Welcome to

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• Welcome to
• OUR UNIVERSE
• University of Western Australia 2004
• a new course designed to introduce students
  whatever their background to the modern
  understanding of the physical universe.
• . we need YOUR input to ensure the course
  optimally meets your needs
• Understand the awesome scale of the universe
• Understand how it seems to be fine tuned for life
  as we know it.
• Are we alone?

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My Expectations for your successful completion of
this course. Lectures are a guide to the course
content Much of the material can be found in the
official text Universe by Kaufmann and
Freedman, 6th edition Freeman Pub. You are
expected and required to read beyond this text,
through recommended books and web
pages. Assignments may be done as 3-person group
exercises. Last year students preferred
individual work. Oral presentations.(3
assignments, 3 presentation sessions.) Astronomy
excursions and tutorials are an essential
component of the course. First starnight Monday
fortnight
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Practical Issues Assignment presentation word
processed, 3 text pages per person( minimum 9
pages images if you want to do a team
assignment) Star nights Practical and social
arrangements Combined with tutorial, barbeque.
Transport for star nights Carpooling? Deadlines W
ritten12pm, Last Friday in March, April and
May Oral presentation during deadline
week? Examination 50Formal exam and 50
continuous assessment? Web access all notes on
Web
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What do you already know? What do you expect to
learn? Mathematics Rational and Irrational
Numbers Powers of Ten Notation Simple
Formulas Physics Laws of Physics Nature of
Matter Astronomy Birth of the Universe Galaxies
and Stars Distance Scales 6 Types of Stars Life
Cycles of Stars Black Holes The Future of our Sun
and Our Universe
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• Module 1 The Universe of Numbers
• 1,0,p,?
• All civilisations have developed numbers.p was
  discovered almost 4000 years ago but zero was
  only discovered 1500 years ago
• Can the Universe Count?
• Why invent zero? the uses of zero
• (bases and notation)
• Does p exist, does the universe of numbers exist?
• What is the difference between a googleplex and
  ??
• Using Big numbers The scale of the universe

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How to Discover the Truth Occams Razor the
Principle of Simplicity Scientific Scepticism
Disputation and Disproof Fundamental principle
Logic Mathematical Proof independent of
physical reality Physical Laws eg gravitation
Universal over all space and time Universal
Constants eg c,G, h Why is the universe
governed by simple mathematical laws, simple
symmetries and fixed universal constants?
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OUR UNIVERSE Assignment 1 Use material from The
Joy of p, The Book of Nothing, From One to Zero,
Fermats Last Theorem and/or other comparable
texts to discuss the following a) Does the
Universe of Numbers and Mathematics have an
independent existence or is it a mere human
invention. b) Review the independent discovery of
p by many civilisations. What is its
significance. Gravity in the universe ensures
that it is both fundamentally and practically
impossible to measure p to more than about 10
significant figures yet it is known to billions
of places explain and comment. c) Zero is a
relatively recent invention by world
civilisation. Why is zero so enormously
significant. Why is it essential to our counting
system. Consider writing one billion in Roman
numerals, and discuss the difficulty. Why is
powers of 10 notation essential for studying the
universe.
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Suggested Reading Mathematics The Book of
Nothing John Barrow, Vintage Books 2000 Fermats
Last Theorem Simon Singh, Fourth Estate
1997 Against the Gods Peter Bernstein, Wiley
1996 From One to Zero Georges Ifrah, Penguin
1985 The Joy of p David Blatner, Viking
1997 Geometry, Gravity and Curved Space Ripples
on a Cosmic Sea David Blair and Geoff McNamara,
Allen and Unwin 1997 Black Holes and Time Warps
Kip Thorne, Norton 1994
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Our Universe Assignment 2 (2003, for your
info) Geometry, Curvature and Gravitational
Lenses The gravitational deflection of starlight
by the sun is an example of gravitational
lensing. Research the history of the prediction
and the discovery of this phenomenon, including
the role of the Wallal Expedition in Western
Australia. Microlensing is the phenomenon applied
to the search for dark matter..investigate the
Macho project and the project Planet. Find and
explain some of the dramatic large scale
gravitational lensing imagesthe phenomenon known
as macrolensing. Explain the difference between
microlensing and macrolensing. Use a balloon to
investigate geometry on curved surfaces.Present
some examples of non-Euclidean geometry on curved
surfaces and show that the formula for the area
of a circle is false on the surface of a sphere.
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Our Universe Assignment 3 (2003, for your
info) The Next Supernova in our Galaxy? Eta
Carina is an extraordinary star. Observe it and
find out about its history. What is a supernova?
Find out about historical supernovae (ref Ripples
on a Cosmic Sea) What is the risk to Planet
Earth? What is the nature of neutrinos and their
role in supernovae?
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History of Numbers and the Origin of Zero

• Note excursion Monday fortnight
• Delayed one week

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Early Sumerian Numbers
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History of Zero see chapter 1, The Book of
Nothing Positional number systems plus place
markers invented 2000BCE Babylon Mayans,
Babylonians used positional system, then zero
symbol followed. India 350BCE Brahmi
numerals 200BCE probably had zerodot Positional
base 10 system 6th century CE, using same
numerals First just a place marker, then becoming
a number in its own right Bramagupta 628CE sunya
arises when one subtracts a number from
itself. when sunya is added or subtracted from a
number, the number remains unchanged, and a
number multiplied by sunya becomes sunya and
infinity arises when one divides by sunya
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Bases and Numbering Systems

• Early systems used separate symbols for big
  numbers.
• (eg L,C,D M in Roman numbers)
• In such systems order of symbols does not matter.
• Very cumbersome
• Positional numbering need a base.
• Popular bases 8(finger gaps),10(fingers),20(ftoe
  s), 60(? joints)

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Relics of Old Bases

• Seconds,minutes,hours60
• 20chains1 furlong.20
• 20 shillings1 pound.20
• 16 ounces1 pound.8
• Zero started as a placekeeper (to stop errors)
  but evolved

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Early Sumerian, before 2700BC
4980 3600 1380 3600 600 600 60
60 60
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Greek, 500BC
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First Positional System Cuneiform
2 x 60 x 60 51 x 60 3 x 10
2x1 bases are blue
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First Positional Decimal System China 200BC
rotation to separate 10s and 1000s from 1s and
100s
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The No-entry Problem in positional systems
Position indicates multiples of 60x60
60 10 1
Our system 10000 1000 100 10
1
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Solving the no-entry problem first use of zero
zero indicates no entry in a certain column
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Mayan Digits Central America
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Mayan tower notation Positional, amazing bases,
need for zero
Bases 20 360 20 x 360 7200 20 x 7200
144,000
Zero is always needed to prevent confusion
between say 7_2 meaning 702 and 72. To prevent
mistakes the Mayans invented a variety of zero
symbols.
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India Base 10, and zero invented first a dot,
then a circle.200BC
The stars shone forthlike zero dotsscattered
in the sky
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Evolution of Zero
First zero was a place marker, then it began to
be used as an Operator to indicate another level
of base. Only posible because of the regular base
system
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The Operator Zero in Indian poetry
The dot on her forehead Increases her beauty
tenfold Just as a zero dot increases a number
tenfold
Brahmagupta 628AD Zero becomes a number
When sunya is added to a number or subtracted
from a number, the number remains unchanged, and
a number multiplied by sunya becomes sunya.
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The History of p
Ahmes 1650 BCE
pr2(16/9)2r2 So p 256/81 3.16049 1
error
8/9d
First known example of squaring the circle. The
Bible (1000BCE?) 10cubits diameter30cubits
circumference (1Kings 723). Hence
p3 Explanations 1) Bible is false, 2)
Scientists are lyingand many more.
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Greeks Antiphon, Bryson 420BCE Polygons inner
and outer polygons Circumferencepd, area pr2
True area is between inner and outer polygon,
more accurate as number of sides
increase. Archimedes 287-212BCE Used
circumferences 3 10/71 lt p lt3 1/7 p3.1419,
0.03 error
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Ptolemy 87-165AD p3 17/120 (3degrees 8minutes
and 30 secondssexagesimal notation), 0.003
error Liu Hui 263CE independently found polygon
method, 3072 sides Zhu Chong-zhi and Tsu
Cheng-zhi.450CE 24,576 sided polygon, p355/113,
3.1415929 Record held for 1000 years, 8 x 10-8
error Chinese advantage they had decimal
notation and they had zero Viete (France) 1579
polygons, p3.1415926535-7 and found first
mathematical series for p Rudolf van Ceulens
1610CE 32-billion sided polygon. 35 digit
accuracy.(sufficient to measure circumference of
universe to resolution of a sensitive
microscope!!) Wallis 1655 p/2 2x2x4x4x6x6x8
1x3x3x5x5x7x7x9...
Lambert 1761 proved p to be irrational
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Recent History 1949ENIAC, 2037 decimal
places 1959 IBM704, 16,167 places-Paris 1966
IBM7030 250,000 places-Paris 1973 1million
places-Paris 1983 16million.KanadaJapan 1989
1billion,Chudnovsky Bros New York 1995
Kanada..6billion 1996 Chudnovsky8 billion 1997
Kanada51.5 billion
There is a beauty to pi that keeps us looking.
The digits of pi are extremely randomand yet
they are precisely defined.
References on p www.joyofpi.com A History of Pi
Petr Beckmann St Martins Press 1971 Pi A Source
Book Len Berggren and JP Borwein 1997
Springer-Verlag
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p, space and geometry

• p describes the ratio between the circumference
  and the diameter of a circle.
• Only on flat surfaces!
• On curved surfaces p (defined experimentally) can
  be larger or smaller.
• Nowhere in the universe has space flat enough for
  p to be useful to more than 20 places.
• Hence the existence of p is purely abstract.
• Does it contain a message?
• Einsteins theory of gravitation matter tells
  space how to curve space tells matter how to
  move

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p and Extraterrestrials

• Interstellar communication by radio or laser
  pulses is easy if you can know what frequency to
  use.
• How can we choose a frequency that they will use?
  
• Remember that 1 second and all other units are
  arbitrary human inventions.
• One choice the interstellar contact channel
  hypothesis.
• Assumption that mathematics and numbers are
  universal

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Interstellar Contact Channel Hypothesis

• Choose a frequency defined by element number 1,
  hydrogen.
• This itself is useless because the universe is
  full of natural radiation sources from hydrogen.
• Multiply or divide this frequency by a number
  that signifies civilisation.
• Is p the unique choice?
• No! p, 2p, 1/p and 1/2p would be equally valid.
• Several searches using Parkes radio telescope
  (led by DGB and AW) yielded null results.

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e and i

• e is another very significant irrational number
  e2.71828
• The natural logarithm of e1
• i is the imaginary number, square root of -1
• Amazingly eip -1
• Maybe we should have searched e x hydrogen
  frequency
• But surely if the aliens wanted to make contact
  they could have tried both!

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The Galactic Club(1)

• Why make radio or laser contact with aliens?
• Because interstellar space travel is impossible!
• Why is it impossible
• a) Because it takes more than the rest mass
  energy of an object to get it there in a
  reasonable time.
• b) Because space is full of damaging radiation.

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The Galactic Club (2)

• Why communicate with aliens?
• For the sake of knowledge and information.
• What does it offer?
• The histories of a million planets and millions
  of civilisations.
• New frontiers of discovery
• Membership of the galactic club

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How to Join the Club

• The galactic club welcomes new membersthe only
  way to expand the frontier of knowledge.
• Search for Beacons
• The galactic club sends out beacons to encourage
  new members
• The big catch it only sends out beacons when it
  knows that a radio civilisation has emerged.

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Planet Earths Radio Sphere

• The radio sphere from the Earth is only 50-60
  light years in radius.
• The nearest star is 4 light years away.
• The radio sphere has only reached a few hundred
  stars.
• Only a few 10s have had time to reply.
• Astronomy can never distinguish between green
  planets with jelly fish and slime (600million
  years ago on Earth), dinosaurs (70m years ago),
  stone age primates (1m years ago) and
  pre-industrial society (1000 years ago)
• Would anybody send out beacons for 100million
  years.

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The Aliens

• Have never visited
• Must be vastly more advanced
• Have already contacted other civilisations
• Have no evil motives (does power have meaning
  without presence and wealth?)
• Are probably at least 100light years away so we
  cannot expect a beacon until at least 2150.
• Contact will change life on earth forever

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Earth in the Galactic Club

• Mathematics and Logic the tool for communication.
• Numbers, primes and primeproducts.
• Images by prime number products.
• Nouns by images, atomic compositions
• Constant streaming data
• Knowledge of civilisations
• Work for billions of social scientists!
• Purpose and meaning when scientific discovery has
  petered out.
• All of the above is open to criticism,
  argumentopinions, not facts.

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