From 2a651ede895c1eabe0afd25890918a44684f6037 Mon Sep 17 00:00:00 2001 From: MEUNIER Thibaud Date: Sat, 11 May 2019 09:47:22 +0200 Subject: [PATCH] ajout du projet des nombres univers --- articles/00190327/content.html | 74 --------------------- articles/00190327/header.html | 50 +++++++++++++- articles/00190327/images/pi_by_xan2_3.jpeg | Bin 0 -> 286910 bytes articles/00190327/spages/01-jansloot.html | 55 +++++++++++++++ articles/00190327/spages/02-pifs.html | 18 +++++ index.php | 7 ++ page.php | 27 +++++++- 7 files changed, 153 insertions(+), 78 deletions(-) delete mode 100644 articles/00190327/content.html create mode 100644 articles/00190327/images/pi_by_xan2_3.jpeg create mode 100644 articles/00190327/spages/01-jansloot.html create mode 100644 articles/00190327/spages/02-pifs.html diff --git a/articles/00190327/content.html b/articles/00190327/content.html deleted file mode 100644 index 1a4c8af..0000000 --- a/articles/00190327/content.html +++ /dev/null @@ -1,74 +0,0 @@ -
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- Dès le début de l'informatique, les ordinateurs ont été utilisés pour codifier l'information. - Leurs grandes facultées calculatoires étaient bien sûr exploitées dans les domaines scientifiques et financiers. - Mais on a rapidement sû tirer profit de ces machines pour organiser, stocker et rechercher des connaissances. - Dans ces systèmes, textes et images sont convertis en suites de chiffres. - Chaque lettre d'un texte est remplacée par sa position dans l'alphabet. - Les images sont vues comme des matrices de points, dont la couleur est codée suivant l'intensité de sa valeur RGB (Red, Green, Blue) -

- La capacité de traitement des ordinateurs augmenta. - Il fallait stocker toujours plus d'information pour alimenter les calculs qui, ainsi, devenaient de plus en plus pertinents. - Pour couronner le tout, ce stockage était mal géré, de nombreuses copies d'un même fichier existaient, parfois intentionnellement (dans le but d'un assurer la conservation), parfois par manque de rigueur. - La capacité de stockage devint un problème, au point de contribuer mettre la planète en péril. - Consommer toujours plus d'énergie, pour alimenter des datacenters de plus en plus nombreux. - Extraire des minerais rares pour fabriquer des composants électroniques en quantité astronomiques. Cela n'était clairement pas viable sur le long terme. -

- C'est alors que l'on trouva un nouvel intêret aux nombres univers. - Il n'était plus besoin de stocker l'intégralité de la suite de chiffres qui représentait une information. - Cette suite existait forcément à l'intérieur d'un nombre univers. - Seule la longueur de l'information et sa position dans le nombre devenaient nécessaires. - Ces deux valeurs étaient bien sûr stockées, mais cela représentait une économie phénoménale de ressources. - On rechercha des nombres univers dont les propriétés mathématiques permettaient de fabriquer des puces électroniques spécifiquement -

- Comme toujours les pionniers furent incompris et passèrent pour des excentriques. - Certains furent même soupçonnés d'escroquerie tant les performances paraissaient extraordinaires. - Mais bientôt les perspectives de bénéfices attirèrent des entrepreneurs, avec des projets réfléchis et des ambitions démesurées. -

- Les plus malins avaient remarqué qu'il leur était possible de monter un modèle économique où leurs clients étaient complètement captifs. - Car la seule information que le client détenait se limitait à deux nombres : une longueur et une position. - A elles seules, ces données ne permettaient pas grand chose. - Il fallait connaître le nombre univers auquel elles se référaient, et il fallait aussi détenir des composants spécifiques capables de calculer très rapidement un grand nombre de décimales du nombre univers choisi. -

- Bientôt, sous la pression de lobbies industriels, les gouvernements cédèrent les uns après les autres. - Ils votèrent une loi permettant de breveter un nombre univers. - Se donner les moyens de découvrir un nouveau nombre univers garantissait l'exclusivité de son usage. - Les mathématiciens avaient devant eux de belles carrières dans des entreprises devenues d'énormes conglomérats mondiaux. -

- Enfin vint le temps des intelligences artificielles. - La boucle était bouclée, les ordinateurs cherchaient eux-mêmes les conditions de l'optimisation de leurs performances. - La singularité fût-elle atteinte ? Les hommes ne le sûrent jamais. -
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La constante e : Le cas Jan Sloot.

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- Inspiré par un post sur Uzbek & Rica
- Certains l'ont découvert par hasard, d'autres y ont consacré des années de recherche : Il existe des "nombres univers".

- La constante e est l'un d'entre eux : 2,718 281 828 459 045 235 360 287 471 352 662 497 757 247 093 699 959 574 966 967 627 724 076 630 353 547 594 571 382 178 525 166 427 427 466 391 932 003 059 ...

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πfs

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- Certains l'ont découvert par hasard, d'autres y ont consacré des années de recherche : Il existe des "nombres univers". -

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diff --git a/articles/00190327/header.html b/articles/00190327/header.html index 478f0f5..4798b3e 100644 --- a/articles/00190327/header.html +++ b/articles/00190327/header.html @@ -8,13 +8,59 @@

Les chroniques des Nombres Univers.

Certains l'ont découvert par hasard, d'autres y ont consacré des années de recherche : il existe des "nombres univers".

- Ces nombres sont des irrationnels, leur représentation comporte une infinité de décimales. + Ces nombres font partie de l'ensemble des irrationnels, leur représentation comprend une infinité de décimales. La suite de leurs décimales ne comporte aucune périodicité. Cela conduit à une propriété un peu étonnante : ils peuvent contenir la représentation de n'importe quel nombre, y compris eux-même.

Nous en connaissons tous au moins un, il s'agit du nombre π : 3,141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 ... -

Mais il en existe d'autres. +

+ Ils furent massivement utilisés par les grandes firmes informatiques à partir du milieu du 21eme siècle. +

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+ Dès le début de l'informatique, les ordinateurs ont été utilisés pour codifier l'information. + Leurs grandes facultées calculatoires étaient bien sûr exploitées dans les domaines scientifiques et financiers. + Mais on a rapidement sû tirer profit de ces machines pour organiser, stocker et rechercher des connaissances. + Dans ces systèmes, textes et images sont convertis en suites de chiffres. + Chaque lettre d'un texte est remplacée par sa position dans l'alphabet. + Les images sont vues comme des matrices de points, dont la couleur est codée suivant l'intensité de sa valeur RGB (Red, Green, Blue) +

+ La capacité de traitement des ordinateurs augmenta. + Il fallait stocker toujours plus d'information pour alimenter les calculs qui, ainsi, devenaient de plus en plus pertinents. + Pour couronner le tout, ce stockage était mal géré, de nombreuses copies d'un même fichier existaient, parfois intentionnellement (dans le but d'un assurer la conservation), parfois par manque de rigueur. + La capacité de stockage devint un problème, au point de contribuer mettre la planète en péril. + Consommer toujours plus d'énergie, pour alimenter des datacenters de plus en plus nombreux. + Extraire des minerais rares pour fabriquer des composants électroniques en quantité astronomiques. Cela n'était clairement pas viable sur le long terme. +

+ C'est alors que l'on trouva un nouvel intêret aux nombres univers. + Il n'était plus besoin de stocker l'intégralité de la suite de chiffres qui représentait une information. + Cette suite existait forcément à l'intérieur d'un nombre univers. + Seule la longueur de l'information et sa position dans le nombre devenaient nécessaires. + Ces deux valeurs étaient bien sûr stockées, mais cela représentait une économie phénoménale de ressources. + On rechercha des nombres univers dont les propriétés mathématiques permettaient de fabriquer des puces électroniques spécifiquement +

+ Comme toujours les pionniers furent incompris et passèrent pour des excentriques. + Certains furent même soupçonnés d'escroquerie tant les performances annoncées paraissaient extraordinaires. + Mais bientôt les perspectives de bénéfices attirèrent des entrepreneurs, avec des projets réfléchis et des ambitions démesurées. +

+ Les plus malins avaient remarqué qu'il leur était possible de monter un modèle économique où leurs clients étaient complètement captifs. + Car la seule information que le client détenait se limitait à deux nombres : une longueur et une position. + A elles seules, ces données ne permettaient pas grand chose. + Il fallait connaître le nombre univers auquel elles se référaient, et il fallait aussi détenir des composants spécifiques capables de calculer très rapidement un grand nombre de décimales du nombre univers choisi. +

+ Bientôt, sous la pression de lobbies industriels, les gouvernements cédèrent les uns après les autres. + Ils votèrent une loi permettant de breveter un nombre univers. + Se donner les moyens de découvrir un nouveau nombre univers garantissait l'exclusivité de son usage. + Les mathématiciens avaient devant eux de belles carrières dans des entreprises devenues d'énormes conglomérats mondiaux. +

+ Enfin vint le temps des intelligences artificielles. + La boucle était bouclée, les ordinateurs cherchaient eux-mêmes les conditions de l'optimisation de leurs performances. + La singularité fût-elle atteinte ? Les hommes ne le sûrent jamais. +

+
+
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+
+
+
+
+
+

La constante e : le cas Jan Sloot.

+

+ Inspiré par un post sur Uzbek & Rica

+ Certains l'ont découvert par hasard, d'autres y ont consacré des années de recherche : il existe des "nombres univers".

+ Le nombre d'Euler (noté e ) est l'un d'entre eux : 2,718 281 828 459 045 235 360 287 471 352 662 497 757 247 093 699 959 574 966 967 627 724 076 630 353 547 594 571 382 178 525 166 427 427 466 391 932 003 059 ...

+

+

+ Jan Sloot surveillait ses braises. + Un large sourire éclairait son visage. + Bien sûr la perspective d'avaler ces délicieuses merguez contribuait à son état d'esprit. + Accompagnées d'une salade et d'une bière blonde bien fraîche, sur la table du jardin en compagnie de la famille, c'était parfait. + Mais c'était surtout parce que demain, toutes ces longues années de travail allaient enfin payer. +

+ L'idée était pourtant assez simple, et il s'étonnait encore que personne avant lui n'y ait pensé. +

+
+
+
+

Voici deux manières de calculer une valeur approchée de la constante e :

+
    +
  • la formule de Bernoulli : \(e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n\)
  • +
  • la série infinie suivante : \(e = \sum_{n = 0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \cdots\)
  • +
+

L'implémentation informatique directe de ces équations pose des problèmes. Soit cela ne converge pas assez vite vers e, soit les calculs sont trop lents.

+

Pour être pragmatique, il faut poser: \(u_n=\displaystyle\sum_{k=0}^{k=n}\dfrac{1}{k!}\) et \(v_n=u_n+\dfrac{1}{n\cdot n!}\)

+

Ce qui donne, par exemple, le programme Python suivant :

+

+# -*- coding: utf-8 -*-
+def e(ndec=1000):
+  n = fn = 1
+  while fn < ndec:
+    fn *= n; n += 1
+  x = u = 10**ndec
+  for k in range(n,0,-1):
+    u = x + u//k
+  return u
+
+print "// Pour 1000 décimales :"
+print e()
+print "// Pour 100000 décimales :"
+print e(100000);
+            
+ NB : L'identité d'Euler est considérée par beaucoup comme la plus belle formule des mathématiques. + Elle met en jeu deux nombre univers.
+ Elle s'écrit : \(e^{i\pi} + 1 = 0\) +
+
+
+
\ No newline at end of file diff --git a/articles/00190327/spages/02-pifs.html b/articles/00190327/spages/02-pifs.html new file mode 100644 index 0000000..04440d5 --- /dev/null +++ b/articles/00190327/spages/02-pifs.html @@ -0,0 +1,18 @@ +
+
+
+
+
+
+

πfs

+

+ Certains l'ont découvert par hasard, d'autres y ont consacré des années de recherche : il existe des "nombres univers". +

+ Nous en connaissons tous au moins un, il s'agit du nombre π : 3,141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 ... +

+

+ Epilogue : + Les sources de pifs sont en ligne sur GITHUB +
+
+
diff --git a/index.php b/index.php index bb89dd0..baf4601 100644 --- a/index.php +++ b/index.php @@ -21,6 +21,13 @@ + + + + + + + + + + + + @@ -41,14 +52,15 @@ if (file_exists('articles/'.$article.'/styles.html')) - - TOPISTO + + TOPISTO

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