Mind Matters Natural and Artificial Intelligence News and Analysis


Science and research of the universe, spiral galaxy and physical formulas, concept of knowledge and education

From Physics to Faith?

A podcast episode looking at how physics points to more than meets the eye

Do you recognize the number 1/137.035999206? It might seem arbitrary, but if the fine-structure constant were any higher or lower than it is, you might not exist! On this episode of ID the Future, host Brian Miller kicks off an engaging conversation with Rabbi Elie Feder and Rabbi Aaron Zimmer, hosts of the Physics to God podcast. Feder has a PhD in mathematics and has published articles on graph theory. Zimmer has training in physics, and has studied mathematics, philosophy, and psychology. Both men also have extensive rabbinical training. Through their podcast, Feder and Zimmer invite both secular and religious listeners on a journey through modern physics as they offer rational arguments for an intelligent cause of the universe. In Part 1 of Read More ›

aerial perspective of a crop circle with mathematical symbols

Does Deep Social Change Underlie the War on Math?

Why is the universal language of science sinking under the weight of claims about trauma and privilege?

Citing a recent article in the journal Urban Education aimed at “healing practices through the use of Social Justice Mathematics.” education watchdog Joanne Jacobs notes a trend, aimed at California schools, toward turning math class into a soap opera: … Another problem read: “I have US$100. I owe 1/4 of my money to my mom, 2/5 to my grandmother, and 4/10 to my brother. Do I have enough money to pay everyone back? How much money should each person get?” After students calculate that this woman owes more money than she has, they watch a video of a single mom struggling to make ends meet. They are then asked questions like, “What are some feelings that you are having when Read More ›

An abstract computer generated fractal design. A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales.

The War on Math Becomes a Fight Over Textbooks

Florida, for example, rejected 54 math textbooks of 132 submitted by publishers on account of political content

About a year and a half ago, I wrote a piece about the war on math, basically an effort to entrench the idea that there is no such thing as reality apart from politics. A slogan for various wars on math has been 2 + 2 = 5. That proposition originated in the totalitarian Soviet Union. It found its way into 1984, in which George Orwell (1903–1950) repudiated totalitarianism, and resurfaced in recent years in the current American education elite. One tactic used that is more subtle than outright messing with the number system is the inclusion of political issues in math problems. Current affairs writer Steven Tucker explains how it works: If you were an author of school textbooks Read More ›

fire infinity

Of Infinity and Beyond

What are the problems and solutions with infinity in mathematics?

The concept of infinity has plagued a great many proofs, both formal and informal. I think that there are two foundational problems at play in most people’s thinking about infinity that causes issues. The first problem people have with infinity is that they treat it as if it were a single value. Because infinity is bigger than all possible natural numbers, people assume that it is bigger than any number, and therefore there is nothing beyond infinity. Therefore, people have the concept that if I have two infinities, then I still have the same number.  They believe that 2 * infinity = infinity. However, using that logic can quickly lead to contradictions. This problem is exacerbated by much mathematical notation. People often will Read More ›

Silhouette of a man, with thoughts in the form of physico-mathematical formulas. The concept of scientific and education topics.

Is Mathematics Discovered or Invented?

Some think math is invented. Evidence, though, points towards discovery.

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 ›

Milky Way over Cordillera Huayhuash

Is Mathematics an Illusion? Lawrence Krauss and Cormac McCarthy Discuss

McCarthy asked, "Would mathematics be here if we weren't?"

In December, physicist and author Lawrence Krauss interviewed the late American novelist Cormac McCarthy, who died on June 13th at the age of 89 in Santa Fe, N.M. McCarthy is famous for his remarkable fictional works like The Road and Blood Meridian, but he was also deeply fascinated with mathematics and science. Apparently, he enjoyed reading science more than he did fiction! He moved to Santa Fe from El Paso to be closer to the Santa Fe Institute, a science think tank where McCarthy would spend time speaking with various physicists, scientists, and mathematicians. His latest two novels, The Passenger and Stella Maris, are about a brother and sister who are both brilliant mathematicians. Towards the beginning of the interview, Read More ›

3D rendering of abstract blocks of mathematical formulas located in the virtual space

Math, Mind, and Matter

The surprising similarities between mathematics and literature

Last October, legendary American author Cormac McCarthy, who wrote Blood Meridian and The Road, released a pair of interconnected novels called The Passenger and Stella Maris. The books arrived after a sixteen-year silence from the desk of McCarthy. The books deal, per usual, with themes of mortality, fate, and the “God question,” and are predictably lyrical, vivid, and dark. But McCarthy plows new ground in these sibling novels. The books are about mathematicians. It’s fiction about math.  The story revolves around the complex relationship between a brother and sister: Bobby and Alicia Western. Bobby is a deep-sea diver with some history in the field of mathematics, while Alicia is a once-in-a-generation math prodigy.  Not Estranged, but Akin After reading these books myself, I marveled at McCarthy’s ability to Read More ›

close up of calculation table, printed in an old book

An Illusion of Emergence, Part 2

A figure can tell a story but, intentionally or unintentionally, the story that is told may be fiction

I recently wrote about how graphs that use logarithms on the horizontal axis can create a misleading impression of the relationship between two variables. The specific example I used was the claim made in a recent paper (with 16 coauthors from Google, Stanford, UNC Chapel Hill, and DeepMind) that scaling up the number of parameters in large language models (LLMs) like ChatGPT can cause “emergence,” which they define as qualitative changes in abilities that are not present in smaller-scale models but are present in large-scale models; thus they cannot be predicted by simply extrapolating the performance improvements on smaller-scale models. They present several graphs similar to this one that seem to show emergence: However, their graphs have the logarithms of Read More ›

3D illustration of Escher's inspired stairs

How Surreal Artist MC Escher Influenced Physicist Roger Penrose

Escher’s mathematical art was all the more remarkable because he had no formal training in mathematics

Last month, Robert Lawrence Kuhn interviewed eminent British mathematical physicist Sir Roger Penrose on a number of topics, including the influence of surrealist artist M. C. Escher (December 9, 2022/32:00 min). Here is a transcribed selection from the second part of the discussion in Part 1 above*, beginning around the 12-minute mark, with some notes: Robert Lawrence Kuhn: We talked about the impossible Penrose triangle which really opens up another area of your life in terms of visual representations of remarkable things. Penrose tiling really new ways of thing of seeing visual representation of fiery fundamental geometric and algebraic transformations and things. But what I wanted to ask you is, as youdeveloped that you had this interaction with the artist Read More ›

Lost and confused man walks puzzled on a penrose triangle. Perplexed person looks disoriented ahead, don't know which way to choose. Surreal and conceptual scene, mental maze, optical illusion

Nobelist Roger Penrose Talks About His Impossible Triangle

At Closer to Truth, the mathematical physicist explains to Robert Lawrence Kuhn how he understands the relationship between mathematics, the mind, and the physical world

Last month, Robert Lawrence Kuhn interviewed eminent British mathematical physicist Sir Roger Penrose on the relationship between mathematics, the mind, and the physical universe (December 9, 2022/32:00 min). Penrose likes to illustrate the relationship between the three with an “impossible” triangle (see below). Here are a couple of transcribed selections from the first part of the discussion in Part 1*, concerning the Penrose Triangle, with some notes: Robert Lawrence Kuhn: Let’s start with your grand metaphysical framework, your three worlds — three mysteries: the physical world, the mental world, the platonic or mathematical world — each connected to the other two in your famous diagram of an equilateral triangle. What’s the origin of this vision of yours of foundational reality? Read More ›

Elements of Infinity

Mathematics Can Prove the Existence of God

Atheist biologist Jerry Coyne finds that difficult to believe but it’s really a matter of logic

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 ›

Blue glowing 4 dimensional object in space abstract fractal background

Hard Problem of Consciousness Solved?: A 4th Spatial Dimension?

Philosopher Peter Sjöstedt-Hughes argues that higher spatial dimensions might hold the key

This story was #4 in 2022 at Mind Matters News in terms of reader numbers. As we approach the New Year, we are rerunning the top ten Mind Matters News stories of 2022, based on reader interest. In “Hard problem of consciousness solved?: A 4th spatial dimension?” (April 20, 2022), our News division looks at philosopher Peter Sjöstedt-Hughes’ view that higher spatial dimensions might hold the key to the uniqueness of human consciousness. In an abridged chapter of his recent book Modes of Sentience (2021), University of Exeter philosopher of mind, Peter Sjöstedt-Hughes, argues that higher spatial dimensions might hold the key to the hard problem of consciousness:” He is a fan of the More–Broad–Smithies theory of consciousness: The word tesseract was Read More ›

spiral aloe vera
Spiral aloe vera with water drops, closeup

Our Physical Universe Is Based on Patterns in Mathematics

In that sense, the underlying basis of our universe is immaterial, not material

Sunny Labh, science writer and “budding astrophysicist,” reminds us that, in our universe, everything from snowflakes to black holes can be described by mathematics: To have a basic understanding of how accurate and loyal this universe is to math, we could visualize our solar system. Back in 1905, scientists discovered that the orbit of Uranus and Neptune was not following Newton’s Gravitational laws, and using mathematical expressions, predicted that there must be some other heavenly body that was influencing their orbit. In 1930 Clyde Tombaugh used the method of comparative plating of astronomical photographs also known as the blink comparator technique. The calculations were made precise to a point where we could even tell where to point our telescope in Read More ›

Congress Spending Your Money.

Celebrating My 2 Billionth Birth-Second: What Big Numbers Mean

Let’s see if we can give a clearer, sharper personality to these big numbers

I have lived for over two billion seconds. In 2013, I celebrated my 2 billionth birth-second. The party did not last long. Today US spending and deficits are going through the roof. References to billions and trillions of dollars of spending and deficit are everywhere. The late US Senator Everett Dirksen of Illinois is purported to have said “A billion here, a billion there; pretty soon you’re talking about real money.” He said this in the middle of the last century. Today we can replace “billion” in Dirksen’s quote with “trillion.” Let’s see if we can give a clearer, sharper personality to these big numbers. A trillion is a thousand times bigger than a billion. If we scale a trillion Read More ›

A sad young female student sitting at the table, studying.

Can We Rewire Our Brains To Be More Fluent in Math?

An artsy who flunked math — but later became an electrical engineering prof — says yes

Barbara Oakley, a self-confessed math phobe, nonetheless became a professor of electrical engineering at Oakland University in Michigan, as well as an author. In 2014, she offered some secrets: at Nautilus. Be warned: Her secrets are not “Forget homework!” or “Math is a tool of oppression!” No, this is quite a different message. It’s about neuroplasticity, the ways our brains adapt to our circumstances, to give us the tools we need. But to adapt, the brain needs practice: Japan has become seen as a much-admired and emulated exemplar of these active, “understanding-centered” teaching methods. But what’s often missing from the discussion is the rest of the story: Japan is also home of the Kumon method of teaching mathematics, which emphasizes Read More ›

Stock Trader Sleeping At Multiple Computer's Desk

More Hard Math Does Not Necessarily Mean More Useful Solutions

It is sometimes tempting to overemphasize the math and underemphasize the relevance

Math is said to be the language of science in that most (but definitely not all) scientific models of the world involve mathematical equations. The Pythagorean theorem, the normal distribution, Einstein’s energy-mass equivalence, Newton’s second law of motion, Newton’s universal law of gravitation, Planck’s equation. How could any of these remarkable models be expressed without math? Unfortunately, it is sometimes tempting to overemphasize the math and underemphasize the relevance. The brilliance of the models listed above lies not in mathematical pyrotechnics but, if anything, in their breath-taking simplicity. Useful models help us understand the world and make reliable predictions. Math for the sake of math does neither. Examples of mindless math are legion. I will give three very different examples. Read More ›

Funny boy and his dog looking at piles of coins

Researchers Are Zeroing In on Animal Number Sense

We’re beginning to find out more about how animals that don’t really “think” much can keep track of numbers, when needed

University College cognitive psychology prof Brian Butterworth, author of Can fish count? (Basic Books, 2022), talks about animal number sense in a recent article in Psyche: He offers many examples of animals counting single digit numbers but then helpfully addresses the question of how they do it. We are talking here about a variety of very different types of neurological equipment — insects vs. amphibians, for example. Neuroscientists are beginning to pinpoint specific brain functions associated with counting for specific tasks: Female túngara frogs benefit by mating with the male that can produce six croaks in one breath, over the male that can manage only five, because this is an indicator of respiratory fitness. Naturally, the male will try to Read More ›

solving algebra equation on whiteboard in classroom

The War on Math Is Becoming an Entrenched Ground War

If math skills are rooted in white supremacy, as alleged, one current solution is tests that don’t require math skills

When we first started talking about the war on math, many readers may have thought we were joking. No. The war on 2 + 2 = 4 is getting some pushback but it continues. The basic idea is that the rules of math are rooted in white supremacy. Last December, the question was mooted at USA Today, “Is math racist?” The context was proposed changes to math education: After Ebri switched to emphasizing real-world problems and collaboration, her students, most of whom are Black, improved their scores on Florida’s math exam in 2020-21 – even with 1 in 3 learning from home. But other, bolder recommendations to make math more inclusive are blowing up the world of mathematics education. Schools Read More ›

Groups of people
Groups of people are connected by lines. Interdependence correlation in workflow. Interacting and joining forces with other teams. Interact to complete tasks. Formation of a more complex community.

Step Away From Stepwise Regression (and Other Data Mining)

Stepwise regression, which is making a comeback, is just another form of HARKing — Hypothesizing After the Results are Known

There is a strong correlation between the number of lawyers in Nevada and the number of people who died after tripping over their own two feet. There are similarly impressive correlations between U.S. crude oil imports and the per capita consumption of chicken — and the number of letters in the winning word in the Scripps National Spelling Bee and the number if people killed by venomous spiders. If you find these amusing (as I do), there are many more at the website Spurious Correlations. These silly statistical relationships are intended to demonstrate that correlation is not causation. But no matter how often or how loudly statisticians shout that warning, many people do not hear it. When there is a Read More ›

abstract ornate illustration

The Vector Algebra Wars: A Word in Defense of Clifford Algebra

A well-recognized, deep problem with using complex numbers as vectors is that they only really work with two dimensions

Vector algebra is the manipulation of directional quantities. Vector algebra is extremely important in physics because so many of the quantities involved are directional. If two cars hit each other at an angle, the resulting direction of the cars is based not only on the speed they were traveling, but also on the specific angle they were moving at. Even if you’ve never formally taken a course in vector algebra, you probably have some experience with the easiest form of vector algebra — complex numbers (i.e., numbers that include the imaginary number i). In a complex number, you no longer have a number line, but, instead, you have a number plane. The image below shows the relationship between the real Read More ›