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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.

Earth and Moon taken by the Galileo spacecraft. 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 east-west from one another see the eclipse at different times, while those located north-south 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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