The End of (Numeric) Error

The End of (Numeric) Error

Crunching numbers was the prime task of early computers. Wilhelm Schickard’s machine of 1623 helped calculate astronomical tables; Charles Babbage’s difference engine, built by Per Georg Scheutz in 1843, worked out tables of logarithms; the Atanasoff-Berry digital computer of 1942 solved systems of linear equations; and the ENIAC of 1946 computed artillery firing tables.

The common element of these early computers is they all used integer arithmetic. To compute fractions, you had to place an imaginary decimal (or binary) point at an appropriate, fixed position in the integers. (Hence the term fixed-point arithmetic.) For instance, to calculate with tenths of pennies, arithmetic must be done in multiples of 10-3 dollars. Combining tiny and large quantities is problematic for fixed-point arithmetic, since there are not enough digits.

Floating-point numbers overcome this limitation. They implement the “scientific notation,” where a mantissa and an exponent represent a number. For example, 3.0×108 m/s is the approximate speed of light and would be written as 3.0E8. The exponent indicates the position of the decimal point, and it can float left or right as needed. The prime advantage of floating-point is its vast range. A 32-bit floating-point number has a range of approximately 10-45 to 10+38. A binary integer would require more than 260 bits to represent this range in its entirety. A 64-bit floating point has the uber-astronomical range of 10632.

A precursor of floating point arithmetic is embodied in the slide rule, invented by William Oughtread in 1620. The slide rule multiplies and divides, but handles only mantissas. The user keeps track of the exponents. Computing machines with floating-point numbers (including exponents) were suggested by the Spanish inventor Leonardo Torres y Quevedo in 1914; they were first implemented in Konrad Zuse’s computers, from the Z1 (1938) to Z4 (1945).

Despite their range, floats have a serious drawback: They are inaccurate. Anybody can try this out on a pocket calculator: Punch in ⅓ and you get 0.333333. You wonder, of course, how close an approximation this is. Now multiply by 3. Most likely you will see 0.999999 and not 1.0. If the result is 1.0, subtract 1.0 from it, which will probably give you something like −1E−10. This is a perfectly simple example—why can’t computers get this right?

John Gustafson, one of the foremost experts in scientific computing, has proposed a new number format that provides more accurate answers than standard floats, yet saves space and energy. The new format might well revolutionize the way we do numerical calculations.


Remember That Awful Scene? Conservatives Sure Do — Pacific Standard

Remember That Awful Scene? Conservatives Sure Do — Pacific Standard

When Donald Trump proclaimed early in his presidential campaign that “This country is a hellhole,” many of us looked at each other and asked: What is he talking about? The economy is getting better, we’re not in a major war, and more people have health insurance than ever before. What’s so horrible?

But Trump was clearly speaking for a sizable minority of Americans. Blue-collar workers faced with bleak employment prospects understandably resonate to this rhetoric, but in Republican primaries, his bleak portrait of America also rings true to more than a few educated, middle-class voters. Why?

While fear of the nation’s changing racial demographics is surely a factor, newly published research reveals another form of deep-seated bias that likely plays a role.

It reports that, when people search their memory banks — which, after all, is how we make emotional sense of our lives, and our world — those on the political right are more likely to remember negative scenes than positive ones.

A research team led by University of Nebraska psychologist Mark Mills reports this dynamic is not found among political liberals. What’s more, it finds such “negativity bias” increases with higher levels of conservatism.

“Our results show that negatively valenced emotional stimuli appear to have a more privileged status in memory the more conservative one is,” Mills and his colleagues write in the journal Behavioural Brain Research. Their findings suggest “emotional memory plays a role in the development of political ideology.”

It has long been established that conservatives tend to pay closer attention than liberals to negative imagery, such as angry faces. This helps explain why conservatives are more likely to view the world as a scary place that demands a defensive response. Hence, their greater support for military action, and a tendency to give police the benefit of the doubt.

Audubon Pranked Fellow Naturalist by Making Up Fake Rodents | Smart News | Smithsonian

Audubon Pranked Fellow Naturalist by Making Up Fake Rodents | Smart News | Smithsonian

In 1818, the prodigious and strange European naturalist Constantine Samuel Rafinesque took a trip down the Ohio River Valley, collecting specimens and accounts of plants and animals along the way. During this venture, he often stopped to visit or stay with fellow botanists and naturalists. That’s how he found his way into the home of artist and naturalist John James Audubon in Henderson, Kentucky, in August of that year, reports Sarah Laskow at Atlas Obscura

During the stay, Audubon pulled a fast one on Rafinesque, describing and sketching for him 11 outlandish fish species, including the 10-foot-long Devil-Jack Diamond fish with supposedly bulletproof scales. Rafinesque even published accounts of the faux fish in his book Icthyologia Ohiensis, writes Kira Sobers, a digital imaging specialist at the Smithsonian Institution Archives.

Researchers identified the prank well over a century ago. But until now they didn’t realize that Audubon fed Rafinesque a lot more than fanciful fish. According to a new paper in Archives of Natural History, Audubon also fabricated two birds, a “trivalve” mollusk-like creature, three snails, and two plants. He also came up with nine “wild rats,” some of which Rafinesque later described in the American Monthly Magazine and Critical Review.

“Audubon may have thought that Rafinesque would realize the prank, and he probably considered it unlikely that the eccentric naturalist would be capable of publishing his descriptions in scientific journals,” writes Neal Woodman, the author of the paper and mammal curator at the Smithsonian Museum of Natural History. “If so, he underestimated both Rafinesque’s trusting naïveté and his ingenuity in finding and creating outlets for his work.”

So why would Audubon, one of the America’s great naturalists, fabricate species? Researchers speculate that the answer lies in a likely embellished version of Rafinesque’s visit Audubon published years later called “The Eccentric Naturalist.”

According to that account, Audubon awoke one night to find a naked Rafinesque running around his room, swinging Audubon’s favorite violin at bats that had gotten in through an open window. Convinced the bats were a new species, Rafinesque wanted to swat the little mammals down. A displeased Audubon took the violin remnants and finished the job, doubting the bats were anything special.

As Allison Meier at Hyperallergenic writes, the fish stunt may have cost Audubon some credibility. He was later accused of making up five of the birds in his 1827 magnum opus Birds of America—species that were likely hybrids, extinct, or rare color morphs.

Woodman points out that Audubon also received karmic retribution for the stunt. His friend John Graham Bell was traveling with him in the 1840s as an assistant and taxidermist when the two separated for a week. While Audubon was gone, Bell sewed together the head, body and legs of different birds. Surprised by the creature, Audubon sent out an account right away. Weeks later, when Bell confessed, Audubon was livid, but soon saw the humor in the trick.

“Audubon himself fell victim to a prank similar to the one he played on Rafinesque,” writes Woodman. “To his credit, Audubon at least had a specimen in hand.”

There Are Almost No Black People Brewing Craft Beer. Here’s Why.

There Are Almost No Black People Brewing Craft Beer. Here’s Why.

I’m in a craft beer bar in Brooklyn, sipping a $9 stout and looking for black people. “Juicy” is on the speakers, and Notorious B.I.G. grew up a five-minute walk from my barstool here on the dividing line between Clinton Hill and Bedford-Stuyvesant. This is a traditionally black neighborhood, but right now, at 10:30pm on a Thursday, the only people in the bar are me (white), the bartender (white), and a stocky guy with a beard down at the end mouthing lyrics and nursing a bomber of what looks like Hill Farmstead (he’s white, too).

My search isn’t going well so far.

That’s because craft beer is white. Whiter than a ski lodge. Whiter than a Whole Foods in the suburbs. Craft beer is so white, in fact, that there’s an entry for “microbreweries” in Stuff White People Like, a book based on a blog written by a white person making fun of white people for being white. The passage concludes with this sentence: “[M]ost white people want to open a microbrewery at some point.”

Do most black people want to open a microbrewery at some point? Do any? The Brewers Association, the craft industry’s leading trade group, doesn’t keep records on the racial breakdown of its membership; nor does the American Homebrewers Association, its DIY-focused branch. Both organizations told me they weren’t aware of the existence of any such data. After digging around, neither am I.

Nearly all craft beer brewers started out as craft beer drinkers, so it stands to reason that if there are to be black brewers, there would have to be black drinkers.

Turns out the latter are few and far between. A recent Nielsen study commissioned by the Brewers Association found that while black drinkers compose 11.2% of the US population, they consume only 3.7% of the country’s craft beer. Compare that with the 80% of craft beer guzzled by whites, who make up 60% of the population, and you’ll start to get a sense of the size of the divide.* (See footnote at the bottom of this page for a word on other racial groups.)

Still, numbers don’t tell the whole story. So I asked a sample of black peers if they drank craft beer, and what they thought about it. “I don’t hate craft beer,” said Owen Rucker, a 29-year-old video editor living in Williamsburg. “But if I had to choose what I dislike most about it, it would have to be the culture.” Which he summed up as, “God forbid you want a ‘regular’ beer instead of an 18% homebrewed bacon-infused IPA. You’d get an earful from the closest neckbeards about how you just have to ‘work’ through the taste.”

Kara Brown, a 27-year-old writer in Los Angeles, feels similarly. “It seems like craft beer has been closely tied to an experience that a lot of people of color either don’t want to be a part of or don’t feel welcome engaging with,” she said. “I think of white guys in thick-framed glasses and flannel shirts drinking at tables crafted out of reclaimed wood next to their Manic Pixie Dream Girl.”

No single moment in American history has had more impact on the beer business than Prohibition. As it turns out, the 18th Amendment carried some grim racial undertones.

Temperance found its way into the Constitution thanks in part to the Anti-Saloon League, which trafficked in racially loaded propaganda to cast alcohol as a dangerous pandemic. “Saloons became code for not only drinking and debauchery, but also code for where immigrants and brown people hang out,” explained J. Nikol Beckham, an assistant professor of communication studies at Randolph College in Lynchburg, Virginia. The Prohibition movement was “always racialized,” she said, pointing to political cartoons like this one, in which faceless blacks are portrayed as willing minions of a Germanic beer baroness.

In 1933, Prohibition was repealed by the 21st Amendment, but the beer business quickly developed — or even cultivated — race problems of its own. “[The post-Prohibition] consolidation of most beer brewing in the US into very large corporations probably hurt all sorts of minorities who would have potentially owned breweries,” said Allison McKim, an assistant professor of sociology at Bard College.

Are Swing Voters Real? — Pacific Standard

Are Swing Voters Real? — Pacific Standard

Mitt Romney got roughly a five percent bump in the polls following his first debate with Barack Obama in 2012, an increase most politicos attributed to swing voters being disappointed with Obama’s phoned-in performance. But there’s a different explanation, according to a new study: Polls shifted not because opinions changed, but because pollsters asked different people for their opinions before and after the debate.

That’s an important distinction not only for our understanding of politics, Andrew Gelman, Sharad Goel, Douglas Rivers, and David Rothschild argue in the Quarterly Journal of Political Science, but also for politicians, who spend billions of dollars trying to persuade swing voters who may, in fact, not exist.

Yet the discovery was largely an accident, Gelman writes in an email. Goel and Rothschild had been studying data from a 2012 Web-based survey of 83,283 people; on any given day, about 7,500 responded to survey questions, so they had a lot of data. Meanwhile, Gelman had been working on figuring out how to adjust polling results for differences between the general population and the people actually polled. “When we did all this, David and Sharad noticed this stunning result that, after adjustment, support for [Romney and Obama] was very stable over time,” Gelman writes.

[The more general problem is that most people do not understand statistics. Reporters do a disservice on how they report the numbers.]

15th-Century Suits of Armor are Way More Ergonomic Than You’d Think – Core77

15th-Century Suits of Armor are Way More Ergonomic Than You’d Think – Core77

Today we look at a sword-wielding woman currently of greater global interest: Brienne of Tarth. As Game of Thrones starts this Sunday, it won’t be long before we’re seeing armor-suited folks like her putting some wear and tear on their weapons. Which makes one wonder: How much range of motion does Brienne and her foils really have in that get-up, with the metal plates and the greaves and all?

The answer is “Quite a lot,” assuming her suit was designed along the same principles as the armor of 15th-Century Europe.* Below we see a very surprising video put together by France’s Le Musée National du Moyen-Âge de Cluny (“The National Museum of the Middle Ages Cluny”), whereby they drop two chaps into 15th-Century armor designs, then make them do everything from jumping jacks to jumping each other:

The Jacob Lego Javits Center – Core77

The Jacob Lego Javits Center – Core77

Next month is the ICFF, which designers both aspiring and established will descend upon to display their wares. But Brooklyn-based Sean Kenney’s work is already inside the Javits Center. Earlier this year, Legomaniac Kenney built a 114,470-piece replica of the Javits that is now on display there.

The model is nearly 7 feet long and over 5 feet wide, contains 114,470 LEGO pieces, built over the course of 2 months with 4 of my assistants.

Nine Wi-Fi gadgets that reflect IoT momentum – RCR Wireless News

Nine Wi-Fi gadgets that reflect IoT momentum – RCR Wireless News

With predictions of billions of new devices that will have wireless connectivity over the coming years, the “Internet of Things” is expected to have a major influence on multiple verticals and consumers’ everyday lives. And it turns out that already, everything from dog dishes to stuffed animals to vacuums and home appliances are getting connected.

Cisco’s Mobile Visual Networking Index for 2016 estimates that machine-to-machine connections will grow from 604 million last year to 3.1 billion by 2020, reflecting five-fold growth.

“M2M connections—such as home and office security and automation, smart metering and utilities, maintenance, building automation, automotive, healthcare and consumer electronics, and more—are being used across a broad spectrum of industries, as well as in the consumer segment,” Cisco concluded. In the wearables market specifically, Cisco projects that there will be 601 million devices globally by 2020 — and most of those devices will be connected by a non-cellular technology such as Bluetooth or Wi-Fi, with only seven percent expected to be cellular-equipped.

While Linksys’ H2O router to provide Wi-Fi coverage up to 10,000 feet underwater was an April Fool’s joke, there are more than enough real envelope-pushing Wi-Fi gadgets on the market or in development to prove that for Wi-Fi, the IoT is already here. Some of these include:

-Amazon’s Wi-Fi-enabled Dash buttons currently serve more than 100 brands with one-touch reordering in the home, enabling consumers to push a button and automatically place an order with Amazon. They are available at $5 a pop, with the cost recouped in a $5 credit on the first product order. Perhaps more interestingly, Amazon is now partnering with other brands to incorporate Dash ordering capabilities in its Dash Replenishment Program and has released an API to encourage such development. Samsung, General Electric and others have signed up to build hardware that can re-order products without any intervention. A Whirlpool Smart Dishwasher, for example, can calculate how much product it has used compared to what’s available in a typical product size and re-order when the supply is running low via Dash.

-San Diego-based start-up BIGaVu connects teddy bears via Wi-Fi to provide music, voice messages from parents, and react to online games to provide comfort and entertainment for children who are in the hospital. The company recently unveiled prototypes of its bears and has a therapies-on-demand hardware and software platform.

-Jenn-Air just added the brand’s first Wi-Fi enabled refrigerator to its line-up, which can be controlled via an iOS or Android application for monitoring or directing tasks such as making extra ice. It will be available starting this winter.

-The June computerized counter-top oven sends updates on cooking process to a smartphone app via Wi-Fi and can provide live video from inside the appliance, as well as a push notification when the dish is done. It also gets software updates via Wi-Fi. June recently raised a $22.5 million Series A funding round and plans to start shipping ovens for the 2016 holiday season.

-In addition to its Bluetooth-enabled wearables, Fitbit has a Wi-Fi enabled scale that integrates with its Fitbit app. The fitness wearables market is a popular one for the integration of both Bluetooth and Wi-Fi; a new fitness tracking solution recently touted by Naked Labs includes a scanning mirror and a scale that doubles as a turntable, so that users are presented with a 360-degree view of their bodies and “heat maps” of changing areas to visually track their fitness progress. That offering is expected to be available in March 2017.

-The Petnet Wi-Fi-enabled SmartFeeder for pets has an app (for iOS only) that allows an owner to schedule automatic feedings while they are away. The app has an easy re-ordering option supported by Amazon’s Dash Replenishment Service and also recently added integration with Google’s Nest Cam.

–Foobot is an indoor air quality monitoring device with Wi-Fi connectivity that measures volatile organic compounds and particulate in the home, along with carbon monoxide, carbon dioxide, temperature and humidity.

-iRobot introduced embedded Wi-Fi connectivity to its Roomba vacuuming robot product line last year, with the Roomba 980 model that can be remotely controlled and scheduled via an Android or iOS app. Previously, workarounds were available for customers who wanted to control their Roombas via wireless, but the newest addition builds in Wi-Fi capabilities.

A River Once Ran through the Sahara [Graphic] – Scientific American

A River Once Ran through the Sahara [Graphic] – Scientific American

No one ever says of the Sahara that a river runs through it. But somewhere between 11,700 and 5,000 years ago, one did. In full flow, it would rank 11th among the largest rivers on the earth today. Paleoclimatologist and geochemist Charlotte Skonieczny of the French Research Institute for Exploration of the Sea and her colleagues report the evidence for the ancient channel in a recent issue of Nature Communications. The team discovered the so-called Tamanrasett River when examining microwave data collected by a Japanese satellite that had been mapping geologic features in the area. The hidden bedrock valley winds for more than 500 kilometers from the Atlas Mountains in northern Africa to the Atlantic Ocean.