Decoding the Heavens

By Jo Marchant

In autumn 1900, Captain Dimitrios Kontos and his crew of sponge divers were sailing home from their summer diving grounds off Tunisia. They were heading for the island of Symi in the eastern Mediterranean, but were blown off course by a storm and sheltered by a barren islet called Antikythera.

After the storm’s retreat, they discovered on the seabed a spectacular shipwreck . A Roman ship from the first century BC, it was carrying stolen Greek treasures, including statues, armour and jewellery.

The divers salvaged the wreck for the Greek government, and the artefacts were taken to the National Archaeological Museum in Athens. Among the haul was a lump of rock no one unnoticed at first. Then it cracked open, revealing gearwheels, inscriptions, and dials. This “Antikythera mechanism” turned out to be the most stunning scientific artefact we have from antiquity. Nothing close to its complexity appears again for more than a thousand years.

For much of the last century this mysterious machine was largely ignored by mainstream historians. But thanks to a succession of men who devoted their lives to decoding the device (see video), its secrets have finally been revealed. It was a clockwork computer for calculating the varying movements of the Sun, Moon and planets, and even predicting future eclipses.

I first heard about the Antikythera mechanism in summer 2006. A paper revealing its workings was due to appear in the science journal Nature, where I was on staff as an editor. The story grabbed me immediately, and I travelled to Athens to see the remains of the mechanism, and meet those who had studied it.

In my new book, Decoding the Heavens, I describe the 100-year quest to understand the device. But along the way I became intrigued by the bigger tale, of where this unexpected technology came from and where it went for a thousand years. I was stunned to discover that the expertise embodied in the device was not lost. Traces were passed to the Islamic world, and back to Medieval Europe, where this ancient knowledge triggered much of the technology that shapes our lives today.

Jo Marchant in the author of Decoding the Heavens: A 2,000-Year-Old Computer and the Century-Long Search to Discover Its Secrets, published by Da Capo Press

Magic Squares

By Ian Stewart

According to a Chinese myth, the Emperor Yu, who lived in the third millenium BC, came across a sacred turtle in a tributary of the Yellow River, with strange markings on its shell. These markings are now known as the Lo Shu ("Lo river writing").

The markings are numbers, and they form a square pattern:

4 9 2
3 5 7
8 1 6

Here every row, every colum and every diagonal adds to the same number, 15. A number square with these properties is said to be magic, and the number concerned is its magic constant. Usually the square is made from successive whole numbers, 1, 2, 3, 4, and so on, but sometimes this condition is relaxed.

In 1514 the artist Albrecht Durer produced an engraving "Melancholia," containing a 4x4 square. The middle numbers in the bottom row are 15-14, the date of the work. This square contains the numbers

16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1

and has magic constant 34.

Using consecutive whole numbers 1, 2, 3,...., and counting rotations and reflections of a given square as being the same, there are precisely:

. 1 magic square size 3 x 3
. 880 magic squares of size 4 x 4
. 275,305, 224 magic squares size 5 x 5

The number of 6 x 6 magic squares is unknown, but has been estimated by statistical methods to be about 1.77 x 10 (19)



From the book Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart. Excerpted by arrangement with Basic Books, a member of the Perseus Books Group. Copyright © 2009.

But She Doesn't Look Like a Witch!

For those of you interested in having a peek at Maria Gaetana Agnesi, the woman for whom the mathematical formula "Witch of Agnesi" was named: here you go.

And for more on witches more generally, here are a few of our favorite posts:

Why Call It A Witch?

Witches and Midwives

Midwives and Witches, oh My!

Image from the book Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart. Excerpted by arrangement with Basic Books, a member of the Perseus Books Group. Copyright © 2009.

Why Call It a Witch?

Witch of Agnesi

Guest Post by Ian Stewart

Maria Agnesi was born in 1718 and died in 1799. She was the daughter of a wealthy silk merchant, Pietro Agnesi (often wrongly said to have been a professor of mathematics at Bologna), and the eldest of his 21 children. Maria was precocious, and published an essay advocating higher education for women when she was nine years old. The essay was actually written by one of her tutors, but she translated it into Latin and delivered it from memory to an academic gathering in the garden of the family home. Her father also arranged for her to debate philosophy in the presence of prominent scholars and public figures. She disliked making a public spectacle of herself and asked her father for permission to become a nun. When she refused, she extracted an agreement that she could attend church whenever she wishes, wear simple clothing, and be spared from all public events and entertainments.

From that time on, she focused on religion and mathematics. She wrote a book on differential calculus, printed privated around 1740. In 1748 she published her most famous work, Instituzioni Analitiche ad Uso Della Gioventu Italiana (Analytical Institutions for the Use of the Youth of Italy). In 1750 Pope Benedict XIV invited her to become professor of mathematics at the University of Bologna, and she was officially confirmed in the role, but she never actually attended the university because this would not have been in keeping with her humble lifestyle. As a result, some sources say she was a professor and others say she wasn't. Was she, or wasn't she? Yes.

There is a famous curve, called the "witch of Agnesi"....The curve looks remarkably unlike a witch--it isn't even pointy.


From the book Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart. Excerpted by arrangement with Basic Books, a member of the Perseus Books Group. Copyright © 2009.

Book of the Week: Cabinet of Mathematical Curiosities

By Holly Tucker

I make before you now an earnest confession: I am a not a math genius.

Thanks to graduate training, I feel pretty darn confident when it comes to historical research and critical theory. But math, well, let's just say that I'd never be able to play the Matt Damon character in Good Will Hunting.

For those more numbers-minded than I am, the history of early mathematics is actually very fascinating: Pascal, Fermat, and a host of others chased after math's greatest secrets.

Long ago, we profiled Kevin Devlin's The Unfinished Game here on Wonders and Marvels. (And I just noticed that I made the same confession about being math illiterate on that post too.)

Up this week is Ian Stewart's Professor Stewart's Cabinet of Mathematical Curiosities.

With the good help of Professor Stewart, I'll be offering up a few examples of why math can be so interesting to historically minded folks.

Extra points for the person who can name the guy in the picture above. It starts with A. He's known as the Father of Mathematics. Christian Huygens' father compared his son to this legend of 287-212 BCE. Anyone?

Give up? Archimedes.

Seventeenth-Century Math

I have to admit that the History of Math is one of my biggest gaps--or lacunes as they say in French--in my education as an early modernist. That probably has something to do with the fact that I barely survived my college math classes. Maybe I would have done better if Pascal or Fermat had been teaching...

To my delight, the good publicist fairies over at Basic Books had this gem delivered to my doorstep yesterday: Keith Devlin's The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern (A Tale of How Mathematics Is Really Done).

Yes, it's a mouthful of a title. But it looks like a great read for number-challenged folks who want to know more about why the early history of mathematics matters to us even now.

Here's the publishers blurb:

Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance.

The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the “unfinished game” problem: how do you divide the pot when players are forced to end a game of dice before someone has won? The idea turned out to be far more seminal than Pascal realized. From it, the two men developed the method known today as probability theory.

In The Unfinished Game, mathematician and NPR commentator Keith Devlin tells the story of this correspondence and its remarkable impact on the modern world: from insurance rates, to housing and job markets, to the safety of cars and planes, calculating probabilities allowed people, for the first time, to think rationally about how future events might unfold.