Workshop: The Seven Greatest Works Of Science



On Sunday the 21st of September, I’ll be conducting a workshop in Bombay hosted by Meera Damji at her residence in Lower Parel. The duration will be from 10AM to Noon.

The theme of the session will be, as usual - the history of science.

However, this time we will try to identify some…


Levinus Vincent. Wondertoonel der Nature, Cabinet of Curiousities. 1715.

The Auroras of Bombay (1872)

A singularly remarkable phenomenon is reported in the Times of India, dated Feb 6, 1872: 

The Wikipedia explains why an aurora in the tropics would be a rare event: 

Most auroras occur in a band known as the auroral zone, which is typically 3° to 6° wide in latitude and observed at 10° to 20° from the geomagnetic poles at all local times (or longitudes), but often most vividly around the spring and autumn equinoxes. The charged particles and solar wind are directed into the atmosphere by the Earth’s magnetosphere. A geomagnetic storm expands the auroral zone to lower latitudes.

The islands of Bombay are notable in the history of geomagnetism also because of the Portuguese admiral and scientist João de Castro, who discovered the first instance of magnetic declination in the compass needle due to underwater rocks “near Baçaim, on 22 December 1538” ( the modern day suburb of Vasai ). This observation might have been the first physical evidence which would culminate in William Gilbert’s theory ( 1600, De Magnete) that the entire Earth is a giant magnet. 


  1. Geomagnetic storms over India: A close look at historic space weather (pdf), by Chanchal Uberoi
  2. The Compass Chronicles Vol. I: “Tales of Attraction
  3. The painting of Bombay harbour shown above (1754) is by Dutch artist Jan Van Ryne. 
  4. Magnetologia Curiosa: BibliOdyssey (image below) 




Athanasius Kircher. Matteo Ricci (Li Madou) and Xu Guangqi. China Illustrata. 1667.

I can’t help but imagine they’re comparing the grandeur of their respective hats.
Matteo: Il mio cappello è più grande!!!
Guangqi: 你讲废话!我的帽子是全世界最大的!!!
Here’s more on the Italian missionary Matteo Ricci, and on Athanasius Kircher, and the Chinese cholar-bureaucrat, agricultural scientist, astronomer, and mathematician Xu Guangqi.



Athanasius Kircher. Matteo Ricci (Li Madou) and Xu Guangqi. China Illustrata. 1667.

I can’t help but imagine they’re comparing the grandeur of their respective hats.

Matteo: Il mio cappello è più grande!!!

Guangqi: 你讲废话!我的帽子是全世界最大的!!!

Here’s more on the Italian missionary Matteo Ricci, and on Athanasius Kircher, and the Chinese cholar-bureaucrat, agricultural scientist, astronomer, and mathematician Xu Guangqi.


Athanasius Kircher. Ars Magna Lucis et Umbrae (The Great Art of Light and Shadow). 1646.

The Icosahedron Of Tipoo Sultan

File:Tipu death.jpg

Mysteriously, the five Platonic solids are almost entirely absent from the history of mathematics and science on the Indian subcontinent, but this gold icosahedron found in Tipoo Sultan’s treasury is an exception. 

This is a small, very well crafted icosahedron with a number in East Arabic numerals on each face. It apparently was in the treasury of Tipu Sultan at the time he was overthrown by the British in 1799 at Seringapatam in southern India, but this object may be much older than from the time of Tipu or his father. The origin of this, where it was created and for what purpose appear to have been lost with time.


Paul Bien speculates about the numerals on this artifact, which are the following, arranged as a net unfolded from the solid by cutting some edges: 

numbered icosahedral folding net

The total sum of the numbers is 5190. The sum of the numbers on the lid is 3206, leaving the sum of the numbers on the rest of the icosahedron at 1984. From these numbers the structure of  the icosahedron yields very close values for the golden ratio, phi= 1.618.

The basic geometric definition of the golden ratio is that the whole is to the larger part as the larger part is to the smaller part. Applying this to  the icosahedron, take the whole = 5190, the larger part = 3206, and the
smaller part = 1984:

whole/larger part = 5190/3206 = 1.6188 = 1.0005 * phi

larger part/smaller part = 3206/1984 = 1.6160 = 0.9987 * phi.

There are many more intriguing results including ones for pi, and the square roots of 2, 3, and 5. These results arise in some very simple ways from the icosahedron that appear to leave little room for these results occurring by chance. Also, it appears that the twenty individual
numbers themselves come about from some very clever number play between pi and phi. There’s little doubt that whomever created this had a very deep and insightful mathematical mind.

However, the actual structure and purpose of the object remains a mystery. 

Update: As soon as I tweeted this post, came a very interesting response from Sayeed Anjum suggesting that this could be related to Abjad numerals. I do not discount that possibility as unlikely: 

Further Reading

  1. Math Baubles, by Brian Hayes
  2. A Numbered Icosahedron From India, by Paul Bien
  3. The sale at Sotheby’s describes Lot 65
  4. The Siege of Seringapatanam (1799): Wikipedia, source of the topmost image. 

[Reading List] The Astronomer & the Chessboard


The latest volume of The Compass Chronicles is about some intersections in the history of chess, astronomy and magic squares. However, there are many things I had to omit while writing it, due to the newspaper’s word limit.

For example, this wonderful quote comparing chess to calculus: 

Major Carl Jaenisch, the mathematician and chess analyst declared chess to be more difficult than the integral calculus , and when it is borne in mind that the position of the pieces (each of which has different powers) varies at each move on each board giving rise to almost infinite variations, and that the blindfold player has to mentally examine the most important ones on each board, without omitting a single link in the chain, and in most instances successfully emerge from this labyrinth…

Blindfold chess by itself has a colorful history, and there seem to be many exhibitionist players who toured the early modern world, including one Greek by the name of Yusuf Chelebi who may have toured India and the Near East. 

At least one respondent on Twitter wanted to know more: 


So here you go, Raya. 

Further Reading

  1. Joseph Needham on the origins of chess
  2. The chess-set of Colonel James Tod, historian of Rajasthan
  3. Maharaja & the Sepoys: a variant of chess that emerged in the late 19th century colonial India. 
  4. The Cox-Forbes theory on the evolution of chess in India, now largely discredited. 
  5. The Wheat & Chessboard problem
  6. Rudrata's Kavyalankara
  7. The Magic hypercube of Nasik
  8. There are no magic knight’s tours on the chessboard
  9. The greatest chess puzzle, by Aryan Argandewal
  10. A short history of chess, Henry A. Davidson
  11. Knight’s Tour

Stunningly appropriate for Compasswallah, this quasi-mathematical quilt constructed by a British soldier stationed in India during 1863-1877, a few years after the Great Mutiny. 


Stunning military quilt by Francis Brayley. Made of wool.


Soldiers were encouraged to take up sewing as a valid alternative to the less salubrious pursuits of drinking and gambling; needlework was also used as a form of therapy for those injured in conflict and recuperating in hospital. Unsigned and undated, it was possibly made by Private Francis Brayley, who served in the 1st/11th Foot in India between 1863-1877. From the Muster Rolls Brayley appears to have enjoyed good health until the latter half of 1875 and most of 1876, when he was hospitalised due to ‘Rifle Drill Fatigue’. Brayley may have embarked on his patchwork during this period.

The Red Rust of Elephanta

The only survivor of an 18th century scientific expedition from Denmark to Arabia - was a German scholar by the name of Carsten Niebuhr. He arrived in September 1763 from Mocha to Bombay, where the last of his expedition members ( its only doctor ) was claimed by malaria.

“Mr. Cramer, sinking at length under his complaints, died at Bombay, on the 10th of February 1764, in spite of the cares of a skillful English physician,” notes his memoir. Given the nature of this expedition and the volatile political spectrum of the subcontinent, Niebuhr’s feverish description of India at that time is important.

His account outlines the struggle of multiple powers wrestling for control: the English empire on its rise, the lurking presence of embittered Marathas, and the waning of Portuguese influence - whom he takes the opportunity to mock in this story:

“A small fleet of merchant ships bound from Goa to Diu, under the protection of two frigates, was seen, one evening, off Bombay. In the night we heard a brisk firing of guns, and imagined that the Portuguese were engaged with the Mahrattas. But in the morning, it appeared that their exploits had ended merely in the destructions of a quantity of bamboos, from 30 to 40 feet high, which the fishermen had set up in a sand bank for the purposes of their fishing. Those valiant Portuguese had taken the bamboos for the masts of an hostile fleet. To crown their glory, the admiral found himself compelled by the governor of Bombay to pay damages to the fishermen.”

Describing the state of Hindu idols in the caves of Elephanta Island (which he visited thrice in order to draw its antiquities) Niebuhr wrote:

“I should suppose that the modern Indians no longer adore their ancient Gods, but have adopted new objects of worship, whom they represent by stones painted red, for want of more artificial statues. In many places through India, indeed, may be seen similar piles of red stones, which are held in high veneration among a people who have almost entirely lost all knowledge of the fine arts. The rest of the temple being perfectly neglected, is now the haunt of serpents and beasts of prey. One dares not enter it without first making several discharges of fire arms…”

The symbolic importance in Hindu culture of the vermilion pigment Niebuhr mentions cannot be over-stated, especially in relation to human blood and fertility. Niebuhr must have wondered, that by applying red color to stones the devout imbue them with a key attribute of life, a soul - or do they in turn imply that the Gods too are human and mortal?

Nevertheless, by the 19th century chemical science had established enough for the Victorian art critic and philosopher John Ruskin to note that the source of red color in earth, clay and blood is an oxide of iron. Ruskin declared eloquently in his 1858 lecture on The Work Of Iron In Nature, Art & Policy:

“It is not a fault in the iron, but a virtue, to be so fond of getting rusted, for in that condition it fulfils its most important functions in the universe, and most kindly duties to mankind. Nay, in a certain sense, and almost a literal one, we may say that iron rusted is Living; but when pure or polished, Dead. You all probably know that in the mixed air we breathe, the part of it essentially needful to us is called oxygen; and that this substance is to all animals, in the most accurate sense of the word, “breath of life.” The nervous power of life is a different thing; but the supporting element of the breath, without which the blood, and therefore the life, cannot be nourished, is this oxygen. Now it is this very same air which the iron breathes when it gets rusty.”

Another naturally magnetized oxide of iron, called magnetite - was known to the ancients in the form of lodestone which was used as a magnetic compass for navigation. That such a thing should exist - which of its own volition foretells the direction of things in the universe, would have been a cause of great mystery and wonderment. One of the investigators of this phenomenon, Guillaume Le Nautonier wrote ( around 1601) of this miraculous device as “that little piece of iron that seems to live and have judgement.”

In a sense, the very life in an object seems to come from either blood or magnetism, both of which are a result of the properties of iron, the element which is now understood to have the most stable nucleus. Soon after Nautonier it began to dawn in the works of William Gilbert and others that the Earth itself was a giant magnet, through which circulated magnetic fields from pole to pole ( like blood through a body ).

There must have been a few who wondered if the Earth too was a living God. What other reason could there be to carve out faces and forms that emerge in bas-relief from the rocks of a mountain, or inside the walls of a cave, rather than to suggest Gods emerging from the strata and body of Earth?

Strangely enough, it was the same John Ruskin who recited a poem titled Elephanta And Salsette, at Oxford in June 1839, which is what Niebuhr’s malarial brain must have felt at the sight of these somnambulant caves of colonial India -

Low in the dust, its rocky sculptures rent,
Thine own memorial proves thee impotent.
thy votaries mourn thy cold unheeding sleep,
Chide where they praised, and where they worshipped,

At the Worcester Art museum’s website, a Chola dynasty granite sculpture of trimurti “with traces of gesso and red pigment” has been described thusly: “…the four faces of Brahma symbolize the four Vedas as well as the cardinal points of the compass.”


  1. Herr Niebuhr & the Remarkable Traverse by C. Braton Crattie
  2. Niebuhr’s Trimurti drawings
  3. The Work Of Iron by John Ruskin

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)