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Problem
Book
(En)
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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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Problem
Book
(En)
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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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