Mind Matters Natural and Artificial Intelligence News and Analysis


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The Universe and its Mathematical Structure

Do humans project mathematics upon nature or vice versa?

This past June, we published an article featuring a conversation between physicist Lawrence Krauss and novelist Cormac McCarthy, where they discussed whether mathematics was “discovered or invented.” Robert J. Marks went on to write his own thoughts on the question shortly thereafter. If you’re further interested in mathematics and whether there is an actual correspondence between math and the natural world, consider watching new podcast episode featuring Dr. Melissa Cain Travis. Do humans project mathematical order onto nature? Or was it there all along? On a new episode of ID the Future, I conclude a three-part conversation with Dr. Melissa Cain Travis about her recent book Thinking God’s Thoughts: Johannes Kepler and the Miracle of Cosmic Comprehensibility.  In Part 3, we look Read More ›

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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 ›

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Science as Insight vs. Science as Power

What are the core purposes of science and math? Evaluating the idea of "knowledge as power" in the computer age

Should machines replace mathematicians? This phrase is the headline of a new post by science writer John Horgan, who comments on the current state of mathematics and the growing potential of AI and computers to do all the “heavy lifting” of the mathematical enterprise. Horgan notes that mathematicians were the ones to develop computers in the first place, but now, with the advent of advanced computing and artificial intelligence, the role of human-driven mathematics is getting vague. However, maybe math is more about input and output but a “way of being human.” For Horgan, data and computation don’t get to the heart of scientific and mathematical endeavors. It needs to mean something more than an impersonal process geared towards calculable Read More ›

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Using Data Like a Drunk Uses a Lamppost

Startup companies can be tempted to use statistics for support instead of real illumination

Karl Pearson, the great English mathematician and statistician, wrote, “Statistics is the grammar of science.” At its finest, it is. Statistical data and methods are the backbone of the scientific method that underlies the astonishing scientific advances that humans have made. Unfortunately, statistics can also be used to provide misleading support for false claims. The examples are numerous and so are the laments: There are three kinds of lies: lies, damned lies, and statistics.—Benjamin Disraeli There are two kinds of statistics, the kind you look up and the kind you make up.—Rex Stout Definition of Statistics: The science of producing unreliable facts from reliable figures. —Evan Esar If you torture the data long enough, they will confess.—Ronald Coase We couldn’t 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 ›

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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 ›

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Iterations of Immortality

If it is beauty that governs the mathematician’s soul, it is truth and certainty that remind him of his duty

by David Berlinski Editor’s note: We are delighted to welcome Science After Babel, the latest book from mathematician and philosopher David Berlinski. This article is adapted from Chapter 7.  The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible, but it was the algorithm that made possible the modern world. They are utterly different, these ideas. The calculus serves the imperial vision of mathematical physics. It is a vision in which the real elements of the world are revealed to be its elementary constituents: particles, forces, fields, or even a strange fused combination of space and time. Written in the language of mathematics, a single set of fearfully compressed laws describes their secret Read More ›

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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 ›

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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 ›

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We Can’t Build a Hut to the Moon

The history of AI is a story of a recurring cycle of hype and disappointment

Once upon a time there live a tribe who lived on the plains. They were an adventurous tribe, constantly wanting to explore. At night they would see the moon drift lazily overhead, and became curious. How could they reach the moon? The moon was obviously higher than their huts. Standing on the highest hut no one could reach the moon. At the same time, standing on the hut got them closer to the moon. So, they decided to amass all their resources and build a gigantic hut. Reason being that if standing on a short hut got them closer to the moon, then standing on a gigantic hut would get them even closer. Eventually the tribe ran out of mud and Read More ›

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What Do We Want With Mathematics Curriculum?

If we are going to dedicate such a large portion of our children's lives to learning mathematics, we had better know why

Modern policy discussions in America almost always leave out the biggest question – why are we doing what we are doing in the first place? Leaving out first principles always leaves people trying to find the most practical way to accomplish nothing in particular. We have become accustomed to not asking questions about first principles because they always sound too doctrinaire, but then we wind up, at best, making the misplaced assumption that everyone is reaching for the same goal, or, far worse, viewing the activities themselves as the goals. One place where this problem repeatedly rears its ugly head is education, and especially mathematics education. Why are we teaching math? What do we want people to get out of Read More ›

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The Fundamental Problem With Common Core Math

Intuition relies on skill, not the other way around

In 2010, a bold effort to reform math curriculum was adopted by the majority of the United States. Known as “Common Core Math,” the goal of this endeavor was to establish a common foundation of mathematics education across the country, and to help bolster not only students’ mathematical abilities, but also their mathematical intuition. The goal was to help students think about math more deeply, believing that this will help them work with mathematics better in later years. Before discussing problems with this approach, I want to say that I appreciate the idea of helping students think more deeply about mathematics. After years and years and years of mathematics education, many students wind up thinking about mathematics as merely a set Read More ›

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Practicing the Basics: Teaching Math Facts in the Classroom

How to help students make deeper connections within mathematics with creative games.

Many people learn to hate math early on. One of the places where people learn to hate math first is in high-stakes speed testing for math facts. This has caused quite a bit of angst in mathematics education for people on both sides of this issue. On the one hand, some have advocated for getting rid of math facts memorization altogether. On the other hand, others have doubled-down, saying that we need speed tests in order to make sure that the cognitive load of arithmetic is limited for later mathematics work. While I fall more into the latter camp than the former, I do think that a more balanced approach to mathematics education may help students in the long run.  Read More ›

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The Chaitin Interview III: The Changing Landscape for Mathematics

How are the fields of mathematics and academic research different today compared to years past? In this week’s podcast, Robert J. Marks and Gregory Chaitin discuss the challenges many mathematicians face today and the unfortunate trend toward bureaucracy that makes academic research difficult. Dropping names of mathematical geniuses past and present, they explore how technology and artificial intelligence are changing Read More ›

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The Chaitin Interview II: Defining Randomness

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. Listen in as Robert J. Marks explores that paper with Chaitin, covering Chaitin’s definition of randomness and his philosophical interest in algorithmic information theory. Show Notes 00:27 Read More ›

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The Chaitin Interview I: Chaitin Chats with Kurt Gödel

In this week’s Mind Matters episode, Robert J. Marks begins a conversation with mathematician and computer scientist Gregory Chaitin. The two discuss Chaitin’s beginnings in computer science, his thoughts on historic scientists in his field such as Leonard Euler and Kurt Gödel, and even the story of how a cold call to Gödel almost led to Chaitin meeting the famed Read More ›

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Bingecast: Selmer Bringsjord on the Lovelace 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 ›

Groupe de Bonobos autour d'un hôtel à insectes

Can Animal Minds Rival Humans Under the Right Circumstances?

Are we just not being fair to animals, as some researchers think?

In 2007, Sue Savage-Rumbaugh, a psychologist and primatologist , published a paper in the Journal of Applied Animal Welfare Science with a remarkable citation: Sue Savage-Rumbaugh, Kanzi Wamba, Panbanisha Wamba, and Nyota Wamba, “Welfare of Apes in Captive Environments: Comments on, and by, a Specific Group of Apes,” Journal of Applied Animal Welfare Science 10:1 (2007): 7–19. What is remarkable about the paper is not the text but the authorship statement. Kanzi, Panbanisha, and Nyota Wamba are not co-author colleagues—they’re apes, bonobos to be specific. Dr. Savage-Rumbaugh (right) is a controversial scientist who believes that animals have intellectual powers that can, under the right circumstances, rival the human intellect. She included her ape subjects as co-authors on the paper because Read More ›

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Gödel and God: A Surprising History

A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God

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.

Read More ›