CHAPTER TWO
SENSATIONAL SYMMETRY
Matter & Motion
The earliest Greek thinkers considered ideas and logic as the purest subjects of study,
scoffing at those who would try to explain observed events as students of imperfect
knowledge. Persons such as Pythagoras who wanted to understand notes and chords struck
at a smith's forge were scorned by Plato  the senses can deceive! Plato held that the
mind alone would create the true realities of ideas. A student would never learn about
the stars and planets by observing them  only with pure thought can one derive the true concepts.
Pythagoras was born in Samos about 580 B.C. so he was a contemporary of Thales
(see Human Ideas on Cosmic Design). He emigrated to the south of Italy to establish
a school in Croton. He and his students studied the properties of numbers,
designating to the numbers for the first time attributes such as even, odd,
triangular, square, cubic, rational, and irrational. Pythagoras and his students
represented the numbers by circular dots of a specific size, one dot for one,
two dots for two, etc., and many of the properties were deduced by observing the
collection of dots that represent a number. The school was also skilled in
geometry, so many of the biases for certain numbers were transferred to figures.
Circles were considered "perfect" shapes since they are the geometric figures
having least perimeter for a given area; similarly, spheres are figures having
least surface for a given volume. This perfection makes these figures suitable
for celestial bodies. The Earth, the Moon, and the Sun must be spheres;
the Moon, the Sun, and the planets must move in circular paths at uniform speed.
Over 150 years after Pythagoras, Plato's students were able to apply about 30
small uniformly rotating circles to the larger circular paths for the five known
planets to represent their irregular motions across the sky, including the
retrograde portions of their motions.
The inclination to describe the celestial bodies with favorable properties follows
from the dire consequences that could befall the thinker who would deduce more
common attributes. The heavens must be occupied by heavenly bodies. To say anything
less could mean a cup of poison or banishment.
Even centuries after Plato, Ptolemy in the 2nd century A.D. took care in choosing
his subject of study, applying mathematics to astronomical measurements because
this subject lies between the incomprehensible theology and the unpredictable physics.
Ptolemy concludes that the Earth is spherical based on observations of the times
of eclipses: Observers located eastwest from one another see the eclipse at
different times, while those located northsouth see it at the same time.
Further, moving northward brings more stars into the collection of those that
never set. Plus, observers on ships approaching shore see a mountain appear
to rise from the sea. Ptolemy concludes that the Moon and the Sun are both
spheres because they appear as circles wherever they are observed on the Earth.
Ptolemy's logic and conclusions are not very different from our present
understanding of these bodies.
So these perfect symmetries, the circle and the sphere, are the most common shapes
we see in the sky. The further we see with our improved telescopes, the greater
are the numbers of spheres and circles we observe. That we now can reason why
these shapes are common makes the simplicity of this symmetry no less beautiful
to our eyes.
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