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Файл:M&Ms. Movies and Maths. Учебно-методическое пособие
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11
Unit 2
A Beautiful Mind
[from https://blimey.pro/a-beautiful-mind-ending-explained/]
Lead-in
A. Do you know any quotes about mathematics? Look at the following three and decide
which one reflects your understanding of what mathematics is.
“Pure mathematics is, in its own way, the poetry of logical ideas.”
Albert Einstein
“Mathematics is the language of the universe. So the more equations you know,
the more you can converse with the cosmos.”
Neil Tyson
“Mathematics is the most beautiful and the most powerful creation of the human
spirit.”
Stefan Banach
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B. Many of us think mathematicians are people who deal with computations. Others
suggest that mathematicians handle categories, spaces and parameters rather than
computations. What is your point of view? What do mathematicians do?
Viewing
A. What are practical applications of math in everyday life?
B. Watch the scene. What achievements of mathematicians are mentioned? What does
the principal of the university say about mathematicians? What stereotype about
genius mathematicians is brought up in this scene?
C. Watch the scene again and fill in the gaps.
The principal: 1) _________ _________ the war. Mathematicians 2) _________
_________ _________ _________ …and built the A-bomb. Mathematicians...
3) _________ _________. The stated goal of the Soviets is global communism. In
4)_________ _________ _________, in technology or space, battle lines are being
drawn. To triumph, we need results – 5) _________ _________ results. Now who
among you will be the next Morse? The next Einstein? Who among you will be
the vanguard... of 6) _________ _________ and _________? Today, we bequeath
America's future into your 7) _________ _________. Welcome to Princeton,
gentlemen.
Man 1: It's not enough Hansen won the Carnegie Scholarship.
Man 2: No, he has to have it all for himself.
Bender: It's the first time the Carnegie Prize... 8) _________ _________ _________.
Hansen's all bent.
Neilson: Rumor is he's got his sights set on Wheeler Lab, the new military think tank
at M.I.T.
Bender: They're only taking one this year.
Neilson: Hansen 9) _________ _________ _________ _________ picked first.
Man 1: Oh, yeah, he's wasted on math. He should be running for President.
Nash: There could be a mathematical explanation for how 10) _________ _________
_________ _________.
13
Neilson: Thank you. Neilson, symbol cryptography.
Bender: Neils here 11)_________ _________ _________ _________. Helped rid
the world of fascism. At least that's what he tells the girls, eh, Neils? The name's
Bender. Atomic 12) _________. And you are?
Sol: Am I late?
Neilson: Yes. Yes, Mr. Sol.
Sol: Oh, good. Uh, hi. Sol. Richard Sol.
Hansen: The 13) _________ _________ _________.
Bender: There he is.
Hansen: So many supplicants, and so little time. Mr.Sol.
Sol: How are you, sir?
Hansen: Ah, Bender.
Bender: Nice to see you. Congratulations, Mr.Hansen.
Hansen: Ah, thank you. I'll 14) _________ _________.
Nash: Excuse me?
Hansen: A thousand pardons. I simply 15) _________ _________ _________
_________ _________.
Bender: Play nice, Hansen.
Neilson: Nice is not Hansen's strong suit.
Hansen: An honest mistake.
Nash: Well, Martin Hansen. It is 16) _________ _________ _________ _________?
Hansen: Why, yes, John, it is.
Nash: I imagine you 17) _________ _________ _________ _________ _________
miscalculation. I've read your pre-prints… both of them. The one on Nazi ciphers, and
the other one on 18) _________ _________, and I am supremely confident that there
is not a single seminal... or 19) _________ _________ in either one of them. Enjoy
your punch.
Hansen: Gentlemen, meet John Nash, that mysterious 20) _________ _________
_________. The other winner of the 21) _________ _________ _________.
Bender: Oh, okay.
14
Sol: Oh, yeah?
Bender: Of course.
D. Reductions. Listen to the following utterances from the scene again. Is there
a difference between the way they are written and pronounced?
1. It is the first time the Carnegie Prize has been split.
2. They are only taking one this year.
3. It is Martin, isn’t it?
4. There is not a single seminal or innovative idea in either1 one of them.
E. Match the utterances from exercise D and the following peculiarities of
pronunciation.
1) dropping plosive sounds, for instance [t], [d], at the end of a word:
I din’ do anything – I didn’t do anything
2) dropping initial [h] in HAVE in perfect forms:
I’ve done that – I have done that
3) dropping [f] in OF:
One o’ these cakes – One of these cakes
4) palatalization – transformation of final consonant sounds because of the following
[j]:
*Dinchu2 say this? – Didn’t you say this?
*Sinschu ast, I’ll do it – Since you asked, I’ll do it
F. Listen again to the utterances in D. Repeat them after the speaker in the scene.
1
You can hear the American pronunciation in EITHER.
2
This is NOT the accepted spelling of the word.
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Vocabulary 1
A. Watch the scene again. What do these phrases mean in the context?
the battle lines are drawn to bequeath(e) to split (split, split)
he’s used to being picked first nonlinear equations able hands
to have one’s sights set on… to run for President to break a code
the burden of genius a think tank to rid smb/smth of
a strong suit seminal ideas miscalculation
publishable applicable vanguard
B. Read the following sentences. Decide which one vocabulary unit from exercise A
can fill all the gaps in one set of sentences. You may want to change the form of
the original expression.
Example:
1) They became just a _______________ to the company, unwanted and unwelcome,
after they have fulfilled their roles.
2) Sam likes me - he never makes me feel like I am a _______________ .
3) The government lowered the tax _______________ on the middle class.
Answer: the word BURDEN fits all the 3 sentences
1. a) Political scientists who were in the intellectual _______________
chose to pay less attention to the constitution.
b) Look at the three _______________ social reforms through the eyes of
a Conservative MP.
c) This innovation puts Japan in a good position to move into
the _______________ in future developments in computers.
2. a) Jack has got _______________ Bella’s money, I am sure.
b) There are not so many young people today with _______________ a career
in industry.
c) Those island boys had _______________ the night life of Fort William.
3. a) There appeared to have been a _______________ – one which Rostov
himself did not yet understand.
b) Henry III’s political _______________ had to be set right, and it was
imperative that the status of the king remain intact.
c) You’ve made a serious _______________. As soon as you realise that,
I suspect, you will be off like greased lightning.
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4. a) James put an end to this squabble, writing: “I _______________
my last penny to London charitable organisations.”
b) Some people choose to _______________ their bodies to medical schools.
c) We want a modernising society, which uses science and technology to
_______________ clear seas and fresh air to future generations.
5. a) I heard of the game, but computer games aren’t exactly my
_______________.
b) Housekeeping doesn’t appear to be the actor’s _______________: the floor
is littered with cigarette butts, dirty coffee cups, overflowing ashtrays are all over
the room.
c) Geography may not be our _______________, but we know a thing or two
about the location of the wells.
C. Think of the scientists shown in the scene – who, in your opinion, looks like a true
scientist? Why? In pairs or small groups, come up with five qualities a true scientist
should have. Use the vocabulary from exercise A.
D. Share your ideas with the rest of the class. What qualities are unanimously
recognized?
E. Role-play. Two students meet in a student café. They talk about Art students and
Science students and discuss if there are any differences between the two. Use
the vocabulary from exercise A. Act out the conversation.
Grammar
A. Study the following example.
Example: Hansen is used to being picked first.
Does the sentence describe the present or the past?
Was Hansen picked first only once?
B. Complete the following sentences using the pattern BE+USED+TO+Ving.
1) He ____________ problems utilizing Euler’s method.
2) When I was at school, we _____________ integral calculus.
3) ____ you _____________ the first prize?
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C. Ask your partner two or three questions figuring out:
● what they are used to doing in the evening,
● if they are used to going in for sport,
● if they are used to staying up late,
● if they are used to solving math problems when they have spare time,
● if they are used to walking in the forest, etc.
Speaking
A. Why do you think the movie is named A Beautiful Mind? What is a beautiful mind
for you? Offer your own definition for this phrase. An example is given below.
Example: A person has a beautiful mind when they give their love to other people.
B. In groups of three, share your definitions – find the similarities and differences
in your definitions. Report the results to the rest of the group.
Reading
A. What do you know about John Nash, the protagonist of the movie?
B. Read the following interview with John Nash (1928-2015). Are the following
statements true or false?
1. Russel Crowe conversed with John Nash before the movie release to learn
what accent he had.
2. The fact that the personal life became known to the whole world didn’t matter
much to John Nash.
3. Winning the Nobel was a pivotal point in Nash’s life.
Return of a 'beautiful mind'
From New Scientist, by Michael Brooks
Interviewer: John Nash was recognised by his colleagues as a genius in 1948 when
he was accepted into Princeton University’s graduate programme at the age of 20.
A year later he found a mathematical way for hostile parties to settle arguments to
mutual advantage. Known as the Nash equilibrium, his major contribution to
mathematics remains as useful today - as shown by recent auctions of bandwidth to
mobile phone companies - as it was in cold war politics. It gained him a Nobel prize
for economics in 1994. He researches problems in cosmology and quantum theory.
An obvious question to kick off with: is there a connection between madness and
genius?
18
Nash: There’s certainly a connection between mental illness and “thinking out of
the box”. If you're going to be anything like a genius you have to think out of the box.
In that sense genius is something other than perfect normality, but I wouldn’t say there
is a strong connection.
Mathematicians are comparatively sane as a group; it’s the people who study logic who
are not so sane. Logical scholars like Kurt Godel are certainly not a good example of
sanity.
Interviewer: What it’s like to have become famous as a mathematician through
Hollywood influence? Do you find it awkward that people now know about your
personal life without knowing much about your work?
Nash: It is a bit of a burden. You become quite well known, without it being the best
type of reputation to have. To be considered a distinguished mathematician by
mathematicians is one thing, but to be considered by the public to be a distinguished
mathematician, well, that’s something else. It does help that there’s a lot of fiction in
the movie. It’s based on my life but there are some variations – and the other characters
are more or less fictional.
Interviewer: Do you even recognize yourself in A Beautiful Mind?
Nash: It’s not me, but Russell Crowe plays the role well. I didn’t meet him before
the movie. Just his speech coach came to see me a few times. The idea was that Crowe
would be modeling my accent and the flavour of my speech. In the end, he simply used
a southern accent, which is not the same as mine. I only met him when they were
actually doing the movie, and at the Oscar event.
Interviewer: At the end of the film, we see a happily-ever-after scenario when you
have recovered from mental illness. Was that really like a second birth?
Nash: It was more like a return than a second birth. I have a son who is disturbed
through mental illness. He is a mathematician. He got as far as PhD and then got
disturbed. If he could come back it wouldn’t be a rebirth, it would be like a return.
Interviewer: What about you? Do you still hear voices?
Nash: I was a long way into mental illness before I heard any voices. Ultimately
I realized I am generating these voices in my own mind: this is dreaming, this is not
communication. This is coming from an internal source, not from the cosmos. And
simply to understand this is to escape from the thing in principle. After understanding
that, the voices died out. My son hears voices, but I haven’t heard any for a long time.
Interviewer: So, was there an element of rational decision-making involved in dealing
with your symptoms?
Nash: There’s a lot of choice in this, I think, I know this is not the standard point of
view. The standard doctrine is that we are supposed to be non-stigmatic in terms of
these people: constitutionally, necessarily schizophrenic. But I think there’s
an element of choice. A person doesn’t pass into insanity when their situations are
good. If their personal life is successful, people don’t become insane. When they are
not so happy, when things aren’t so good, then they may become clinically depressed,
and then maybe schizophrenic. Wealthy people are less likely to become schizophrenic
than people who are not wealthy.
Interviewer: Are you saying that some people simply choose to opt out of a difficult
reality?
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Nash: It provides an escape. In another way, a person might choose a monastic life:
become a monk or a nun. There are various forms of escape in human societies, leading
to another life where you do not face the same challenges, the same burdens.
Interviewer: When you came up with the Nash equilibrium, the United Nations had
just formed, and a few people were pushing for a world government. Your colleagues
were thinking only about optimistic bargaining situations involving mutual
cooperation. You solved the problem of finding bargaining solutions for situations
where people won’t cooperate. Is that why your work seemed so radical – because it
ran contrary to the zeitgeist and exposed the fact that there’s always a way to get by
without cooperation?
Nash: At the time my idea was offbeat or radical. But in a sense it was classical. After
all, economics works this way. I know that von Neumann and Einstein thought that
there could be some sort of coordinating world leadership. It’s easy to say that there
should not be any war. When the Pope talks about war and peace, you know without
listening what he will say. But war is not in the ideal world, it’s in the real world. It
will happen.
Interviewer: Did the Nobel Prize change anything for you?
Nash: It changed everything for me. Before the Nobel I wasn’t recognised at all,
I was quoted and cited in economics and game theory, but beyond that I didn’t have
any recognition. And without the Nobel Prize there wouldn’t have been any movie.
Vocabulary 2
A. Match the following words from the interview and their counterparts or
definitions.
1. stigmatic
a) marked by disgrace
2. to opt out of
b) to manage with difficulty to
accomplish smth
3. the zeitgeist
c) to be opposed to
4. other than
d) to explore ideas that are not
limited by rules or tradition
5. offbeat (coll.)
e) the ideas and beliefs of the time
6. to run contrary to
f) apart from
7. to think out of the box
g) to choose not to participate in
smth
8. to get by
h) unconventional
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B. Fill in the following gaps with the words or phrases from the exercise above.
1. Such a turn in the solution of the problem ______________ to the fundamental
principle of our theory.
2. Your transformative research is in full accord with ______________.
3. This university would be a good step-up in the career, but I ____________ of it.
4. Alex didn’t manage to do anything ______________ his algebra assignment.
5. All the students were making tremendous efforts to pass this exam and avoid
______________ consequences.
C. Writing. Compose a paragraph (80 words) about an outstanding mathematician
from Akademgorodok.
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