' and a 'theorem', which bears a superficial resemblance to the OED's distinction between the two senses of 'theory'. A conjecture is a proposition that looks true but has never been proved. It will become a theorem when it has been…
Theory, Sense 1: A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; a hypothesis that has been confirmed or established by observation or experiment, and is propounded or accepted as accounting for the known facts; a statement of what are held to be the…
Suppose someone describing something to me from postulates like. "Here's a computer and here are the op codes." I can visualize the structure of programs and how things are efficient or inefficient based on those op codes, by seeing the bottom and imagining the hierarchy. And i can see the same thing with programs. If…
He was 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and 'twas the 47 El. libri I. He read the proposition. 'By G—,' sayd he, (He would now and then sweare, by way of emphasis) 'By G—,' sayd he, 'this is impossible!' So he reads the…
The contents of a Doomsday Chest will include stainless steel or titanium sheets, laser etched with an archive of the fundamentals of human knowledge. Each sheet would be carved, front and back, in the five most widely spoken languages of the 21st Century; Mandarin, Spanish, English, Arabic and Hindi. To aid in their…
Asymmetric attention is the key to another important concept, celebrity. Being famous means that a lot of people pay attention to you--after all, by definition it is famous people who appear on the cover of magazines, which are purchased because lots of people want to know what's happening with their favorite…
Web topology contains more complexity than simple linear chains. In this section, we will discuss attempts to measure the global structure of the Web, and how individual webpages fit into that context. Are there interesting representations that define or suggest important properties? For example, might it be possible…