Log24

Tuesday, November 1, 2005

Tuesday November 1, 2005

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM
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The above seal is from an ad (pdf) for an Oct. 21 lecture, "The Nature of Space," by Sir Michael Atiyah, sponsored by the American Mathematical Society.

The picture in the seal is of Plato's Academy.

"The great philosopher Plato excluded from his Academy anyone who had not studied geometry.  He would have been delighted to admit Sir Michael Atiyah, who was for a time Savilian Professor of Geometry at Oxford…"

 

Would he?

Sir Michael Atiyah's
Anti-Platonism

"Mathematics is an evolution from the human brain, which is responding to outside influences, creating the machinery with which it then attacks the outside world. It is our way of trying to reduce complexity into simplicity, beauty and elegance….

I tend to think that science and mathematics are ways the human mind looks and experiences– you cannot divorce the human mind from it. Mathematics is part of the human mind. The question whether there is a reality independent of the human mind, has no meaning– at least, we cannot answer it."

— Sir Michael Atiyah, interview in Oslo, May 2004

"For Plato, the Forms represent truth, or reality…. these Forms are independent of the mind: they are eternal, unchanging and perfect."

—  Roy Jackson (pdf)

Atiyah's denial of a reality independent of the human mind may have something to do with religion:

"Socrates and Plato were considered 'Christians before Christ'; they paved the way for the coming of Christianity by providing it with philosophical and theoretical foundations that would be acceptable to the western mind.
    In the analogy of the cave, the sun represents the Form of the Good. In the same way that the sun is the source of all things and gives light to them, the Form of the Good is over and above the other Forms, giving them light and allowing us to perceive them. Therefore, when you have awareness of the Form of the Good you have achieved true enlightenment. In Christianity, the Form of the Good becomes God: the source of all things."

— Roy Jackson, The God of Philosophy (pdf)

See also the previous entry.
 

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