Sunday, June 15, 2008

Aleph

Georg Cantor was a brilliant mathematician who devised 'transfinite set theory,' working from the 1870's to 1884... Cantor also proved that real numbers were more numerous than natural numbers...Set theory is now foundational to mathematics, providing proofs for algebra, analysis, and topology. In 1904,the British Royal society gave Cantor their Sylvester award, the highest honor it could bestow. Cantor died in 1918.

Cantor's ideas attracted hostility from his academic peers; the area of math that Cantor mostly worked with dealt with infinity, and the result could be interpreted as proofs for God's existence. This was a time when most scientists were moving away from any notion of deity; reductionism, materialism, and determinism, were the norm ( and these ideas still are, partly).

"Cantor's theorem" implies the existence of an "infinity of infinities." Set theory was thought to be represent reality better than any other sense object or concept...From set theory, Cantor discovered or proved the existence of Infinity and human free will. These ideas so stirred Cantor that he once wrote to the Pope, in an attempt to change official church doctrine- Cantor thought God had chosen him to reveal to the world the ultimate truth of about actual infinity...a pantheistic theology could be viewed as a logical result of Set theory.

Cantor's struggles with authority contributed to his mental erosion- he suffered from a bi-polar type condition, eventually ending up in a padded cell.

" The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in it's highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds." (Cantor)

David Hilbert was the mathematical successor to Cantor. After Cantors death, Hilbert said...

"No one shall expel us from the Paradise that Cantor has created."

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