Tuesday, April 7, 2026

Cardano's Consoltation

TRIGGER WARNING: This post mentions Hamlet's To Be or Not To Be soliloquy and the dark themes contained therein. If you are currently feeling life to be a "sea of troubles," you may want to skip this post and find a different one to read. Wishing you well, dear reader!

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)
 
Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

On the title page of Cardano's Three Books of Consolation English'd is printed the statement, "Of great use in these times." This is the 1683 English translation of the 1542 original, which had also been translated into English in 1573, and which I read in 2026, and I would say it is of great use in all these times.

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Reading this book by Cardano put me in mind of the poem If Still Your Orchards Bear by Edna St. Vincent Millay that ends with the stanza

I think you will have need of tears;
I think they will not flow;
Supposing in ten thousand years
Men ache, as they do now.

Both her poem and this book are testimonie to me that the experience of being human doesn't change - not with decades and not with centuries - no matter the rise and fall of empires or advances in technology. We still feel joy and sorrow, still experience loss and gain, still feel hope and despair. We still wonder about the purpose of life and what, if anything, comes after it.
Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)
This small volume consists of three "books," each of which is broken up into chapters. At the head of each chapter is a summary of what the chapter is about. For example, in the picture below, we see that in chapter 1 of book 1 we will find: Good discourses a necessary remedy against all misfortunes. Opinion makes many things good or evil.
Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Though Cardano does cover many areas of human experience, I'm moving here into a deep diver into his reflections on death - hence the "trigger warning" at the beginning of this post. In chapter 1 of book 2 some potentially familiar sentiments. As you read them, see if they remind you of anything else you've come across elsewhere in literature:

I have felt more grief than pleasure in this world. Seeing then this love of life availeth nothing, nay tho it were desirable, tis better to cast off this burden of cares . . .

 . . . what can Death be better compared to than a Dream?

Death may be fitly compared to a sound sleep.

What is our life by continual toil, perpetually attended with labor, suspicious, and dangers . . .

If what comes to mind is Hamlet's To Be or Not to Be soliloquy, you are not alone. In that soliloquy, Shakespeare speaks through Hamlet of the "sea of troubles" and the "slings and arrows of outrageous fortune" that we experience in life and of the "heartaches and the thousand natural shocks that flesh is heir to." He ponders further: "To die - to sleep; to sleep, perhance to dream."

While there is currently no scholarship providing a direct link between Shakespeare and Cardano's book, this book has been included by some academics in lists of potential influences on Shakespeare - as one of the widely circulating humanist texts that drew on stoic philosophy and belonged to the tradition of books of consolation.

I work hard to keep my posts as factual as possible, but I hope I can be allowed a small, reasonable flight of fancy on occasion - fully acknowledged as such. I like to think that there IS a link here. Here is some of my thinking on the matter:

Girolamo Cardano and John Dee had met - Cardano's writing did circulate widely - Dee was influential in Elizabethan circles - and Shakespeare and Dee (though decades apart in age) both moved in those Elizabethan circles - I, personally, like to think that the book Shakespeare has Hamlet holding in Act 2, Scene 2, when Polonius walks in and asks, "What do you read, my lord?" is Cardano's book. This scene is followed not long after by Act 3, Scene 1 where Hamlet speaks the To Be or Not To Be soliloquy.
The Globe Theatre, London

The Globe Theatre, London

Again, just to be clear, there is no PROOF that this is THE book that Hamlet is holding (though there's no evidence against it either), but when I read or see Hamlet, I think of it being Cardano's book in his hands. Though not proven (and probably not provable), it is certainly plausible.

Here are two further glimpses into Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9). These pages form the closest connection for me between Cardano's thoughts and Hamlet's speech.
Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Well, the Hamlet connection became a rather lengthy side-trip from where I began. But I'll end by zooming out a bit once more. Cardano writes of so many things in this book. He touches on how without experiencing illness we cannot appreciate health, and without having experienced troubles, we cannot fully appreciate ease. He puts things in perspective. He addresses our appetites, writing, "whatsoever is profitable or necessary to any creature that is naturally desirable in which desires brute beasts (who are guided only by sense) do not transgress. Whereas man, who has most reason in his understanding has least in his actions, for [man] eats, drinks, and sleeps more than either conveniency or necessity require."

He addresses poverty and riches and our perspectives on them: "Should it come to pass now as it did in the time of Noah that all money, provisions, cattle, and other commodities were carried away in a universal Flood, I believe then no man would think himself injured by poverty. Why then dost thou complain having whereon to live? This plainly evidences 'tis not poverty but envy that molests thee."

I'll close out with some comparisons he makes - the last line of which made me laugh out loud.

“Perhaps thou wilt say I would have Pleasure without Pain: ‘Tis contrary to nature, for Joy is continually attended by Sorrow, Glory with Envy, Wisdom is not gotten without labor, Wealth is not obtain’d without care, Children are kept with trouble, Banqueting is attended by sickness, Ease with poverty, Power with envy, Quiet with weariness. Every man has something to complain of. Some be afflicted with Poverty, others want Children, this man is Sick, that man wants a Wife, and this man would be rid of his.”

Our dear mathematician Cardano had many thoughts on many subjects, and these are but some of them. If interested, and perhaps headed to London, here is a link to this item in the catalogue of the British Library.

Saturday, March 14, 2026

Einstein and Pavia

Ponte Coperto, River Ticino, Pavia, Italy
Normally on today's date - March 14 - I'm encouraging people to celebrate Pi Day. But this year I've decided to post in honor of the birthday of Albert Einstein. I'm choosing to write about one slice of his life :-)

Ponte Coperto, River Ticino, Pavia, Italy

Ponte Coperto, River Ticino, Pavia, Italy

Ponte Coperto, River Ticino, Pavia, Italy - dome of Duomo di Pavai in background
Einstein's family moved to Pavia from Munich, seeking better possibilities for his father's electrical business. Einstein was a teenager at this time, and still in gymnasium (high school), so he stayed behind in Munich to finish his schooling and joined his family during school holidays. Young Albert quickly fell in love with this beautiful city. Because of this, much of my post is simply pictures of the beauty of Pavia - with a splash of humor at the end.
Duomo di Pavia

Pavia University

Pavia University

Ancient Towers outside Pavia University

Walking through Pavia

Walking through Pavia
Einstein would take walks through the city with his sister Maja - something he still reminisced about decades later and looked back on fondly. He especially enjoyed the covered bridge, Ponte Coperto, over the River Ticino that flows through Pavia, which is why I opened this post with so many pictures of the covered bridge.
Riverside walk in Pavia, Italy - Ponte Coperto in the distance

View from Ponte Coperto, Pavia, Italy
More than 50 years later, Einstein mentioned Pavia in a letter. A phrase from that letter is engraved on a plaque inside the bridge memorializing Einstein's time in Pavia:

AN DIE SCHÖNE BRÜCKE IN PAVIA HABE ICH OFT GEDACHT . . .

I have often thought of the beautiful bridge in Pavia . . .

Einstein Plaque, Ponte Coperto, Pavia, Italy
And now for the silly ending that I can't help but include. 

Just a bit of a walk down-river from the bridge is an intriguing sight that I like to believe inspired some of Einstein's whimsy.
Walking alongside the Ticino River, Pavia, Italy

Walking alongside the Ticino River, Pavia, Italy


 La Linguacciona, Pavia, Italy


 La Linguacciona, Pavia, Italy


 La Linguacciona, Pavia, Italy

 La Linguacciona, Pavia, Italy
I mean, he was still thinking of his time in Pavia half a century later, so might La Linguacciona have inspired Einstien's pose in a picture taken many years later? We'll never know for sure, but I like to think it did.
Albert Einstein on his birthday in 1951



Monday, January 26, 2026

The Humble Grave of Henry Briggs

 

Grave of Henry Briggs (Henricus Briggius) in the chapel of Merton College, Oxford.
Today's post honors mathematician Henry Briggs who died on this date, January 16, in the year 1630. He was a man who held two prominent professorships and who contributed tremendously to the development and speedy adoption of logarithms - an invention that revolutionized calculation so dramatically that they were said to have "doubled the life of the astronomer."

Despite his prominence, Briggs was modest, humble, uninterested in wealth, and content with a quiet life of study. Fittingly, his tombstone in the chapel floor of Merton College bears only his name: no dates, no titles, no heraldic sheild, no list of achievements. Just the Latin form of his name: Henricus Briggius. Compare this with the memorial - also in Merton Chapel - of his contemporary and patron Henry Savile - heraldic sheild around his head, bust situated atop the world and flanked by Chrysostom, Ptolemy, Euclid, and Tacitus, and above it all, an angel playing a trumpet.
Memorial to Henry Savile (1549-1622) - Merton College, Oxford
Prior to teaching in Oxford, Briggs was the first professor at Gresham College, London, from which later arose the Royal Society. It was during his time at Gresham that he made the arduous journey to Edinburgh to meet the inventor of logarithms, John Napier; the journey today is about 4 hours by train; back then it was a formidable 4-day-long journey by horse and coach.
Gresham College, London today

Lion atop the gates to Napier's castle of Merchiston (Edinburgh)

Napier's Home, Merchiston Castle, from above
Briggs first visited and collaborated with Napier in the summer of 1615 and then went back in the summer of 1616 - each time staying for a month. He had plans to return in the summer of 1617, but Napier died in April. Briggs picked up the baton, constructing tables of base-10 logarithms, and promoting them in the scientific community, leading to their wide adoption.
Merton College, Oxford
A few years after these visits with Napier, Briggs moved from Gresham College, London to Merton College, Oxford, when he was appointed first Savilian Professor of Geometry at Oxford by Henry Savile himself. When I visit here, I feel I've traveled back in time - all the way back to the time of Briggs himself.

Merton College, Oxford

Merton College, Oxford
Chapel Tower, Merton College, Oxford
Chapel Door (left), Merton College, Oxford
Merton College, Oxford
The magnificence of the organ in Merton College Chapel never fails to take my breath away, but this organ, of course, was not there in Briggs's time (was installed only about a decade ago).
Merton College, Oxford
Merton College, Oxford

Merton College, Oxford
Barely visible on the left and right of the pillars on either side of the organ are the elaborate memorials to Henry Savile, pictured earlier in this post, and of Thomas Bodley, he of the Bodleian Library. About 15 feet to the left of where I'm standing to take this picture is the simple stone of the humble, yet brilliant man, Henry Briggs, and it is from my vigil at his stone that I take my leave of you today.
Tomb of Henry Briggs, Merton College, Oxford



Tuesday, December 30, 2025

Time to Raise a Glass

 

Guinness Storehouse - "Tick Followed Tock" - Guinness Advertisement 1999

As the clock winds down on 2025, as we toast the old year and look forward to the new, I find myself remembering my mathematical visit to the Guinness Storehouse in Dublin, Ireland earlier this year. Mathematics certainly provides great excuses to visit a wide variety of places!

A Visit to Guinness Storehouse - Dublin, Ireland
The Storehouse is a 7-story extravaganza of all things Guinness from ingredients to brewing to adverisiting to shipping and more! It includes a restaurant and multiple bars, including the Gravity Bar that makes up the entirety of the 7th floor, which has one of the best views over the city of Dublin. Most tickets include a pint in the Gravity Bar at the end of your tour.
Guiness Storehouse - Dublin, Ireland
One floor is enirely devoted to Guiness's famously whimsical ads.
Guiness Storehouse - Dublin, Ireland
All of my travels involve mathematics in some way, so what's the math connection here? 
Guiness Storehouse - Dublin, Ireland
Guinness faced a practical quality-control problem: testing barley to ensure consistent brewing required destroying some of the product; therefore, only small samples could be used. Traditional statistical methods required large sample sizes and didn’t work well with such limited data. William Sealy Gosset, a brewer at Guinness with training in mathematics and chemistry, developed a new way to draw reliable conclusions from small samples. 
Guiness Storehouse - Dublin, Ireland
This method became what we now call the Student’s t-test. The name is due to a company policy. Guinness allowed Gosset to publish his work only under a pseudonym. The name he chose to use was “Student.” That pseudonym is why the test still bears that name today.
St. James's Gate Brewery - Dublin, Ireland

Guinness Storehouse - Dublin, Ireland

Guinness Storehouse - Dublin, Ireland

Guinness Storehouse - Dublin, Ireland
More than a century later, the Student's t-test still matters because it remains one of the most widely used tools for making sense of small data sets, from scientific research to medicine, economics, and more! So, if you raise a glass this New Year's Eve - especially if it's a pint of Guinness - be sure to remember the name William Sealy Gosset.
Heidi &Toby at Gravity Bar - Guinness Storehouse - Dublin, Ireland
To all my reader's - I wish you a happy, healthy, and prosperous New Year!