Christian Mathematician – Page 5 – GOD & MATH: Thinking Christianly About Math Education

Christian Mathematicians – Hamilton

March 29, 2012June 10, 2012joshwilkerson10 Comments

By Steve Bishop

(Disclaimer: The views expressed by guest authors do not necessarily reflect those of GodandMath.com. Guest articles are sought after for the purpose of bringing more diverse viewpoints to the topics of mathematics and theology. The point is to foster discussion. To this end respectful and constructive comments are highly encouraged.)

Sir William Rowan Hamilton (1805-1865)

Hamilton has been described as ‘one of the most imaginative mathematicians of the nineteenth century’ (Hankins ) and as a ‘mathematical genius’ (Wilkins, 2005). Hamilton was born in 1805 in Dublin, the son of a solicitor. He lived with his clergyman uncle James from the age of three.

He studied at Trinity College Dublin where he excelled. Before going to Trinity he had read many mathematical papers and had even spotted a mistake, which he rectified, in some of Laplace’s work. There he did work on optics. He then became the Royal Astronomer of Ireland. He remained the Royal Astronomer until his death in 1865.

In an obituary De Morgan (1866) had this to say of Hamilton:

In the case of Hamilton there is no occasion to state anything but the simple fact, known to all his intimates, that he was in private profession, as in public, a Christian, a lover of the Bible, an orthodox and attached member of the Established Church, though of the most liberal feelings on all points. He had some disposition towards the life of a clergyman, but preferred to keep himself free to devote all his time to science: he was offered ordination by two bishops.

And Charles Pritchard (1866) in another obituary wrote:

This memoir would be incomplete if we did not add, that our deceased member, together with the character of a scholar, a poet, a metaphysician, and a great analyst, combined with that of a kind-hearted, simple-minded Christian gentleman; we say the latter because Sir William Hamilton was too sincere a man ever to disguise, though too diffident to obtrude, his profound conviction of the truth of revealed religion.

Gene Chase writes of the link between Hamilton’s faith and his mathematics:

In Hamilton’s Calvinistic[1] theology, as in that of his Scottish friend and pupil Clerk Maxwell, God is the creator both of the universe and of the laws governing it. This means that the lawful relations among material objects are as real as the objects themselves. As a Christian, Hamilton was convinced that the stamp of God is on nature everywhere. He expected a Triune God to leave evidence of the Trinity on everything from three-dimensional space in geometry to an algebra involving triples of numbers. This “metaphysical drive,” in the words of Thomas Hankins, his best twentieth-century biographer, “held him to the task” of looking for a generalization of complex numbers to triples.”

It was this search for triples that led him to the discovery of quaternions. This occurred when out walking with his wife, he then carved the formula on the Broome Bridge – there is now a plaque on a bridge marking the spot:

His formula is even celebrated on a Irish stamp:

He was knighted in 1835. Other contributions made by Hamilton include work in optics, dynamics, complex numbers and a board game ‘icosian’ based on his work in graph theory.

He gave his name to the Cayley-Hamilton theorem and to the Hamiltonian.

References:

Chase, Gene B. 1996. ‘Has Christian theology furthered mathematics‘ In Facets of Faith and Science vol 2: The Role of Beliefs in Mathematics and the Natural Sciences: An Augustinian Perspective. Jitse M. van der Meer (ed.) University Press of America/ Pascal Centre for Advanced Studies: Lanham/ Ancaster.

De Morgan, Augustus. 1866 ‘Sir W. R. Hamilton’ Gentleman’s Magazine and Historical Review, vol. I. (new series) : 128-134.

Hankins, Thomas L. 1980. Sir William Rowan Hamilton. John Hopkins University Press.

Pritchard, Charles 1866. William Rowan Hamilton. Monthly Notices of the Royal Astronomical Society 26, 109-118.

Wilkins, David R. 2005. ‘William Rowan Hamilton: mathematical genius’ Physics World (Aug), 33-36.

[1] It seems Chase may be mistaken in assuming that Hamilton’s faith was Calvinistic. However, his sister certainly was see e.g. E. P. Graves, 1889, Life of Sir William Rowan Hamilton p. 112.

Steve Bishop is the compiler of A Bibliography for a Christian Approach to Mathematics and the author of several articles on the relationship between faith and math. Look for future posts from him in this series on Christian Mathematicians.

Previous Entries in this Series:

Christian Mathematicians – Bayes

March 22, 2012June 10, 2012joshwilkerson10 Comments

By Steve Bishop

Thomas Bayes (1702-1761)

Thomas Bayes (1702-1761) was the minister of the Presbyterian Chapel in the English spa town of Tunbridge Wells from around late 1733. By all accounts he was a better mathematician than he was a church minister! The Protestant Dissenter’s Magazine of 1814 describes Bayes as a respected minister, however, he was not according to Timpson (writing in 1859) a popular preacher (Bellhouse, 2004).

As a non-conformist he was prevented from attending the English universities, so he began study in 1719 at Edinburgh University in Scotland.

In 1731 he published a work entitle Divine Benevolence and in 1742 he was made a fellow of the Royal Society after defending Isaac Newton against Bishop Berkeley in a ‘pamphlet war’.

Bayes did work with fluxions, infinite series as well as in probability. In the late 1740s Bayes set out his theory of probability that eventually bore his name. His theorem was discovered after his death. It had no practical applications in his lifetime. He didn’t even bother to publish it. It was his friend and fellow mathematician and church minister Richard Price who discovered it among Bates’ effects after his death and had it published as “An Essay towards solving a problem in the doctrine of chances,” Philosophical Transactions of the Royal Society of London 53 (1763): 370–418. Available here: http://rstl.royalsocietypublishing.org/content/53/370.full.pdf+html

Price suggested that the theory could be used to defend Christianity against the skepticism of David Hume. Price was at the time the minister of the non-conformist chapel in Newington Green, England.

Laplace re-rediscovered it and modified it into the form we largely recognise today.

The statistical community who largely accepted the frequentist view of statistics rejected it; they thought that the bayseian approach was subjective and hence ‘unscientific’. It is only in the last few decades that the bayesian approach is starting to be dominant. McGrayne (2011) writes:

In discovering its value for science, many supporters underwent a near-religious conversion yet had to conceal their use of Bayes’ rule and pretend they employed something else. It was not until the twenty-first century that the method lost its stigma and was widely and enthusiastically embraced.

Today it is used among other things to forecast weather, to identify e-mail spam, to improve low-res images on computers and has been used to identify forgeries.

The formula is known today in this form:

P(A|B)=P(B|A)P(A)/P(B)

where P(A) denotes the probability of A and P(A|B) is the probability of A given that B has occurred.

Sharon Bertsch McGrayne’s (2011) book title summarises its impact: The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant from Two Centuries of Controversy (Yale University Press, 2011)

A recent book by Andrew Hartley, Christian and Humanist Foundations for Statistical Inference (Resource, 2008), suggests that a subjective bayesian approach comports well with a Christian perspective on statistics.

Interestingly, Bayes’ theorem has been used by philosophers of religion such as Richard Swinburne to try and prove God’s existence and by others such as philosopher John Mackie and the atheist evangelist Richard Dawkins in an attempt to disprove God’s existence.

Bill Bryson on Thomas Bayes:

References

Bellhouse, D. R. 2004. “The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth,” Statistical Science 19 (1) 3–43.

Sharon Bertsch McGrayne (2011) The Theory That Would Not Die (Yale University Press, 2011)

Previous Entries in this Series:

Christian Mathematicians – Nightingale

March 15, 2012June 10, 2012joshwilkerson11 Comments

By Steve Bishop

Florence Nightingale (1820-1910)

Florence Nightingale was born in Florence to a family of high standing. Her family were there as part of a grand tour of Europe. She shocked them by wanting to become a nurse. She felt called into that service by God. She is perhaps best remembered as the “lady of the lamp.”

In 1854 she went to serve as a nurse in Sutari during Crimea War. As a result of her work the death rate in war hospitals fell from 42% to 2%. She did this by collecting data; she was a good statistician. She pioneered the idea that social phenomenon could be quantified. She declared:

“To understand God’s thoughts, we must study statistics for these are the measure of His purpose.”

For her there was no conflict between faith and statistics. She was elected to membership of the Statistical Society of England in 1858. Karl Pearson is alleged to have called her a ‘prophetess’ of statistics. In 1874 she was made an honorary member of the American Statistical Association.

Her data collection and statistical analysis changed the nursing profession. She provides a great example of how mathematics can be a useful tool in stewarding the creation.

She was the originator of coxcombs, a polar area diagram – the forerunner of the pie chart. She used it to show the causes of mortality during the Crimea war.