Mathematician and predicting the future of computers

 In “The Scientific Letters and Papers of James Clerk Maxwell, Vol I (1846-62), Vol II (1862-1873), and Vol III (1874-1879)” published by Cambridge University Press, in December 1873 (150 years ago), Maxwell wrote: “A mathematician is one who endeavors to secure the greatest possible consistency in his thoughts and statements, by guiding the process of his reasoning into those well-worn tracks by which we pass from one relation among quantities to an equivalent relation. He who has kept his mind always in those paths which have never led him or anyone else to an inconsistent results, and has traversed them so often that the act of passage has become rather automatic than voluntary, is, and knows himself to be, an accomplished mathematician. The very important part played by calculation in modern mathematics and physics has led to the development of the popular idea a mathematician as a calculator, far more expert, indeed, than any bankers’ clerk, but of course immeasurably inferior, both in resources and in accuracy, to what the ‘analytical engine’ will be, if the late Mr. Babbage’s design should ever be carried into execution.”

Interestingly, this was written by one of the greatest mathematical physicists of all time. Charles Babbage (1791- 1871) originated the concept of a digital programmable computer had died just over two years before Maxwell wrote the above.

 We can see Maxwell pass from one relation to an equivalent relation in a picture I took from in a museum where he was born. 

 The next paragraph goes on, “But although much of the routine work of a mathematician is calculation, his proper work - that which constitutes him a mathematician - is the invention of methods. He is always inventing methods, some of them of no great value except for some purpose of his own; others, which shorten the labour of calculation, are eagerly adopted by all calculators. But the methods of which the mathematical is content to hang his reputation are generally those which he fancies will save him and all who come after him the labour of thinking about what has cost himself so much thought.” 

That is a good description of many of the files I’ve put together on my TI-Nspire to teach AP Calculus. Some files, like Volume by Cross Section, were challenging to figure out, but they have been of help for my students and other teachers to help student visualize the mathematics. (For example, see https://sites.google.com/site/tinspiregroup/classroom-news/3dparametric )

Interestingly, I read in Maxwell’s biography (pg. 71) from a letter he wrote his father that 178 years before I was there, that he and a friend visited the beach at Portobello. My friends with Texas Instruments shared about how some of their mathematicians or software engineers have been active inventing methods to make 3D graphing work and many other functionality, including the programming language Python work on the TI-Nspire handheld. A student gave me a Python option to have the flag of Scotland, the oldest flag in the world, on my TI-Nspire as it posed on the beach. 

The Scots Worthies

 The first edition of this book, “The Scots Worthies,” was  published in 1870. That would be 9 years before James Clerk Maxwell passed away. 

In the author’s preface (pg.xx) John Howie notes that if their example is not followed then “the Church of Christ is so far from gaining ground, that it loses what it hath already gained in the world; of which the Church of Scotland is a most glaring example…” He goes on to give a few cautions so that there will be great advantage through the Divine blessing by reading about the lives of people like Knox, Alexander Henderson, Donald Cargill, Richard Cameron, George Wishart and many others.

1. Don’t rely on “the person, principle, or practice of any man, yea, the best saint we have ever read or heard of, but only to seek those gifts and graces that most eminently shone forth in them… For it is the peculiar honor and divinity of Jesus Christ alone, to be worthy of being imitated by all men absolutely.” As it says in Philippians 3:17 “Be imitators of me as I am of Christ.”

2. “Neither are we, on the other hand, to dwell too much upon the faults or failings that have sometimes been discovered in som of God’s own dear children; but at the same time to consider with ourselves, that, although they were eminent men of God, yet at the same time they were sons of Adam also… So says the apostle, they are “earthen vessels,” “men of like passions with you” (2 Cor 4:7; Acts 14:15).

So I wonder if Maxwell read this book? Yes, I think it is likely. I know from a biography about Maxwell by Campbell (pg 321-322,371) that he was learned in John Owen (1616-1683) and Jonathan Edwards (1703-1758).  “A considerable portion of the evening would often be devoted to Chaucer, Spenser, Milton, or a play of Shakespeare, which he would read aloud to Mrs. Maxwell. On Sundays, after returning from the kirk [church], he would bury himself in the works of the old divines.” But I also know that he read modern books and articles. From a letter James Clerk Maxwell wrote in 1876, three years before his death, he cited articles that were published in 1851,1874 and even cited a commentary that by Lightfoot that was published that year. He wrote, “ I think that each individual man should do all he can to impress his own mind with the extent, the order, and the unity of the universe, and should carry these ideas with him as he reads such passages as the 1st Chap. of the Ep. to Colossians (see Lightfoot on Colossians, p. 182), just as enlarged conceptions of the extent and unity of the world of life may be of service to us in reading Psalm viii.; Heb. ii. 6, etc.”

 

These are pictures taken from my visit to Maxwell’s birthplace. We scheduled a tour (https://clerk Maxwell foundation.org) and had a delightful time. 

Here is a paper I wrote called “James Clerk Maxwell and Why Read Biographies”

150 years ago Maxwell wrote in his preface to his Treatise on Electricity and Magnetism “It is of great advantage to the student of any subject to read the original memoirs on that subject … If by anything I have here written I may assist any student in understanding … I shall regard it as an accomplishment of my principal aims - to communicate to others the same delight which I have found myself…” 

   

   I say amen to that. My prayer is that I may assist students to understand and help them have some of the delight I receive. Psalm 111:2 “Great are the works of the Lord, studied by all who delight in them.

This is some of Maxwell’s handwriting.

On my last day Saturday in Scotland I visited the local library and read some of Maxwell’s letters and original writings. I could have spent longer there, but the library closed at 5pm.  It was an exciting visit.

 (This picture was taken in Maxwell’s birth place on 14 India Street in Edinburgh.)

Scotland - week 1 part A

 Outline of days

Day 1, flew from Indy to JFK and then arrived in Edinburgh, Scotland on the morning of  

Friday, June 16 - After getting the rental car (stick shift and driving on the left side of the road) we stopped by Pentland Hills and went for a walk. 

We arrived at our airbnb in Portobello beach area and visited some thrift shops. 

Saturday, June 17 - Got up to enjoy some tea and crumpets and McVitie’s Digestive biscuits and a 4:30 sunrise. After a helpful nap, we drove downtown to visit the Edinburgh Castle. The girls had an Explorer Pass and I did the Historic Scotland Membership. We enjoyed dinner at a restaurant and had fried bree, haggis, fish and chips and dessert. I loved everything. 

Then we went on a self guided walking tour of Edinburgh and saw the James Clerk Maxwell statue. 

We stopped by a Tesco on the way home and had a great time at the beach around sunset (10pm).

Lord’s day morning we went to North Edinburgh Reformed Presbyterian Church. They use what is called the split leaf Psalter. The words can be sung from a variety of tunes. 

That week my daughters and I visited the Dunfermline Abbey and Palace where people dressed in period outfits told us about blacksmithing, games in the Middle Ages, and actors performed as Queen Margaret and her lady in waiting.  We learned that nails used in doors were bent and couldn’t be reused - thus, it was dead … dead as a door nail. While in the village we happened upon the birthplace of Andrew Carnegie and the accompanying museum. This museum was free and the abby was included with our Explorer Pass and Historic Scotland membership.

Betsy and I climbed to Arthur’s Seat and made it back to our bnb in a pleasant ran. The next morning we got up in time for the 4:30 sunrise. It was beautiful.  

After a little nap we were off to Sterling Castle. We heard the tale of the unicorn, the official animal of Scotland - a symbol of strength, purity, etc. We temporarily usurped the thrones, had our Scotch pies and strawberry tarts we had picked up that morning.

 Once the delightful tours were completed we headed to Finnich Glen (a.k.a. The Devil’s Pulpit, which we later found out appeared in shows like Pokémon and Outlander). Parking was limited and we missed the stop, but providentially we found a car park the led to a path up a hill with impressive vistas. Off in the distance I could even see Loch Lomond. The GPS said we were outside of Glasgow in Blanefield.

Then back to Finnich Glen and a perfect parking spot. Finnich Glen is a steep sided sandstone gorge carved by the Carnock Burn. The sign informed us that visitors should be aware of unstable gorge edges and hidden, sheer drops. It took us some exploring to find the way down, but it was worth it.

 

By 6pm we had made it to the village of Balmaha on the bonnie banks of Loch Lomond. We got some crisps and an ice cream cone and hiked a bit, but needed to drive to find a more impressive beach. It was brilliant.

We had one more adventure in us for the night. We hiked up Abbeyhill in Holyrood Park to capture amazing sunset photos at 10pm.

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