'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/
>
>
>
>
> >
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Received on Sun Feb 08 2009 - 09:44:53 PST