^{
Type
post
AuthorRobert J. Marks
Date
July 6, 2023
Categorized
Mathematics
Tagged
Elements by Euclid, Euclidean geometry, Gottfried Wilhelm Leibniz, Isaac Newton, Mathematics, Physics, Robert J. Marks, Royal Society
}

_{Some think math is invented. Evidence, though, points towards discovery.}_{
Robert J. Marks
July 6, 2023
5
Mathematics
}

Some think math is invented. (See the article by Peter Biles.) Evidence, though, points towards discovery. Simultaneous mathematical discovery supports this viewpoint. Many mathematical breakthroughs are sometimes independently reported by two or more mathematicians at roughly the same time. The most famous is the simultaneous discovery of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Newton was secretive about his discovery and shared his results with only a few members of the Royal Society. When Leibnitz published his discovery of the calculus, Newton charged him with plagiarism. Today, historians agree that the discoveries were independent of each other. Here are some other lesser-known examples of simultaneous discovery. The Papoulis-Gerchberg Algorithm (PGA). The PGA is an ingenious method for recovering lost Read More ›

^{
Type
post
AuthorMichael Egnor
Date
December 29, 2022
Categorized
Mathematics, Philosophy, Religion
Tagged
Augustine of Hippo, Augustinian proof (of God), Featured, Gottfried Wilhelm Leibniz, Jerry Coyne on God, Platonic forms, Realism (in philosophy), Scholastic realism
}

_{Atheist biologist Jerry Coyne finds that difficult to believe but it’s really a matter of logic}_{
Michael Egnor
December 29, 2022
6
Mathematics, Philosophy, Religion
}

This story was #3 in 2022 at Mind Matters News in terms of reader numbers. As we approach the New Year, we are rerunning the top ten stories of 2022, based on reader interest. In “Mathematics can prove the existence of God” (July 31, 2022), neurosurgeon Michael Egnor offers this thought: Because mathematics can show infinity, eternity, and omnipotence, it can only have proceeded from a mind with those characteristics. That’s God. In a recent post, atheist biologist Jerry Coyne takes issue with a commenter who asserts that God exists in the same sort of way mathematics exists. Here’s the analogy the commenter offered, as quoted by Coyne: Think of numbers for example, or mathematical equations, these are metaphysical things, Read More ›

^{
Type
post
AuthorMichael Egnor
Date
July 31, 2022
Categorized
Mathematics, Philosophy, Religion
Tagged
Augustine of Hippo, Augustinian proof (of God), Featured, Gottfried Wilhelm Leibniz, Jerry Coyne on God, Platonic forms, Realism (in philosophy), Scholastic realism
}

_{Atheist biologist Jerry Coyne finds that difficult to believe but it’s really a matter of logic}_{
Michael Egnor
July 31, 2022
7
Mathematics, Philosophy, Religion
}

In a recent post, atheist biologist Jerry Coyne takes issue with a commenter who asserts that God exists in the same sort of way mathematics exists. Here’s the analogy the commenter offered, as quoted by Coyne: Think of numbers for example, or mathematical equations, these are metaphysical things, that have not been created, however were discovered. The number 7 was the number 7 before anything at all came into existence. This is also true concerning the nature of God. He is not some material being that has come into existence, he is like a number that has always existed, (and by the way nobody will deny this logic with the number, however when someone mentions God a problem occurs). Jerry Read More ›

^{
Type
podcast
AuthorRobert J. Marks
Date
December 30, 2021
Tagged
A Mathematician's Apology, Active Information in Metabiology, Alan Turing, Andrew Wiles, Automacoin, Bitcoim, But Bang. Ls nascita della filosofia digitale, Carl Friedrich Gauss, Chris Calude, Claude Shannon, Collatz Conjecture, Consciousness and information classical quantum or algorithmic, Dangerous Knowledge, David J. Chalmers, Elements of Information Theory, Elon Musk, Fermat's Last Tango, Fermat's Last Tango (musical), G.H Hardy, George Cantor, Geroge Gilder, Goldbach Conjecture, Gottfried Wilhelm Leibniz, Gregory Chaitin, Guilio Tononi, Hector Zenil, Jack Schwartz, Karl Popper, Kurt Gödel, Legendre's Conjecture, Leonard Euler, Lofti Zadeh, Marvin Minsky, Mathematica, Meta Math The quest for the Omega, Neuralink, ON the length of programs for computing finite binary sequences, Paul Erdős, Proving Darwin Making biology mathematical, Ray Solomonoff, Robert J. Marks, Roger Penrose, Selmer Bringsjord, Srinivasa Ramanujan, Stephen Hawking, Stephen Wolfram, The Conscious Mind, The Emperor's New Mind, The Unknowable, Twin Prime Conjecture, Unravelling Complexity The Life and Works of Gregory Chaitin, William Sealy Gosset, WolframAlpha
}

In the 1960s, mathematician and computer scientist Gregory Chaitin published a landmark paper in the field of algorithmic information theory in the Journal of the ACM – and he was only a teenager. Since then he’s explored mathematics, computer science, and even gotten a mathematical constant named after him. Robert J. Marks leads the discussion with Professor Gregory Chaitin on Read More ›

^{
Type
post
AuthorNews
Date
September 23, 2021
Categorized
Philosophy, Science
Tagged
Augustine, Augustinian proof (of God), Featured, Fifth Way (Aquinas), First Way (Aquinas), Five Ways (Aquinas), Fourth Way (Aquinas), Gottfried Wilhelm Leibniz, Matt Dillahunty, Michael Egnor, Moral law (as proof of God), Mystic proof (of God), Neoplatonic proof (of God), Plato, Plotinus, Second Way (Aquinas), Theology Unleashed, Third Way (Aquinas)
}

_{First, how did a medic, formerly an atheist, who cuts open people’s brains for a living, come to be sure there is irrefutable proof for God?}_{
News
September 23, 2021
16
Philosophy, Science
}

“Does God exist?” On September 17, in a dramatic debate, Christian neurosurgeon Michael Egnor and atheist broadcaster Matt Dillahunty squared off on the question at Theology Unleashed. The debate hosts are Arjuna Das for Theology Unleashed and Nathan from Digital Gnosis as the moderator. A partial transcript and notes follow. Egnor has been a guest at Theology Unleashed, before, debating materialist philosopher David Papineau. The ten proofs of God that he presents as his opening argument below are not drawn from sacred texts but from philosophical reasoning: Michael Egnor: There are, broadly speaking, two different kinds of theology. There’s natural theology and there’s revealed theology. Revealed theology is the use of scripture, personal experiences, or relationships to God. And that’s Read More ›

^{
Type
post
AuthorRobert J. Marks and Samuel Haug
Date
June 7, 2021
Categorized
Mathematics, Religion
Tagged
Anselm of Canterbury, Axioms, Definitions, Descartees, God's existence, Gottfried Wilhelm Leibniz, Kurt Gödel, Kurt Gödel (belief in God), ontological proof, Theorems
}

_{Here is a line-by-line explanation of his proof}_{
Robert J. Marks and Samuel Haug
June 7, 2021
8
Mathematics, Religion
}

Kurt Gödel, an intellectual giant of the 20th century, offered a mathematical proof that God exists. Those who suffer from math anxiety admire what the theorem (shown below) claims to do, but have absolutely no idea what it means. Our goal is to explain, in English, what Gödel’s existence of God proof says. Gödel’s proof shows the existence of God is a necessary truth. The idea behind the truth is not new and dates back to Saint Anselm of Canterbury (1033-1109). Great scientists and philosophers, including Descartes and Leibniz, have reconsidered and refined Anselm’s argument. Gödel appears to be the first, however, to present the argument using mathematical logic. Lexicography In any development of a mathematical theory, there are foundational axioms Read More ›

^{
Type
post
AuthorNews
Date
April 1, 2021
Categorized
Mathematics, Philosophy of Mind
Tagged
Bit Bang (book), Conscious Mind (book), Consciousness, David Chalmers, Featured, Gottfried Wilhelm Leibniz, Gregory Chaitin, hard problem of consciousness, Information (types), Materialism, Monad, Panpsychism, Panpsychism (vs. materialism), Robert J. Marks, Universe (as information not matter), Universe (mathematics as origin)
}

_{Gregory Chaitin asks, what if the universe is information, not matter? }_{
News
April 1, 2021
12
Mathematics, Philosophy of Mind
}

In last week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin, best known for Chaitin’s Unknowable Number, on, among other things, consciousness. What can mathematics contribute to the discussion. Also, what does Chaitin think about panpsychism (everything is conscious”)? The discussion began with reference to David Chalmers’s 1996 book, The Conscious Mind: In Search of a Fundamental Theory, in which Chalmers coined the term “Hard Problem of Consciousness.” The term acknowledged what everyone knew, that human consciousness is a very difficult problem to understand, especially from a materialist perspective.Are there other approaches? Chaitin offers a look at the challenge panpsychism presents to materialism: https://episodes.castos.com/mindmatters/Mind-Matters-127-Gregory-Chaitin.mp3 This portion begins at 28:25 Read More ›

^{
Type
podcast
AuthorRobert J. Marks
Date
April 1, 2021
Tagged
Automacoin, bitcoin, Chaitin's Constant, Chaitin's number, Chris Calude, Collatz Conjecture, Elon Musk, G.H. Hardy, Georg Cantor, George Gilder, Goldbach Conjecture, Gottfried Wilhelm Leibniz, Gregory Chaitin, Halting Probability Omega, Hector Zenil, Legendre's Conjecture, Marvin Minsky, Omega, Philosophy, Ray Solomonoff, Stephen Wolfram, Twin Prime Conjecture
}

Listen in as Robert J. Marks picks the mind of Professor Gregory Chaitin about Chaitin’s number – a number that has been called “mystical and magical”. How does this number work? Why do some people call it “Chaitin’s constant”? What is the usefulness of philosophizing in mathematics? Show Notes 00:27 | Introducing Gregory Chaitin and Chaitin’s number 01:32 | Chaitin’s Read More ›

^{
Type
podcast
AuthorRobert J. Marks
Date
March 25, 2021
Tagged
Algorithmic Information Theory, Chaitin's Constant, Christof Koch, computable, Consciousness, Creativity, David Chalmers, Giulio Tononi, Gottfried Wilhelm Leibniz, Gregory Chaitin, Halting Probability Omega, halting problem, Jack Schwartz, knowability, Lovelace test, non-computable, Panpsychism, Paul Erdős, Roger Penrose, Selmer Bringsjord, Stephen Hawking, unknowability
}

What does it mean for something to be unknowable? Is creativity non-computable? Do all things have a level of consciousness? Jump into today’s podcast, where Robert J. Marks continues his discussion with Gregory Chaitin about mathematical theory and philosophy. Show Notes 00:23 | Introducing Gregory Chaitin 00:40 | What is unknowability? 06:07 | Does non-computable mean unknowable? 09:43 | A Read More ›

^{
Type
post
AuthorNews
Date
March 22, 2021
Categorized
Artificial Intelligence, Mathematics, Programming
Tagged
Creativity (and computers), Elon Musk, Featured, Gottfried Wilhelm Leibniz, Gregory Chaitin, Mathematica (math program), Robert J. Marks, Software (extendability), Stephen Wolfram, Unravelling Complexity (book), Wolfram Alpha (math program)
}

_{Wolfram has not made computers creative but he certainly took a lot of the drudgery out of the profession }_{
News
March 22, 2021
11
Artificial Intelligence, Mathematics, Programming
}

In last week’s 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 why math or engineering geniuses (Elon Musk came to mind, of course) can’t just follow the rules. This week, we look at Stephen Wolfram’s new program that checks your hard math. What can — and can’t — it do for mathematicians? https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 13:22 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: Now, there is what I regard as a piece of AI, so it might be interesting to talk about it. My friend Stephen Wolfram (pictured), the system he’s created, Read More ›

^{
Type
post
AuthorNews
Date
March 12, 2021
Categorized
Mathematics, Programming
Tagged
Algorithmic Information Theory, David Hilbert, Discours de Metaphysique (book), Featured, Gottfried Wilhelm Leibniz, Gregory Chaitin, Hermann Weyl, Incompleteness (information theory), Karl Popper, Logic of Scientific Discovery (book), Randomness, Randomness (definitions), Robert J. Marks
}

_{He found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data}_{
News
March 12, 2021
12
Mathematics, Programming
}

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 Read More ›

^{
Type
podcast
AuthorRobert J. Marks
Date
September 24, 2020
Tagged
Abstract thought, Ada Lovelace, Alan Turing, Algorithm-of-the-Gaps, AlphaGo, Charles Babbage, Claude Shannon, Cognition, computer, Computers, Consciousness, Creativity, David Gelernter, disjunctive syllogism, Eugene Goostman, Gottfried Wilhelm Leibniz, Kurt Gödel, Language, Lovelace test, Marcel Proust, Mathematics, Natural Language Generation, Natural Language Processing, non-algorithmic, novels, ontological argument, ontological proof, Ray Kurzweil, Saint Anselm, Selmer Bringsjord, Singularity, Sports, Theorems, Turing Test
}

The Turing test, developed by Alan Turing in 1950, is a test of a machine’s ability to exhibit intelligent behaviour indistinguishable from a human. Many think that Turing’s proposal for intelligence, especially creativity, has been proven inadequate. Is the Lovelace test a better alternative? What are the capabilities and limitations of AI? Robert J. Marks and Dr. Selmer Bringsjord discuss Read More ›

^{
Type
post
AuthorNews
Date
May 10, 2020
Categorized
Artificial Intelligence, Mathematics, Religion
Tagged
___longform, Featured, Formal logic, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, Rene Descartes, Robert J. Marks, Saint Anselm, Selmer Bringsjord
}

_{A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God }_{
News
May 10, 2020
11
Artificial Intelligence, Mathematics, Religion
}

In an unsanitized, politically incorrect (but factual) history, Selmer Bringsjord talks about how the tormented genius Kurt Gödel took up a quest that dated back a thousand years to prove the existence of God by formal logic. His original version didn’t quite work but his editor’s version passed an important logic test.

^{
Type
podcast
AuthorRobert J. Marks
Date
May 7, 2020
Tagged
disjunctive syllogism, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, ontological argument, ontological proof, Saint Anselm, Selmer Bringsjord, Theorems
}

Kurt Gödel toppled a tall tower of mathematical reasoning with publication of his work showing no formal system of math could be both complete and consistent. He also gave a mathematical proof of the existence of God. Is Gödel’s proof valid? Robert J. Marks and Dr. Selmer Bringsjord discuss mathematics, Kurt Gödel, and the ontological argument. Show Notes 01:05 | Read More ›