Original image

Benjamin Banneker, the African-American Mathematician Who May Have Saved Washington, D.C.

Original image

Wikimedia Commons // Public Domain


Many people who have a passing familiarity with Washington, D.C. know it was originally styled after famous European locales by architect Pierre Charles L’Enfant, then completed by Andrew Ellicott after L’Enfant was given the boot in 1792. Too few tourists and history fans, however, know that the U.S. capital might have been a very different place if not for the surveying work of Benjamin Banneker—a highly accomplished mathematician, astronomer, and scholar who challenged Thomas Jefferson and his peers to recognize African-American achievement when it was right under their noses (and feet).

Benjamin Banneker was born November 9, 1731, in Baltimore County, Maryland, to Robert and Mary Banneker. While scholars still debate almost all the specifics of his background and early life, according to the most popular story, both sides of his family suffered under enslavement in the soon-to-be United States. Although records are scarce, it's said that Benjamin’s maternal grandmother, a woman named Molly Welsh, was falsely convicted of theft in England and sentenced to indentured servitude in Maryland (not an uncommon practice at the time). After earning her freedom, she rented land in Baltimore County and purchased two slaves to help farm it. Several years later, after the farming operation was established, she freed both men.

One of them, who is said to have been abducted from a royal family in Africa earlier in his life, displayed a keen interest in astronomy and other scientific subjects. He was called Bannake or Bankka, and Molly Welsh married him, violating state law that forbid marriage to slaves. Later, their daughter Mary and her husband—a Guinean man who’d been abducted, enslaved, and then baptized as Robert and freed—chose to adopt the surname Banneker at the time of their own marriage. Just a few years after regaining his freedom, records show that Robert was able to purchase a 100-acre farm (possibly the same one his mother-in-law rented), where his family would live out much of their lives and where his son’s scholarship would bloom.

Benjamin Banneker grew up as one of only 200 free African-Americans among 13,000 whites and 4000 slaves in Baltimore County. His experience with formal instruction was limited to a brief stretch in a one-room, mixed-race Quaker schoolhouse, but he was a keen study from his earliest years. Perhaps with his doting grandmother Molly’s help, he learned to read and soon became especially interested in mathematics and mechanics, often performing calculations and experiments on his own.

Once he was old enough to work on the family farm, Banneker settled into a lifestyle that combined this work with scholarly achievement. After his father’s death when Banneker was 27, he continued running the farm with his mother and sisters. The horses, cows, garden, and multiple beehives he kept enabled a simple, comfortable life for the family, according to one 19th-century account presented to the Maryland Historical Society. Using crop rotation and irrigation techniques that wouldn’t catch on in the U.S. for many decades, he also raised profitable tobacco crops that were sold alongside his produce in the Ellicott family’s store. Taking heed of food shortages during the Revolutionary War, Banneker also swapped tobacco out for wheat to help feed American soldiers.

Throughout his life, Elizabeth Ross Haynes writes, Banneker “found time to study all the books which he could borrow.” He became well-versed in topics throughout the sciences and humanities. The 19th-century account presented to the Maryland Historical Society remembered Banneker as “an acute observer, whose active mind was constantly receiving impulses from what was taking place around him.”

For example, one rather illustrative 1797 journal entry reads:

Standing at my door I heard the discharge of a gun, and in four or five seconds of time, after the discharge, the small shot came rattling about me, one or two of which struck the house; which plainly demonstrates that the velocity of sound is greater than that of a cannon bullet.

Some historians have speculated that Banneker’s many childhood lessons with his grandmother Molly, who may have gained a sophisticated understanding of astronomy from Bannake, could have fostered his particular expertise with the subject. However, it was his prowess with mathematics for which he first became renowned throughout Baltimore County, according to a 1912 article. As word spread of his exceptional skills, far-away scholars began sending Banneker complex mathematical problems, and they continued to do so throughout his life. Banneker reportedly always solved them, often responding in verse and with a fresh problem.

As a young man, Banneker also gained fame and admiration for miles around due to one of his earliest known mechanical feats: building a working clock almost entirely out of wood from scratch. It may have been the first clock ever assembled completely from American parts, according to Haynes (although other historians have since disputed this). Banneker reportedly only had a borrowed pocket watch to use for reference on clockwork mechanisms, while his wooden version contained functioning, carved-to-scale components. The clock continued working until a few days after Banneker’s death, when a fire destroyed his cabin home and many of its contents—clock included.

However, Banneker’s accomplished scholarship remained mostly unknown outside the region until he encountered the Ellicott family. In 1772, the Quaker Ellicotts purchased the land next door to Banneker’s and began building new gristmill facilities there. Banneker’s fascination with the mill’s mechanics made him a frequent visitor to the site. In keeping with Quaker tradition, the similarly scholarly Ellicotts were adamant proponents of racial equality, and they collaborated with Banneker as well as encouraged wider application of—and recognition for—his unique skills.

George Ellicott, a close friend of Banneker’s for decades, was himself a student of astronomy and eagerly shared both his resources and queries with his neighbor. Banneker took great advantage of the borrowed tools and books in performing exquisite astronomical calculations, such as predicting a solar eclipse near-exactly in 1789. He also began building the foundations for several atlases and technical treatises he’d release in the decades before his death. In 1791, George’s cousin, Major Andrew Ellicott, gave Banneker a national stage, after Andrew had gone to George requesting help with a new job. George, being otherwise busy, suggested Banneker's assistance. The job was surveying land along the Potomac River for what would soon be the nation’s capital, Washington, D.C.

Ellicott's plan for Washington, D.C. Image credit: Leeann Cafferata, Flickr // CC BY-SA 2.0

The plans for the large city were laid out by French architect and engineer Pierre Charles L’Enfant, who volunteered for service in the American Revolution’s Continental Army and was hired for the project by George Washington in 1791. Before long, however, tensions mounted over its direction and progress of the project, and when L’Enfant was fired in 1792, he took off with the plans in tow.

But according to legend, the plans weren’t actually lost: Banneker and the Ellicotts had worked closely with L’Enfant and his plans while surveying the city’s site. As the University of Massachusetts explains, Banneker had actually committed the plans to memory “[and] was able to reproduce the complete layout—streets, parks, major buildings.” However, the University of Massachusetts also points out that other historians doubt Banneker had any involvement in this part of the survey at all, instead saying that Andrew and his brother were the ones who recreated L’Enfant’s plan. It's an intriguing myth, but it may only be that.

Yet Banneker’s valuable contributions to the project drew attention, and set the stage for later correspondence with Thomas Jefferson. During the project, the Georgetown Weekly Ledger made public note of Banneker as “an Ethiopian, whose abilities, as a surveyor, and an astronomer, clearly prove that Mr. Jefferson's concluding that race of men were void of mental endowments, was without foundation."

Gelman Library, George Washington University // Public Domain

In 1791, Banneker had finished his “painstakingly calculated ephemeris,” or table of the position of celestial bodies, which he would publish alongside charts, literature, and humanitarian and political essays in six almanacs with 28 editions in the following six years. Upon its initial completion, he first sent a copy of the ephemeris to then-Secretary of State Thomas Jefferson, along with a famously direct, yet perfectly polite, letter challenging Jefferson’s opinion that African-Americans suffered an innate intellectual disadvantage [PDF]. Among other things, the letter observed:

Sir, I have long been convinced, that if your love for yourselves and for those inestimable laws, which preserved to you the rights of human nature, was founded on sincerity, you could not but be solicitous that every individual ... might with you equally enjoy the blessings thereof, neither could you rest satisfied [short of] their promotion from any state of degradation, to which the unjustifiable cruelty and barbarism of men may have reduced them.

Sir, I freely and cheerfully acknowledge that I am of the African race ... and it is under a sense of the most profound gratitude to the supreme ruler of the Universe, that I now confess to you, that I am not under the state of tyrannical thraldom, and inhuman captivity to which many of my brethren are doomed, but that I have abundantly tasted of the fruition of those blessings, which proceed from that free and unequalled liberty, with which you are favored, and which, I hope you will willingly allow, you have received from the immediate hand of that being ... [and] that the present freedom and tranquility which you enjoy, you have mercifully received, and that it is the peculiar blessing of heaven.

Jefferson’s letter of response the same year was significantly shorter than Banneker’s, and not without traces of the mindset Banneker sought to defeat. But it also documented the scholar’s triumph in gaining some respect for his accomplishments, and in helping to dislodge certain prejudices from the minds of the era’s most learned men.

On August 30, 1791, Jefferson wrote:


I THANK you, sincerely, for your letter of the 19th instant, and for the Almanac it contained. No body wishes more than I do, to see such proofs as you exhibit, that nature has given to our black brethren talents equal to those of the other colors of men ; and that the appearance of the want of them, is owing merely to the degraded condition of their existence, both in Africa and America. I can add with truth, that no body wishes more ardently to see a good system commenced, for raising the condition, both of their body and mind, to what it ought to be, as far as the imbecility of their present existence, and other circumstances, which cannot be neglected, will admit.

I have taken the liberty of sending your Almanac to Monsieur de Condozett, Secretary of the Academy of Sciences at Paris, and Member of the Philanthropic Society, because I considered it as a document, to which your whole color had a right for their justification, against the doubts which have been entertained of them.

I am with great esteem, Sir, Your most obedient Humble Servant,


The discrimination African-Americans suffered from Jefferson and other bigwigs is well-documented, and Banneker’s brave, considered opposition to it stands forever among his many admirable achievements. The 1854 document A Sketch of the Life of Benjamin Banneker reflected:

He appears to have been the pioneer in the movement in this part of the world, toward the improvement of his race; at a period of our history when the negro occupied almost the lowest possible grade in the scale of human beings, Banneker had struck out for himself a course, hitherto untravelled by men of his class, and had already earned a respectable position amongst men of science.

Records suggest that Banneker also suffered discrimination by lower-profile white Americans, and had his achievements belittled and questioned. Despite the many pushbacks he withstood, however, Banneker remained joyfully curious and generous of spirit throughout his life. According to A Sketch of the Life of Benjamin Banneker, he was able to slough off the bitterness of others in part thanks to his prevailing interest in study. “His equilibrium was seldom disturbed by the petty jealousies and inequalities of temper of the ignorant people,” the book notes, “with whom his situation obliged him frequently to come in contact.”

Benjamin Ellicott, who prepared extensive notes on Banneker’s life for the Maryland Historical Society, remembered him as such in a letter:

Although his mode of life was regular and extremely retired, living alone, having never married,--cooking his own victuals and washing his own clothes, and scarcely ever being absent from home, yet there was nothing misanthropic in his character … [He was known as] kind, generous, hospitable, humane, dignified and pleasant, abounding in information on all the various subjects and incidents of the day; very modest and unassuming, and delighting in society at his own home.

Given Banneker’s wide-ranging interests and enthusiasm, then, it is perhaps fitting that a variety of parks, schools, awards, streets, businesses, and other public and private institutions and facilities all bear his name today. Admirers can learn about the accomplished scholar at Benjamin Banneker Park and Memorial in Washington, D.C., for example, or at Baltimore, Maryland’s Benjamin Banneker Historical Park and Museum. Others can choose to follow in his footsteps by exploring their passions and hobbies at community centers named for Banneker in Washington, D.C., Bloomington, Indiana, and Catonsville, Maryland. It seems possible, however, that the man himself might have been most fond of—or, at least, a very frequent visitor to—Maryland’s own Banneker Planetarium.

Header images via Wikimedia Commons // Public Domain

Know of something you think we should cover? Email us at

Original image
iStock // Ekaterina Minaeva
Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
May 21, 2017
Original image
iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

Original image
Stephen Missal
New Evidence Emerges in Norway’s Most Famous Unsolved Murder Case
May 22, 2017
Original image
A 2016 sketch by a forensic artist of the Isdal Woman
Stephen Missal

For almost 50 years, Norwegian investigators have been baffled by the case of the “Isdal Woman,” whose burned corpse was found in a valley outside the city of Bergen in 1970. Most of her face and hair had been burned off and the labels in her clothes had been removed. The police investigation eventually led to a pair of suitcases stuffed with wigs and the discovery that the woman had stayed at numerous hotels around Norway under different aliases. Still, the police eventually ruled it a suicide.

Almost five decades later, the Norwegian public broadcaster NRK has launched a new investigation into the case, working with police to help track down her identity. And it is already yielding results. The BBC reports that forensic analysis of the woman’s teeth show that she was from a region along the French-German border.

In 1970, hikers discovered the Isdal Woman’s body, burned and lying on a remote slope surrounded by an umbrella, melted plastic bottles, what may have been a passport cover, and more. Her clothes and possessions were scraped clean of any kind of identifying marks or labels. Later, the police found that she left two suitcases at the Bergen train station, containing sunglasses with her fingerprints on the lenses, a hairbrush, a prescription bottle of eczema cream, several wigs, and glasses with clear lenses. Again, all labels and other identifying marks had been removed, even from the prescription cream. A notepad found inside was filled with handwritten letters that looked like a code. A shopping bag led police to a shoe store, where, finally, an employee remembered selling rubber boots just like the ones found on the woman’s body.

Eventually, the police discovered that she had stayed in different hotels all over the country under different names, which would have required passports under several different aliases. This strongly suggests that she was a spy. Though she was both burned alive and had a stomach full of undigested sleeping pills, the police eventually ruled the death a suicide, unable to track down any evidence that they could tie to her murder.

But some of the forensic data that can help solve her case still exists. The Isdal Woman’s jaw was preserved in a forensic archive, allowing researchers from the University of Canberra in Australia to use isotopic analysis to figure out where she came from, based on the chemical traces left on her teeth while she was growing up. It’s the first time this technique has been used in a Norwegian criminal investigation.

The isotopic analysis was so effective that the researchers can tell that she probably grew up in eastern or central Europe, then moved west toward France during her adolescence, possibly just before or during World War II. Previous studies of her handwriting have indicated that she learned to write in France or in another French-speaking country.

Narrowing down the woman’s origins to such a specific region could help find someone who knew her, or reports of missing women who matched her description. The case is still a long way from solved, but the search is now much narrower than it had been in the mystery's long history.

[h/t BBC]