Материал: Гвоздева Пхысицс фор адванцед студентс 2011

Vocabulary Notes

1.a meaning – a sense

2.to be amenable to calculations – to be calculable

3.at the bottom – at the root

4.stuff – substance, material, ideas

5.mean – average

6.to derive something from – to get something from

7.a consideration – an examination

8.the mean proportionals – relationship of numbers

POST-READING TASK

(To be done at home in writing)

I. Change the sentences using the complex object.

1.Heraclites believed that the world was a scene of perpetual change.

2.Pythagoras believed that the universe at the bottom displays the combination of pure numbers.

3.The Pythagoreans considered that numbers are the stuff of which the universe was made.

4.The Pythagoreans considered that the relationships between numbers and geometrical figures are built into the foundation of the universe.

5.The Pythagoreans considered that the mean proportionals are the actual bond which holds together the unrelated elements of reality and welds them into a whole.

6.Edenton believed that the universe is fundamentally a mathematical construction.

III. Explain.

1 Numbers 1, 2, 3, 4 in the interpretation of the Pythagoreans

2 Edenton’s ideas of the nature of number and mean proportionals

IV. Look for the information concerning the Pythagoreans’ view of pure numbers in the Internet and add some more facts.

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CLASS EXERCISES

Exercise 1 (do it yourself)

Translate the sentences. Follow the passage.

1.В атомном масштабе наши представления о причине и следствии не имеют смысла.

2.По мнению физиков-математиков в атомном масштабе жёстко детерминированные законы не применимы.

3.Всё, что мы знаем, это то, что поток материи и энергии поддаётся вычислениям.

4.Вселенная основана на сочетании чисел.

Exercise 2 (do it yourself) Outline the Russian passage.

You will find these words helpful: to report, specific, to unify, on the basis of, the latest data, to be interrelated, destruction

1. «Nature» (www. nature. com/news) сообщает о том, что обна-

ружено конкретное число, объединяющее все существующие параметры и фундаментальные законы, на которых строится вселенная. Основываясь на последних данных о существовании темной материи и темной энергии, профессор Скот Фанкхаузер, США, пришёл к выводу, что число 10 в 122 степени (ten to the one hundred twenty second power) есть некое универсальное число, которое объединяет все физические параметры Вселенной. Это значит, что все параметры связаны друг с другом и нарушение этой связи сделало бы наше существование невозможным.

UNIT 13

GOD CREATED THE INTEGERS

DIMENSIONLESS NUMBERS

PRE-READING TASK

Study some grammar points.

I. Unreal situations (Improbable)

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We use special tenses with if when we are talking about unreal or imaginary situations.

a. To talk about improbable present or future situations we use:

If S + V2, S + would + Vo Study a sentence.

If there were more than three spatial dimensions, the orbit of planets around the sun or electrons around a nucleus would be unstable and they would tend to spiral inwards.

Note:

could, might = would be able to

Study a sentence.

If stars could shrink to as small as 10 or 20 miles across to become neutron stars, one might expect other stars to shrink even further to become black holes.

b. To talk about improbable situations that did not happen we use:

If + had V3 (were), S + would + have V3 Study some sentences.

1.If the initial expansion of the universe had been slightly smaller or slightly greater, the universe would either have collapsed or have expanded very rapidly.

2.If the gravitational mass of the proton were significantly different, one wouldn’t have had stars.

II. We use for +N + to V to talk about the purpose of doing something.

Study the sentences.

1.There could be different universes with different densities. Only those that are very close to the critical density would last for long enough and contain enough matter for stars and planets to form.

2.Is there a need for a general public to be closely in touch with scientific developments?

3.Is it possible for a particle to travel faster than light?

4. Notice, the below sentence is emphatic. To emphasize a part of the sentence, we change the word order. To understand it, restore the usual word order: S + V + O + where + when

Study the sentence.

Only in a small number of the universes, with conditions and parameters like our own universe, will it be possible for intelligent life to develop.

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III. The infinitive after a noun N + to V (to be + V3) characterizes it and expresses an action that must be done, or could be done in the future.

Study the sentences.

1.There wouldn’t be anyone to ask the question.

2.Only in the universes that are very close to the critical density will there be intelligent beings to ask the question: why is the density so close to the critical density?

3.Hawking intends to form a theory to explain the origin of the universe.

Give Russian correspondence:

neither … nor, either ….. or, initial (original), on the other hand, since (as, for, because), before, by the same amount, so (thus, therefore), otherwise (differently), close to (near)

INITIAL CONDITIONS AND THE VALUES

OF THE PARAMETERS ARE CHOSEN

Study the passage. Mind the underlined grammar points.

In fact it seems that neither the initial conditions, nor the values of the parameters in the theory are arbitrary but that they are somehow chosen very carefully. For example, if the proton-neutron mass difference were not about twice the mass of the electron, one wouldn’t obtain the couple of hundred or so stable nuclides that make up the elements and are the basis of chemistry and biology. Similarly, if the gravitational mass of the proton were significantly different, one would not have had stars in which these nuclides could have been built up, and if the initial expansion of the universe had been slightly smaller or slightly greater, the universe would either have collapsed before such stars could have evolved or would have expanded so rapidly that stars would never have been formed by gravitational condensation. If the density of the universe one second after the big bang had been greater by one part in a thousand billion, the universe would have collapsed after ten years. On the other hand, if the density of the universe at that time had been less by the same amount, the universe would have been essentially empty since it was about ten years old.

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According to one version of the anthropic principle, there is a very large number of different, separate universes with different values of the physical parameters and different initial conditions. Most of these universes will not provide the right conditions for the development of the complicated structures needed for intelligent life. Only in a small number, with conditions and parameters like our own universe, will it be possible for intelligent life to develop and ask the question, “Why is the universe as we observe it?” The answer, of course, is that if it were otherwise, there wouldn’t be anyone to ask the question.

Stephen Hawking

Vocabulary Notes

1.arbitrary – random – approximate – not exact

2.similar – like; similarly – we use similarly to say that an action or an event is similar to the one that you have just described

3.to build up – to accumulate

4.slightly – a bit

5.essentially – basically

POST-READING TASK

(To be done at home in writing)

I. Study grammar point I and answer the questions: What would happen (have happened) if

1.the proton-neutron mass difference were not about twice the mass of the electron?

2.the gravitational mass of the proton were significantly different?

3.the initial expansion of the universe had been slightly smaller or slightly greater?

4.the density of the universe one second after the big bang had been greater by one part in a thousand billion?

5.the density of the universe at that time had been less by the same amount?

6.the conditions and parameters of our universe were different?

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