Nothing really matters

Nothing really matters
I.
Lesson 2
Your special number
Is there a number that you specially like ?
Is there a number that you don’t like at all ?
Do you think some numbers have “special meanings” ?
II.
A powerful invention
Listen to the first extract from Simon Singh’s radio programme, fill in the gaps,
and then answer the questions in your notebook.
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So, where does the history of zero start ? Well there was a time when
mathematicians didn’t even know about zero. The word, the symbol, the
very concept of 0 hadn’t been invented ; or is that discovered ? Either
way, as Ian Stewart of Warwick University points out, there came a time
when mathematics couldn’t progress without 0.
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Arithmetic works much better if you think of 0 as a number. What’s 3
take away 3 ?
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Zero.
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Exactly. And it’s a physical thing you can do.
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So you need 0 in order to represent nothing in an equation.
Questions :
1. What is this programme about ?
2. What mathematical operation is Ian Stewart talking about when he says “3 take
away 3” ?
3. What is an equation ?
4. Can you think of other reasons why zero is such an important number ?
5. Simon Singh says, “Zero hadn’t been invented ; or is that discovered ?”
Do you think zero was invented or discovered ?
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Monday, September 15th, 2008
III.
How do you relate to zero ?
In the next extract, Simon Singh interviews Adam Spencer, an Australian mathematician.
When I’ve spoken to mathematicians, they tend to give numbers personalities. How do you relate to zero ?
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Zero. Underrated, stubborn, at times helpful, at times very irritating,
refuses to go away.
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And if you really want to see the irritating side of 0 then try dividing
by it.
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Questions :
1. What happens if you try to divide by zero ?
2. Do you know why ?
IV.
A question of irreversibility
To find out exactly why you can’t divide by zero, Simon Singh finally interviews
Charles Seife, author of “Zero, biography of a dangerous idea”.
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In short, never divide by 0, because the result is chaos, logic breaks down,
paradoxes proliferate. The root of all these problems is irreversibility.
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For instance if you multiply 2 by 3 you get 6. To get back, you divide
6 by 3 and get to 2. That’s a reversible operation.
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Right.
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Multiplying by 0 is not a reversible operation. Because multiply 0 by 3
you get 0. But if you multiply 2 by 0 you get 0.
So, if you try and work backwards there’s no obvious way to tell where
you came from.
Questions :
1. Can you find other examples of reversible operations ? of irreversible operations ?
2. Let a and b be two numbers, with a = b.
What do you think of the following proof ? :
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Monday, September 15th, 2008
a=b
this is the hypothesis
a×a=a×b
multiply by a
a2 = ab
a2 − b2 = ab − b2
subtract b2
(a − b)(a + b) = b(a − b)
factorise
a+b=b
divide by a − b
a+a=a
because a = b
2a = a
2a a
=
a
a
2=1
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divide by a
isn’t that interesting ? !
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Monday, September 15th, 2008