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TagKarl Popper

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black mathematics board with formulas

Why Don’t We See Many Great Books on Math Any More?

Decades ago, Gregory Chaitin reminds us, mathematicians were not forced by the rules of the academic establishment to keep producing papers, so they could write key books.

In our most recent podcast, “The Chaitin Interview III: The Changing Landscape for Mathematics,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on many things mathematical, including whether math is invented or discovered. This time out, Chaitin talks about why he thinks great books on math, advancing new theorems, aren’t written much any more: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 02:49 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: You don’t hear the word “scholarship” very much anymore in academia. Gregory Chaitin: And people don’t write books. In the past, some wonderful mathematicians like G. H. Hardy (1877–1947, pictured in 1927) would write wonderful books like A Mathematician’s Apology (1940)…

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Infinite random numbers, original 3d rendering background, technology and science concepts

Chaitin’s Discovery of a Way of Describing True Randomness

He found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data

In this week’s podcast, “The Chaitin Interview II: Defining Randomness,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on randomness. It’s a subject on which Chaitin has thought deeply since his teenage years (!), when he published a journal paper on the subject. How do we measure randomness? Chaitin begins by reflecting on his 1969 paper: https://episodes.castos.com/mindmatters/Mind-Matters-125-Gregory-Chaitin.mp3 This portion begins at 1:12 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: In particular, my paper looks at the size of computer programs in bits. More technically you ask, what is the size in bits of the smallest computer program you need to calculate a given digital object? That’s called the program…

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Stack of papers isolated on white background

Einstein’s Single Journal Paper Ended WWII

Does that mean that a thousand papers could multiply the effect? Think again.

It was Albert Einstein’s work on matter and energy, captured in e = mc2 that enabled the atomic bomb that ended World War II. Modern anonymous peer review today works well except that it is muddied with bias, incompetence, and ignorance. The review processes of Einstein’s day were better. A renowned expert’s approval was sufficient for a paper’s publication.1 The current system has only been in force since the end of World War II when pressure was applied to professors to write papers. The mantra “publish or perish” looks to have been coined soon after the war in 1951 by Marshall “The Medium is the Message” McLuhan.2 Earlier, professors were often discouraged from publishing. Karl Popper, one of the most…

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Photo by mrjn Photography

Why the Mind Cannot Just Emerge from the Brain

The mind cannot emerge from the brain if the two have no qualities in common

In his continuing discussion with Robert J. Marks, Michael Egnor argues that emergence of the mind from the brain is not possible because no properties of the mind have any overlap with the properties of brain. Thought and matter are not similar in any way. Matter has extension in space and mass; thoughts have no extension in space and no mass.

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