Showing posts with label Maxwell. Show all posts
Showing posts with label Maxwell. Show all posts

Thursday, May 19, 2016

James Clerk Maxwell

James Clerk Maxwell (1831-1879) is comparable to Isaac Newton and Albert Einstein in terms of the importance of his work, but he is not as well known.  As well as being a mathematician and mathematical physicist he was a published poet, and his Christian faith was central to his life.  
It was in 1861 that he unified electricity, magnetism and light with his equations, so the 150th anniversary of this discovery was recently celebrated.  The year 2011 was quite a year of anniversaries in physics, from Boyle's publication of "Sceptical Chymist" to the discovery of superconductors to Rutherford's model of the atom and more!

I said earlier that Maxwell is comparable to Einstein and Newton.  I think this quote from a 2011 article in The Economist puts it well:

"Worthy intellectual accomplishments, all.  Yet they pale in comparison with Maxwell's.  This is not just because, unlike a lot of subsequent theoretical advances, his insight has already yielded a century's worth of tangible results, from radio to mobile phones.  (Only a century because it took scientists several decades before they had grasped the theory's full significance and put it into practice.) . . . . He showed that nature ought not to be taken at face value, and that she can be cajoled into revealing her hidden charms so long as the entreaties are whispered in mathematical verse.  In doing so he paved the way for the pursuit of physicists' holy grail: the grand unified theory, a set of equations which would explain all there is to know about physical reality. . . . Maxwell remains the great unsung hero of human progress . . . . His life's work, which also includes remarkable contributions to thermodynamics (not to mention taking the world's first colour photograph, also 150 years ago) is among the most enduring scientific legacies of all time, on a par with his more widely acclaimed peers, Isaac Newton and Albert Einstein.  It deserves to be trumpeted."

Maxwell was born at the house pictured above, at 14 India Street, Edinburgh, though not long after his birth his family moved to their home in Glenlair in the countryside of Scotland where his natural curiosity was soon apparent, and he always wanted to know how everything worked.  The family planned his education to be carried out by his mother until it was time for him to attend Edinburgh University.  Sadly, his mother died when he was 8 years old, and, after an unsuccessful attempt at having a tutor work with him at home, he was sent to the Edinburgh Academy.

Maxwell was 14 years old when he wrote his first mathematical paper, an exploration of the ellipse and of curves with more than two foci.  This work was read to the Royal Society of Edinburgh, though not by Maxwell, as he was considered too young to present his work. 

At age 18, while attending the University of Edinburgh, he wrote two further papers for the Transactions of Edinburgh's Royal Society, but he was still considered too young to read them, so they were read to the society by his tutor instead.
Main Campus, Edinburgh University

Though Maxwell had chosen to do his undergraduate work at Edinburgh University he did head to Cambridge for his graduate work and earned his degree in mathematics there.  In the famous tripos testing he earned the position of "second wrangler."  He is better known as a physicist or a mathematical physicist but his degree was in mathematics.
Looking down on Trinity from Great St. Mary's - Clock Tower, Chapel, Great Gate

While a student at Trinity he decided to examine his faith deeply.  He wrote:

"Now my great plan, which was conceived of old, . . . is to let nothing be wilfully left unexamined. Nothing is to be holy ground consecrated to Stationary Faith, whether positive or negative. All fallow land is to be ploughed up and a regular system of rotation followed. . . . Never hide anything, be it weed or no, nor seem to wish it hidden. . . . Again I assert the Right of Trespass on any plot of Holy Ground which any man has set apart. . . . Christianity — that is, the religion of the Bible — is the only scheme or form of belief which disavows any possessions on such a tenure. Here alone all is free. You may fly to the ends of the world and find no God but the Author of Salvation. You may search the Scriptures and not find a text to stop you in your explorations . . ."
Trinity Great Court
He was elected a fellow of Trinity - eventually also accepted a professorship in Marischal College in Aberdeen, Scotland - and later moved to London and became professor at King's College there.  His time in London was a very productive period of his life - perhaps the most productive.  
King's College London
He resigned his chair there in 1865 and returned to his Scottish family home with his wife, but in 1871 he accepted, somewhat reluctantly, an offer from Cambridge to be the first Cavendish Professor of Physics.  He was there in charge of developing the Cavendish Laboratory, overseeing every element of its construction and design.

The photographs below are of the "Maxwell Lecture Theatre" in the Old Cavendish (which currently belongs to the Sociology Department, and for a time until quite recently had been being used for storage; the fate of this historic hall is uncertain at this point.)




Maxwell died of cancer at the age of 48 in Cambridge.  He remained calm and firm in his faith through to the end.

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Edinburgh University has expanded over time, and in 1919 an area to the south of the town of Edinburgh was purchased for the relocation and expansion of its science departments.  One of the buildings here is named for Maxwell.  (You can see more about Edinburgh's Universities at this link.)


In his youth, while at the Edinburgh Academy, Maxwell had a bit of a rough start socially.  He was looked upon by some of the other students as a bit of a "country bumpkin" and because of that had the nickname "Dafty," which didn't seem to bother him.  Eventually he met two other boys who were close in age and intellect to him who remained lifelong friends.  One of these was the future mathematician Peter Guthrie Tait (1831-1901), who, along with Maxwell and Thompson (aka Lord Kelvin) pursued topology and knot theory for a time.  When I read the following poem I see a confluence of Maxwell's faith and his work - knots, divine intellect, higher dimensions and the soul.


My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect, in the Unseen residing,
And thine cloth like a convict sit,
With marlinspike untwisting it,
Only to find its knottiness abiding;
Since all the tools for its untying
In four-dimensional space are lying

Full poem can be found at this link.

Monday, April 11, 2016

Cambridge

Punting on the Cam - The Bridge of Sighs



I haven't been sure where to begin with my time in Cambridge, and I figured punting was as good as anything.  It's sort of classic, and it shows of the colleges of Cambridge University well.

As I write this I am sitting in the Centre for Mathematical Sciences, Cambridge - in the common room of one of the pure math pavilions with a bust of Ramanujan overlooking my work.  I don't know how anyone could possible beat that situation!

Before leaving on my sabbatical travels I wrote a professor here, Dr. Piers Bursill-Hall, with one question about the location of rooms of two mathematicians I was particularly interested in: John Edensor Littlewood and G. H. Hardy.  I'd been told he'd be the best person to ask.  Rather than receiving just an email answer I have been hosted in the most gracious and solicitous manner imaginable - so much so that I'm feeling almost too humbled and awed to really write much about it at this point.  I'm still pinching myself and wondering if this is real.

He first connected me with one of his doctoral students, Richard Chapling, who is in maths at Trinity College and who is very knowledgeable about Hardy, among many other things.  Richard pointed out places and items related to Newton, ushered me into the Trinity Great Court in time to hear the famous clock chime noon, showed me various of Littlewood's, Hardy's and Ramanujan's room locations from over the years (there was some moving around), and then treated me to lunch in Trinity's hall, which just about knocked my socks off as I sat under the hammer beam roof and under the gaze of Henry VIII.  When the three of us were having dinner together the next day I remarked on what a privilege that was for me, Piers said, "No big deal.  Hardy ate there every day."  To which I replied, "Yes!  EXACTLY!"

To make a very long story short, on Friday after the tour and lunch at Trinity, Piers met up with me and Richard and took us to Ely Cathedral, which was fascinating.  Saturday involved visits to many of the colleges and chapels - concluding with my first visit to the Centre for Mathematical Sciences, time to work here, take-out Chinese in "The Core," and lots of stories told.  Today involved an amazing visit to James Clerk Maxwell's laboratory (lots of stories about that - what a privilege! - same lab bench still there that Maxwell, Rutherford and Einstein taught on), a second visit to King's College Chapel, finally getting in to Trinity College Chapel, time in Clare, St. John's, etc.  And now back to the CMS where Piers and Richard are working in the office on their stuff while I work alone in the common room on this.

ASTOUNDING!

I'm here in Cambridge because of the "non-trivial" number of phenomenal mathematicians (and mathematical physicists and mathematical philosophers) throughout history that are associated with Cambridge, and particularly Trinity College, Cambridge - people such as the following:

Charles Babbage
Mary Cartwright
Arthur Cayley
Augustus de Morgan
Paul Dirac
William Timothy Gowers
G. H. Hardy
James Jeans
John Maynard Keynes
John Edensor Littlewood
James Clerk Maxwell
Sir Isaac Newton
Roger Penrose
Srinivasa Ramanujan
Bertrand Russell
Peter Swinnerton-Dyer
Sir George Gabriel Stokes
James Joseph Sylvester
Alan Turing
John Venn
John Wallis
Alfred North Whitehead
Andrew Wiles

  .  .  .  to name a few.

I'm having rather a hard time processing all the information I've taken in in the last few days, so I think for now I'll just post some pictures of Cambridge and will try to sort things out into separate posts later.

Newton's Apple Tree at Cambridge - a descendant of the one at his home in Woolsthorpe

Trinity Great Gate with founder Henry VIII holding a rather interesting scepter
This fountain in the middle of the Great Court has been here since before Newton's time

Trinity Clock Tower (Chapel to the right)
Statue of Newton in Trinity College Chapel


A few plaques among many in Trinity's chapel - 



Wren Library, Trinity College Cambridge (from Nevile's Court)

King's College Chapel

King's College Chapel
Detail of King's College Chapel (west door)

Inside King's College Chapel
Henry Rex
H&A - didn't work out so well for A
Fan Vaulted Ceiling of King's College Chapel

Fan Vaulted Ceiling of King's College Chapel
Here are some images of James Clerk Maxwell's laboratory/lecture hall.  My host taught in this room for 20 years, but it has now been taken over by Sociology <gasp> because physics was more interested in nice new rooms than in their incredibly sacred history.  It was recently used for storage space and now is not being used for anything.  Maths faculty is hoping it is not gutted in a couple of years to make a modern classroom  .  .  .





Trap doors in the ceiling allowed things to be lowered in.

Original bench over which Maxwell, Rutherford, Einstein and Bursill-Hall taught
Student's-eye View - Dr. Bursill-Hall at front
There are MANY more Cambridge photos I could share, and some of the ones I have shared I probably should have waited with until I wrote on specific mathematicians, but this is just all too cool not to jump in right now and post all this.

Oh - one last closing shot - about to go under the Mathematical Bridge on the punt - couldn't be happier:


Wednesday, March 30, 2016

Mathematicians of Edinburgh

When first planning these mathematical travels I had only planned a couple of days for Edinburgh.  My interest was in John Napier, a very interesting character who also invented logarithms and is responsible for popularizing the use of the decimal point.  After seeing Merchiston Tower, which is all that remains of his castle in Edinburgh and is now part of Edinburgh Napier University, and after touring Lauriston Castle, home of his brother, I was going to be on my way to my myriad of mathematical stops in England.

However, as I began to look into Edinburgh I became aware of more and more mathematicians and mathematical physicists of note who were associated in some way with Edinburgh.  Along with Napier, these are:

Girolamo Cardano
Colin MacLaurin
John Playfair
Mary Somerville
William Thompson, Lord Kelvin
James Clerk Maxwell
Peter Guthrie Tait

and, currently, Sir Michael Atiyah, geometer and Fields Medal winner.

Clearly my Edinburgh sojourn needed to be extended, and I ended up reserving six days in Edinburgh rather than the two I had initially planned.  Even at that I need to focus on two or three and just touch on the others.  In this post I am sharing landmarks that all of these mathematicians would have been familiar with - that's not to say that some changes may not have been made to certain places such as Edinburgh Castle and Holyrood Palace between the time of Napier (b. 1550) and Atiyah (b. 1929).

EDINBURGH CASTLE




HOLYROOD PALACE




HOLYROOD PARK AND ARTHUR'S SEAT



St. Anthony's Chapel ruins in Holyrood Park - partway up to Arthur's Seat
Overlooking the city from near the top of Arthur's Seat
ST. GILES' CATHEDRAL



EDINBURGH UNIVERSITY

Main Campus

"New College" Campus - now a divinity school

"New College" Campus
"New College" Campus (with John Knox)
THE FIRTH OF FORTH

I haven't gotten close yet, but here it is from a bit below Arthur's Seat
CALTON HILL (with or without observatory and various monuments)

Observatory and Playfair Monument

Edinburgh - the Athens of the North

Viewing across Old Calton Burial Ground

Top left - looking over Holyrood Palace
Post Script - this idea of common landscapes was confirmed today (March 31, 2016) when I visited the National Portrait Gallery and saw the piece below from 1820 showing Calton Hill and Arthur's Seat behind it.