Fun with numbers!

The integers are one of the most studied areas of mathematics and yet we keep keep learning new things about them. Today comes this bit of knowledge: Any positive integer can be written as the sum of three palindromes. More precisely, this is based on a paper Every Positive Integer Is A Sum Of Three Palindromes by Javier Cilleruelo, Florian Luca, and Lewis Baxter that makes the claim that “For integer g ≥ 5, we prove that any positive integer can be written as a sum of three palindromes in base g.”

Here is an interactive site based on this result. It invites you to write down any number, however large, and then watch as it is given as the sum of three palindromic numbers. Go on, try it!

Numbers are fascinating things. it is not surprising that number theory attracts some of the finest mathematicians.

The myth of scientific manipulation of data

America has this curious strain of anti-intellectualism that sees expert opinion on any topic as somehow suspect. While skepticism is a good quality when practiced in moderation, what Bertrand Russell referred to as ‘heroic skepticism’ that takes a stance in direct opposition to expert opinion, such as that human-caused global warming is not happening and that hence climate change is a fiction, is foolish.
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Rewriting religious anticipations of science history

Nir Shafir is a historian of the early modern Ottoman Empire at the University of California, San Diego. In preparing to teach his class on Science and Islam he was looking at some books and discovered something about the illustrations that seemed a little off.

As I prepared to teach my class ‘Science and Islam’ last spring, I noticed something peculiar about the book I was about to assign to my students. It wasn’t the text – a wonderful translation of a medieval Arabic encyclopaedia – but the cover. Its illustration showed scholars in turbans and medieval Middle Eastern dress, examining the starry sky through telescopes. The miniature purported to be from the premodern Middle East, but something was off.

Besides the colours being a bit too vivid, and the brushstrokes a little too clean, what perturbed me were the telescopes. The telescope was known in the Middle East after Galileo invented it in the 17th century, but almost no illustrations or miniatures ever depicted such an object. When I tracked down the full image, two more figures emerged: one also looking through a telescope, while the other jotted down notes while his hand spun a globe – another instrument that was rarely drawn. The starkest contradiction, however, was the quill in the fourth figure’s hand. Middle Eastern scholars had always used reed pens to write. By now there was no denying it: the cover illustration was a modern-day forgery, masquerading as a medieval illustration.

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Henrietta Swan Leavitt: An ignored and forgotten scientist

In recent times, there has been greater awareness of the major but overlooked contributions that women have played in the sciences, and attempts to lift them out of the obscurity to which they had been consigned. The recent film Hidden Figures told of the women mathematicians, African-American women in particular, who worked in the US space program in the 1960s doing critical complex calculations despite the Jim Crow laws that heaped all manner of indignities on them.
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Big step towards open-access science publishing

When it comes to science, the coin of the realm, the measure by which ideas and scientists are evaluated, is by being published in peer-reviewed journals. The journals are run either by professional organizations of scientists as a non-profit arm, such as all the journals run by the American Institute of Physics or the American Physical Society or are purely commercial private operations, such as the prestigious journal Nature. Journals subscriptions are then sold to individuals and libraries. But over time, a combination of rapidly rising subscription costs, shrinking library budgets, and the rise of the internet has created both a crisis and an opportunity for radical changes.
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Myths about human sperm

I suppose I am like most people who have a model of conception as a great race, involving a male emitting a vast number of sperm that then race towards the egg waiting for them in the female and one of the sperm, the victor, gets to fertilize the egg. Robert D. Martin, emeritus curator of biological anthropology at the Field Museum in Chicago and a member of the Committee on Evolutionary Biology at the University of Chicago, writes about the history of studies into sperm and that this idea of ‘macho sperm’ is one of the many myths that surround conception.
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The environmental impact of animal farming

Two arguments are advanced in favor of veganism and vegetarianism. One is the moral one, that the animals we eat are sentient beings that are similar to humans and that it is wrong for us to kill and eat them, even if we eliminate the cruelty of factory farming. The second is an economic and environmental argument, that animals are a highly inefficient source of protein, requiring the expenditure of a vast amount of resources. The rough rule of thumb is that as we go up the food chain, we lose 90% of the energy at each stage. In other words, by feeding grain to animals for the meat, we get only 10% of the energy that was initially stored in the grain. If the animals are fed a diet of animal protein, then we lose another 90%, leaving us with only 1% of the initial energy. This is highly wasteful.
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Correcting false assertions about the history of science

As a scientist interested in the history of science, I have become acutely aware that much of the science ‘history’ we picked up in the course of our scientific training is largely folklore (what Richard Feynman referred to as ‘myth-stories’) and highly unreliable. Hence it is advisable not to make sweeping conclusions based on them. Via PZ Myers over at Pharyngula I came across an interesting article that looks at a recent discussion between Sam Harris and Ben Shapiro, where they use history to draw conclusions about the relationship of science to religion. You could not pay me enough to listen to these two people but Tim O’Neill, an Australian atheist who writes the blog History for Atheists: New Atheists Getting History Wrong did, and he has done a thorough analysis of the historical assertions made by both and finds them, especially those of Harris, utterly wanting.
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Why did hell go from being hot to cold to hot again?

In response to the Satanists installing a statue of Baphomet on the grounds of the state capital in Little Rock, Arkansas in response to the installation of a Ten Commandments monument, Republican state senator Jason Rapert, a minister and lead sponsor of the law allowing the Ten Commandments monument, promised to have the Satanist statue removed, saying that it will be a “very cold day in hell” before a statue of Baphomet would be installed.
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Fact-checking The Galaxy Song

This song from the Monty Python film The Meaning of Life is an extraordinarily good one, inviting us to marvel at the wonder and vastness of the universe and putting into perspective our place in it.

I knew that the facts in the song were roughly correct but Bill Andrews has done a detailed, line-by-line, fact check and finds that it is remarkably accurate except for two or three items. Pretty good, Eric!