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Sunya – Zero – chiffre - code
…
For Annick de Souzenelle, mathematician and
Author of reference books using the sources of the hebrew language
Zero does not come from as sifr but from the hebrew Zerca (semence)
Le semence va mourir en terre. De cette mort jaillit la vie.
De même Dieu se retire:
présence d’une absence
One of the greatest discoveries in the history of mankind, made
more than 15 centuries ago, among certain learned circles in India,
then transmitted to the Arabs, and which later undoubtedly
constituted one of the fundamental contributions of the Middle Ages
to the intellectual equipment of western science
G. Beaujouan
La science dans l’occident chrétien
in Histoire générale des sciences (1957)
Some opposition to the introduction of zero
Medieval hostility to zero rested
on a Christian antagonism to
« nothing »: give credence to
that which was not and could not
be in God’s world was to risk
blasphemy
During the fourteenth century,
the handling of numbers passed
from church educated clerks to
merchants
By early seventeenth century
Hindu numerals had completely
replaced Roman ones as the
dominant mode of recording
and manipulating numbers
throughout Europe
B. Rotman
The abacists versus the algorists
The introduction
of zero in the practice of arithmetic,
the vanishing point in perspective art,
and imaginary money in economic
exchange
are three isomorphic manifestations.
In all three codes, the sign introduced is
a sign about signs, a meta-sign,
whose meaning is to indicate,via a syntax
which arrives with it, the absence of certain
other signs.
Brian Rotman
Signifying Nothing
The Semiotics of Zero
At the end of the sixteenth century the Dutch mathematician Stevin advocating in
his treatise The Dime the extension of the Hindu system of numeration from finite to
infinite decimals, expressed great wonderment at the creative power of zero,
at the ability it gave the principle of place notation to manufacture an infinity of
number signs.
For Stevin it was not the unit that was the arche of number, but the nought.
Zero was the proper origin of number, the true and natural beginning.
He called zero the poinct de nombre, for zero gives rise to the numbers.
Stevin rejected numbers as signs conceived in terms of positive content,
as names for « things » in favour of signs understood structurally, as having meaning
only in relation to other signs within the sign system of mathematics.
Stevin insisted to transfer zero’s lack of referentiality, its lack of « positive content »
to all numbers.
A number like any other
ex: a cheque number 045664
There are 151200 (= 10.9.8.7.6.5) possible cheques with the 6 places filled with a digit, without repetition
226800 different cheques with two repetitions, as in this cheque
Zero neutral
Present
10 + 3 + 5 + 7- 3= 10 + 5 + 7
5a2 + 3ac + 2b –5a2 = 3ac –2b
Or a warning:
A needed tool:
2x + 3 = 7
2x + 3 – 3 = 7 - 3
The loaned camel
• The heritage: 11 camels.
• 1 for the eldest son,
• 21 for the second
• 14 for the youngest
6
11 11 11
1
   10 
2 4 6
12
12 12 12
 
= 11
2
4
6
Zero in disguise
It is nothing, and yet.
This nothing has untied knots!
Which is the cercle:
x2 + y2– 4x –6y = 12?
x2 –4x + 4 – 4+y 2 –6y +9 – 9 = 12
(x –2) 2 + ( y – 3)2 – 4 – 9 = 12
(x –2) 2 + ( y – 3)2 = 12 + 4 + 9
(x –2) 2 + ( y – 3)2 = 25
A circle with center ( 2, 3) and radius 5
1-1, 4 - 4, 9 - 9
nothing….and yet
A nothing that transforms deadends into tresholds…
On condition that one struggles with the difficulties up to
finding a solution.
Such tricks will then be remembered.
Zero nothing interferes
This zero « nothing » which helps the passage over thresholds designates them too.
This weightless zero, this « zero nothing » may illegitimately interfere in operations other than addition and substraction.
Its ravages then reveal the profound intuitions beyond the forms of language.
Sandrine:
Zéro c’est rien
0.4=4
Pierre:
4x = 4

Marie Alix:
3x=3

4
x=
x=0
4 Reste rien (Nothing left)
x=0
3 x =J’ai3 
simplifié (
All that can disappear
has to disappear
and disappearance
is linked to nought
I cancel out)
Guy:
0-4=0
If you have nothing and take away 4, it still
makes nothing.
1
Ricardo gives me the graph of the function y =
and the V.A: x=1 et x= 1/2
2
2 x  3x  1

I ask him whether there is an H.A ( H.A.
Y = 0, it’s the horizontal axis)
Ricardo: Il n’y en a pas parce que c’est 0. 0 c’est rien, çà compte pas.
When I compute the asymptote with him
Ricardo: Ah c’est pas rien alors, çà existe
Is zero nothing?
In 3 – 3 = 0
there were 3 things that are gone.
3.0=3
Yasmine:
nothing, don’t bother!
0 . 3 = 0 don’t take 3
3 / 0 = 3 nothing, don’t bother
I corrected her: 1,01
Yasmine: Je ne comprends pas. Zéro çà compte pas.
0 / 3 = 0 there is nothing to be
divided
Marie: Et en € que dis tu de 2,5 et de 2,05€?
Dans un cas tu as 2€ et 50 cents.
Dans l’autre tu as 2€ et 5 cents.
We observe with children that it is extremly difficult for them to respect a void
( both in writing numbers and texts). Digits and words are gathererd, the void disappears
A. Michelot The notion of zéro for children
Ce qu’il aurait fallu faire pour
.........
f(x)= ( x  1).(3x  5)
What about something = zero?
x
3
Trouvez x
Le voici
10
2x+3 = 0
Kadoyi:
« if it comes to zero, there is
nothing I can say about it ».
Jérôme:
2
4
2
4
If x  x then x  x that’s x.
3
5
3
5
Marie:
Nathalie changes
And where is your =?
x4
Jérôme:
 0 into x - 4= x-2 because
x2
Zero is nothing isn’t it?
« =0, çà n’a pas de sens »
m.(x+3) = 4

if m
 O x + 3 = 4/m
if m = 0 0(x+3) = 4 which can never happen, there
are no solutions S=O
Searching an impossible value
The thing « x » cannot exist here because the sentence in which it appears is absurd
Jérôme:


0(x+3) = 4
x+3= 4
x=1
0 x= 7
Sol = O
0x=0
Sol = R
Aurélia:
7x – 7x = -9
x = -9

Let’s note that the search for the value of x is in fact a search that aims to fill a void
And what about dividing by zero?
A speaker in a scientific conference told me:
4/0: 4it must be = 0 since 4. 0 = 0
0
Do not learn without reserve.
A whole life will not suffice to unlearn what, naïve and submissive,
you have allowed – innocent – to be put into your head without
dreaming of the consequences.
Henri Michaux
Caroline:
2=1 isn’t right, but because you have
established it, I thought the whole process
must make it right.
I know that 2 isn’t equal to 1, but I can accept that in
mathematics 2 = 1
Marie, flabbergasted:
Really?
Caroline, serenely:
Oh yes, in maths there are so many strange things
that I accept 2 = 1
Mathemagic!
The forbidden zero
5=5
25 = 5 . 5
25- 25= 5.5 - 25
(5-5)(5+5)= (5-5)5
5+5=5
2.5=5
Dividing by 0 is forbidden
1 is said not to exist
0
1
0
Brushing away existence when
it becomes cumbersome?
All the rectangles with a surface of 36 cm2
To be or not to be?
These functions do not exist when x = 0
Does that means that there is a hole in the
paper when x = 0 ?
in f(x)=
x 2  4 x x ( x  4) x  4


5x
5x
5
there is a hole in the
graph when x = 0
1
0
-2
-1
0
x.y = 36 ou y = 36 / x
-1
in f(x)= 36/x the situation is different
1
2
3
4
5
Zero repulses
Zero points up the differences between equalities:
The scale like equality:
36

0
When we divide by
the smallest,
we get the biggest
result
2x + 3 = 5
And the deployment: when x
0, 1/x

Plus le diviseur devient petit, et plus le quotient devient grand.
Si le diviseur se réduit à la plus extrême petitesse,
le quotient grandit au delà de toute mesure.
Cependant, tant qu’on peut dire qu’il a telle ou telle grandeur,
il n’a pas encore atteind sa limite extrême car il est toujours possible
de trouver un nombre plus grand.
Le quotient est donc une grandeur indéterminable et peut,
à juste titre, être dit infini.
Baskara, savant hindou du 12eS
Abdoul
To tend to zero …and find 1
Each inner square worthes
Of the initial square
1 1 1 1
, , , ,...
2 4 8 16
Putting side by side the
inner squares and adding
their surface:
1 1 1 1
   ... = I ( the outer square)
2 4 8 16
( while
1 1 1 1
    ....  )
2 3 4 5
Horus eye
Zero absorbs
Homothétie de rapport
2 , ½ et 0
0 . (a+b) = 0 . b
ZERO IN MULTIPLICATION IS ABSORBANT
i.e. it permits us, in multiplication, to completely
ignore the nature of what it affects
In multiplication, zero doesn’t go unnoticed!
Unless it is still the « nothing » of mother language.
Then 0 . 4 = 4
0 is neutral in addition and substraction
1 is neutral in multiplication and division
« If neutrals are going to start having colours now »
Hélène
Zero absorbs onto 0 … and 1!
In multiplication: a. 0 = 0
But when the multiplication is repeated: an = ? if n = 0

a0= 1
0
0 =?
In most cases
00 = 1
Multiply nothing zero times by itself
=1
A metaphor for the one attained
without ego?
The value of 00 may vary from problem to problem.
00 =
where x and y approach 0 along all possible paths in the x-y plane.
We get different limits by approaching along different paths.
Nicolas: pourquoi log x n’existe pas quand x = 0?
or
10? = 0

In 10X When x
10X
0,
but won’t reach 0 anymore than x would reach
Therefore there is no answer to 10?

= 0, no value for log 0
But for
logi x = 0,

there is a unique answer which ever base is chosen
( among an
number of possibilities).
The only « zéro » of the function log is 1
logi 1 = 0
And what about
0.

Looking at all the rectangles with
Surface = 25cm2 and 36 cm2
One observes that
0.

= 25 or 36 or….
Depending from which family comes the rectangle whose length is
and whose width is 0

« Idéalités »: power and precision in measurements
(Desanti)
With zero, it is mathematically possible to:
Divide 128 by 1 million: 0,000128
Multiply 128 by one million: 128 000 000 or even by one milliard or more:
it is just a matter of zeros
In Physics, the taking of measurements depend on the instruments and the
techniques used. It can be upset by interfering phenomenas. Therefore one has
to define a degree of precision and reliability and a margin of error or uncertainty.
Zero stroke or cipher stroke is the name created by German physicians
for prevalent nervous malady brought about by the present fantastic
currency figures. Score of cases of the stroke are reported among men and
women of all classes, who have been prostrated by their efforts to figure
In thousands of millions. Many of these persons apparently are normal, except
for a desire to write endless rows of ciphers.
Significant positions:
In 0,000128 and in 128 000 000 the zeros are
significant.
They are not so in 00128,000….excepts for Sabrina
If her calculation is written:
But if all places are marqued
She obtains:
Similarly, for her
132,98 – 31 = 132,67
unless the question is 132,98 – 031,00
She gets the
right result:
( 98 – 31 = 67)
Sabrina shows how much zero is nothing positioned…and it positions others
A little worm who knows that all
numbers come from zéro?
Péano’s axiomatic:
0= card 0
1= card {0}
2= card {0,{0}}
The Budhist notion of existence is pervaded by emptiness.
It’s understanding is made possible by the discovery of the concept of zero.
The Budha’s teaching is similar in dimension
to the mathematical zero which is neither space
nor time but without whose nature and function
all operations cease
Matsuo
Without zero we cannot make ten or a hundred.
Similarly with emptiness.
It is emptiness and at the same time,
it is the basis of everything
H.H. Dalaï Lama
To René Weber
Emptiness is silence, absolute silence.
But absolute silence defines all means of expression.
The Western mind takes emptiness as the climax of abstraction,
the highest conceptual abstraction.
The Oriental mind takes it as more concrete.
Everyday feeling…
Something must be done, and at the same time, that nothing done is expressed that
way.
D.T.Suzuki
You live in the illusion and the world of appearances
But there is a reality:
You are that reality, but you don’t know it yet.
When you’ll wake upin this reality, you’ll recognize that you are nothing
and that being nothing you are all.
Kalu Rimpoche
One has seen for my form, which is a worthless zero,
some use in counting it along with alif.
Khagani
Alif, the first letter of the alphabet, is a straight line, and stands also for 1.
Besides, it is the cipher for the slender stature of the beloved.
The lover has value only together with the beloved.
Anne Marie Schimmel quoting the Diwan
I am under constraint yet with free will in the execution of every work.
I am acting and non-acting.
I am the zero in counting
Ali Khan Ni’mat
In the Heart Sutra: (Prajnaparamita Sutra):
Form is nothing but emptiness
Emptiness is nothing but form
What is form is empty
What is empty is form
Form is not differentiated from emptiness
And emptiness is not differentiated from form.
Form is at once emptiness
And emptiness is at once form.
Consciousness is not differentiated from emptiness
And emptiness is not differentiated from
Consciouness
Consciousness is at once emptiness
And emptiness is at once consciousness.
=1
Zero nothing?
=0
Il (x) ne peut pas disparaître tout de même
(y-2). 3/2 = 0
Équation impossible,
S= O
Sunya qui signifie le vide et devint notre zéro servait aussi
aux hindous à désigner l’inconnue.
(Sunya that signifies the void and became our zero was also used by the hindus to designate the unknown /the
variable)
Tobias Dantzig Le nombre langage de la science
0 and x are both meta-signs:
0 initiate the activity of the counting subject
x indicates the possible but not actual presence of number signs
This requires a new mathematical subject, the algebraic subject,
whose relation to the one-who-counts mirror the relation between
a variable and a number.
Thus the algebraic subject has the capacity to signify the
absence of the counting subject, the displacement from the onewho-counts from an actual to a virtual presence.
B. Rotman
Nothing comes of nothing
SHAKESPEAR’S King Lear
This is perfect
That is perfect
Take away the perfect from the perfect
And what is left is perfect