jeudi 20 janvier 2011

Les nombres et le réel


Les mathématiques nous permettent d'appréhender cet univers dont nous sommes des poussières d'étoiles.

Cependant, sans même avoir recours aux mathématiques les plus élaborées, restons en à l'arithmétique qui nous renseigne par exemple sur la distance qui nous sépare d'Andromède, notre plus proche galaxie. Tout juste quelques années-lumière. 

Cela peut se compter en kilomètres, en mètres, en millimètres en microns même, il est toujours possible d'écrire un chiffre qui représentera la plus grande ou la plus petite mesure possible dans l'univers.

Que ce soit des distances, des masses, des particules, des durées, des températures, toutes pourront être quantifiées, de la position, la vitesse et la masse d'un neutrinos aux mêmes attributs d'un trou noir ou de la matière manquante.

Mais les nombres sont-ils toujours significatifs quand ils ne se rapportent plus au réel?

Ainsi, il est possible d'écrire 10 milliards puissance 10 milliards à l'infini mais cela ne peut plus correspondre à quoi que ce soit dans l'univers.

Les nombres étant le produit de notre faculté cognitive peut-on en conclure qu'il y a "plus" d'infini en nous que dans l'univers? Ce qui bien sûr est une impossibilité logique, le plus ne pouvant être dépassé par lui-même. Comme l'infini est un concept qui d'une certaine façon désigne l'Absolu dans toutes les civilisations passées et présentes, ne sommes-nous pas, nous humains, créateurs et porteurs de l'Absolu?

Ce que les hommes ont cherché pendant des millénaires dans un au-delà du monde, dans des déités imaginaires et toutes différentes les unes des autres, c'est en eux-mêmes que cela réside.

L'infini, l'absolu, quel que soit le nom qu'on lui donne, c'est l'homme lui-même qui en est détenteur ou plutôt l'intelligence humaine comme le montre le portrait d'Homer Simpson!

43 commentaires:

Anijo a dit…

Flocon,
You've got me reading about numbers and infinity this morning. Yesterday I was working on the painting of the "two Romans" and that used up that part of my brain. All I had left in me was talking politics and basking in the sun.

Did you notice that Google is celebrating Cézanne's 172nd birthday?

Anyway, to continue with my homework

Flocon a dit…

Anijo,

You sure know much, much more about guns, firearms and weaponry than I do in mathematics. My level is that of an 11 year old lame pupil... pathetic :-(

re Cézanne, no it doesn't appear on my Google page nor does it on the US Google. Maybe am I too late?

Anijo a dit…

Flocon,

When we're on line at the same time we'll have to compare notes as to what image we see on the Google page.

Anijo a dit…

Right now Google.com is celebrating the inauguration of JFK as 35th President of the U.S. On Google.fr there is nothing.

Flocon a dit…

Anijo,

Je crois en effet qu'il doit y avoir des spécificités nationales célébrées pour chaque Google.

Si ça se trouve Google Italy celebrates Garibaldi the day he was born and Google Germany the day the wall fell.

Go figure what Google India or Google Japan have in store for people living over there?

Mais je n'ai pas vu Google Cézanne and yet I land 25 times a day on Google...

I can't access to Google web from France. What I can get access to is the Google American news page which is neutral.

Ned Ludd a dit…

"L'infini, l'absolu, quel que soit le nom qu'on lui donne, c'est l'homme lui-même qui en est détenteur ou plutôt l'intelligence humaine comme le montre le portrait d'Homer Simpson!"

Et l'infini n'existerait pas s'il n'y avait pas un être comme l'homme à le perçevoir ou imaginer? Comme le son d'un arbre tombé dans un forêt s'il n'y avait personne pour l'entendre?

En fait, comme j'ai dit une autre fois, il y a des infinis. On peut consulter un livre dont je mentionné une fois, "From Here to Infinity".

Flocon a dit…

Ned,

Je suis content que tu soulèves la question objet/sujet par le biais du thème de l'infini.

C'est Berkeley qui le premier je crois, en tout cas en Occident, a poussé aussi loin l'idéalisme absolu (ou subjectif) avec son Esse est percipi aut percipere.

Le problème est que cela débouche sur le solipcisme dont on ne peut plus sortir.

Ton interrogation est celle de l'étonnement spontané.

"Et l'infini n'existerait pas s'il n'y avait pas un être comme l'homme à le perçevoir ou imaginer? Comme le son d'un arbre tombé dans un forêt s'il n'y avait personne pour l'entendre?"

C'est ce que je pense en effet.

Ta position est celle des matérialistes dont Schopenhauer disait qu'ils s'oublient dans leur calculs.

De ce couple objet/sujet, Nietzsche écrit qu'il est vrai mais trivial. Trivial peut-être il n'empêche...

L'arbre qui tombe dans la forêt est comme une éruption volcanique sur une planète appartenant à une galaxie éloignée de la nôtre de 50 millions d'années lumière.

Qui est au courant? Existe-t-elle cette éruption si aucune conscience n'est là pour la percevoir?

L'infini mathématique dont il est question dans le billet est un produit de notre cerveau donc de notre conscience. Où d'autre peut-on le trouver?

"comme j'ai dit une autre fois, il y a des infinis"

Où???

Ned Ludd a dit…

Je crois que j'ai parlé des infinis quand j'ai fait un poste sur Lawrence Krauss. A la fin de son conférence pendant les questions, il a adressé le sujet.

Flocon a dit…

Ned,

Excuse-moi mais je me suis mal exprimé quand je te demandais "où?" (last word of the comment).

Le "où" ne se rapportait pas à la vidéo de Krauss dont tu parles mais à la "localisation", si je puis dire, de l'infini.

L'infini lui-même est un concept humain, comment pourrait-il exister sans l'humain qui l'a créé?

Même le Brahman hindouiste, tout absolu de l'absolu qu'il soit, transcendant la transcendance de tout ce qui est et de tout ce qui n'est pas, En soi universel et âme cosmique éternelle, n'existe pas s'il n'y a pas une conscience pour ne serait-ce que l'imaginer.

Mais cela ne répond pas aux question que je pose dans ma réponse.

J'ai mal formulé ma question d'ailleurs;

"L'infini mathématique dont il est question dans le billet est un produit de notre cerveau donc de notre conscience. Où ailleurs peut-on le trouver?"

J'ai évoqué l'hypothèse d'une éruption volcanique à 50 millions d'années-lumière d'ici.

Est-ce une création imaginaire de ma part ou est-ce "vrai"?

Sujet d'un billet à venir.

En attendant, Ned, please, pray and tell me: où sont les infinis dont tu parles? Particulièrement les infinis mathématiques ou géométriques?

Ned Ludd a dit…

Just because we haven't observed or perceived something, doesn't mean it doesn't exist. I would say that "zero" existed before Indian mathematicians discovered or invented it for our minds.

As to infinities, one example. There are an infinite number of rational numbers and there are an infinite number of irrational numbers. Indeed, between any two rational numbers there are an infinite number of irrational numbers, like Pi.

You can add or multiply it by whatever number and get another infinity. So it would seem that there are more irrational numbers than rational numbers, though both are infinite.

I have to review my math to be more explicit.

Flocon a dit…

Ned,

I know you're always right but sometimes maybe not entirely right yet.

Les mathématiques et la géométrie sont des créations exclusivement humaines, elles sont le produit de nos capacités cognitives.

Le zéro, la racine carré ou tout ce que tu peux imaginer n'existent pas hors de notre conscience puisque c'est nous qui les avons créés.

"You can add or multiply it by whatever number and get another infinity."

J'ai donné l'exemple de 10 milliards puissance 10 milliards à l'infini qui ne peut correspondre à rien de réel car c'est une pure création de l'esprit.

En imaginant un infini hors de nos consciences, tu te places dans la situation du matérialiste qui s'oublie dans ses calculs.

"Just because we haven't observed or perceived something, doesn't mean it doesn't exist."

That something exists only because you can imagine it exists.

L'éruption volcanique sur une planète de notre galaxie (not to mention the billion other galaxies that we know do exist) a-t-elle eu lieu il y a 50 millions d'années? How do we know?

Le temps est continu et il y a (sans doute) des éruptions volcaniques en continu sur les milliards de milliards de planètes que nous savons exister dans l'univers. Mais c'est éruptions nous les imaginons, nous n'en connaissons rien.

Le choix est entre imaginer et savoir. Donc elle n'existent pas puisque nous ne savons pas.

Pour qu'une chose existe il faut qu'elle soit perçue par une conscience réfléchissante.

A cet égard, les animaux qui nous ont précédés sont comme des vitres transparentes alors que nous sommes des miroirs. Ce qui fait toute la différence dans la perception de la matière qui en nous peut se "reconnaître".

Tu ne peux pas trouver l'infini hors de notre conscience puisque c'est un concept créé par notre conscience.

Remember Ned: The world as Will and Representation.

Flocon a dit…

J'ajouterai pour bien marquer la distinction entre imaginer et savoir le concept du divin.

Tu peux imaginer que Dieu existe (beaucoup le font) mais tu ne peux pas en inférer qu'il existe réellement. Tu ne peux pas dire : je sais qu'il existe.

C'est un peu comme l'essence et l'existence. Tu ne peux inférer l'existence de quoi que ce soit seulement parce que tu en connais l'essence qui n'est jamais qu'un création de ton imagination.

Sans le savoir peut-être, en croyant que les choses existent indépendamment de notre perception, tu défends l'argument ontologique de Descartes qui conclut à l'existence de Dieu uniquement parce qu'il a mis en nous l'idée de l'infini, idée que nous sommes incapables de concevoir par nous-mêmes parce que nous sommes finis.

Ned is a theist! Who would have thought?

Anijo a dit…

Flocon,

This notion that infinity as well as mathematics are both concepts understood by a conscious mind has been occupying my thinking today. Thank you for expanding the way that i view the world.

Can we 'observe' infinity? No, of course not. So then what exactly is infinity if not a concept conceived by humankind?

Flocon a dit…

Anijo,

"So then what exactly is infinity if not a concept conceived by humankind?"

My point yes.

I already wrote a post about infinity last July.

Exponantiation, Factorial, Squares, Prime numbers and all those mathematical tools lead us to infinity but where, save in our heads, are these infinities to be found or observed?

The quote by Planck that you gave the other day (on Monisme) is much appropriate here:

I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness."

Slightly OT but not that much, here is what I read on the English Wiki re Schopenhauer:

Many interpreters[who?] see Schopenhauer's account of the Will as closely resembling classic examples of Monism, especially as propounded by Upanishads and Vedanta philosophy"

Si l'infini est en nous cela veut dire qu'il y a interdépendance entre la matière et l'esprit. The one cannot go without the other.

Cela ne va pas changer ma vie au quotidien évidemment mais comme tu l'écris justement it expands the way you view the world.

Vivre en ville perturbe très profondément notre relation à la Nature évidemment et plus encore notre relation au cosmos.

Being in the desert or at sea in the night, comtemplating the seemingly so far away stars is an awesome experience.

If one takes the time to wonder and meditate, one will slowly perceive there's another way of relating to what we perceive as being outside whereas we belong to the universe as much as it belongs to us.

We're all one but our modern living conditions add more and more blinders on our eyes and more and more hindrances on our ability to stray away from the received modern "right path".

Here is the last sentence of the World as Will and Representation loosely translated from German to English:

For those in which the Will has turned and has denied itself, our so very real world with all its suns and galaxies is... Nothing

Ned Ludd a dit…

"C'est un peu comme l'essence et l'existence. Tu ne peux inférer l'existence de quoi que ce soit seulement parce que tu en connais l'essence qui n'est jamais qu'un création de ton imagination."

On peux imaginer pleine des choses qui n'exist pas, comme dieux. Nous avons evidence par calcul et experimentation des choses qui existe.

Franchement, je ne comprends pas qu'est ce que tu veux dire par "essence". Est-ce qu'on peut l'observer ou la mésurer? Le même pour "l'esprit".

L'infinities et zero existent même s'il n'y a personne qui en a connaissance.

Toutes les galaxies et étoiles que nous ne connaissions pas jusqu'a Hubble ont existaient avant que nous les avons decouvertes. Il y a 650 millions d'années, la terre était couverte de glaciers. Même si nous n'avons pas decouvert cette période, il aurait toujours existée.

Ned Ludd a dit…

J'ai oublié la formule d'un écrivain sur la science: zero, the nothing that is.

Flocon a dit…

Ned,

Je ne veux pas te convaincre bien sûr but I think you haven't made the great leap yet and still are in the position where there is you on the one side and the rest of the world on the other side.

C'est la position dualiste traditionnelle qui oppose le sujet et l'objet.

"L'infinities et zero existent même s'il n'y a personne qui en a connaissance.

Toutes les galaxies et étoiles que nous ne connaissions pas jusqu'a Hubble ont existaient avant que nous les avons decouvertes. Il y a 650 millions d'années, la terre était couverte de glaciers. Même si nous n'avons pas decouvert cette période, il aurait toujours existée"


Parce que tu es là à présent, hic et nun pour reconstituer mentalement ce qui a été.

Mais il faut une conscience réfléchissante pour que le temps ou l'espace soient les conditions d'apparitions des phénomènes par lesquels l'en-soi des choses se laisse deviner.

Après tout il est possible qu'aient existé il y a des millions et des millions d'années des consciences dans lesquelles la matière s'est reflétée.

Mais quand (ou si) ces consciences (dont on ne sait pas si elles ont existé) ont disparu, la matière s'est "évaporée" avec elles.

De même que lorsqu'un individu meurt, le temps, l'espace et la matière disparaissent avec lui.

Bien sûr, d'autres consciences lui survivent et avec elles le temps, l'espace et la matière se perpétuent.

Pour ce qui est de l'essence:

essence is the attribute or set of attributes that make an object or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity

L'article est intéressant car il prend en compte la métaphysique occidentale comme les pensées bouddhistes et hindouistes.

Flocon a dit…

"L'infinities et zero existent même s'il n'y a personne qui en a connaissance."

And once again I must ask you: Where?

Ned Ludd a dit…

Flocon, your position demands the answers to several questions.

- Do we know anything?

- Can we know anything?

-If so, how do we know that we know something.

Are we reacting to sort of a video game or are reacting to a "real" universe?

My answer is that what we "know" works. When something doesn't work, we look for other solutions, like other animals or plants.(do you know that there are hunter plants?).

In the developing world there are people who believe in magicians or sorcerers and who believe that miracle water or chants can cure them(and not only in the developing world). Sometimes these people get well spontaneously, but mostly not.

Vaccination and antibiotics have proven themselves.

Even in the developed world there are millions of people who believe in homeopathy. The treatment won't cure them, but won't kill them either unless the water included is polluted.

I refer you again to Bierce for his comments on homeopathy, and for good measure, his comments on Christian Science.

Flocon a dit…

Ned,

"Flocon, your position demands the answers to several questions."

Funny you start your comment with that line but you don't care to answer to my own previous question ;-)

Je ne conteste évidemment pas la réalité du réel et je n'ai rien à redire à ce que tu écris sur la maîtrise du réel que nous procure le savoir (Nous rendre comme maître et possesseur de la Nature as Descartes wrote).

Unless we live on two parallel universes (which would explain everything), I question the reality of anything when there is no reflecting consciousness whereas you state that reality does exist since we know it and are able to act upon it, the necessity of reflecting consciousness being irrelevant.

This is where we disagree.

Je ne peux pas mieux exprimer ma position qu'en répétant ma question: Comment le réel peut-il exister sans une conscience qui puisse le percevoir?

Quand existe une conscience réfléchissante such as the one you possess bien sûr qu'il y a du réel.

Mais quand il n'y a pas ou plus de conscience?

Pour celui qui dort, est évanoui ou est médicalement anesthésié, le réel est déjà bien problématique et quand il est mort il n'y a plus de réel, as simple as that.

Ta position est celle du matérialiste absolu (not that there's anything wrong with that) qui s'oublie dans ses calculs alors que ma position est celle de l'idéaliste qui tient, comme Planck par exemple, que la conscience est la condition d'existence du réel.

Je reviens au point de départ (il faut être cohérent): Où existeraient ou pourraient être observés un ou plusieurs infinis (ou du moins des modes différents de l'Infini) si ce n'est dans notre cerveau?

Back to my post: Where are prime numbers (which are infinite) or exponantiations (which give infinite numbers) save in our heads?

I doubt we can reach an agreement since one of the two of us has gone astray... Don't know which one anyway.

Thanks for giving me the opportunity to better understand my own position on that issue of reality and consciousness.

Ned Ludd a dit…

Flocon, I that I had answered your question with the various examples I gave. "Comment le réel peut-il exister sans une conscience qui puisse le percevoir?"

Does the boson of Higgs exist or not because we haven't discovered it? Even if we never find it, it may exist.

Does the expansion of the universe only exist because we found out about it? I think it would be occurring, i.e. real, even if the dinosaurs stilled ruled the earth and we never developed.

Not exactly on topic, but here is a series of videos with late physicist Richard Feynman. "The Pleasure of finding things out".

the pleasure of finding things out

I have tried the "blue link", hope it works.

Flocon a dit…

Ned,

"I that I had answered your question"

Another tense I didn't know of...

Quoiqu'il en soit, tu ignores systématiquement (au sens you discard) le point crucial de notre affaire, à savoir la conscience réfléchissante (cogito ergo sum) et tu affirmes que les choses existent de par elles-mêmes.

C'est une pétition de principe totalement irrationnelle ça.

We'll have to agree to disagree on that one but at the end of the day the issue isn't a vital one anyway.

---------

Kudos de chez kudos pour les liens bleus! Je n'y croyais plus :-D

Isn't it more elegant that way?

Yours works indeed and, just in case, you can always check if they will work in the "aperçu" window before you post your comment.

Merci de t'y être mise, cela évite à chacun de faire un copier/coller et d'ouvrir une nouvelle fenêtre.

Did the blue links exist before they were discovered?

Just kiddin' Ned, just kiddin'...

Anijo a dit…

You can add or multiply it by whatever number and get another infinity. So it would seem that there are more irrational numbers than rational numbers,

Ned, I was curious about this comment and Googled it and found these interesting comments

By "more" we should clarify that you mean comparison of cardinalities, and is defined in terms of bijections (or maps in general) between sets, otherwise this is crank bait.

and since the reals are the (disjoint) union of the rationals and irrationals, if the irrationals were countable, as the rationals are, then the reals would be countable, when they aren't.

When dealing with infinite sets, traditional notions of more don't work, because, we run into questions like "Is infinity plus one more than infinity?" that the usual notions of more don't really handle well. Similarly, you can't count an infinite number of things.

So, let's say that to show two sets are the same size if we can put the elements into pairs, one from each set, so that each element is in only one pair, and each element is in a pair. This type of relationship is called a bijection.

Now, it's possible to show that there is a pairing even if there are infinitely many pairs.

Anijo a dit…

And then I found this discussion re infinity

NOVA: Does feeling comfortable with the concept of infinity mathematically help you to feel comfortable with it philosophically?

Netz: That's a very interesting question. There are philosophers who think that because of the rigorous establishment of the calculus in the 19th century, and because of the rigorous treatment of the concept of infinity in set theory from Cantor onward, the philosophical problem of infinity has been solved.

On the other hand, there are interesting complications there..

*****

Once again you see that the philosophical question—What kind of infinities exist?—is not really answered. It's left as a philosophical puzzle. I think it's fair to say that mathematics shows you what's coherent, but what's actually true about the universe is left a philosophical question.

Anijo a dit…

another interesting comment here

Infinity" in mathematics is only a semantic term we attribute whenever it is intuitively appropriate. We can say that a set if "infinite", but formally we may mean that there is an injection from the natural numbers to the set. We can say that a straight line in the real plane is infinitely long, but formally mean that it has a parametrization as such: x = t, y=at+b for real t. "Infinite" is just a label; the mathematical equivalent in each situation has nothing to do with infinity per se.

We can extend the real numbers with by incorporating the symbol with applicable formal rules which allow us to say e.g. that for all real numbers r - and appropriately call the symbol infinity - but is only a syntactical statement and has no "deeper" philosophical meaning beyond what ordinary real numbers have.

Ned Ludd a dit…

Flocon, of course I meant that "I had thought that I had..."

I dropped out a word. Yes, I guess we will have to disagree. If you watch the Feynman interview, you will see that he is rather dismissive of "soft sciences", like philosophy.

Anijo, you mention the real numbers, but then there are also the imaginary numbers. They were first thought to be useless, but today many of our gadgets wouldn't exist without them.

As you undoubtedly know, but for others, imaginary numbers are multiples of the square root negative 1, written as "i".

imaginary number

Ned Ludd a dit…

I would just like to add that I once again have to go to the lecture by Lawrence Krauss that explains some things quite clearly I think. So I become repetitive and boring.

Flocon a dit…

Ned,

"Flocon, of course I meant that "I had thought that I had..."

Of course I knew and it's the stupid side of me which took the upper hand and noticed it. I shouldn't have.

Re the video by Krauss, it's not that you're repetitive or boring it's just that I can't stand in front of my computer for more than one hour and try to undestand what he says for the reasons that I already have provided.

I'd very much welcome a transcript if one were available. Not sure I would understand anything anyway when I consider my non existent level in all that pertains to maths and sciences.

Some people are rightly dismissive of soft sciences yes, but it's been a long time now that philosophy has ceased to believe it could boast being a science.

Save for analytic philosophy.

Et un deuxième lien bleu! Un! Bravo.

Flocon a dit…

Anijo,

This is why I still "hate" my teachers of mathematics who tried to persuade me that I was a moron (exponantiation simpleton) from the age of 12 till the age of 18 because I was unable to get into maths.

These jerks have succeeded in disgusting me for ever with maths, geometrics and al (also I'm a bit dyslexic which doesn't help).

I don't know what real numbers are, rational or irrational ones, what a function is. I can't even solve 8/11 : 4/7 or anything similar.

40 years after I've left school I still feel the rage that they made me believe I was a dunce.

I had to keep to myself that I knew I wasn't entirely and irretriviabily a complete imbecile!

That's how I turned to hard drugs!

Anijo a dit…

Flocon,

It is clear from everything that you post that you understand science a lot more than you claim to understand it. As for mathematics, it has to do with the details of science. I don't understand the more intricate and complex details of mathematics.

Science and philosophy are interconnected. Any of the great scientists who came up with new ideas had to first develop a new hypothesis (which may or may not have lead to a workable theory), but to come up with said hypothesis, they had to first be a philosopher.

Einstein was a philosopher and that is why he was a powerful thinker/intellectual. Add to that his knowledge of mathematics and science and we have a man who contributed a lot to the knowledge of our world as we know it.

Anijo a dit…

Ned,

It would be helpful if instead of just posting a link to something that L. Krauss said, you would refer to the particular statement that you find pertinent.

Flocon a dit…

Anijo,

I'm an impostor and I owe you the truth re maths and sciences.

As I previously wrote, my level in maths is 0! Zéro, Null, nada, zilch ad infinitum.

As pertains to sciences (only physics) between the age of 11 until 14 I was an avid reader of this magazine plus another one. When I turned 15 I read Toute la science which was kind of Sciences for junior until I was 17 I guess.

I knew the structure of atoms or how a nucular reactor worked (yeah, nuclear), the solar system, the universe, black holes, dark matter etc.

Then I went into electronics, radio and television with the help of these books and built a small radion receptor in 1968.

The result was that in physics class I knew much more than all pupils together (by far), simply I desastrously fared at all exams because, even if I knew what it was all about, I hardly understood the enunciation of the problems and was absolutely incapable to translate my knowledge with maths.

Judging by my grades, anybody would have concluded I was an hopeless idiot!

By the age of 18 I got my Baccalaureate (a miracle!) and made to myself the promise never to have to do with maths for the rest of my life.

I owe much to my mother, nothing to my father who was a complete failure, not much to my teachers and a little bit to the French Education Nationale system which, thanks to its inertia, let me sail my way up to the baccalaureate (and it was a very, very close shave, although I got 12/20 altogether)

If it were for some teachers, I would have ended in a pit, scraping for coal.

I don't know Jack about maths and even less in geometry [which was an impediment when I read Schopenhauer because he knew (how lucky you are to have such articles in the English Wiki!)].

Now you know it all Anijo :-D

Anijo a dit…

Impressive resume Flocon (and no I"m not being sarcastic. I mean it)

Yes, now I understand. You have a hands-on understanding.

Ned Ludd a dit…

Anijo, I have mentioned specific things said by Krauss. For one, in a few billion years the universe will have expanded so much that any new civilization like ours will only know our galaxy, the Milky Way. Everything else will be too far away.

Therefore, they can discover everything about the galaxy that we know, but will have a wrong idea about the universe and not know about the Big Bang, etc.

This is why I mentioned that the expansion of the universe exists whether we were here or not to observe it.

As to the link on infinities, I rather like the end:

"NOVA: What about you personally? Do you believe, for instance, that space is infinite?

Netz: That's the question really: Do things exist?! There are many people who say that we should adopt what's known as Occam's razor—namely, don't assume things that are not necessary. Very often this is taken as an argument in philosophy. If you can produce something without a particular assumption, then don't assume the existence of this particular assumption. If you can do without it, better assume it doesn't exist.

I actually don't see the validity of Occam's razor. I think that things can exist even if they don't serve any purpose. My tendency is to be pluralistic. Yeah, I think infinity is a coherent concept. I think I tend to like it. So yes, I tend to believe that infinities exist—all of them, all the way up.

NOVA: Time and space?

Netz: Yes, time and space, and infinities that go far beyond that, the infinities of pure, abstract mathematics, which are much, much bigger than whatever you need for the development of space and time. I seem to believe those things exist in some mathematical universe. But it's a matter of temperament. There are people who like the universe big and people who like it small. I'm a pluralist; I like to believe things exist."

I too like to believe that things exist.

Ned Ludd a dit…

I know it is long to watch some of the videos, so here is an extract from the interview(part 5) with Richard Feynmen.

"A very fundamental part of my soul is to doubt, and to ask. When you doubt and ask, it gets a little harder to believe. You see, one thing is I can live with doubt and uncertainty and not knowing. I think it is much more interesting to live not knowing than to have answers which might be wrong. ... I am not absolutely sure about anything and there are many things I don't know anything about. ... But I don't have to know an answer. I don't feel frightened by not knowing things."

Science is also about doubt.

Anijo a dit…

Science is also about doubt

aye

I too like to believe that things exist.

Belief is not science, therefore there is doubt vis-à-vis what's actually true about the universe as concerns infinity and it is thus a philosophical question.

Anijo a dit…

Some people like to believe that some sort of God or Yahweh or Allah exists. Liking to believe that something exists does not make it so.

Flocon a dit…

Ned,,

I find this topic extraordinary fascinating and I'll write another post about it next month. I just fear to be repetitive and boring...


"Do you believe, for instance, that space is infinite? is a question which recalls of the first Kantian antinomy (the limitation of the universe in respect of space and time).

Conclusion: the question of the limits of time must be regarded as meaningless.

As pertains the quote by Feynman it very much looks like the Discourse on the method redux.

"A very fundamental part of my soul is to doubt, and to ask. When you doubt and ask, it gets a little harder to believe."

Also known as Cogito ergo sum...

Anijo a dit…

Flocon,
here is a transcript to the Feynman youtube interview that Ned provided a link to.

I can't see that he is addressing anything that has to do with the topic of this post though.

Flocon a dit…

Anijo,

For whatever reason your comment landed in the basket??? Mystères etc.

You're my sweet caring nurse Anijo; merci ;-)

I didn't know it was possible to find transcripts of these videos.

Now, I've some reading to do this afternoon...

Flocon a dit…

Right, I've read the interview with Hitchens.

I noted some very interesting parts such as this one which I should have included in the Dieu est mort post (the debate between Hitchens and Blair).


"Basically, says that Christianity is OK because it makes people do good works and give money to charity, which it – no one denies its true, but has nothing to do with the relevance or the truth of the matter"

I liked that one also:

"What if we secularists stop going to hospitals and walking around the wards and asking if people are religious when they are in extremeness and in their last days and saying look, you’ve still got a little time, why don’t you live the last few days of it as a free person. You’ll feel much better. All that nonsense they taught you. You know you could still have every chance to give it up. Experience the life of a free thinking autonomous person. Don’t live in fear, don’t believe in mythology. They – I don’t think they’d welcome it"

Coincidentaly (?)for some times I've had an idea for a post with the tiltle Je n'aime pas mon prochain and I discover Hitchens had a video "where you talk about how hating people can be a good thing".

Of course I enterely agree with what he says about mother Teresa

I keep the interview in my bookmarks for good use later on.

"the thing to note about stage four is that there is no stage five."

Dry humour...

Ned Ludd a dit…

This subject will soon pass to page two, but I would like to respond to Anjio. When Netz talked about "believe", I don't think he meant it in the sense of some religious or mystical belief. As far as we know, what we think we know is based on science.

Richard Feynman described it well in mentioning mystics. They think they know all the answers. In science, one knows, if you like, that one doesn't have all the answers. Furthermore, he said he wasn't looking for all the answers and that he just wanted to find out more about the world.

Not being a scientist, I won't know, or at least understand, what Feynman knows. That doesn't imply that I am a theist, :), as Flocon suggested.

In fact, saying that "God did it", is not an explanation of anything. It is a cop out. That leads to the question of who did God.

I am reminded of an episode of "Mr. Diety" on internet where Lucy(Lucifer)talks about astronomy to Mr. Diety. Mr. Diety mistakes it for astrology. Lucy explains to him she means astronomy. Mr. Diety asks, "What is the difference?". Lucy responds, "About 50 IQ points." Mr. Diety, "Oh, I'm at least a 50."

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There was a documentary on ARTE comparing the genomes of apes, neanderthals, and humans. The latter two are very close and must have mated because a small number of neanderthal genes are found in humans in a large part of the world. The researchers asked the question of why the humans created representative art around 40,000 years ago, but the neanderthals didn't at the same time. They think they have found a gene that may be responsible for the ability to do so, which is found in humans but not in neanderthals. So maybe our ability to think about and represent abstract things comes down to our genes.

Also, neanderthals ate exclusively meat while humans are omnivorous, and the researchers think that perhaps some climate change or something else may have led to a lack of meat for the neanderthals helping to lead to their extinction. Humans were more adaptable. For me, that leads to a question: why didn't the neanderthals learn art and nutrition variation from their neighboring humans? Perhaps it was this genetic difference.

Flocon a dit…

"As far as we know, what we think we know is based on science."

C'est un sujet intéressant: comment savons-nous que nous savons?

J'ai un vieux billet (pas encore écrit) sur ce thème.

..."mystics. They think they know all the answers"

Ils se situent au-delà de l'expérience sensible qui, pour eux, n'a plus aucune valeur heuristique ni pratique.

I liked the Mr. Diety story...