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
> 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
>> 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 ....
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
>> 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.
>> 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?
>> 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,
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