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Mathematics

At NPR: For social justice’s sake, get rid of algebra!

From Kayla Lattimore and Julie Depenbrock at NPR: Algebra is one of the biggest hurdles to getting a high school or college degree — particularly for students of color and first-generation undergrads. It is also the single most failed course in community colleges across the country. So if you’re not a STEM major (science, technology, engineering, math), why even study algebra? That’s the argument Eloy Ortiz Oakley, chancellor of the California community college system, made today in an interview with NPR’s Robert Siegel. … Oakley is among a growing number of educators who view intermediate algebra as an obstacle to students obtaining their credentials — particularly in fields that require no higher level math skills. More. Hmmm. If we dropped Read More ›

Fun: Laws of math don’t apply in Australia?

New Scientist’s Scare of the Month: From Timothy Revell at New Scientist: Mathematicians around the world are rushing to check millennia of calculations, as the Australian prime minister Malcom Turnbull has explained that their discoveries aren’t as concrete as we thought. “The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia,” said Turnbull. Turnbull’s comments came as he proposed a new law to force tech companies to give security services access to encrypted messages. Apps like WhatsApp currently prevent any snoopers from reading your messages using end-to-end encryption, jumbling it up in such a way that only the recipient can de-jumble it.More. What he really means is that his government Read More ›

Is Mathematics a Natural Science? (Is that important?)

In our time there is a tendency to treat Mathematics as though it is a natural science. This reflects in part the shift in meaning of the term Science in recent centuries, from knowledge and systematic bodies of more or less established knowledge, to the natural sciences based on inductive reasoning on observation and experiment. Where, inductive here denotes arguments whereby evidence — typically empirical — supports but does not logically demonstrate a conclusion, as a rule provisionally. Such has been multiplied by Scientism, the view, assumption or implication that Science ring fences and monopolises reliable, serious knowledge. (Of course, such Scientism is self-referentially incoherent as this is an epistemological and thus philosophical claim; it fails its own test.) In Read More ›

What accounts for humans’ math ability?

Various foolish explanations are on offer: the adaptationist hypothesis, the byproduct hypothesis, and the sexual selection hypothesis. From Bill Dembski and Jonathan Wells at Evolution News & Views: Leaving aside whether mathematical ability really is a form of sexual display (most mathematicians would be surprised to learn as much), there is a fundamental problem with these hypotheses. To be sure, they presuppose that the traits in question evolved, which in itself is problematic. The main problem, however, is that none of them provides a detailed, testable model for assessing its validity. If spectacular mathematical ability is adaptive, as the adaptationist hypothesis claims, how do we determine that? What precise evolutionary steps would be needed to achieve that ability? If it Read More ›

Neuroscientist: Consciousness is theology, not neurology

From neurologist Robert J. Burton at Nautilus: As a fledgling neurologist, I’d already seen a wide variety of strange mental states arising out of physical diseases. But on this particular day, I couldn’t wrap my mind around a gene mutation generating an isolated feeling of being spied on by the FBI. How could a localized excess of amino acids in a segment of DNA be transformed into paranoia? Though I didn’t know it at the time, I had run headlong into the “hard problem of consciousness,” the enigma of how physical brain mechanisms create purely subjective mental states. In the subsequent 50 years, what was once fodder for neurologists’ late night speculations has mushroomed into the pre-eminent question in the Read More ›

Would math best communicate with ET?

From Leonard David at LiveScience: The idea is that mathematics is as much a part of our humanity as music and art. And it is mathematics that might be understandable — even familiar — to extraterrestrial civilizations, allowing us to strike up star-speak repartee. Carl DeVito, an emeritus faculty in the mathematics department at the University of Arizona in Tucson, has proposed a language based on plausibly universal scientific concepts. He recently detailed his work at the Astrobiology Science Conference 2017, held from April 24 to April 28 in Mesa, Arizona. [13 Ways to Hunt Intelligent Alien Life] Designing a signal that attracts attention and, on examination, is “clearly” the work of intelligence, is a complex problem, DeVito told Space.com. Read More ›

Confusing Probability: The “Every-Sequence-Is-Equally-Improbable” Argument

Note to Readers: The past few days on this thread there has been tremendous activity and much discussion about the concept of probability.  I had intended to post this OP months ago, but found it still in my drafts folder yesterday mostly, but not quite fully, complete.  In the interest of highlighting a couple of the issues hinted at in the recent thread, I decided to quickly dust off this post and publish it right away.  This is not intended to be a response to everything in the other thread.  In addition, I have dusted this off rather hastily (hopefully not too hastily), so please let me know if you find any errors in the math or otherwise, and I will be happy Read More ›

“Western” math as a dehumanizing tool?

Well, we knew that math does NOT lead to a more interesting social life but… now get this from American Thinker: One thing you realize when following the follies and foibles of social justice warriors is that there is no limit to their idiocies – that anything and everything can be declared “racist” or “sexist” if they stretch logic and reason beyond the breaking point. Case in point: a course designed to teach high school kids that mathematics, as taught in the Western world, is a “dehumanizing tool” that has been used to “trick indigenous peoples out of land and property.”More. But can anyone imagine a world without math? And how did it get to be “Western” math anyhow? Isn’t math Read More ›

The unreasonable effectiveness of math vs evolution

A friend draws attention to an old paper, “The Unreasonable Effectiveness of Mathematics vs. Evolution” (The American Mathematical Monthly Volume 87 Number 2 February 1980) by R. W. Hamming: If you recall that modern science is only about 400 years old, and that there have been from 3 to 5 generations per century, then there have been at most 20 generations since Newton and Galileo. If you pick 4,000 years for the age of science, generally, then you get an upper bound of 200 generations. Considering the effects of evolution we are looking for via selection of small chance variations, it does not seem to me that evolution can explain more than a small part of the unreasonable effectiveness of Read More ›

Reader: Weirdness of infinity shows that the universe is not infinitely old

In response to: Math prof: Be careful what we do with infinity. Weird things can happen: “Some weird things are like 1 = 0, not just weird, but undesirable. So we try to build our mathematical ideas to avoid those. But other weird things don’t contradict logic, they just contradict normal life,” a reader writes, Indeed, when you introduce ‘infinity’ into your equation, one of the (far worse than “weird” or “undesirable”) results you get is that 1=0 , which is a logical contradiction/impossibility (which is to say, utterly impossible). Or, to put this another way, you can “prove” anything with a false premise. And, this “result” that 1=0 is one more way we can know that the age of Read More ›

Math prof: Be careful what we do with infinity. Weird things can happen.

From Eugenia Cheng at ScienceFriday: What has gone wrong? The problem is that we have manipulated equations as if infinity were an ordinary number, without knowing if it is or not. One of the first things we’re going to see in this book is what infinity isn’t, and it definitely isn’t an ordinary number. We are gradually going to work our way toward finding what type of “thing” it makes sense for infinity to be. This is a journey that took mathematicians thousands of years, involving some of the most important developments of mathematics: set theory and calculus, just for starters. The moral of that story is that although the idea of infinity is quite easy to come up with, Read More ›

Absolute zero proven mathematically impossible?

From Leah Crane at New Scientist: It’s an absolute. Mathematics has put speed limits on cooling, finally proving a century-old law – that unless you have infinite time and resources, you can’t get to the absolute zero of temperature. … Now Jonathan Oppenheim and Lluís Masanes at University College London have mathematically derived the unattainability principle and placed limits on how fast a system can cool, creating a general proof of the third law. … By applying mathematical techniques from quantum information theory, they proved that no real system will ever reach 0 kelvin: it would take an infinite number of steps. More. Paper is open access. Abstract: The most accepted version of the third law of thermodynamics, the unattainability principle, Read More ›

Is celeb number pi “normal”?

Yesterday was pi day (3.14) From Tia Ghose at LiveScience: Pi is definitely weird, but is it normal? Though mathematicians have plumbed many of the mysteries of this irrational number, there are still some unanswered questions.   Mathematicians still don’t know whether pi belongs in the club of so-called normal numbers — or numbers that have the same frequency of all the digits — meaning that 0 through 9 each occur 10 percent of the time, according to Trueb’s website pi2e.ch. In a paper published Nov. 30, 2016, in the preprint journal arXiv, Trueb calculated that, at least based on the first 2.24 trillion digits, the frequency of the numbers 0 through 9 suggest pi is normal. Of course, given Read More ›

Blowing up mathematics

From Jordana Cepelewicz at Nautilus, on mathematician Harvey Friedman: The foundations of mathematics is also a field—in stark contrast to the casual and light tone of Friedman’s emails—that has been in crisis for nearly a century. In 1931, the Austrian mathematician and philosopher Kurt Gödel proved that any logical system adequate to develop basic arithmetic gives rise to statements that cannot be proven true or false within that system. One such statement: that the system itself is consistent. In other words, no system can ever prove itself to be free of contradiction. The result seemed to present an insurmountable problem for mathematicians, not so much because it prevented them from ever knowing whether the system their work is built on Read More ›

Deep problem created by Darwinian Ron Fisher’s p-values highlighted again

Maybe this time it will matter. From Frank Harrell at Statistical Thinking: In my opinion, null hypothesis testing and p-values have done significant harm to science. The purpose of this note is to catalog the many problems caused by p-values. As readers post new problems in their comments, more will be incorporated into the list, so this is a work in progress. The American Statistical Association has done a great service by issuing its Statement on Statistical Significance and P-values. Now it’s time to act. To create the needed motivation to change, we need to fully describe the depth of the problem. We thought that Darwin’s reputation in pop science would be enough to frustrate any inquiry, but maybe not. Read More ›