The Real World

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The Real World Chapter 2 From Unifying the
Universe By H. Padamsee
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A New Period
Athens Declines

• The center of culture shifts away from Athens
• So does the center of intellectual activity.
• We move to Alexandria, Egypt, founded by and
  named after the Greek conqueror Alexander
• Tutored as a youth by Aristotle.

Sunset Over Greek Culture
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Alexander Defeats the Persians
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Modern Rendition of Alexanders Battles
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Greek culture and science spread over Alexander's
Empire

• Alexandria grew from a booming center of trade
  into a fabulous cosmopolitan city.
• People of many lands and cultures converged here
  Greeks, Jews, Arabs, Hindus...
• Most interesting for the development of science
• Alexandria became the converging point for the
  knowledge of Egypt, the science of Greece as well
  as new knowledge from remote areas of the world.

Alexander founded a city that bears his name.
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Great Library of Alexandria

• The rulers of Alexandria were patrons of arts and
  sciences, ready to put resources into large
  educational and research projects.
• They financed a gigantic Library at Alexandria,
  a single place where all the knowledge of the
  whole world came together.
• The collection at the Library grew to 400,000
  rolls of papyrus
• Each equivalent to a modern book of 60 pages. A
  strip of papyrus was called biblion, the origin
  of our word bible.

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Q How did the library of Alexandria acquire a
collection of nearly one million books? (a) They
had many bright scientists and writers. (b) They
copied the works of many cultures and collected
them. (c) They had a printing press. (d) All of
the above.
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Renaissance Artist Raphaels RenditionWill
discuss many aspects later...
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The intellectuals of Alexandra made enormous
advances in many fields.

• Mathematics Euclid, Archimedes, Apollonius,
  Hypatia
• MechanicsArchimedes
• Fluids Ctesibos, Hiero
• Geography Eratosthenes
• Astronomy Apollonius, Aristarchus, Hipparchus,
  Ptolemy

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Elements of Geometry

• Euclid wrote a book called the "Elements of
  Geometry".
• This is the geometry we learn in High School.
• It is the most widely printed book in the world
  today, after the Bible.

"See the bold shadow of Urania's glory Immortal
in his race, no less in story, An artist without
error, from whole line Both Earth and Heavens, in
sweet proportions twine Behold great Euclid. But
Behold him well, For 'tis in Him that Divinity
doth dwell... G. Wharton
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The modern poet, Edna St. Vincent Millay, pays
tribute to the geometer "Euclid alone Has
looked on Beauty bare. Fortunate they Who,
though once only and then but far away, Have
heard her massive sandal set on stone. "
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The Size of the Earth Eratosthenes
Through close attention to details Erathosthenes
discovered a way to measure the earth
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At noon, on the day of the summer solstice, an
auspicious time, a strange report from Syenne
Whenever a paradox occurs we can be sure that
there is a serious flaw in the way we think about
reality. Resolution of the paradox leads to a
radical new vision.
Observation
Expectation
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-The rays from the sun are all parallel -Alternate
angles are equal Euclid. Angle of sun Angle
at earths center
-The earth is spherical
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Measurement
360/7 51

486 miles x 51 25,000 miles
486 mi
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What new methods did Eratosthenes apply to
advance science? a) Close attention to the
details of the world b) Measurements of angles c)
Measurements of distances d) Euclids geometry e)
All of the above
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Resolution Through Precise Measurement

• So the earth appears flat because it is much
  larger than the human scale (1-2 meter)

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The early Greeks narrow focus on abstract
idealism broadened to include detailed features
of the real world
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Compare Idealistic vs. RealisticInterest in
Details
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Measurement plays a crucial role in the
advancement of science
The ancient of Days, by William Blake, 1757-1827
Later, artist and poet William Blake imagines the
words of Wisdom, who was present with the Lord
through the time of Creation When he prepared
the heavens, I was there When he set a compass
upon the face of the depth When he established
the clouds above When he gave to the sea his
decree When he appointed the foundations of the
earth
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Archimedes and p

• Q What is the meaning of pi?
• Archimedes was a mathematician
• He figured out how to determine the value of pi.
• A mathematical advance well ahead of its place
  in science.

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1/2s
2R
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Archimedes Discovered a New Mathematical Curve -
The Parabola
But he missed recognizing the parabola in the
real world
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Like other scientists of Alexandria, Archimedes
grew interested in details of nature.

• Some of these emerged from practical questions
• King Hiero asked Is my crown really made out of
  gold?

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• Archimedes Eureka Moment

Details, Details, Details! Measure, Measure,
Measure
Density Weight/Volume
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• Approximate Densities of Common Substances
• Important to be Quantitative (numbers describe
  nature)
• Units kg/m3
• Important Remember Mars probe lost!
• Units of weight, volume, area, density
• Some other units of density gm/cm3
• Must learn how to convert (section)
• Water 1 x 103 kg/m3
• How big is a cubic meter?
• Learn how to use scientific units (section)

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Archimedes Lever Principle F1d1 F2 d2

• "Give me a lever and a place to stand and I will
  move the earth."

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Archimedes Practical Accomplishments
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Q Suppose I weigh the aluminum block in air and
then in water. The weight in water will be
A) the same as in air B) more than it weighed in
air C) less than in air D) It will weigh zero
(weightless)
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Archimedes Buoyancy Principle
Density Weight in Air/Loss of Weight in Water
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A block if steel and a block or aluminum have the
same weight in air. Steel has a higher density
than Aluminum. Now weigh both in water, one at
a time. The weight of the steel block in water
will be
A) less than the weight of the aluminum block in
water B) more than the weight of the aluminum
block in water C) the same as the weight of the
aluminum block in water
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Archimedes Buoyancy Principle
Take the same volumes
Density Weight in Air/Loss of Weight in Water
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Alexandrian Experiments and Applications with Hot
Air

• Philo of Alexandria Heated air expands
• Hero of Alexandria practical application of
  heated air

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Maria the Jewess Developed Chemical Science