Mind Matters Natural and Artificial Intelligence News and Analysis

Tag__featured

Intelligent robot machine pointing finger 3D rendering
Intelligent robot machine pointing finger 3D rendering

New Book Massively Debunks Our “AI Overlords”: Ain’t Gonna Happen

AI researcher and tech entrepreneur Erik J. Larson expertly dissects the AI doomsday scenarios
AI researcher and tech entrepreneur Eric J. Larson has just published a book debunking the claims that AI is taking over. Read More ›
world-mental-health-day-concept-silhouette-of-human-standing-to-worship-god-in-meadow-autumn-sunset-background-stockpack-adobe-stock.jpg
World mental health day concept: Silhouette of human standing to worship God in meadow autumn sunset background

Here’s Why an Argument for God’s Existence Is Scientific

The form of reasoning and the type of evidence accepted is the same as with Newton’s theories or Darwin’s

Atheist evolutionary biologist Jerry Coyne is a fountain of nonsensical arguments against the existence of God. If a scholar wanted to write a review paper on the most ridiculous arguments against God’s existence so far in the 21st century, he would need look no further than Coyne’s blog. Coyne’s latest post denying God’s existence takes issue with an essay by Samuel Benson in the Deseret News in which Benson makes the case that invoking both a miracle and a scientific achievement in the development of the COVID vaccine is not necessarily contradictory. Benson points out that the natural world, properly understood, can only be explained using both science and theology. In support of his view, he quotes the president of…

pray-stockpack-adobe-stock.jpg
Pray.

Why Should We Believe Atheists on the Subject of God?

Logic and evidence both point to the existence of God, whatever atheists may think

Noting a recent article by philosopher Steve Meyer at The Federalist, neurosurgeon Michael Egnor comments, The public square is replete with books and articles written by atheist scientists claiming that cosmology or genetics or evolution properly understood disproves the existence of God. These atheist scientists profoundly misunderstand the implications of their science; they couldn’t be more wrong. As in his new book, The Return of the God Hypothesis, Dr. Meyer points to three particularly clear advances in modern science. Michael Egnor, “The God Hypothesis Versus Atheist Science Denial” at Evolution News and Science Today (April 5, 2021) The three arguments he addresses are ● The Big Bang: “The existence of a moment of beginning of our universe in an almost…

surprised-nerd-student-stockpack-adobe-stock.jpg
Surprised nerd student

Fermat’s Last Tango: Lively Musical For Nerds

The ghost of Fermat and other giants from the Aftermath Club help (frustrate?) a mathematician’s effort to prove Fermat’s famous Last Theorem

If you are a nerd, the musical Fermat’s Last Tango (2001) is hilarious. Mathematician Pierre de Fermat proposed his last theorem around 1637. He wrote a note in the margin of a copy of Arithmetica, a book written by a 3rd-century Alexandrian mathematician, Diophantus. Fermat’s short scribble claimed that he could prove that a specific Diophantine equation had no solution. But whatever Fermat was thinking died with him in 1665. A proof of Fermat’s last theorem eluded mathematicians over 300 years until Princeton’s Andrew Wiles proved it in 1995. Fermat’s Last Tango is a fantasy account of Wiles’s life while he was working on the proof. The play is a musical sprinkled with nerdy inside jokes. For example, part of…

connect the dots.jpg
Anti social man, business connection or social network concept, miniature people businessman standing on colorful pastel chalk line link and connect between multiple dot or tiers on blackboard

What Is the Essential Feature of Creative Intelligence?

Creative intelligence is easier to describe by what it is not than by what it is. But there is a clue in that very fact…

I’ve spent the past couple articles debunking artificial intelligence. It is just as artificial as its name suggests. It takes on the appearance of intelligence through speed but it lacks the fundamental ability to create a well-matched start and end. So a perceptive reader has returned with another good question: “What is creative intelligence?” The reader is right to ask. Yes, telling someone that the exquisite dessert is not celery and not cod liver oil does not help us understand what the dessert itself is. There is a mystery regarding the very nature of human intelligence. Like its antithesis, randomness, creative intelligence is easier to describe by what it is not than by what it is. But, we can try!…

big red numbers.jpg
random numbers

The “Jump” of Chaitin’s Omega Number

Gregory Chaitin explains, “For any infinity, there’s a bigger infinity, which is the infinity of all subsets of the previous step”

In last week’s podcast, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks asked mathematician Gregory Chaitin (best known for Chaitin’s unknowable number) if the unknowable number could prove (or disprove) Goldbach’s Conjecture that every even number can be expressed as the sum of two primes. This task is harder than it first appears because even numbers go on indefinitely. A proof that Christian Goldbach (1690–1764) was right or wrong must show that even numbers must be like that, no matter how big they are or how many of them there are. This time out, Dr. Marks and Dr. Chaitin discuss what we can know about Omega numbers — and where famous mathematicians are buried. This…

list-of-prime-numbers-below-100-vintage-type-writer-from-1920s-stockpack-adobe-stock.jpg
List of Prime Numbers below 100, Vintage type writer from 1920s

Could Chaitin’s Number Prove Goldbach’s Conjecture At Last?

Chaitin notes that the problem grows exponentially and the calculations get quite horrendous

In last week’s podcast, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks continued his conversation with mathematician Gregory Chaitin, best known for Chaitin’s unknowable number. One thing they discussed was the usefulness of philosophy, with Chaitin saying that if he had had to do practical work 60 years ago, there wouldn’t be practical research today based on the Omega number. But then they turned to the question of whether the unknowable number could prove Goldbach’s famous Conjecture: This portion begins at 17:17 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks (pictured): The poster problem for the Turing halting problem, is Goldbach’s Conjecture, which says that every even number can be…

Logical Diagrams
Making business plan. Businessperson drawing diagrams. Many graphs and hand drawn diagrams.

Why Impractical Things Like Philosophy Are Actually Quite Useful

Chaitin argues that the human spirit is capable of doing both practical things and impractical things which may have practical consequences later

In last week’s podcast,, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks continued his conversation with mathematician Gregory Chaitin, best known for Chaitin’s unknowable number. Last time, they looked at how Chaitin’s unknowable number relates to computer pioneer Alan Turing’s vexing halting problem in computer science. This time, they look at the way pure mathematics has a way of being highly practical: It creates a basis for new understanding, leading to technical breakthroughs: This portion begins at 09:50 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: There are always going to be a few of us who like to do practical things. That’s part of my personality too, but there’s also,…

xray of brain.jpg
X-ray.

Why a “Budding” Neuroscientist Is Skeptical of Brain Scans

After reading her perceptive essay about the problems in fMRI imaging in neuroscience, I’m sad that a gifted student has doubts about a career in the field

Kelsey Ichikawa has just published a superb essay about the pitfalls of functional magnetic resonance imaging (fMRI) of the brain. Ms. Ichikawa (pictured), who describes herself as a ”budding” neuroscientist who graduated last year from Harvard, discusses the snares into which misinterpretation can lead us. fMRI brain scanning is a relatively new technology in which researchers and clinicians use magnetic resonance images (MRI) of the brain to detect brain activity almost as it happens. The technique is widely used, both for clinical care of patients (neurosurgeons use it to map sensitive parts of the brain prior to surgery) and for research purposes. A major thrust of neuroscience research in the last couple of decades has been the use of fMRI…

businesswoman-protect-wooden-block-fall-to-planning-and-strategy-in-risk-to-business-alternative-and-prevent-investment-insurance-business-risk-control-concept-stockpack-adobe-stock.jpg
Businesswoman protect wooden block fall to planning and strategy in risk to business Alternative and prevent. Investment Insurance ,Business risk control concept,

Chaitin’s Number Talks To Turing’s Halting Problem

Why is Chaitin’s number considered unknowable even though the first few bits have been computed?

In last week’s podcast,, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks continued his conversation with mathematician Gregory Chaitin( best known for Chaitin’s unknowable number) on a variety of things mathematical. Last time, they looked at whether the unknowable number is a constant and how one enterprising team has succeeded in calculating at least the first 64 bits. This time, they look at the vexing halting problem in computer science, first identified by computer pioneer Alan Turing in 1936: https://episodes.castos.com/mindmatters/Mind-Matters-128-Gregory-Chaitin.mp3 This portion begins at 07:16 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: Well, here’s a question that I have. I know that the Omega or Chaitin’s number is based…

young-blind-man-with-white-cane-and-guide-dog-sitting-in-park-in-city-stockpack-adobe-stock.jpg
Young blind man with white cane and guide dog sitting in park in city.

The Mystery of Blindsight Helps Us Understand the Mind Better

How can a blind person demonstrate awareness of an object in his visual field — and yet not be conscious of it?

Blindsight is the remarkable ability of some blind people to sense objects that they cannot actually see. It occurs when the blindness is caused by damage to the main part of the brain that processes visual information (the striate cortex). But the eyes themselves are intact. The eyes continue to see (sensation) but nothing is receiving the messages (perception). Or so we would think, except for this: One of the most contentious discussions in philosophy of mind and neuroscience is the nature of perception as opposed to sensation. How can we perceive objects in our environment? On a deeper level, what do we mean by “perception”? In what ways does perception differ from sensation, if at all? The neurobiology of…

omega-the-letter-of-a-greek-alphabet-greek-numerals-mathematical-eight-hundred-number-concept-abstract-digital-wireframe-low-poly-mesh-raster-blue-neon-3d-illustration-triangle-line-dot-stockpack-adobe-stock.jpg
Omega, the letter of a Greek alphabet. Greek numerals, mathematical eight hundred number concept. Abstract, digital, wireframe, low poly mesh, Raster blue neon 3d illustration. Triangle, line dot

Is Chaitin’s Unknowable Number a Constant?

One mathematics team has succeeded in the first 64 bits of a Chaitin Omega number

In this week’s podcast, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks continued his conversation with mathematician Gregory Chaitin, best known for Chaitin’s unknowable number. In this segment, Dr. Marks and Dr. Chaitin discuss whether the unknowable number is really a number… or is it a constant? In earlier podcasts linked below, they have discussed a variety of topics ranging from gifted mathematicians of the past through how to understand creativity in a mathematical way—and more. https://episodes.castos.com/mindmatters/Mind-Matters-128-Gregory-Chaitin.mp3 This portion begins at 01:32 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks (pictured): I want to clear up something first of all. Stanford’s Thomas Cover and Joy Thomas wrote a book that…

evolving-abstract-visualization-stockpack-adobe-stock.jpg
Evolving Abstract Visualization

Can Mathematics Help Us Understand Consciousness?

Gregory Chaitin asks, what if the universe is information, not matter?

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…

teamwork-and-brainstorming-concept-with-businessmen-that-share-an-idea-with-a-lamp-concept-of-startup-stockpack-adobe-stock.jpg
Teamwork and brainstorming concept with businessmen that share an idea with a lamp. Concept of startup

Why Human Creativity Is Not Computable

There is a paradox involved with computers and human creativity, something like Gödel’s Incompleteness Theorems or the Smallest Uninteresting Number

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 a number of things, including whether computers can show creativity. Chaitin has thought a lot about that: https://episodes.castos.com/mindmatters/Mind-Matters-127-Gregory-Chaitin.mp3 This portion begins at 21:34 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: We’re talking, just in general, about the unknowable. Roger Penrose recently won a Nobel Prize for his work with Stephen Hawking on black hole theory. He also wrote a book called The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics (1989) and he followed it up with The Shadows of the Mind:…

metallic numbers.jpg
abstract metallic number background

The Paradox of the Smallest Uninteresting Number

Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on how he proved that the number that determines whether computer programs are elegant (in the sense of maximally efficient) is “unknowable.” As Dr. Chaitin explained in the segment published yesterday, any solution would be contradictory. Thus, his proof is a proof by contradiction. By way of illustrating the concept of proof by contradiction, Dr. Marks then offered his proof by contradiction that “all positive integers — numbers like 6 or 129, or 10 100 — are interesting.” This portion begins at 19:45 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: If [some…

abstract-virtual-binary-code-illustration-on-blurry-modern-office-building-background-big-data-and-coding-concept-multiexposure-stockpack-adobe-stock.jpg
Abstract virtual binary code illustration on blurry modern office building background. Big data and coding concept. Multiexposure

Why the Unknowable Number Exists But Is Uncomputable

Sensing that a computer program is “elegant” requires discernment. Proving mathematically that it is elegant is, Chaitin shows, impossible

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on his “unknowable number.” That’s the topic of this series, based on the fourth podcast. Last week, we tried getting to know the unknowable number. Today, let’s look at the question of how we know that the number is unknowable — instead of merely non-computable. Lots of things are non-computable but we do not expect that to be true of numbers. Let’s see what’s happening here, as Chaitin offers a walk through his proof that it really is unknowable: https://episodes.castos.com/mindmatters/Mind-Matters-127-Gregory-Chaitin.mp3 This portion begins at 09:43 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks:…

human-brain-on-technology-background-represent-artificial-intelligence-and-cyber-space-concept-stockpack-adobe-stock.jpg
human brain on technology background represent artificial intelligence and cyber space concept

Why “the Mind Is Just a Computation” Is a Fatally Flawed Idea

Much modern neuroscience can be characterized as a collection of weak metaphors about the mind and brain. This is one of them

The computational theory of mind (CTM) is the theory that the mind is a computation (calculation) done by the brain. That is, the mind works by rule-based manipulation of symbols, which is what a computer does — computation. Thus our mental states are computational states. Several prominent philosophers have held this view, notably Hilary Putnam (1926–2016) and Jerry Fodor (1935–2017) , and more recently Matthias Scheutz, among several others. I believe that the computational model of the mind is fatally flawed. Here are some reasons: The most obvious reason is that all mental states have meaning — that is, they are intentional. Intentionality means that our thoughts are about something — there is always an object to which a thought…

matrix-made-up-of-math-formulas-and-mathematical-equations-illustration-rendering-stockpack-adobe-stock.jpg
matrix made up of math formulas and mathematical equations - illustration rendering

Getting To Know the Unknowable Number (More or Less)

Only an infinite mind could calculate each bit

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on his discovery of the “unknowable number.” How can a number that is unknowable exist? Some numbers go on indefinitely (.999999999… ) but we can describe them accurately even if they don’t seem to come to an end anywhere. Some numbers, like pi (π), are irrational — pi goes on and on but its digits form no pattern. However, what does it mean to say that a number exists if it is unknowable? How do we even know it exists? That’s the topic of this series, based on the fourth podcast between Dr. Marks and Gregory Chaitin. Note:…

afro-american-boy-hiding-in-ruined-building-escaped-from-dysfunctional-family-stockpack-adobe-stock.jpg
Afro-american boy hiding in ruined building, escaped from dysfunctional family

Woke Medicine Is Very Bad for Everyone’s Health

The issues raised by Critical Race Theory are real but I believe that the diagnosis is deeply flawed

Critical Race Theory and claims about structural racism in American society are infiltrating medical care and education. There is a major effort in medical education today to indoctrinate students and resident physicians into Critical Theory. This is, in my view, a deeply misguided approach.The issues raised by Critical Race Theory are real but I believe that the diagnosis is deeply flawed. The question we face is: how can we protect medical education and practice from this latest iteration of Marxism, and at the same time work to improve deficiencies in education and medical care that Critical Race Theorists correctly point out? It is undeniable that there are structural problems in medicine. Many of these problems impede good medical care, especially…

castaway-in-bureaucracy-stockpack-adobe-stock.jpg
Castaway in bureaucracy

Gregory Chaitin on How Bureaucracy Chokes Science Today

He complains, They’re managing to make it impossible for anybody to do any real research. You have to say in advance what you’re going to accomplish. You have to have milestones, reports

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 how Stephen Wolfram’s software has taken much of the drudgery out of math. At the same time, in Chaitin’s view, a threat looms: A new, more bureaucratic, mindset threatens to take the creativity out of science, technology, and math: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 19:45 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: I was sitting down tallying, I think, the intellectual giants that have introduced new mathematical ideas, brand new. I was thinking of people like Claude Shannon, Lotfi Zadeh, yourself… I don’t know if we…