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You might expect 10 ÷ 5 is the same as 10/5 is the same as 10 over a 5 with a vinculum between them, but each has its own eccentricities. We’ve already noted that ÷ can mean “divide the number on the left by the number on the right” or “divide the expression on the left by the expression on the right.” But it gets really tricky when people assume that a slash replaces a vinculum. Does ab/cd = (ab)÷(cd) or ((ab)÷c)÷d? Does a/b/c mean (a)÷(b)÷(c) or a÷(b/c) or (a/b)÷c? (Answer: Use some parentheses!)

The bottom line is that “order of operations” conventions are not universal truths in the same way that the sum of 2 and 2 is always 4. Conventions evolve throughout history in response to cultural and technological shifts.

An exhibition at the British Library in London reveals the importance that visualising data has had on the scientific process – from 19th Century ship logs that still influence climate science, to models used to forecast the 2009 influenza pandemic.These images not only aid scientific progress, but also help to change the world.

Discover 1,200 Romantic and Victorian literary treasures, new insights by 60 experts, 25 documentary films, 30 inspirational teachers’ notes and more.

How large is Africa compared to the United States, or Western Europe? Most inhabitants of the latter places might guess it is a little larger, but few would have any idea of the scale of the difference. This has led German graphics designer Kai Krause to produce this map to shake people's perceptions a little.

Any attempt to map a spherical planet onto a flat map will involve distortions of size, shape or both. There is a passionate debate among cartographers about the best way to hang the world on a wall, but most agree that the most common maps we get our sense of the world from are very bad ways to do it. The problem is that these maps exaggerate the size of the countries at high  latitudes, and shrink places near the equator - leading to a perception that Europe is larger than South America, to pick just one example among many.

Africa, which spans the equator, fares particularly badly on these sorts of projections: Krause says, "Africa is so mind-numbingly immense, that it exceeds the common assumptions by just about anyone I ever met: it contains the entirety of the USA, all of China, India, as well as Japan and pretty much all of Europe as well - all combined!”  Some have argued that since people associate size with importance this encourages the already strong tendency of the world's wealthiest nations to disregard those who live in the tropics. 

Language, Darwin believed, was not a conscious invention but a phenomenon “slowly and unconsciously developed by many steps.” But what makes a language a language? In this short animation from TED Ed, linguist John McWhorter, author of the indispensable The Power of Babel: A Natural History of Language (public library), explores the fascinating world of fantasy constructed languages — known as conlangs — from Game of Thrones’ Dothraki to Avatar’s Na’vi to Star Trek’s Klingon to Lord of the Rings’ Elvish. Though fictional, these conlangs reveal a great deal about the fundamentals of real human communication and help us understand the essential components of a successful language — extensive vocabulary, consistent grammar rules but peppered with exceptions, and just the right amount of room for messiness and evolution.

The first page of my notebook holds a column of place names, some cuneiform letters taken from a tomb in the British Library and a collection of oddly-named English meadow flowers (wet-the-bed, yellow rattle, adder's tongue fern).

Documents such as medal and grave records, census information, family photographs and battalion diary entries record their lives, but the IWM says it is still seeking more details about them. The project, which is free to use, is being supported by DC Thomson Family History, which runs several online ancestry websites. Each person in the archive will have their own web page, where the public can upload photographs, write stories and recollections or add links to other records. The IWM says the centenary of WW1 will see many families showing a renewed interest in documents, diaries, letters or photographs handed down by relatives or picked up from museums, libraries and archives.

tanding at the turn of the millennium, how odd it seems that women, the majority of the human species, have not, over the course of so many centuries, intervened successfully once and for all on their own behalf. That is, until you consider that women have been trained to see themselves as having no relationship to history, and no claim upon it. Feminism can be defined as women's ability to think about their subjugated role in history, and then to do something about it. The 21st century will see the End of Inequality -- but only if women absorb the habit of historical self-awareness, becoming a mass of people who, rather than do it all, decide at last to change it all. The future is ours to lose.

"The idea was to look more at the more moral and ethical implications of how alcohol might affect decision-making," said Aaron Duke, one of the researchers.* His team found a correlation between each subject's level of intoxication and his or her willingness to flip the switch or push the person—the drunker the subject, the more willing he or she was to kill one hypothetical person for the sake of the hypothetical many. This choice follows the logic of utilitarianism: More good is done by saving five people than harm is done by killing one. This "really undermines the notion that utilitarian preferences are merely the result of more deliberation," said Duke, who also co-authored a paper on the study, charmingly titled, "The drunk utilitarian: Blood alcohol concentration predicts utilitarian responses in moral dilemmas." There's a fabulous irony in the idea that drunk people are emotionally steeled rationalists who are willing to do whatever it takes to save lives. But Duke and his research partner, Laurent Bègue, aren't necessarily arguing that drunk people are ace philosophers and logicians; it's more that their findings challenge common assumptions about how people make decisions.

“News of Boston public schools’ decision to go with the Peters projection has gone viral over the past week, and my teeth have not stopped itching,” Jonathan Crowe writes on his blog, The Map Room. “It is incredibly short-sighted and narrow-minded to say it should be one or the other,” says Mark Monmonier, author of Rhumb Lines and Map Wars: A Social History of the Mercator Projection. Even Ronald Grim, curator of the Norman B. Leventhal Map Center at the Boston Public Library, had concerns: “In my mind, both the Mercator and the Peters are controversial projections,” he says in a phone interview. “But we were not asked to be part of the decision.” Choosing between map projections is a necessarily difficult task. The Earth is resolutely three-dimensional, and any attempts to smooth it out are going to add a certain amount of warping. It’s a balancing act: the more accurate you make the continents’ relative area, the more you have to distort their shapes, and vice versa. The art of cartography lies in choosing to privilege one or another of these accuracies—or finding a sweet spot between them that serves your particular purpose.