Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryMathematics

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Black female student in front of chalkboard

If Reality Is Fundamentally Mathematical, Why the War on Math?

Just as physicists are recognizing the mathematical nature of reality more clearly, the basic idea of getting math right is under fire in our schools

Sam Baron, a philosophy prof at Australian Catholic University, whose specialty is the philosophy of mathematics, argues in a new paper that mathematics is not a human invention. It gives structure to the world we live in. We simply observe it. So do many life forms, it seems. He offers an example: There are two subspecies of North American periodical cicadas that live most of their lives in the ground. Then, every 13 or 17 years (depending on the subspecies), the cicadas emerge in great swarms for a period of around two weeks. Why is it 13 and 17 years? Why not 12 and 14? Or 16 and 18? One explanation appeals to the fact that 13 and 17 are…

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multiverse conceptual illustration

Multiverse Cosmology Is Not a Good Argument Against God

Or against fine tuning of our universe. God could have created countless universes on various principles for a variety of reasons

New Scientist’s executive editor Richard Webb, a “recovering particle physicist,” offers a look at the current state of the idea that there might be an infinity of universes out there. Why believe it? Mainly, it turns out, to avoid believing something else: Gods and their intelligent designs are less in the mainstream of scientific thought now, yet similar ideas about an optimal universe still trickle through cosmology. That is principally down to some mysterious numbers that determine its workings. Tot them all up in the standard models of particle physics and cosmology, and you end up with about 30 constants of nature – numbers like the strengths of the fundamental forces and the masses of elementary particles that our theories…

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Colorful numbers background

How Even Random Numbers Show Evidence of Design

Random number generators are actually pseudo-random number generators because they depend on designed algorithms

In Define information before you talk about it, neurosurgeon Michael Egnor interviewed engineering prof Robert J. Marks on the way information, not matter, shapes our world (October 28, 2021). In the first portion, Egnor and Marks discussed questions like: Why do two identical snowflakes seem more meaningful than one snowflake. Then they turned to the relationship between information and creativity. Is creativity a function of more information? Or is there more to it? And human intervention make any difference? Many questions arose during the discussion. Does Mount Rushmore have no more information than Mount Fuji? Does human intervention make a measurable difference? That’s specified complexity. Putting the idea of specified complexity to work, how do we measure meaningful information? How…

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multiverse and alternative universes concept

Why Just Anything Can’t Happen via Infinite Universes

We can see why not, using simple mathematical reasoning in this universe

Can anything happen if there are an infinite number of universes each with an infinite number of possibilities in each? Can you be bald in one universe and fully haired in another? Can you have two eyeballs in this universe and three in another? The answer is no. In a nutshell, the reason is that some infinities are bigger than other infinities. (And this is not a claim like infinity plus one is bigger than infinity. Infinity plus one is still infinity.) The number of points on a line segment from, say zero to one, is a bigger infinity than the number of counting numbers {1,2,3,…}. We can label the infinite number of universes in the multiverse as universe #1,…

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Black hole illustration

13. Egnor vs. Dillahunty: Are Singularities a Part of Science?

Also, an audience member asks the debaters: Does atheism make better predictions than theism?

In the “Does God exist?” debate at Theology Unleashed between theist neurosurgeon Michael Egnor and atheist broadcaster Matt Dillahunty (September 17, 2021), we now look at questions from the audience on whether singularities are really a part of science and whether atheism is really a belief system that can make predictions. Readers may recall that the debate opened with Egnor explaining why, as former atheist, he became a theist. Then Dillahunty explained why, as a former theist, he became an atheist. Michael Egnor then made his opening argument, offering ten proofs for the existence of God. Matt Dillahunty responded in his own opening argument that the propositions were all unfalsifiable. When, in Section 4, it was Egnor’s turn to rebut…

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double moon above Crater Landscape on alien Planet.

Would ET Intelligences Understand the 1974 Arecibo Message?

Probably not, says astrobiologist Dirke Schulz-Makuch, who raises the question of whether we could ever really communicate with extraterrestrial intelligences

In early, easily-mocked sci fi, a little green man points his raygun at an unsuspecting passerby and barks “Take me to your leader.” Fast forward: If the little green man didn’t have the technology to figure out who the leader was before landing, he certainly wouldn’t have the technology to get here. In any real-world scenario, we must assume that extraterrestrial intelligences are doing common sense logical things that we would do: Check Earth’s inhabitants out first by monitoring our communications. Some analysts have pointed out that there are places they could even hide technology in our solar system (Lagrange points, for example) with much less chance of being noticed. But then the question is, what to say to them?…

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Cute white English Bulldog puppy in a graduation cap

Tested!: Are the Least Expert People the Most Confident? No.

The claimed Dunning–Kruger effect in psychology is a very shakeable truth frequently exploited by online social bullies

Have you ever been in an online discussion where a vocal proponent confidently claimed that his opponent was the victim of the dreaded “Dunning–Kruger” effect? At Vox, Brian Resnick explains, “That’s where people of low ability — let’s say, those who fail to answer logic puzzles correctly — tend to unduly overestimate their abilities”: An obvious example people have been using lately to describe the Dunning-Kruger effect is President Donald Trump, whose confidence and bluster never wavers, despite his weak interest in and understanding of policy matters. But you don’t need to look to Trump to find an example of the Dunning-Kruger effect. You don’t even need to look at cable news. Brian Resnick, “An expert on human blind spots…

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Two piles of coins

Are Our Neurons Really Wired for Numbers?

Some neuroscientists say they have shown hardwiring in studies of crows and macaques but others say no, these life forms differ too much

University College London cognitive neuroscientist Brian Butterworth, author of a forthcoming book, Can fish count? (Basic Books, 2022), reckons that, one way or another, in a modern urban society, we process about 16,000 numbers in an average day. Numbers create conceptual relationships between vastly different things. From the publisher’s introduction to his book, we learn, “The philosopher Bertrand Russell once observed that realizing that a pair of apples and the passage of two days could somehow both be represented by the concept we call “two” was one of the most astonishing discoveries anyone had ever made.” At The Scientist, Catherine Offord, discussing his work, offers a critical distinction between estimations of quantity and actual counting: “Our perception of quantity, separate…

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Small kitten

In an Infinity of Universes, Countless Ones Are Run by Cats…

Daniel Díaz notes that most of the talk about the multiverse started to appear once it was realized that there was fine-tuning in nature

Walter Bradley Center director Robert J. Marks has been doing a series of podcasts with Swedish mathematician Ola Hössjer, and Colombian biostatistician Daniel Díaz in connection with a recent co-authored paper on the fine-tuning of the universe for life in the Journal of Cosmology and Astroparticle Physics. In the first portion of this episode, podcast 153, “Why is there fine-tuning everywhere?” they look at whether life was seeded in our universe by advanced life forms (directed panspermia), as advocated by some prominent scientists. In the second portion, they discuss the view — again, held by prominent science figures — that our universe is an advanced computer sim. In the third segment, they tackle the idea that there is nothing to…

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Robot eyes closeup

Sure, AI Could Run the World — Except for Its Fundamental Limits

But many of the basic errors, problems, and limitations have no easy solution

We are told that not only will AI take our jobs but it will take our bosses’ jobs and their bosses’ jobs and pretty soon., AI will be running the world… We can see those films on Netflix any night. Science writer and science fiction author Charles Q. Choi offers, in a longish piece at the Institute of Electrical and Electronic Engineers’ online magazine, Spectrum, talking about the real world where “Neural networks can be disastrously brittle, forgetful, and surprisingly bad at math.” AI frequently flubs and it is not clear how to make it flub less. Here are brief notes on three examples of the seven he offers: ➤“Brittle” 97% of AIs could not identify a school bus flipped…

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Soup With Letter Noodles On Spoon

Can There Be a General Theory for Fine-Tuning?

If you make a bowl of alphabet soup and the letters arrange themselves and say, good morning, that is specified. What are the probabilities?

In Episode 2, the first part, (September 9, 2021), Swedish mathematician Ola Hössjer discusses fine tuning in biology with Walter Bradley Center director Robert J. Marks the way “Life is so finely tuned that it is frightening,” Put another way, the billions of cells in our bodies are each like a city. Not as a group but each of them. No wonder we feel so sick when things are going wrong with our cells. It is like billions of dysfunctional cities… Anyway, Hössjer has been working on a general theory for fine-tuning: https://episodes.castos.com/mindmatters/Mind-Matters-Episode-151-Hossjer-Diaz.mp3 This portion begins at 12:07 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: Ola, you came up with a general theory. We…

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Vaccine or flu shot in injection needle. Doctor working with patient's arm. Physician or nurse giving vaccination and immunity to virus, influenza or HPV with syringe. Appointment with medical expert.

COVID-19, Bayes’ Rule, and Simpson’s paradox

Israeli data, when studied carefully, confirm the effectiveness of COVID-19 vaccines

Israel has a very high COVID-19 vaccination rate and yet, on August 15, 2021, 58% of those Israelis hospitalized for COVID-19 were fully vaccinated — suggesting that vaccinations are ineffective or even harmful. This is a great example of two common statistical traps. The first is confusion about inverse probabilities. One hundred doctors were once asked this hypothetical question: In a routine examination, you find a lump in a female patient’s breast. In your experience, only 1 out of 100 such lumps turn out to be malignant, but, to be safe, you order a mammogram X-ray. If the lump is malignant, there is a 0.80 probability that the mammogram will identify it as malignant; if the lump is benign, there is a 0.90 probability that…

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Guaranteed Likely Probable Certainty Measuring Confidence Level

Fine-tuning? How Bayesian Statistics Could Help Break a Deadlock

Bayesian statistics are used, for example, in spam filter technology, identifying probable spam by examining vast masses of previous messages

In the earlier part of podcast episode 150, “Ours is a finely tuned — and No Free Lunch — universe,” Swedish mathematician Ola Hössjer and University of Miami biostatistician Daniel Andrés Díaz-Pachón discussed with Walter Bradley Center director Robert J. Marks the many ways in which the universe is finely tuned for life. Many theorists are not happy with the idea of fine-tuning because they are uncomfortable with its theistic implications. In this second portion of the episode, they discuss how a method of estimating probability called Bayesian statistics or Bayes theorem could help break a deadlock around fine-tuning: https://episodes.castos.com/mindmatters/Mind-Matters-Episode-150-Hossjer-Diaz-.mp3 This portion begins at 13:00 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: Bayes’ theorem…

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Set of numbers 1, 2, 3 made of leather. 3D render font with skin texture isolated on black background.

Further Dispatches From the War on Math

Discussions of social policy where math is relevant can be useful. But a student who does not understand how an equation works will fail at both math AND social policy

Earlier this year, I reposted an article that originally ran at Salvo on the war on the teaching of mathematics as a discipline in publicly funded schools in North America. The war continues so here are some updates: Recently, three mathematicians who immigrated to the United States weighed in: The United States has been dominant in the mathematical sciences since the mass exodus of European scientists in the 1930s. Because mathematics is the basis of science—as well as virtually all major technological advances, including scientific computing, climate modelling, artificial intelligence, cybersecurity, and robotics—US leadership in math has supplied our country with an enormous strategic advantage. But for various reasons, three of which we set out below, the United States is…

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Piano tuning process. closeup of hand and tools of tuner working on grand piano. Detailed view of Upright Piano during a tuning

Ours Is a Finely Tuned — and No Free Lunch — Universe

Mathematician Ola Hössjer and biostatistician Daniel Andrés Díaz-Pachón explain to Walter Bradley Center director Robert J. Marks why nature works so seamlessly

Our Walter Bradley Center director Robert J. Marks had a chance, recently, to talk with Swedish mathematician Ola Hössjer and University of Miami biostatistician Daniel Andrés Díaz-Pachón on the many ways in which the universe is finely tuned for life. This is Part 1. Part 2 will shortly follow. https://episodes.castos.com/mindmatters/Mind-Matters-Episode-150-Hossjer-Diaz-.mp3 This portion begins at 00:00 min. A partial transcript, Show Notes, and Additional Resources follow. Today on Mind Matters news on the podcast, we’re going to talk about fine-tuning of the universe for life. Scientists know that Earth is is finely tuned for life to come into existence. For example, pronounced atheist Sir Fred Hoyle (1915–2001). Hoyle was a great astronomer, maybe known best for his coining the term, Big…

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Joke

Why Animals Can Count But Can’t Do Math

A numerical cognition researcher outlines the differences between recognizing numbers and doing math

At The Conversation, psychology professor Silke Goebel offers some perspective on the differences between the way animals and small children process numbers and the way adults do. As a researcher in numerical cognition, she tries to focus on how brains process numbers. Her research shows that Humans and animals actually share some remarkable numerical abilities – helping them make smart decisions about where to feed and where to take shelter. But as soon as language enters the picture, humans begin outperforming animals, revealing how words and digits underpin our advanced mathematical world. Silke Goebel, “Why animals recognise numbers but only humans can do maths” at The Conversation (July 28, 2021) Essentially, she says, there are two different types of counting…

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solving algebra equation on whiteboard in classroom

How Eccentric Mathematician Kurt Gödel Opened the World

Science writer: As often happens, few people understood the significance of what had just happened. The one exception was John von Neumann.

Albert Einstein, Jogalekar tells us, considered it a privilege to walk home with Gödel every day. Why?: In an exceptionally elegant essay, science writer Ashutosh Jogalekar (no stranger to controversy) talks about the huge difference Kurt Gödel (1906–1978) made by eliminating the idea that some single, simple explanation would put an end to all questioning about the nature of the universe in favor of some simple materialism. In a review of Stephen Budiansky’s biography of Gödel, Journey to the Edge of Reason (Harvard 2021), Jogalekar explains how Gödel dashed such hopes: In September 1930, a big conference was going to be organized in Königsberg. German mathematics had been harmed because of Germany’s instigation of the Great War, and Hilbert’s decency…

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Close up of math formulas on a blackboard

Is Our “Number Sense” Biology, Culture — or Something Else?

It’s a surprisingly controversial question with a — perhaps unsettling — answer

British science writer Philip Ball, author of How to Grow a Human, offers an even-handed account of a controversy on the origin of our ability to understand numbers (numeracy). Numeracy is the beginning of mathematics, the most abstract of all human pursuits. It isn’t possible to get very far in mathematics without some ability to abstract. Ball cites as an example the difference between 152 and 153. Many life forms, competing for a pile of food items, can distinguish between 2 and 3. But distinguishing between 152 and 153 clearly requires abstraction. It’s the same principle as the chiliagon, a geometric figure like a triangle except that it has 1000 sides. A triangle can be envisioned concretely. A chiliagon can…

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Father And Son Competing In Video Games At Home

Why Did Video Gamers Uncover Fraud More Easily Than Scientists?

Video gamers are subject, a psychologist tells us, to much more rigorous constraints than scientists

In a recent article at The Atlantic, King’s College psychologist Stuart Ritchie, author of Science Fictions: How Fraud, Bias, Negligence and Hype Undermine the Search for Truth (2020), has noted a curious fact: Video gamers are much quicker to spot fraud than scientists. The video game fraud he focuses on involved a gamer’s claim that he had finished a round of Minecraft in a little over 19 minutes, a feat he attributed, Ritchie tells us, to “an incredible stretch of good luck.” “Incredible” is the right choice of word here. “Dream,” as the player was known, later admitted — in the face of skepticism — that he had “inadvertently” left some software running that improved his game — thus disqualifying…

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Space and Galaxy light speed travel. Elements of this image furnished by NASA.

No Free Lunches: Bernoulli is Right, Keynes is Wrong

What the Big Bang teaches us about nothing

Jacob Bernoulli made a now obvious observation about probability over three-and-a-half centuries ago: If nothing is known about the outcome of a random event, all outcomes can be assumed to be equally probable. Bernoulli’s Principle of Insufficient Reason (PrOIR) is commonly used. Throw a fair die. There are six outcomes, one for each face of the cube. The chance of getting five pips showing on the roll of a die is therefore one sixth. If a million lottery tickets are sold and you buy one ticket, the chances of winning are one in a million. This reasoning is intuitively obvious.  The assumption about the die is wrong if the die is loaded. But you don’t know that. You know nothing. So Bernoulli’s PrIOR…