The Magic Hypercube Of Nasik



The Whipple Museum of the History of Science contains, among other mathematical objects, a magic hypercube constructed in 1877 by Andrew Hollingworth Frost at Nasik ( India ). 

This 3-dimensional Nasik square is the analogue of a magic square, whose rows, columns and diagonals all add up to the same number.

A Nasik magic cube is a magic cube with the added restriction that all 13m2 possible lines sum correctly to the magic constant. This class of magic cube is commonly called perfect

 The Nasik square of Frost was the first magic cube discovered. 

Frost had been a missionary in a city named Nasik in India. Thus, his cube is called a “Nasik cube”, and was published in 1866, in an English scientific magazine, The Quarterly Journal of Pure and Applied Mathematics.


Frost (A. H.), “The Properties of Nasik Cubes,” Quarterly Journal of
Mathematics, London, 1878, p. 93. ( I don’t have access to this paper yet, if you do - please let me know. ) 

East India Company & the scientific revolution

I have mentioned the British East India Company at least twice this week in connection with the scientific revolution. Its fleet and merchants acted as pollinators of European science everywhere they went, knowingly or accidentally. 

Firstly, in the context of company sailors providing tidal data that would be used to support the theory of universal gravitation by Newton and his colleague Edmund Halley. 

Secondly, the history of logarithmic tables provides another connection with navigation: 

It was not until 1614 that Napier’s first work on this subject, Mirifia logarithmorum canonis descriptio (known as the Descriptio), was published. In addition to tables of logarithms the Descriptio also contains an account of the nature of logarithms and a number of examples explaining their use. The East India Company was so impressed by Napier’s Descriptio that it asked Edward Wright, a Cambridge mathematician and expert in navigation, to translate it into English for the benefit of the Company’s seafarers. From the very beginning of logarithms their utility to navigators has been of supreme importance in their development. (Graham Jagger, The Making of Logarithmic Tables)

David Arnold also observes that: “Company rule in India was contemporaneous with one of the most momentous phases of modern science, from the rise of Enlightenment natural history to the eve of Darwinian biology. “

The East India Company’s Court of Directors in London exercised a commanding position in relation to science in India. One of the leading patrons of science in Britain itself, on the subcontinent the Company and its servants enjoyed a near monopoly over Western scientific activity. Anxious to preserve its commercial privileges and prevent outsiders from undermining its authority, the Company closely regulated European access to India. Its approval was essential for any kind of scientific expedition to be undertaken and the Company was disinclined to allow scientific visitors, however eminent they might be. Apart from the French naturalist and traveller Victor Jacquemont, who died in India in 1831, the greatest exception to the scientific monopoly of Company servants was the expedition to India in 1848-50 of Joseph Dalton Hooker, the foremost botanist of nineteenth-century Britain. The German naturalist Alexander von Humboldt sought, but was never granted, permission to visit India. Many leading British scientists of the period – Joseph Banks, Charles Lyell, and Charles Darwin among them – showed great interest in the natural history of India without ever visiting the country in person. Europe’s scientists and collectors relied instead on informal networks of contacts with army officers, doctors and officials – or on the magnanimity of the Company itself – to provide them with specimens, drawings and scientific information. ( David Arnold, Science, Technology & Medicine in Colonial India


  1. Newton On The Ganges, by Rohit Gupta being Volume 5 of The Compass Chronicles. 
  2. Telescopes, Logarithms & Computers: A 400 Year Journey on Zetatrek. 
  3. Image source


Camera Obscura.

Reading List #003: A Garden Of Stars

Below are some of the interesting articles that I came across while writing my monthly column The Compass Chronicles Vol. 5 for The Hindu BusinessLine. Here are Volume 4, Volume 3, Volume 2 and Volume 1.


  1.  The Fall Of Shergotty (pdf), by Kevin Kinchka
  2. Mystery of the meteorite in Bihar’s opium fields, by Amitava Ghosh
  3. A survey of Bengali writings in science and technology (1800-1950) by various authors. 
  4. Introduction of Modern Astronomy In India during 18-19 centuries, (pdf) by S.M. Razaullah Ansari
  5. The Growth of modern astronomy In India, R.K. Kochhar
  6. Modern Astronomy in Indo-Persian Sources, by S.M. Razaullah Ansari
  7. Transit Of Mercury, 1651: Earliest telescopic observation in India by R. K. Kochhar 
  8. The Philosopher Burmese Prince & the Air Pump, by Jonathan Saha

Clockwork To Chaos: an online workshop (19 July-19 Oct 2014)



This manuscript page from 1665 shows a 23-year old Isaac Newton calculating the area under a hyperbola ( the curve drawn on the top left of the page).

He calculates no less than 55 decimal places, meticulously adding values from each term of an infinite series. The series emerges…


We close pollinator week with this animated tribute to the bees, bugs, birds, bats, and others who make life a little sweeter.
Original from Maria Sibylla Merian’s Raupen wunderbare Verwandelung und sonderbare Blumennahrung , 1730


We close pollinator week with this animated tribute to the bees, bugs, birds, bats, and others who make life a little sweeter.

Original from Maria Sibylla Merian’s Raupen wunderbare Verwandelung und sonderbare Blumennahrung , 1730

(via scientificillustration)

[Lecture] Secrets of the 3rd Dimension


In this workshop, Compasswallah will use 3D-printing technology to showcase cosmic visions of solid geometry from the 16th century in Germany.

Artists, philosophers and mathematicians have studied the beauty of the five Platonic solids for thousands of years. The astronomer Johannes Kepler proposed in his 1592 book that these shapes were embedded into the very structure of the universe. A wide variety of such structures - known as polyhedra were subsequently discovered - and used as models to explain atoms, crystals, viruses, radiolaria, or simply as ornamental motifs.

Even before Kepler, artists and goldsmiths such as Wenzel Jamnitzer in Nuremberg had begun to use Platonic geometry in their designs. Most of these designs remained imaginary for centuries, but today we can use modelling software like AutoCad or Solidworks to bring them into reality with 3D printers. Maker’s Asylum is a community workshop in Bandra (Mumbai), dedicated to spreading technical know-how around this technology.

The lecture will outline a history of 3-dimensional geometry and its role in biology, physics and chemistry. Alongside, the audience will see a live demo of a solid object being printed out by the machine.

Registration: There is a minimum donation of INR 400, to be paid on arrival. Seats will be limited to first 20 people who register online.

Time: Wednesday June 25, 6-8pm

Links: ,

Venue: Maker’s Asylum, Rizvi Palace Building, Next to Mamma Mia’s Pizza, Opp Yoko’s Sizzlers, Chinchpokli Road, Off Hill Road, Bandra West, MUMBAI 400050, MH, INDIA

Contact: Vaibhav: +91 7710991000 or Rohit: +91 97847 09366

About the speaker: The term Compasswallah is 19th century colonial slang for British surveyors roaming the Indian countryside with telescopes and sextants. It is also the assumed identity of Rohit Gupta, an artist, writer and historian of mathematics and science. Gupta’s corpus of work from 2000-2014 includes a published collection of science-fiction, comics, a variety of essays, innovations in new media art and technology, lectures, film and workshops. ( He tweets as @fadesingh )


Carnivalesque Vol. 102: A Midsummer Dream


Carnivalesque is an interdisciplinary blog carnival dedicated to pre-modern history upto the year 1800 CE. Compasswallah is proud to host the 102nd edition putting the history of science in focus, with an eye turned to the farthest fringes of human art & culture

Perhaps the most famous figure in pre-modern western literature, William Shakespeare “was born just twenty-one years after Copernicus’ De revolutionibus was published and lived through the period in which Kepler and Galileo, among others, made the heliocentric hypothesis..”. This correspondence has inspired a book on Shakespearean science by Dan Falk, which is examined closely for historical accuracy by The Renaissance Mathematicus. The bard’s 450th birth anniversary also marks the release of a book by two antiquarian booksellers who claim to be in possession of a dictionary Shakespeare often consulted. 

At the H-word Rebekah Higgitt looks at another famous literary persona, of the marooned sailor Robinson Crusoe, explicating that it was a hoax: ”While the book is seen today as an important precursor to the novel, as part of a new genre of realistic fiction, it was designed, at least in part, to confuse and to question. Robinson Crusoe was its purported author, not its title.” The theme of nautical adventures is continued by Benjamin Breen at The Appendix in “A Pirate Surgeon in Panama" describing a curious encounter of European medical thought with that of the natives circa 1670:

But if [Lionel] Wafer is far from the only seventeenth-century European to leave a report of his adoption into an Indian tribe, there are aspects of his story that are virtually unique. As we’ve seen, he practiced a form of hybrid Kuna-European medicine.

The untimely death of two negro crewmen aboard Captain Cook's  circumnavigation of the globe in 1769 are the subject of Richard Conniff's short note at Strange Behaviors. And Michiel van Groesen looks into the iconography of Columbus’s 1592 landing in Americas. 


Although sea voyages were rendered less dangerous by maps, cartography has always had deeper implications than just to navigation, such as psychogeographical diagrams of belief or cosmology. David Bressan outlines a concise history of geological maps, in a series of four posts

Following a bunch of recent open-access initiatives, the New York public Library has released thousands of historical maps online. Following close on its heels is the Leiden Library with 12,000 Dutch colonial maps from Indonesia, Antilles & Surinam. 

A Memorial & Miscellany

The ensemble of 34 posts remembering the passing of art historian Hasan Niyazi are a rich memory of the art historian himself, and also the subjects touched upon by him. In this context Daydream Tourist writes on the painting technique of sfumato and its science

Sfumato, which come from the Italian word for smoke, is the effect of creating transitions from light to dark without any discernible lines.  An invention of the Renaissance, it is a technique most closely associated with its champion Leonardo da Vinci.

In Luca, Leonardo, Albrecht and the search for the third dimension, Thony Christie carves a circuitous route in the history of renaissance mathematics and finally connects it to Hasan Niyazi’s favorite painter, Raphael. 

Two experiments in the digital domain worth mentioning are Wilfried Hou Je Bek’s comparative recipes of 16th versus 20th century food, and  B4XVI, where hip hop meets the middle ages. Also worth reading is the latest in a continuing series of discussions around the reboot of a TV series called Cosmos, in which they talk about Kepler and the age of the Earth

Finally, the world’s oldest decimal multiplication tables were found in a market in Hong Kong, and an archaeological trail of grains has pushed back the period of Silk Road interactions by 2000 years.   

[ Image sources: Top> unidentified image from British Library Or. 5259 f29 Middle > Ebstorf Mappa Mundi ] 

The Compass Chronicles Vol. I: Tales of Attraction

(This is the annotated version of my new column for The Hindu Business Line’s magazine BLink, published on April 4, 2014. The image is a depiction of the Konark Sun temple from James Fergusson’s 1847 text Ancient Architecture in Hindoostan. 

That the Sun Temple of Konark once contained a giant lodestone magnet, which held the entire edifice together by its force — is a story often told. And in the telling, this tale becomes taller, whence idols in the sanctum sanctorum begin to levitate, and the temple’s magnetic field is said to disorient the mariner’s compass on any ship passing in the Bay of Bengal. Or imagine, the holy magnet pulling out all the iron nails of a Chinese wooden ship causing it to fall apart. Some have even tried to explain the infamous Indian rope trick using various magnetic contrivances.

Another tall story, both incredible and uncertain, attributed to an American general named Benjamin Alvord in a letter to the poet Longfellow (circa 1842), is about a magnetic plant: “There has been discovered in the forests of India a strange plant (philotacea electrica) which possesses, to a very high degree, astonishing magnetic power. The hand which breaks a leaf from it receives immediately a shock equal to that which is produced by the conductor of an induction coil. At a distance of six metres a magnetic needle is affected by it, and it will be quite deranged if brought near. The energy of this singular influence varies with the hours of the day. All powerful about two o’clock in the afternoon, it is absolutely annulled during the night. At times of storm its intensity augments to striking proportions. While it rains the plant seems to succumb: it bends its head during a thunder-shower and remains without force or virtue even if one should shelter it with an umbrella. No shock is felt at that time in breaking the leaves, and the needle is unaffected by it. One never by any chance sees a bird or insect alight on this electric plant; an instinct seems to warn them that in so doing they would find sudden death. It is also important that where it grows none of the magnetic metals are found, neither iron, nor cobalt, nor nickel — an undeniable proof that the electric force belongs exclusively to the plant. Light and heat, phosphorescence, magnetism, electricity, how many mysteries and botanical problems does this wondrous Indian plant conceal within its leaf and flower!”

Apart from a few scattered references, the history of magnetism in India prior to the British Raj is poorly documented, much to the chagrin of science historians. That Indian sailors were already using the magnetic compass had been noted by Vasco Da Gama (circa 1497). A few decades later, while sailing near Goa and Bombay, the Portuguese naval officer João de Castro discovered magnetic declinations in his compass caused by nearby ferrous rocks. Even Sawai Jai Singh II, the astronomer-king of Jaipur — although his artistic sundials are singular — seems to have had little interest in magnetism.

The first major character in magnetism from India appears to be Jagadish Chandra Bose in the late 19th century, by whose time the relationship between electricity and magnetism had been firmly established. And for some reason Bose began to investigate the electrical and magnetic signals in plants through his invention, the magnetic crescograph. There is no public record, but one wonders whether Bose knew of that mysterious Indian plant mentioned by Alvord, the philotacea electrica. His early biographer Philip Geddes does mention a similar American “compass plant” (silphium laciniatum) in the book The Life & Work Of Sir Jagadis C Bose (1920).

More importantly, Geddes describes Bose’s spectacular experiments with radio waves: “Bose himself had as early as 1895, in a public lecture in Calcutta, demonstrated the ability of electric rays to travel from the lecture-room, and through an intervening room and passage, to a third room 75 feet away from the radiator, thus passing through three solid walls on the way, as well as the body of the chairman (who happened to be the Lieutenant-Governor). The receiver at this distance still had energy enough to make a contact, which set a bell ringing, discharged a pistol, and exploded a miniature mine.”

This ability to transmit signals through space would soon evolve with better engineering into sophisticated radar systems in the build-up to World War II, and radar — in as much as it was being used for the purpose of sea and air navigation, was really an advanced avatar of the magnetic compass. Both the radio and the compass were for Bose, ways of seeing “invisible light”, they were his prosthetic Third Eye — for visible light and radio waves were different slices of the same electromagnetic spectrum.

Bose’s vision is both romantic and eloquent, he writes: “From amongst the innumerable octaves of light, there is only one octave, with power to excite the human eye. In reality, we stand, in the midst of a luminous ocean, almost blind! The little that we can see is nothing, compared to the vastness of that which we cannot. But it may be said that out of the very imperfection of his senses, man has been able, in science, to build for himself a raft of thought by which to make daring adventure on the great seas of the unknown.”

Further Reading

  1. The Life & Work Of Sir Jagadis C Bose (1920) by Geddes
  2. João de Castro, the Portuguese officer and scientist is notable in this regard:”..the comments made by João de Castro are the most important record of values of magnetic declination in the Atlantic and Indian oceans, in the sixteenth century, and useful for the study of terrestrial magnetism. He made 43 determination of magnetic declination through rigorous measurements of geomagnetic declination over the entire circum-Africa route. The instrument used by him was the Bussola de Variacão, also developed by Felipe Guillen a decade earlier in Seville. João de Castro undertook many observations and can in a way be considered as one of the discoverers of crustal magnetism. He discovered spatial variations of Declination in that Bay of Bombay (near Baçaim), which he attributed to the disturbing effects of underwater rock masses (this is near where the large basaltic and rather strongly magnetized Deccan traps outcrop). In the 1890s, G. Hellman, quoted by Chapman and Bartels (1940), considered Castro to be the most important representative of scientific maritime investigations of the time, and the method he tested was universally introduced on ships and was used until the end of the sixteenth century.
  3. On The Compass Plant by Benjamin Alvord
  4. Silphium Laciniatum, the compass plant: Wikipedia
  5. Gautam Pemmaraju asked if there were some ancient sources for magnetism and I found this from Magnetism In Medicine: A Handbook by Nowak & Andra: 

E. Morieu. Astronomy Plate for Charles Bouret’s Geographic Atlas. Mexico, Paris. 1878.


E. Morieu. Astronomy Plate for Charles Bouret’s Geographic Atlas. Mexico, Paris. 1878.