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Ivan Brazhkin

Alexandr Burlaka

Anastasia Ryabova

Vladislav Shapovalov

Maxim Spivakov

Tzuchien Tho

Dmitry Vorobyev

supostat.org

textandpictures


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[*] In May 2012, large numbers o Russian

citizens took walks in the streets o major

cities to show their disagreement with thepresidential election results. The walks

were deliberately not announced as political

events and were designed to test whether

the authorities would disperse an unsanc-

tioned procession that involved no slogans,

ampliying equipment or speakers. Similar

tactics had to be adopted due to the increas-ing practice o brutality by the authorities

in charge o suppressing organized protests.

The authorities did not interere.

1. Area o unseen luxury

Businessman decides to show solidarity with the Test Walk [*]

by strolling with his wie along the tree-lined walk around his

house in the Zhukovka Hills community.

On the other side o the Moscow River, an activist equipped

with a reel o cord, measuring tape and a protractor marks o a

line segment between points M and N, rom which two diametri-

cally opposed trees (points A and B) can be seen on the walkway

surrounding the house.

Segment MN and the angles it orms with the lines connecting

its endpoints to points A and B:

b= MN = 32.94 m

= AMN = 88.33

= BMN = 62.52

= ANM = 85.45

= BNM = 111.98

N

M

B

A

Fig. 1

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Problem:

How long will the solidarity walk take, assuming that the com-

munity is protected by a security service and that the businessman

and his wie have an average strolling speed o 2.196 km/hour?

Answer:

Thesolidaritywalkwilltake12minutes.

2. Molecular cuisine

December. A ventilation duct leading to the surace rom a sushi

bar in an underground shopping center emits saturated vapor at

a temperature o +40 C. A hungry homeless person warms himsel

by the grating. When breathing normally, he inhales 0.35 liters

o vapor into his lungs in a single breath (0.50 liters) and exhales

50 ml o water per hour.

Problem:

How long will it take or one portion o miso soup (350 g) to

be absorbed into his lungs i respiratory rate is 14 breaths

per minute, relative humidity = 100% and the vapors mois-

ture content = 51 g/m3? How much moisture will he lose

through breathing in this same period o time?

Answer:

Oneportionomisosoupwillbeabsorbedintothehomelesspersons

lungsin23.34hours.Duringthistime,hewilllose1.167literso

moisturethroughbreathing.

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3. An activists dream

The number o protesters is constantly rising. On November 7,

40,000 people show up on Red Square to demonstrate against

government abuses. In May, a crowd o 80,000 lls Red Square.

On July 14, there are 120,000 demonstrators, exceeding the

squares capacity by several thousand. The walls o the buildings

surrounding Red Square are gradually pushed back by the sheer

political power o these human masses ...

Red Square, bordered by the Historical Museum, GUM,

St. Basils Cathedral and the Lenin Mausoleum, is a rectangular

area with sides measuring: = 85 m, b = 4a = 340 m. Crowd densityat demonstrations averages three demonstrators per square meter.

Problem:

How many meters do the buildings bordering Red Square have to

be moved in order to accommodate 120,000 demonstrators?

Answer:

TheKremlinwalls,MausoleumandGUMhavetobemovedback7.5m.

TheHistoricalMuseumandSt.Basilshavetobemovedback30m.

4. Useul area o a stadium

Ninth-grader Pete runs three laps around the school stadium in

3.4 minutes at an average speed o 17.654 km/hour. The length o

the stadium is 3.5 times its radius.

Problem:

How many 22-storey oce buildings with foor space o 26,400 m2

each will t inside the stadium?

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Answer:

Theschoolstadiumwillhold6.63ocebuildings.

5. Stop capitalism! Pressurized slogans.

The political slogan Stop capitalism! contains ourteen letters,one space and one exclamation point. It takes about one second to

write a single letter or exclamation point 30 cm 35 cm in size.

The entire slogan (35 cm 5 m on average) takes around thirty

seconds. A 400-ml can o aerosol paint is used up in 496.1 seconds.

One such can costs 180 rubles.

R

lO2

O1

R

C D

a

b

Fig. 2

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Problem:

How many Stop capitalism! slogans can be made using one

400-ml can? How much does each anti-capitalism slogan cost?

Answer:

1.16.5sloganswilltinsideasingle400-mlcan.

2.Eachanti-capitalismslogancosts10.90rubles.

6. Hired demonstrators

With the surge in mass political activity in Russia, the services

o hired demonstrators are becoming increasingly popular. Orga-

nizers o political movements oten use the services o the mes-

sage board massovki.ru [crowds o extras] to recruit manpower.

According to the inormation posted on the site, the average pay

or a hired demonstrator is 500 rubles per event.

The working conditions o these hired laborers are oten deplor-able, including irregular hours as well as workplaces and sanitary

conditions that ail to meet even minimal standards. Their compensa-

tion may be held up or not paid at all, and they have no social benets.

Lets say that Citizen N works regularly as a hired activist.

Knowing the heavy demands o his proession, he decides to orga-

nize a demonstration o one thousand o his colleagues in support

o workers rights or hired demonstrators. Citizen N must pay the

standard ee to each demonstrator.

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Problem:

How many demonstrations must Citizen N work in order to save

enough money to pay these hired demonstrators, taking into

account the act that brigade leaders (one brigade leader per

twenty fag-wavers) are paid ten times more than rank-and-le

demonstrators (a2) and that party unctionaries (one spin-doc-

tor per 5 brigade-leaders) are paid ten times more than brigade

leaders (a3).

Answer:

CitizenNmustwork2,500demonstrationsinordertopayathou-

sandcolleaguestoattendhisdemonstrationinsupportowork-

ersrightsorhireddemonstrators.

7. Mattresses block rivers, but open new ways!

The not-too-distant uture. Moscow has been taken over by police

orces. Near the Kremlin, the Moscow and Yauza rivers are teem-

ing with protesters. People are using infatable mattresses to orm

foating camps. Navigation is completely blocked, and barges and

tourist boats are unable to pass. The city has thus ound new chan-

nels o protest.

The surace area o the Yauza and Moscow rivers inside the Gar-den Ring is 76.7 ha. Protesters are equipped with our types o mat-

tresses. There is an equal number o each type o fotation device.

Mattress sizes:

1. childrens mattress with pillow, 157 88 cm, large enough

or two adults and our children

2. foating mattress, 189 76 cm, gray with headrest,

large enough or two adults and two children

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3. foating mattress, 183 69 cm, with colorul headrest,

large enough or two adults and two children

4. Intex Supreme 66724 air mattress, 191 137 cm, large enough

or three adults and six children

Problem:

How many air mattresses o each type will be required to block all

Moscow rivers and canals inside the Garden Ring? How many peo-

ple should there be on fotation devices in order to block the citys

waterways inside the Garden Ring?

Answer:

1.116,920airmattresseswillberequiredtoblockallMoscowriv-

ersandcanalsinsidetheGardenRing.2.Thereshouldbe613,830

people(263,070adultsand350,760children)onfotationdevices

inordertoblockthecityswaterwaysinsidetheGardenRing.

8. Cobblestone as a Weapon o the Proletariat [*]

Sergey Sobyanin, in his rst two months ater taking oce as mayor

o Moscow in late 2010, replaced 400,000 m2 o asphalt sidewalk in

the capitals central district with standard concrete paving stones,

190 90 50 mm in size. The cost per square meter was 3,700rubles [**]. In clashes with riot police during the March o Millions [***]

[*] Cobblestone as a Weapon of the Proletariat

is a well-known work by Soviet sculptor

Ivan Shadr, modeled in plaster in 1927 and

cast in bronze in 1947. The plaster cast is

stored in the Tretyakov Gallery. In 1967 a

bronze copy was erected in the Park o the

December Uprising in Moscows Presnensky

District. The gure depicted is a generalizedrepresentation o an early-twentieth-cen-

tury proletarian ghting or revolutionary

ideals and reedom.

[**] The rate o the Russian ruble against the

euro when these problems were being pre-

pared was 39.65 rubles.

[***] On May 6, 2012, ollowing the presidential

inauguration, citizens marched to protest

the start o yet another Putin presidency.

According to the organizers, around 70,000

people took part in the march, and some2,000 activists were detained as a result

o clashes with police. When this text was

being prepared, 16 people had been charged

with rioting.

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in May, protesters used pieces o asphalt paving as weapons, since

Bolotnaya Square and the surrounding area, where the events o

May 6 unolded, had unortunately not been paved with the easier-

to-handle stones.

Problem:

How much would it have cost city authorities to arm

70,000 marchers (as estimated by the events organizers) with one

standard-size paving stone each or one well-aimed throw?

Answer:

Itwouldhavecostcityauthorities4,428,900rublestoarm

70,000demonstrators.

9. Reduction actor

According to police statistics, 300 people showed up at the March

25 demonstration or honest elections in ront o Mariinsky

Palace in St. Petersburg. According to human rights activists,

350 demonstrators were arrested. Ater the arrests had been

made, at least 500 demonstrators remained on the square.

Problem:How many people took part in the May 4 solitary picket against the

law prohibiting homosexual propaganda, assuming the reduc-

tion actor used by the Department o Internal Aairs?

Answer:

0.353persontookpartinthesolitarypicketagainstthelaw

prohibitinghomosexualpropaganda.

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10. Social rent agreement

The City o Pskov has a population o 200,000 and spends

177,000,000 rubles a year on the citys administration.

Problem:

How much would each city resident have to pay per month so that

they could hire away the entire city government and ensure its loy-

alty by oering three times as much money?

Answer:

EachresidentoPskovwouldhavetopay222rublespermonthin

ordertohireawaythecityadministration.

11. A Lesson in Disobedience

On June 6, 2012, the Federation Council approved amendments

to the Law on Assemblies, Rallies, Demonstrations, Processions

and Pickets that would increase the nes or various violations

to 300,000 rubles or demonstrators and 600,000 rubles or

organizers.

As o summer 2012 (when these problems went to press), it is

planned to implement Federal Law No. 83. The law, adopted twoyears ago, eectively abolishes the right to ree primary educa-

tion, turning teachers into competing entrepreneurs in a govern-

ment institution.

According to the minister o education and science, a teachers

average monthly salary in 2012, prior to the implementation o

Federal Law No. 83, is 21,100 rubles.

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Problem:

How long must a teacher set aside his entire monthly salary so

that he can aord to take part in or help organize an unauthorized

demonstration against the ederal law at the rates proposed in the

amendments?

Answer:

Theteacherwillhavetosetasidehissalaryorourteenmonthsin

ordertopaytheneorparticipatinginanunauthorizeddemon-

stration,andtwenty-eightmonthsoractingasanorganizer.

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The Dicult Truth about Mathematics

In our situation, that o Capital, the reign o number is thus the

reign o the unthought slavery o numericality itsel. Number

which, so it is claimed, underlies everything o value, is in actual

act a proscription against any thinking o number itsel. Number

operates as that obscure point where the situation concentrates its

law; obscure through its being at once sovereign and subtracted

rom all thought, and even rom every investigation that orients

itsel towards some truth.

Alain Badiou, Number and Numbers (1990) [1]

What is the relation between mathematics and politics? An obvious responseto this question is to see that numbers, measurements, charts and graphs are

the means by which our world is managed. Despite what liberals might say,

this management, including o the election gures that determine who will

occupy the seats o power, is not politics. So, i mathematics is the means by

which the state and the ruling class manage us, would our resistance to domi-

nation and exploitation also be a resistance to mathematics itsel?

There are reasons or thinking so, and some philosophers in the recent

past have advocated skepticism about anything techno-scientic due

to its associations with modern technological hubris, quanticational

normalization, biopolitical control and state repression. In this case, the

relation between mathematics and politics would be something like an

emancipationfrom mathematics.

By recognizing the instrumentalization o mathematics or the mana-

gerial unctions o the state and capital, could we instead understand the

relationship between mathematics and politics to be one o the emancipa-tion ofmathematics? I mathematics is a means to certain ends, might we

make it serve emancipation rather than oppression?

What i we measure the state in the same way that it measures us? What

i we evaluate, or a change, how ecient the private is, how much govern-

ment money private enterprise consumes on behal o taxpayers. This has

always been a tool o critics and revolutionaries. Mathematics is then some-

thing that allows a orm o communication that puts the public in direct

contact with a given position. This is precisely also because it reduces the

world to those same numbers, measurements, charts and graphs that pull

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the levers o power and opinion. O course, in any movement, no matter

how small, we nd that we can learn to manipulate numbers as well. These

numbers take us back to the classroom o obedience to objectivity. First we

want to be lied to by the gures o politicians; then we want to be outraged

by the numbers o the critics.

In the epigraph above, rom Alain Badiou, we nd a proposal to liberate

mathematics rom its operation as a orm o unthought precisely by the

audacity to think numbers. This orm o emancipation, one that asks us to

think beyond the obuscation o economic models, stock and bond prices

and election tallies, is an engagement with number itsel, a struggle with

an ideological scaolding which employs number as an objective alibi or

lies and thievery. Financial experts and state unctionaries give us numbers

best let to the experts: they are only asking or our vote and consumer

condence. Some o the best mathematical minds o our generation havebeen drated into this army o ventriloquists who make numbers speak or

them, inventing more and more complex puzzles o virtual time and pro-

jected value. Could it be that it is now time to take time and value, in the orm

o numbers, back rom them?

Another sense o mathematical emancipation attacks precisely this

notion o thinking mathematics. As Gilles Deleuze and Flix Guattari

argue inA Thousand Plateaus, the problem is that there are two dierent

paths in mathematical thought itsel.

[I]t is o the nature o axiomatics to come up against so-called

undecidable propositions, to conront necessarily higher pow-

ers that it cannot master. Finally, axiomatics does not constitute

the cutting edge o science; it is much more o a stopping point,

a reordering that prevents decoded semiotic fows in physics and

mathematics rom escaping in all directions. The axiomaticians are

the men o the state o science, who seal o the lines o fight thatare so requent in mathematics, who impose a new nexum, i only a

temporary one, and who lay down the ocial policies o science.[2]

On this view, the state exists in mathematics as well, and its name

is axiomatic thought. Here Deleuze and Guattari suggest a nomadic

science more devoted to experimentation and intuition than the aspects

o necessity and systematic consistency. This statist element that they

point out may be too metaphorical to warrant serious consideration.

The political prejudice in reading systematic or axiomatic mathemat-

ics as something locked in necessity and hence incapable o thinking (and

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grasping) the contingencies in intuition and experimentation is precisely

to miss the point. In a counterintuitive way, it is precisely the balance

between necessity and contingency in mathematics that puts it in relation

with politics. The deep surprise that mathematics, in its history, reveals

is that its relation with (logical) necessity is precisely what renders inno-

vation in mathematics so intriguing. That is to say, when we encounter

mundane worldly acts, social situations and the like, we are dealing with

contingency. When I say that worldly acts are contingent, I do not mean

that they are random. Randomness is o course also something dened

mathematically. Yet what I mean here is that acts could also not be; they

are contingent. It is not a necessary act that I am writing these words now,

or that I exist, or even that the solar system and lie on planet Earth came

into being. This is not the case with mathematical acts. Mathematical

acts cannot not be. This is not a mere external determination o math-ematics but a real tool in mathematical practice. Mathematicians since

antiquity have used what we call reductio ad absurdum, a orm o proo

that demonstrates something by showing that its contrary is inconsistent

or leads to a contradiction. I, or example, we want to prove that there are

an innite number o prime numbers, which is impossible to show directly,

we start with the proposition that there are only a nite number o prime

numbers and then show that this proposition is contradictory. It then ol-

lows, as Euclid tried to show us, that there are an innite number o prime

numbers.

Although necessity is oten seen as constraint, mathematical necessity

also has a proound sense o reedom. This can be traced most readily in the

historical development o mathematical thought. How is it that we have

punctually arrived at new mathematical breakthroughs throughout his-

tory when mathematics appears to be locked in a demonstratively closed

realm o necessity? Radical changes within mathematics as a practice, a seto theorems, a series o truths, mirror historical change precisely because

they allow us to see what real change can mean, a change o the context o

necessity itsel. We casually expect rule-governedchange in the world since

things are contingent, but they are inclined to order and we deduce natural

laws on this basis. But these changes are commonplace and do not extend

beyond the rameworks within which they take place. On the other hand,

a shit in mathematics is systematic precisely because what we contest in

those contexts o change is something undamental: a deeply entrenched

intuition, a set o interlocking axioms. In radical cases, we encounter an

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unexpected reutation that throws o a whole system in part precisely

because we require necessary global and universal consistency. When a

system (which is axiomatic) implies an error, the entire system has to be

re-examined.

Because mathematical change is so undamental, its vanguard is con-

stantly maligned as delivering something false. In the case o Leibniz and

Newton, who concurrently gave orm to the dierential and integral calcu-

lus, this sort o alsity was the very dynamism o discovery. Newton and

Leibniz, Marx remarked in his mathematical manuscripts,

believed in the mysterious character o the newly discovered

calculus, that yielded true (and moreover, particularly in the

geometrical application, astonishing) results by a positively alse

mathematical procedure. They were thus sel-mystied, valued

the new discovery all the higher, enraged the crowd o old ortho-dox mathematicians all the more, and thus called orth the cry o

opposition, that even in the lay world has an echo and is necessary

in order to pave the way or something new.[3]

This positively alse mathematical procedure is the correlate o the

peculiar sort o reedom that I suggest. It is deeply subjective and only real-

izes itsel in the uture anterior: This will have been true.

Falsity plays a special role in reedom in mathematics, but also in the

very notion o reedom as such. When we speak subjectively about reedom,

we usually speak o reedom o opinion or reedom o action. However, as

we can deduce rom the ancient dialectic o reedom, reedom conceived as

merely being open to a set o opinions or choices is not reedom at all. Over-

coming this impossibility o reedom is reedom itsel. To think, to claim, to

seize or to act on something beyond the constraints o given or commonsensi-

cal determination, beyond the set o given choices, seems as impossible as

liberty itsel. It is this impossibility that gives shape to liberty.Mathematics thus presents a mirror in which the strictest orm o neces-

sity encounters its double in the most subjective and absolute orm o lib-

erty. This mirroring can also oer a deeply humanist picture that praises

the unathomable depths o human creativity, the progressive evolution

and transcendence o the human spirit. This, I claim, is also a mistake.

There is something decidedly inhuman about mathematics that grips us

rom the outside. This is not only the intuition and experimentation that

Deleuze and Guattari speak o. Beore those impasses, those undecid-

able statements popularized by Gdel, there is rst the resistance o

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mathematics to thinking. Pace Descartes, the resistance o mathematics is

one that not even the god o the theologians could overcome. We do not sim-

ply axiomatize by pure decision. Mathematics resists us at every step. It is

this resistance against the human that makes us submit our intuition, our

given belies, to the inhuman avant-garde o consistency. The long history

o the imaginary number i, or the square root o negative one -1, attests to

centuries o coming to terms with a mathematical existence which cannot

be reduced to our human experience, our intuition, our experiments. The

history o the imaginary number i is the history o the stubbornness o a

sign, a mathematical thought that orces a person to think; a continuous

mathematical kick rom behind. It is perhaps this inhumanity that is the

perect mirror or liberty. In being orced to think necessity, we are orced

by necessity to think.

The inhuman orce o necessity is not only one o thought. When thephilosopher o mathematics Jean Cavaills decided to become an active

resister in the Second World War, he emphasized that he took this deci-

sion by means o logic.[4]For him, this reedom o action was dictated by

deductive necessity, and being orced to take up the antiascist struggle

was inherent in his relationship with mathematics. I we were in any

doubt about the question, his struggle was political, and his decision, like

proving a theorem, involved persisting in accepting the necessary conse-

quences. He was killed by a Nazi bullet in February 1944, his body buried in

a mass graved marked Unknown No. 5.

Tzuchien Tho, Paris, 29 July 2012.

[1] Alain Badiou, Number and Numbers, trans.

by Robin Mackay, Cambridge: Polity Press,

2008, 213.[2] Gilles Deleuze and Flix Guattari, A Thou-

sand Plateaus: Capitalism and Schizophre-

nia, Volume II, trans. by Brian Massumi,

London: Continuum Press, 2003, 416.

[3] Karl Marx, Mathematical Manuscripts,

London: New Park Publications, 1983, 168.

[4] Georges Canguilhem, La vie et mort deJean Cavaills, Paris: Allia, 1996, 38.


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Translated by:

Carleton Copeland

Christopher Doss


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