Category Archives: Mathematics


Can anyone give a geometric reason why an imaginary number raised to the power of an imaginary number generates four real numbers and no imaginary ones? Continue reading

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What is e exp (-i π) ?

I posted a long answer on where it sort of didn’t do so well. Answers given by others were much shorter but lacked geometric insights. After two days my answer was the most read but least upvoted. It did receive a few positive replies, though.
I can’t help but believe that there must be nerds in cyberspace who might enjoy my answer. Why not post it on my blog? Maybe someday one of my grandkids will get interested in math and read it. Who knows? Continue reading

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There’s a big problem inside the science of science; there always has been. People noticed the problem as soon as they started doing science. Continue reading

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Fine-Structure Constant

What is the fine-structure constant?
Many very smart physicists wonder about it; some obsess over it; a few have gone mad. Physicists like the late Richard Feynman said that it’s not something any human can or will ever understand; it’s a rabbit-hole that quantum physicists must stand beside and peer into to do their work; but for heaven’s sake don’t rappel into its depths. No one who does has ever returned and talked sense about it. Continue reading

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Is it possible for humans to tell the truth always; to never lie? Psychologists say it is not possible; most reasonably informed people agree. It’s a trait that can distinguish humans from some forms of artificial intelligence, which engineers at Google and other companies are working furiously to bring on-line.

People’s ideas—their belief systems—are inconsistent, incomplete, and almost always driven by logically-unreliable, emotionally-laden content, which is grounded in their particular life experiences and even trauma. Does anyone disagree? Continue reading

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Why Something, Not Nothing?

Because we are evolved biological creatures who are mostly blind to the things which exist in our Universe, we have become hard-wired over the eons to accept the concept of nothingness as a natural physical state when, it turns out, there is no evidence for it. Continue reading

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Bell’s Inequality

John Stewart Bell’s Theorem of 1964 followed naturally from the proof of an inequality he fashioned (now named after him) which clearly demonstrated that quantum particle behavior in experiments violated certain rules of logic. It is the most profound discovery in all science, ever, according to Henry Stapp — retired member of the Lawrence Berkeley National Laboratory, and a former associate of both Wolfgang Pauli and Werner Heisenberg. Other physicists, like the late Richard Feynman, have said Bell simply stated the obvious. Here is an analogy to help give an idea of just what it is in these quantum experiments that violates Bell’s Inequality: imagine Continue reading

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Blaise Pascal: Thoughts

Blaise Pascal was a man who suffered terribly his entire life until he died at age 39 from a metastasizing stomach cancer. His mother died when he was three years old; his father when he was twenty-eight.  For those who … Continue reading

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