Mathematics

And that’s not a good thing for understanding numbers, says Priceonomics: Many analysts believe that the unthinking use of the average damages our understanding of quantitative information. This is because when people look at averages, they think it is “the norm”. But in reality, it might be highly impacted by just one huge outlier. Imagine an analyst who wanted to know the representative value for the cost of real estate on a block with five houses. Four of the houses are worth $100,000 and one is worth $900,000. Given these numbers, the average would be $200,000 and the median $100,000. In this case, and many others, the median gives you a better sense of what is “typical”. … The median Read More ›

Not to start up the infinity battle again (okay, maybe we are … ), from New Scientist: Explanimator: Does infinity exist in the real world? … Some mathematicians are trying to rebuild the foundations of mathematics without the infinite. But if there is a biggest number, what would happen when you add one to it? The solution could be thinking of numbers as a cycle rather than a linear series, some sort of loop where you revert back to the beginning. It’s a little strange, but then so is infinity. More. The reader who forwarded the tip comments, “Compared to William Lane Craig’s lectures, this article seems shallow and infantile.” Here’s Craig. Readers can decide: See also: Durston and Craig Read More ›

  From Peter Woit at Not Even Wrong: Erica Klarreich at Quanta has the story of a surprising new result about prime numbers from Kannan Soundararajan and Rober Lemke Oliver. They have found that, given a prime number with a certain last digit, there are different probability for the last digit of the next one (among the various possibilities). This violates usual assumptions that such things are in some sense “random”, indicating just how subtle this “randomness” is. More. From Klarreich at Quanta: Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers — those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that Read More ›

One common criticism of the upcoming Alternatives to Methodological Naturalism conference has been that “scientists just follow the evidence where it leads.” Even among fellow ID’ers who disagree with methodological naturalism, they find it difficult to envision why we would need an alternative that is different from “just go with the evidence.” The answer is simple – the scientific imagination. One of the reasons why I started the conference is because Methodological Naturalism (hereafter, MN) constrains thinking in ways that I am not sure even people led entirely by the evidence are aware of. Theory construction is often treated by both scientists and observers of science as an automatic given once the data is in. In actuality, though, it is Read More ›

And literacy. From qz: Nine- and 10-year-old children in England who participated in a philosophy class once a week over the course of a year significantly boosted their math and literacy skills, with disadvantaged students showing the most significant gains, according to a large and well-designed study (pdf). More than 3,000 kids in 48 schools across England participated in weekly discussions about concepts such as truth, justice, friendship, and knowledge, with time carved out for silent reflection, question making, question airing, and building on one another’s thoughts and ideas. More. Unlike many edu-advocacy findings, this one makes sense. Philosophy teaches us to think in a systematic way. It’s hard to see how that wouldn’t help with math and literacy. But Read More ›

Philosopher and photographer Laszlo Bencze was complaining to us recently, The real problem with infinity as I have come to realize is not the mathematics and logic of it. Rather it’s that just about everybody has a firm opinion on the topic. Yes they do. Average people who haven’t cracked a math text since they failed Algebra I, know exactly what infinity means, how it functions, and how it is the answer to many perplexing questions. They KNOW that actual infinities exist and no amount of reasoning can argue them out of their certainty. Yes, I’ve tried. They regard all explaining as mere trickery. Furthermore, they KNOW that our universe is infinite, time is infinite, energy is infinite, and that Read More ›

From Mashable: The geometric wonders are by Kerby Rosanes, an illustrator from the Philippines, who wields an ink pen and plastic compass like a straight-edge wizard. More of Rosanes’ work can be found on his Society6 page and Instagram. See also: At PBS: Puzzle of mathematics is more complex than we sometimes think Follow UD News at Twitter! More of Rosanes’ work can be found on his Society6 page and Instagram.

Over the past month in response to a suggestion on an infinite temporal past (and the counter argument that such is dubious), there has been quite an exchange on numbers. In that context, it is worth headlining FYI/FTR, HT DS, a unification with continuum — oops, link —  based on surreals discussed by Ehrlich: where also: Such of course provides a lot of breathing room for exploring numbers and relationships in a unified context. Attention is particularly drawn to various ellipses of endlessness (not able to be traversed in finite stage stepwise do forever processes) and to both the trans-finites . . . do not overlook ellipses of endlessness within transfinite ranges — and the infinitesimals including what we could Read More ›

In recent days, the issue of an infinite temporal past as a step by step causal succession has come up at UD. For, it seems the evolutionary materialist faces the unwelcome choice of a cosmos from a true nothing — non-being or else an actually completed infinite past succession of finite causal steps. Durston: >>To  avoid  the  theological  and  philosophical  implications  of  a  beginning  for the  universe,  some  naturalists  such  as  Sean  Carroll  suggest  that  all  we  need  to  do  is  build  a  successful  mathematical  model  of  the  universe  where  time  t runs  from  minus  infinity  to  positive  infinity. Although  there  is  no  problem  in  having  t run  from  minus  infinity  to  plus  infinity with  a  mathematical  model,  the real Read More ›

In the current UD thread on Darwinism and an infinite past, there has been an exchange on Spitzer’s argument that it is impossible to traverse an infinite past to arrive at the present. Let me share and headline what is in effect the current state of play: DS, 108: >>KF, DS, ticking clocks meet dying stars and death of cosmos as useful concentrations of energy die out. There are oscillating universe models which are consistent with an infinite past, as I stated. Replace each tick with a big bang/crunch cycle. And that an actually transfinite number of ticks can in principle occur is the precise thing to be shown. No. I am saying that Spitzer assumes that an infinite number Read More ›

Yes, in certain ways, says mathematician at the University of Adelaide. From Science Daily: The old adage that says ‘If it sounds too good to be true, it probably is’ has finally been put to the test — mathematically. A team of researchers has found that overwhelming evidence without a dissenting opinion can in fact weaken the credibility of a case, or point to a failure of the system. … The team put three different scenarios to the test based on mathematical probability: the use of witnesses to confirm the identity of a criminal suspect; the accurate identification of an archaeological find; and the reliability of a cryptographic system. They found in each case that there was a point at Read More ›

Learn how. Or so they say. From Mashable: It’s an age old question: Can cutting pizza ever be truly equal? … But mathematicians Joel Haddley and Stephen Worsley at University of Liverpool in England believe they have cracked the code for perfect equality at the dinner table by cutting somewhat complex, curved slices — also known as monohedral disc tiling. More. From Phys.org: “I’ve no idea whether there are any applications at all to our work outside of pizza-cutting,” said Haddley in New Scientist. He has tried slicing a pizza in this way for real. But the results are “interesting mathematically, and you can produce some nice pictures.” In short, the math is beautiful, but the pizza was probably a Read More ›

Further to early humans preferred the Golden Ratio (1.618) too?: Repeated use of the numbers 2, Pi and Phi and the relationship between them could not have been chance. I, O’Leary for News, wish to thank bornagain for consistently helpful notes in the comments over the years, and to draw attention to his notes on the Golden Ratio in particular: The golden ratio is found throughout nature and has often been referred to as ‘the fingerprint of God’ (vid ): From the shape of some galaxies to quantum mechanics, the golden ratio is found throughout nature. Do We Live in a “Golden Ratio” Universe? (Evolution News & Views December 2, 2014) *The curl of an elephant tusk *The shape of Read More ›

Further to Robert Marks on the math paradox that challenges physics because it may be unanswerable, Rob Sheldon writes to say, Without reading the full paper, it sounds like a familiar problem in many-body QM, how do you add up all the distant interactions in an infinite crystal to find the energy of the system at a single point? Sometimes the interactions fade away, and the series converges. Sometimes the interactions stubbornly refuse to fade, and the series diverges. This paper is saying “there is no a-priori way to know if you have a convergent or divergent series.” I think for mathematicians, this is a Thales moment, when they get to tell the physicists that math really does have application Read More ›

Or physics problems unanswerable due to a math paradox? From Nature: In 1931, Austrian-born mathematician Kurt Gödel shook the academic world when he announced that some statements are ‘undecidable’, meaning that it is impossible to prove them either true or false. Three researchers have now found that the same principle makes it impossible to calculate an important property of a material — the gaps between the lowest energy levels of its electrons — from an idealized model of its atoms. The result also raises the possibility that a related problem in particle physics — which has a US$1-million prize attached to it — could be similarly unsolvable, says Toby Cubitt, a quantum-information theorist at University College London and one of Read More ›