A Mathematical Passage to India: Nirvana By Numbers

A Mathematical Passage to India was the working title for a 30 minute Radio 4 feature I produced with best selling author and journalist Alex Bellos as presenter.  The programme is scheduled for broadcast on Radio 4 on 7th October, 11 am and is now entitled, Nirvana By Numbers.  It looks at some of the great contributions of Indian mathematics through ancient and medieval history and asks if Indian philosophical and religious culture had any influence on the emergence in India of inventions such as mathematical zero and the decimal place order number system. The following are photos we took along the way, recording interviews and sounds.

This is Professor Krishnamurti Ramasubramaniam at the Indian Institute of Technology Mumbai - a theoretical astrophysicist turned Sanskrit scholar. Ram told us about the extraordinary ways in which complex numerical information was coded into Sanskrit poetic verse, so it could be memorised by other mathematicians down the centuries.

After Mumbai came Puri, on the coast of the eastern state of Orissa.  Every year the seaside town is the location for the Rath Yatra chariot festival.  Three gigantic wooden chariots - each containing a statue of a deity, most importantly Lord Jagannath (an incarnation of Vishnu) - are pulled by armies of pilgrims and policemen from a temple at one of the street to another at the far end.

It's a well attended event.  The local newspaper speculated that 1.1 million people came for it.

Everyone had a good time and hoped that their sins would be absolved.

To prove this was a working trip.  In fact I was not resting my microphone on that gentleman's head.

The Rath Yatra chariot procession is kicked off by one of Hinduism's four top holy men, blowing a conch. That's His Holiness Jagadguru Shankaracharya Swami Shri Nischalananda Saraswatiji Peethedheeshwar.

His Holiness is the figurehead of Vedic Mathematics.  These are 16 sutras/algorithms/speed maths tricks which were claimed to have been divined from ancient vedic texts by the grand guru Tirthaji.  He was the Shankaracharya in Puri between 1925 and 1960.  The story is amusingly and well told in a chapter in the book 'Alex's Adventures in Numberland', by Alex Bellos (see below).

Alex clutches a mango following his interview with His Holiness.  Topics covered ranged across the spiritual importance of zero and whether mathematics is a path to Nirvana.

Our interview with His Holiness was secured with the assistance of Gaurav Tekriwal, the president of Vedic Maths Forum India.

Outside the Shankaracharya's Math (monastery).  Alex Bellos, Gaurav Tekriwal and Anushree Goenka Tekriwal.

A great gaudy blue temple in Puri.

Here's another of our interviewees with Alex: Professor Rajesh Kochhar, an historian of astronomy.  This is in New Dehli at the Jantar Mantar Observatory - a collection of early 18th century structures built by Moghul ruler Jai Singh.  They were supposed to function as astronomical measuring instruments.  Not Indian at all by tradition and owe more to observatories of earlier Central Asia.

I can recommend the monumental and delicious chicken biryani enclosed in a chapati casing at the Chutney restaurant in the Metropolitan hotel in New Delhi.  I can also give a thumbs up for the hotel as a place to stay.  Lovely staff and pleasing 1970s Japanese decor.  Handy for New Delhi railway station.

We didn't stay in Delhi for long.  Waiting and recording at New Delhi railway station for the Shatabdi Express to Gwalior in northern Madhya Pradesh.

We couldn't pass through Agra without getting off the train and visiting the spine-tinglingly beautiful Taj Mahal.

Marital devotion was also in the air when we arrived in Gwalior.  A wedding party at our hotel, the Usha Kiran Palace Hotel.  Highly recommended and booked at a great rate by travel agent Outbound Travels.  I cannot praise this Delhi-based travel company enough!  See more reasons further on.

Gwalior is interesting enough because of the great fort and its 15th-16th century palaces which sit on the steep hill above the city.  But we had come for some old numbers.

There's a tiny temple dedicated to an incarnation of Vishnu, carved in the sandstone cliff beneath the fort.  An inscription inside the temple dates it at around 875 AD.  The inscribed tablet also contains the oldest precisely dated symbols for the number zero in the world.

The photo above shows one of the special zeros in its use in '270'.

Alex was most excited, given that India was where mathematical zero (not to mention the misnamed Arabic decimal numeral system) was invented.

We have Professor Renu Jain of the Department of Mathematics at Jiwaji University to thank for our visit and recorded interviews here.  She sought permission for us and arranged additional interviewees on the inscription at the temple.

Professor Jain is a follower of the Jaina religion.  She told us that early Jain philosophers and mathematicians conceived of mind-numbingly gargantuan numbers including 10 to the power of 400 plus.  They also mused about different kinds of infinity - centuries ahead of western thinkers.

Towards the base of the Gwalior fort's cliff are several stunning ancient Jain temples.

Everything had gone so well on this trip that the end of our last recording day had to end with a mishap.

Ironically, given this whole trip was about numbers, I failed to identify the number of the train which we should have boarded back to New Dehli.  So I had us waiting for a delayed train going south rather than the punctual one heading the 300 kilometres north to the capital, and from where we were supposed to be flying home the next day.

And we failed to get on the last jam-packed train to Delhi that night, departing at 10.30 pm and scheduled to arrive at 6 am the next morning.  Perhaps it's a blessing we couldn't squeeze on that train.

Anyway, a call to the magnificent Outbound Travels saved the situation.  The wonderful Prateek Chawla scrambled a driver from Agra to pick us up at 4.30 am from our hastily rebooked hotel.  We got to New Delhi airport with more than enough time for a masala dosa for lunch before the flight to London.  

A Trip Around Mars - Mud for Life and Young Glaciers

Orbital view of the north polar region of Mars

There is a fascinating aspect of Mars which we rather rushed over in the second part of A Trip Around Mars, now on BBC World Service.  This post seeks to address the issue.  It's about the periodic melting of the water ice in its north polar regions and the growth of glaciers elsewhere, every few million years.

In the programme, it cropped up towards the end with Chris McKay of NASA's Ames Research Center.  He was the principal investigator on the Phoenix lander mission which went to the far North in 2008.

Chris mentioned how the occasional warming of the permafrost just under the high northern plains might create a "muddy mix" of dirt and water in which Martian microbes might persist - if they exist.  My editing of the show left out the mechanism for the warming and melting.

Wayward Tilting

It turns out that the angle at which Mars' north and south poles tilt changes dramatically over a period of several million years.  The Earth's axis of rotation remains at an angle of about 24 degrees; it is stabilised over time by the presence of our Moon.  Mars lacks this stabilising influence, meaning there are times when its north polar region tilts right over and becomes significantly more exposed to the Sun's radiation each year.  Ice warms, melts and/or sublimes into the atmosphere.

Greg Crater and its Young Glaciers

We heard another fascinating story about Mars connected with this.  It concerns a crater called Greg.  Greg is 66 kilometres across, lies in the middling latitudes of the southern hemisphere (east of the Hellas basin) and was named after a Victorian romantic and proto-science fiction writer.  Most remarkable are what look like glaciers on the inner slopes of its northern rim.

The story of Greg's glaciers was told to us by another of our interviewees, the eminent planetary geologist and astronomical painter, Bill Hartmann of the Planetary Science Institute, University of Arizona.

Kevin Fong and Bill Hartmann

Here is an audio clip of Bill describing the initial discovery and the appearance of the glaciers on the northern slopes of the crater, and 'glacial' landforms in southern parts of the crater.



This image shows the tongue-shaped glaciers in more detail.  My understanding is that white ice is not exposed at the surface in these structures.  They have a covering of regular red-brown Mars dust and rock.

The next image shows the unusual landforms around the crater's south inner wall.

Bill Hartmann's count of small craters that have hit the glaciers since their formation suggests they are extremely recent in Martian geological history.  As he says, between 5 and 20 million years.

How could you get ice accumulating and then flowing as glaciers so recently in this region of Mars?  Answers emerged from a collaboration with scientists in France, including global climate modeller Francois Forget.  Forget took his computer climate model and plugged in the Red planet's parameters instead of terrestrial ones - Martian gravity, atmospheric pressures and composition, Martian topography et cetera.  Then they used the computer models to estimate climate variation around Mars at various tilts of the planet's north-south axis.  Bill Hartmann takes up the story in this next clip.



To sum it up: a few million years ago, Mars was tilted over more extremely than today.  Ice in the north evaporated and sublimed into the atmosphere.  The model suggests it was most likely to snow out and accumulate as ice in Greg crater's region of Mars.

Radar Evidence for Ice Flows in the Greg Neighbourhood

Greg's glaciers are too small for existing orbiters with ground-penetrating radar to confirm that they are made of ice.  But not so far away, there are larger landforms that are.  Here's Bill again plus an image showing an ice apron around a mountain, in the general 'neighbourhood of Greg.

 Bill Hartmann thinks this fascinating story has a lesson for us here on Earth - particularly for certain brands of politicians and commentators who pour scorn on anthropogenic climate change and global climate modellers. 


Ice on Canvas - Bill Hartmann's Latest Astronomical Painting

Science aside but continuing the ice theme, Bill showed us one of his astronomical paintings in progress - a view of Saturn from one of its ice moons, Enceladus (if my memory is correct).

A Trip Around Mars - Steve Squyres and the Mars Exploration Rovers

The image is a montage panorama from the Mars rover Spirit (RIP) at the summit of Husband Hill, looking into the floor of Gusev Crater.  It's known as the Everest pan and is a favourite of Steve Squyres, the lead scientist for both Mars Exploration rovers, Spirit and Opportunity.  Kevin Fong and I interviewed Steve at his office in Cornell University for the BBC Radio series A Trip Around Mars.  On this page, I have posted excerpts of this superb interview - much of which didn't make it into the broadcast programmes.

Steve and Kevin with part of the 20ft Everest pan as background

In this first clip, Steve talks about the making of the Everest pan.



"A Desolate Kind of Beauty"

Sand dunes at Gusev Crater

Another image taken by Spirit.  Both rovers far exceeded their expected working lives.  They landed in 2004.  Spirit lost power for good six years later.   Opportunity is still going.  In this next clip, Steve talks to Kevin about the harsh beauty of the landscapes through which both robots have trundled.

Victoria Crater from above

"Some Things on Mars are Just Uniquely Martian"

The point of the rovers' explorations has been to characterise the conditions under which the rocks in their paths formed.  Was there water there?  What kind of watery environments?  Could these have been places hospitable to Martian microbes?  As you can hear in this next clip, Spirit found a place suggestive of geysers and volcanic steam vents (possibly as long ago as 4 billion years) and Opportunity discovered evidence of something like a dessicating acidic salt pan.   Steve and Kevin then go onto discuss the wider evidence for a lot of water in the planet's deep past - catacylsmic floods and the controversy of Martian oceans.

Opportunity's view of the Meridiani Plains

"Humans very much belong on Mars - it can't happen soon enough"

The Columbia Hills were named after the lost space shuttle, and each peak is named for a crew member.
In this last clip Kevin asks Steve Squyres about his hopes and inspirations.  His daily hope is that Opportunity remains alive for at least one day longer.  Then talk turns to the search for evidence of life on Mars, how Steve came to spend his working life on Mars and the place of humans in the Martian landscape.

Victoria Crater from rim edge

Mars lander sites

A Trip Around Mars - Kim Stanley Robinson in conversation

How do you get people into the landscapes of Mars by radio, rather than by rocket?    Kevin Fong and I faced the challenge in our BBC radio project, A Trip Around Mars.  We were lucky to secure a stellar cast of planetary scientists –  William Hartmann, Chris McKay, Steve Squyres et al. "We should interview Kim Stanley Robinson," said Kevin.  Stan is the author of Red Mars, Green Mars and Blue Mars – collectively known as the Mars Trilogy.  The books were published in the late 1980s and early 1990s.

The three novels tell an epic story of colonisation, terraforming and the making of a new global society.  More importantly for our programmes, KSR takes the reader just about everywhere on Mars with his descriptions of the planet’s myriad landscapes.  The Martian terrain is the narrative bedrock.

We interviewed Stan at his home in Davis, California in February and most of the interview didn’t make it into the broadcast BBC programmes.  So here’s more of it in three segments. 

This first clip covers Stan’s synchronous interest in the images of Mars from the Viking missions and his own exploration of the Sierra Nevada mountains.  It then moves to Mars’ greatest volcano Olympus Mons and the topographic giganticism of the Red Planet.



Olympus Mons

KSR elaborates on why he chose to set his story on Mars – an explanation encompassing the Viking missions, the Sierra Nevada, the Vietnam war, utopias and the end of the Cold war.   He’s happy to confine his exploration of Mars to the imagination.



A Martian landscape by William Hartmann

In the last audio clip, Kevin and Stan talk about how data from Martian orbiters influenced the writing of the novels.   We hear that KSR was led astray by miscalculations of the topography of the Hellas basin.  It's the largest impact crater in the southern hemisphere.  Stan filled it with a sea.  Kevin and Stan also discuss the relationship between scientists and science fiction writers.

 

As an aside, it's said that the lowest region of Hellas is deep enough for liquid water to be stable at the surface.  There's enough atmospheric pressure to prevent water boiling away as it would do elsewhere on Mars (except at the bottom of Eos Chasma in Vallis Marineris).  On the warnest days, it would be liquid, say Pascal Lee of the Mars Institute and Margarita Marinova of NASA Ames Research Centre.



Chasma Borealis in the Martian north polar ice cap

Kim Stanley Robinson's next novel is set on the Earth during the last ice age, 20,000 years ago.  It's called Shaman and is out in September 2013.