PROJECTIONS
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PROJECTIONS
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ПРОЕКЦИИ
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Je peux projeter les géodésiques d’un cône sur le plan.
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You can project the geodesics of a cone on to a plane.
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Мога да проектирам геодезическите линии на конус върху равнина.
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PLAN
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PLANE
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РАВНИНА
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toutes ces lignes incurvées, cela évoque des TRAJECTOIRES
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You know, those lines remind me of TRAJECTORIES of particles.
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Всички линии са криви, напомнят на ТРАЕКТОРИИ.
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Exact !
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Precisely !
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Точно така!
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masse m
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Mass m
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Маса m
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L’idée de base de la RELATIVITÉ GÉNÉRALE consiste à assimiler les MASSES à des altérations locales de la courbure de l’espace.
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Der idea at der basis of GENERAL RELATIVITY is to replace MASS by local variations in der curfature of space,
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Основната идея на ОБЩАТА ТЕОРИЯ НА ОТНОСИТЕЛНОСТТА се състои в свързването на МАСИТЕ със собствените изменения на кривината на пространството.
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Vous voulez dire que la masse est un angle ?!?
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Are yer tryin' to tell me that mass is a bunkin' ANGLE ?
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Искате да кажете, че масата е ъгъл?
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Hi Hi !.. mettez m’en pour π/8 ....
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Hi Hi ! Put me down for π/8
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Ха-ха! Нарисувайте ме като π/8 ....
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Oui, dans la mesure où les masses sont des concentrations de courbure
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Yes – provided you measure mass as a kind of concentrated curvature.
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Да, при условие, че масите са концентрични кривини.
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En somme, ce que vous voulez dire, monsieur Albert, c’est que les inflexions des trajectoires, dues aux FORCES, ne sont qu’un effet de PROJECTION, dans notre monde sensible, d’une trajectoire tracée sur une autre surface, et qui est une GÉODÉSIQUE de celle-ci.
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Let me check I've got all this straight, Mr Albert. You're saying that bends in trajectories,
caused by FORCES, are really just an effect of the PROJECTION, into our usual world,
of a GEODESIC trajectory on some other surface.
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В крайна сметка, господин Албер, искате да кажете, че тези извивки на траекториите, причинени от СИЛИТЕ, не са нищо друго, освен ПРОЕКЦИИ в нашия свят на траектория, начертана върху друга повърхност, която е нейната ГЕОДЕЗИЧЕСКА ЛИНИЯ.
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encore de la métaphysique !
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More ruddy metafizzicks !
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ПАК МЕТАФИЗИКА!
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mais non, c’est de la géométrie
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No, just geometry.
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Не, това е геометрия.
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Je vais te donner un exemple. Imagine que nous soyons dans une capsule spatiale, en
orbite autour de la Terre.
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I gif' you an example. Imachin' yourself to be in a space capsule, in orbit around der earth.
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Ще ти дам пример. Представи си, че се намираме в кабината на космически кораб и сме в орбита около Земята.
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Nous échappons alors à toute pesanteur
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Crikey ! We've gone weightless !
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Значи сме в безтегловност.
Ah non !
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Oh 'eck !
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О, не-е-е!
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mi !
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Mi !
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Почти!
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Nous allons jouer à une sorte de billard
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Now we can play a rather unusual kind of BILLIARDS,
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Сега ще поиграем на особен вид билярд.
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Apparemment, cet objet est constitué de deux surfaces transparentes, pleines de plis, de
cloques, mais identiques et proches l’une et l’autre
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As far as I can tell, this thing seems to be built from two transparent surfaces, with lots of folds and dents, both exactly the same and lying parallel to each other.
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Очевидно този обект се състои от две прозрачни повърхности, изпълнени с гънки и издутини, но които са еднакви и са близки една до друга.
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Ce qui permet de Tirer des petites billes entre les deux et d’observer leurs trajectoires
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Dat permits me to shoot der tiny marples between dem and observe dere trajectories.
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Това позволява да изстреляме две малки топчета между тях и да наблюдаваме траекториите им.
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Celles-ci ne dépendent pas de la vitesse initiale V qui est conservée pendant tout le mouvement.
La Direction
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The trajectories do not depend on the speed V because this is deemed to be constant throughout the motion.
The Boss
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Траекториите не зависят от началната скорост V, която се запазва през цялото време на движение.
Ръководството
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Dans ce cas précis, il se trouve que toutes les trajectoires possibles sont des GÉODÉSIQUES
(s’il y avait de la pesanteur cela ne serait plus le cas).
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In yust dis case, it follows dat all possible trajectories are GEODESICS. (If we weren't weightless, dis wouldn't be der case.)
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В този конкретен случай всички възможни траектории са ГЕОДЕЗИЧЕСКИ ЛИНИИ.
(При наличието на притегателна сила това никога няма да се случи).
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Oh, regardez, la lampe projette les trajectoires sur le plancher de notre capsule spatiale !
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Oh, look : the lamp is projecting the trajectories on to the floor of the capsule !
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О, вижте, лампата проектира траекториите върху пода на нашата кабина!
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Quelqu’un qui ne verrait que ces ombres penserait que les objets qui se déplacent sur
ce PLAN sont soumis à un CHAMP de FORCES. Alors que cela n’est qu’un problème
de courbure d’une surface.
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Anyone who could only see der shadows would think dat der objects moofing in der plane were affected by a FIELD of FORCES. But really it's all due to der curvature of der surface.
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Някой, който види само тези сенки, ще помисли, че обектите, които се местят по тази РАВНИНА, са под влияние на СИЛОВО ПОЛЕ. А всъщност това е проблем на кривината на повърхността.
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Alors, quand j’observe la trajectoire d’une comète autour du Soleil, en supposant qu’elle s’effectue dans un espace tridimensionnel euclidien, sans courbure, en fait cette comète suit une GÉODÉSIQUE d’une sorte d’espace dans lequel .... elle va TOUT DROIT !!!!
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So when I observe the path of a comet around the sun, imagining that it's taking place in
a three-dimensional euclidean space, without curvature, in fact the comet is following a GEODESIC in some other space, where it's traveling ... STRAIGHT AHEAD !!!!
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Значи, когато наблюдавам траекторията на една комета около Слънцето, предполагайки, че тя преминава през триизмерно евклидово пространство, без кривина, всъщност тази комета следва ГЕОДЕЗИЧЕСКАТА ЛИНИЯ на това пространство, в което... тя се движи САМО НАПРЕД.
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On ne perçoit que l’ombre des choses
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We see only the shadows of reality.
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Ние виждаме само сянката на предметите.
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c’est très platonicien, ce que vous dites, mon cher Tirésias
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That's a very platonistic sentiment fer a snail, Tiresias old bean.
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Това, което казвате, уважаеми Тирезий, е съвсем в духа на Платон.
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On ne peut aller que TOUT DROIT !
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The only way to go is STRAIGHT.
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Можем да се движим САМО НАПРЕД!
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la LUMIÈRE suit aussi une GÉODÉSIQUE
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LIGHT always follows a geodesic, too.
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СВЕТЛИНАТА следва и ГЕОДЕЗИЧЕСКАТА ЛИНИЯ.
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Tiens, c’est amusant, les géodésiques, quand on les projette suivant un autre angle,
n’ont pas du tout la même tête !
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Y' know, they're funny things, these goedesics. If you project them in a different direction, they don't work. The same way at all !
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Я виж, колко забавно! Когато геодезическите линии се проектират под друг ъгъл, те не изглеждат по същия начин!
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?!?
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?!?
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Tirésias !
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Tiresias !
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Тирезий!
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Bon, bon ....
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I don't mean it, honest !
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Добре, добре...
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MASSE - MATIÈRE
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MASS AND MATTER
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МАСА - МАТЕРИЯ
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Mais alors, le Soleil est un ... cône ?
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Are you saying that the sun is a ... cone ?
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Значи Слънцето е... конус?
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Terre
Mercure
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Earth
Mercury
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Земя
Меркурий
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On sait que le Soleil dévie les rayons lumineux venant de Mercure
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Well, we know it bends light rays from Mercury.
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Знаем, че Слънцето отклонява лъчите на Меркурий.
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Nous croyons que l’espace, au voisinage du SOLEIL, est PLAT. En fait, cet astre, par
sa masse importante, représente une certaine quantité de courbure. Mais, comme le Soleil
n’est pas une masse ponctuelle, nous devrions représenter cette région de l’espace à l’aide d’un cône émoussé :
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We usually think of space near the sun as being FLAT. But in fact, because of its large
mass, this star represents a certain amount of curvature. But because the sun's mass isn't
concentrated at a point, we'll think of this region of space as a smoothed-out cone.
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Предполагаме, че пространството, съседно на СЛЪНЦЕТО, е ПЛОСКО. Всъщност тази звезда със своята голяма маса има известна кривина. Но тъй като Слънцето няма точна маса, то ние можем да представим тази част от пространството като тъп конус.
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étoile
objet massif
observateur
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star
massive object
observer
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Звезда
Масивен обект
Наблюдател
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Des objets extrêmement massifs peuvent courber l’espace au point qu’un observateur
pourra percevoir DEUX images I1 et I2 d’une même étoile E :
c’est l’effet de LENTILLE GRAVITATIONNELLE, récemment mis en évidence par
l’observation.
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Very massive objects can curve space to such an extent that an observer can see two images I1 and I2 of the same star E. This effect, known as a GRAVITATIONAL LENS, has recently been observed in light from quasars.
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Два много масивни обекта могат да изкривят пространството до такава степен, че един наблюдател да вижда две изображения I1 и I2 на една и съща звезда E: това е ефектът на ГРАВИТАЦИОННАТА ЛЕЩА, който бе доказан чрез наблюдение.
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Les masses des atomes, des particules, constituent la courbure générale de l’Univers.
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The masses of atoms and particles all contribute to the general curvature of the universe.
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Масите на атомите, частиците, които съставляват основната кривина на Вселената.
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On donne à la MASSE une signification GÉOMÉTRIQUE
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So MASS has a GEOMETRIC significance.
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МАСАТА има ГЕОМЕТРИЧНО значение.
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mais, entre les atomes il y a bien du ... VIDE ?
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'ang on, wot abaht between the atom ? There’s nuffin’ there !
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Но, между атомите има... ПРАЗНОТА?
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ou alors je ne comprends plus rien ...
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I lorst the thread again ...
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Вече нищо не разбирам...
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mais non, cher ami, cette vieille opposition entre matière et vide est complètement
dépassée ; il n’y a plus que de la .... géométrie
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Now my dear fellow, haven’t you HEARD that the old opposition between MATTER and the VOID is totally OUTMODED ? The ONLY thing NOWADAYS is GEOMETRY.
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Не, приятелю, това противопоставяне между материята и празнотата вече е надживяно. Всичко е... геометрия.
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Plus que de la géométrie !!?!
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Nuffin’ but ... geomatry ???
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Само геометрия?
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Et les négacônes ?
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Wot abaht NEGACONES, smart aleck ?
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А отрицателните конуси?
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Ils évoquent des "masses négatives", génératrices de forces répulsives. Un univers empli
de masses négatives serait bien étrange. Au lieu d’engendrer des galaxies, des étoiles, il
se peuplerait de bulles, de grands vides :
Ainsi semblent se distribuer les amas de galaxies, qui forment un étrange tissu cellulaire, chaque cellule ayant quelque 200 millions d’années-lumière de côté.
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Those conjure up the idea of "negative mass", producing a repulsive force. A universe
full of negative masses would be very peculiar. Instead of galaxies, there would be lots of bubbles – enormous voids. In fact, the mass of the galaxies seems to be distributed like this, forming a strange cellular tissue. Each cell is about 200 million light = years across.
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Те напомнят за „отрицателна маса”, която предизвиква сили на отблъскване. Вселена, изпълнена с отрицателни маси, ще изглежда много странно. Вместо в нея да има галактики и звезди, тя ще бъде населена с балони, големи празноти. Всъщност масата на галактиките ще бъде разпределена по този начин, образувайки странна клетъчна мрежа, в която всяка клетка ще бъде на около 200 милиона светлинни години.
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Les forces de gravité pourraient alors se révéler répulsives à très grande distance.
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Perhaps gravitational forces become repulsive at a very large distance.
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Тогава гравитационните сили ще могат да отблъскват на много голямо разстояние.
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36
POLYÈDRES
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POLYHEDRA
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МНОГОСТЕНИ
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Anselme, tu vas matérialiser les géodésiques d’une surface à l’aide, par exemple, d’un
ruban adhésif.
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Now, Archie : remember that you can produce geodesic on a surface usong sticky tape ? what happens if you bend the surface ?
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Анселм, сега ще материализираш геодезическите линии на една повърхност с помощта, например, на тиксо.
Le fait de plier ce cône (θ = 90°), ne change rien aux géodésiques, et il épouse alors parfaitement le sommet d’un cube.
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If you bend this cone (θ = 90°) the geodesics don’t change. (the sticky tape just bends with the surface.) In fact you can fold it to fit perfectly over the corner of a cube.
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Ако сгънеш този конус (θ = 90°), геодезическите линии няма да се променят и той ще приеме формата на връх на куб.
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De même, tu peux ménager trois plis sur ce cône (θ = 180°) pour lui faire épouser le
sommet d’un tétraèdre régulier.
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Similarly, you can make three folds in this cone (θ = 180°) so that it fits over the corner of a regular tetrahedron.
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По същия начин можеш да прегънеш конуса на три места (θ = 180°) и той ще приеме формата на връх на правилен тетраедър.
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