CategoryMathematics
Gregory Chaitin’s New Books About Math Make It Actual Fun
He is a favorite podcast guest of ours and, it turns out, a fan of Mind Matters
Does Mathematics Belong to an Eternal Realm?
Let’s Dispose of Exploding Pie Charts
Pie charts are seldom a good idea. Here's why.
Why Do People Who Want to Dumb Down Education Pick Math?
When right and wrong answers are clear, rewarding the wrong answer is an easier victory for them to celebrate.
Can AI Open Doors to Ancient Human History?
It’s not a time machine, to be sure, but it may help bring the past to life by motoring through dull, time-consuming translation tasks
From Physics to Faith?
A podcast episode looking at how physics points to more than meets the eyeDo 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 ›
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?
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
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 ›
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 ›
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 ›
Math, Mind, and Matter
The surprising similarities between mathematics and literatureLast 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 ›
An Illusion of Emergence, Part 2
A figure can tell a story but, intentionally or unintentionally, the story that is told may be fictionI 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 ›
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 mathematicsLast 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 ›
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 worldLast 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 ›
Mathematics Can Prove the Existence of God
Atheist biologist Jerry Coyne finds that difficult to believe but it’s really a matter of logicThis 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 ›
Hard Problem of Consciousness Solved?: A 4th Spatial Dimension?
Philosopher Peter Sjöstedt-Hughes argues that higher spatial dimensions might hold the keyThis 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 ›
Our Physical Universe Is Based on Patterns in Mathematics
In that sense, the underlying basis of our universe is immaterial, not materialSunny 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 ›
Celebrating My 2 Billionth Birth-Second: What Big Numbers Mean
Let’s see if we can give a clearer, sharper personality to these big numbersI 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 ›