Mind Matters Reporting on Natural and Artificial Intelligence

TagMathematics

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The robot writes with a pen and looks at the computer monitor. Artificial Intelligence

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…

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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…

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If Then logic statement written in white chalk on a black chalkboard isolated on white

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.

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E-mc2 written on chalkboard

Kurt Gödel’s Proof of the Existence of God

Kurt Gödel toppled a tall tower of mathematical reasoning with publication of his work showing no formal system of math could be both complete and consistent. He also gave a mathematical proof of the existence of God. Is Gödel’s proof valid? Robert J. Marks and Dr. Selmer Bringsjord discuss mathematics, Kurt Gödel, and the ontological argument. Show Notes 01:05 |…

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Architectural curves

Don’t Leave Home Without These Three Curves

Three mathematical curves explain a lot of what happens—and doesn’t happen—in everyday life

One of the problems with modern secondary mathematics education is that it teaches lots of details about how to solve problems but provides very little insight into how to understand problems. You may have learned to solve a quadratic equation but you may not have learned what life situations generate a quadratic equation.

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Girl pushing big stone hard, impossible and useless concept

Doing the Impossible: A Step-by-Step Guide

Often, in life as in calculus, when our implicit assumptions as to why something can’t be done are made explicit, they can be disproven
Calculus textbooks are the most dry and boring presentations of mathematics I have ever seen, even though calculus offers some of the most amazing insights. Unfortunately, most mathematics texts teach only the mathematics, never the insights. Read More ›
Old calculator
Detail of an old office machine used for calculations

Machine Learning Dates Back To at Least 300 BC

The key to machine learning is not machines but mathematics

Machine learning is not a new technique, but is simply a modern extension of a tool that we have had in our toolbox since the days of the Babylonians. It continues to serve us well to help us extrapolate our data to estimate the value of unknown results and to help find the signal in noisy data.

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A pen on top of several math equations

Walter Bradley Center Fellow Discovers Longstanding Flaw in an Aspect of Elementary Calculus

The flaw doesn't lead directly to wrong answers but it does create confusion

The lead author, Jonathan Bartlett, noted that the likely source of the bad notation was a philosophical issue. Because no one wanted to give differentials that same ontological status as other numbers, everyone presumed that the notational problems were simply the result of this fact, and no one pursued it further.

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blue digital binary data on computer screen
blue digital binary data on computer screen. Close-up shallow DOF

The Flawed Logic behind “Thinking” Computers, Part II

There is another way to prove a negative besides exhaustively enumerating the possibilities

I am publishing, in three parts and with his permission, an exchange with Querius, who is looking for answers as to whether computers can someday think like people. In the first part, we discussed why human thinking cannot be indefinitely compressed. Here is the second part: Recapping for myself what I said in Part I and mulling it over: “If all symbol strings do have a shorter representation, then so must their shorter representations. Thus, we’d end up concluding that all symbol strings can be represented by nothing, which is incoherent.” Wait, I’m getting lost. “Therefore, we conclude that only some symbol strings have a compressed representation. As a consequence, compression intelligence is only true if the physical effects of…

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STEM Education 7: Sell the Sizzle

The mathematics underlying our world is fascinating and full of surprises

In my experience, true STEM nerds are always pursuing some type of sizzle even in their spare time. Generally, the higher the academic degree, the greater the freedom STEM nerds have to pursue their sizzle of choice.

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Boy and blackboard filled with math formulas
boy in glasses, blackboard filled with math formulas background

STEM EDUCATION 2. Not Everyone Is Lucky Enough to be a Nerd

How do you identify extroverted nerds? When you are talking to them, they look at YOUR shoes
If I am made to confess that college courses in Shakespearean sonnets will make me a better person, then English literature majors had better confess that calculus makes them better people. Read More ›