'Tis poetry! Kim, Bruno, thanks for this wonderful dialog. Most beautiful stuff I've read in a long time - and so spontaneous.
Cheers, Günther Bruno Marchal wrote: > Hi Kim, > > I have not the time to think deeply on zero, so I will answer your last > post instead :) > > > On 05 Feb 2009, at 12:30, Kim Jones wrote: > >> >> >> On 05/02/2009, at 4:23 AM, Bruno Marchal wrote: >> >>> >>> >>> Hi Kim, >>> >>> Still interested? >>> >>> I must say I was wrong. >> >> >> Only a scientist admits he can be wrong. > > > Yes. I would even say that someone who can admit to be wrong *is* a > scientist. > > > > >> Everyone else will risk their >> life in the attempt to "prove" how right they are. > > > Either they just lack trust in *themselves*, or they are preprogrammed > robot or low animals (if that exists). > > > >> >> >> How "right" can one be? Considering the emotion and passion some >> people invest in defending their righteous viewpoint you would perhaps >> be led to believe that one can be "very right" if not "extremely >> right" or even "totally right". > > > I like to "define" truth by a Queen who wins all battles without any > army (albeit She *can* take time, infinite time). I am an optimist. > It is more difficult to convince people of falsities, you need bodies, > clothes, armies, churches, temples, academies, relations, money, bad > faith, and other rhetorical skills. > > Of course once you have bodies, clothes, armies, churches, temples, > academies, relations, money, bad faith, and other rhetorical skills, you > can even make people liking and needing the falsities. Leading to my > (late) father's, more pessimistic definition of truth: truth is what > humans don't want to hear. > > > > > >> >> The project is highly ambitious and you should follow your own best >> counsel in how to go about it most effectively. The burden is upon me >> to come up to your level of description in my understanding. > > > To understand math you will have to develop a sense of naivete. > Somehow a mathematician is someone who abandons metaphysics, who somehow > is capable of stopping, at the right place, the questioning. The right > place is of course dependent of the goal you have in mind. > Of course this makes applied mathematics to metaphysics a bit subtle and > hard (many traps). > > > > > > >> >>> >>> >>> After all, I am supposed to explain to you how, when we assume the >>> comp hypothesis, the ultimate realities become mathematical in nature, >>> even arithmetical or number theoretical. But how could I explain this >>> to you without doing a bit of mathematics. >> >> >> It may seem strange, but, without demonstrating my understanding in >> any technical sense, I can at least assure you of my "faith" in the >> power of your reasoning. > > > To be franc this will not be enough. yet I know about your mathematical > experience. So I formally promise that I will never ask you to > demonstrate your technical skills. But you will have to develop that > skill up to some point. To taste the deep flavor, you will have to trust > your own power of reasoning, or more precisely your own ppwer to > convince yourself by a reasoning made by another. I hope that you will > have the serenity to tell me when you don't understand something. A > minimum of "easy" exercises is needed to be sure the understanding does > not diverge. My way of teaching you seem appreciate is anything but > questioning (you, and then the "amnesic" universal machine). > I would like you to understand in some deep way the seventh step, which > asks for few but important insight in theoretical computer science. Only > then can I explain to you in some layman language what really AUDA > consists in. > > I could say this. Although machines can only scratch Cantor's Paradise, > there is no part of Cantor's paradise which does not throw light on the > behavior of possible machines. You know, little numbers cannot > distinguish a Big Number with a *Very* Big Number. > > > > >> I understand music when I hear it - why >> should it be any different for this discourse? > > > Hmmm... First there are musical pieces that I have understood, or > appreciated, only after many listening. Then, mathematics is usually > understood after many readings and rereadings, and many > personal thought experiments, some time with aspirin (if not better). > I can test on you, with your permission, a sort of particular > pedagogical path, sort of shortcuts. I have to think. > > > > >> I somehow sense the >> music in the logic. If you choose well your words, I accept that they >> emerge from a mind that has already mapped language to arithmetical >> truth. Of course, I do not expect to pass any high level logic tests >> using this argument... > > > I have to choose well the words, and I have to choose well the path. > Expect some dead end alleys. I have to figure out some tradeoff between > between different kind of efforts. > > > >>> >>> Mathematics is a curious music that only the musicians can hear. >> >> >> It has always struck me as a possible advantage the musician has over >> the mathematician. You can fill your whiteboard with your arcane >> script, but you can not play any of it on your violin. Why I want to >> compose music derived from my understanding of all this. That is my >> ambitious project. > > > > Of course this will be impossible literally, but I can get the feeling. > > > > >> >> >> >>> >>> Mathematicians play with instruments that only them can hear. >>> To listen to a mathematician, you have to be a mathematician and play >>> the instrument. Fortunately, all universal machine like you, are a >>> mathematician, and when a human seems to feel he is not a >>> mathematician, it just means the mathematician living within is a bit >>> sleepy, for a reason or another. >> >> >> Or merely terrified of his lack of education over it. Nobody loses >> sleep thinking they are tone-deaf, because you can still live >> successfully without an inner "pitch model" but it is the same fiction >> as you describe. If you actually were tone deaf, you could not change >> gears in your car - you could not recognise a happy-sounding voice >> from an angry voice, you could not distinguish your mother's voice >> from your father's, you could not distinguish waves on the beach from >> the wind in the trees. Music is where our natural tonal recognition >> faculty is concentrated like a laser beam. I miss greatly the same >> concentrated ability with numbers. > > > From the order point of view, the numbers provide the simplest rhythm: > > BAM ... BAM ... BAM .... BAM ... BAM ... BAM ... BAM ... BAM ... BAM > ... BAM ... BAM ... BAM .... > > or > > I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I > ... I ... I ... I ... I ... I ... > > The first stroke, the second stroke, the third stroke, > > > > From the quantity point of view, it is the same, except each numbers > seems to want to memorize his past: > > I ... II ... III ... IIII ... IIIII ... IIIIII ... IIIIIII .... IIIIIIII > ... IIIIIIIII ... IIIIIIIIII ... IIIIIIIIIII ... IIIIIIIIIIII > ... IIIIIIIII ... IIIIIIIIIIIII ... > > > And then reality kicks back, we have to add the empty or null quantity, > making 1 the second number. Even the Greeks I love could have sent me > away from the Academy for daring making 1 the *second* number. The > "Plotinus" in me is still unders the shock. Order, and Quantity: there > is already a discrepancy, a conflict. How dares the number zero take the > first place? > > Charles Seife, in his book "ZERO, the biography of a Dangerous Idea" > said that zero is the twin of Infinity (if I remember well). And this > indeed has many mathematical interpretation (1/0 = infinity, the > intersection on the empty set gives the universe, the conjunction of > zero argument is true, etc. That's probably why a theory of NOTHING can > be tolerated in a EVERYTHING debate :) > > To begin math at zero? perhaps it is more easy starting with one, or > even two. Perhaps zero should be taught only to hyper-super-qualified > people, with password, and special permission from authorities from the > government. We should make zero illegal, perhaps, and cut the head of > for those who dare to divide by zero. > > Thanks to Platonia, nobody can divide by zero, in a finite time. No > reason to panic, if your computer divides a number by > zero, inadvertently, you can still cut the electrical power. The galaxy > will not disappear. > > > >> >> >> >>> >>> >>> Especially that I am realizing that some people confuse a computation >>> with a description of a computation, which are two very different >>> mathematical objects (albeit relative one) existing in Platonia. >> >> >> You can burn all musical scores (partitions) of any piece and the >> piece is still there. > > You could be right here, but you could be wrong. There is a big and > important ambiguity. Exactly the kind of ambiguity which can make people > to confuse a computation and a description of a computation, or to > confuse numbers and ciphers. We know today that numbers and ciphers are > handled in different part of the brains. > > > > >> A thought once thought cannot be unthought. You >> cannot delete information from the universe. > > > Vast subject, but let us not anticipate too much. > > > > > >> >> >> I think. >> >> >> >> >> >>> This >>> plays a key role in the articulation of the step seven with the step >>> eight. It plays a key role to understand the computationalist >>> supervenience thesis, and thus where the laws of physics come from, >>> and of course it is strictly needed when ultimately we interview the >>> universal Lobian machine. >> >> >> I walk slowly in this direction. I am drawn to it by the beauty of the >> distant music I already hear. > > > Scientists search the truth, and are driven by beauty. They find some > ugliness there, and have to change their mind or admits they were wrong. > Real concrete scientist will not admit the error, but eventually their > students will, and indeed will develop a new taste and criteria for > beauty, and the cycle continues. > > > >> >> >> >>> >>> >>> So, the time has come I cure your math anxiety, if you or some others >>> are still interested. >> >> >> You teach me maths for free, I translate your theses for free > > > You did a very good job. Good deal, thanks. > > >> >> >> >> >>> I can awake the mathematician in you (like I can >>> awake the mathematician living in any universal entity, btw :). >> >> >> OK - so you have NO excuse for not applying for a Templeton Foundation >> grant. Awaken the musical mathematician in the widest possible >> audience. Us musicians, we play very sweetly when somebody throws big >> money at us!!! > > > I should. I guess. Thanks for reminding me. > > > > >> >> >> >> >>> >>> >>> I propose we begin with the numbers, and, to keep our motivation >>> straight, I propose we meditate a little bit on the distinction >>> between numbers and descriptions of numbers, and notations for >>> numbers. It is a bit like the difference between a symphony and a >>> symphony's partition .... >> >> >> Parfaitement entendu >> >> >> >> >> >>> >>> >>> Given the importance of such distinction in the whole drama, it is >>> worth to get those conceptual nuances clear right at the beginning. >>> >>> I really propose to you to begin math at zero. >>> >>> But now I am already stuck: should I explain first the number 1, >>> or ... the number zero? >>> A tricky one that number zero ... :) >> >> >> Zero was "invented" (discovered?) only AFTER 1. >> Yet, zero precedes one >> in the natural scheme of things. > > > > Ah! Like above. It belongs to the natural scheme of quantities, but not > on the natural scheme of order, at least not obviously so. > Armstrong is not the zeroth man on the moon, nor the zeroth winner of > seven the France Cyclist Tour, all right? > > > > > > >> In systems analysis it is axiomatic >> that the sequence of the arrival of information determines the >> ordering of all subsequent information, just as rain falling on a >> landscape creates channels and river basins that channel all >> subsequent rainfall. I believe that civilisation should have started >> with zero - had this happened, we would be 400 or so years ahead of >> where we currently are in our understanding of reality. I do not know >> why I believe this, perhaps you can explain my intuition here. I >> believe we are suffering from a historically ingrained perceptual >> error about zero and one. > > > Sure, one is also quite a weird one. > Two too, isn't it? > > And if you think twice about three, and four ... > > Believe me: mathematicians are at ease *only* with *infinities*. They > invented them to get some clues on zero and one, and two ... > > The term "Number" has the same roots as "Numerous". For the greeks > numbers really begin with three. zero was just unthinkable those days. > And how could 1 be a number? 1 is certainly not numerous, nor is two. > I agree with you that zero is a BIG discovery, which asks for some time > to be swallowed, if that's possible. > > >> Music begins with silence. The silence that >> precedes the upbeat is part of the music. Sometimes the Nothing is >> inserted into the midst of the music, Listen to the opening 20 or so >> bars of Claude Debussy's "L'après midi d'un faune" for a glowing >> illustration of what I mean. He starts with the one, then remembers >> the zero ( an inexplicable and mystical silence takes place, not long >> after the beginning. People have long wondered why this silence.) > > > Yeah, zero is a bit mystical, 0 notes, at the right place, can even be > dissonant, frightful ... > > To begin with a silence is almost perverse, you mean this? > http://www.youtube.com/watch?v=B7tE1PvoSYI&feature=related > <http://www.youtube.com/watch?v=B7tE1PvoSYI&feature=related> > > > >>> >>> >>> PS I now you are busy. I propose we go at the minimum of your rhythm >>> and mine. But I tell you that "the poem is long". >> >> >> Qu'il ne finisse jamais > > > It can't. The symphony is infinite. But like the posts or papers, or > partitions, we have to put a last point without which we perish, > paradoxically enough. > > > > Kind regards, > > > B. > > > http://iridia.ulb.ac.be/~marchal/ > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
