Saturday, March 28, 2020

Modern Day Math

I'm going to take a quick jump out of the 16th century and into the 21st century for this math history blog post.  While in London to study John Dee, I had a landmark in mind that I really wanted to see that has nothing to do with Dee (although now that I'm writing this I realize there may be a tie in, but more on that later).  The landmark I was interested in is 20 Fenchurch Street, also known as the Walkie-Talkie Building, which is the sky-scraper to the right on the pictures above and below.
I became interested in this building while doing a teaching observation in the classroom one of my colleagues.  The topic being introduced that day related to foci of conic sections.  Being the great teacher that she is, she began the class by sharing some engaging real-life examples with her students - one of them being this building and it's properties.  So  .  .  .  other than the fact that it's pretty cool looking, what's so interesting about this building?  And what does it have to do with math?
A curved glass surface can reflect the sun's rays in such a way that they are focused on a point and thus concentrated.  And that is what happened with this building.  The focus was at or near ground level at a nearby street, and the concentrated rays resulted in temperatures at that spot of up to 205 degrees Fahrenheit.  Before the parking areas were blocked off with orange cones, a Jaguar was damaged: its side-view mirror being melted by the heat, and a van was damaged: the plastic of the dashboard becoming melted, as well as a bottle that was inside ending up basically baked.  Tiles on a storefront in that area were baked to the point of cracking off, and a carpet inside a nearby store started to burn and smoke.  As news of this "heat-ray" spread, people turned up with frying pans and were able to fry eggs out on the sidewalk here.
As far as I know, this building doesn't have the shape of a specific conic section that is studied in the classroom.  If it had -- for instance, it if were a paraboloid -- the heat intensity at the focus would have been even higher.
I say I've jumped to the 21st century out of my 16th-century posts, but such properties of curved glass or mirrors were actually known even in ancient times.  Archimedes used this idea to create his famous "burning mirrors" as a weapon of war to protect Syracuse from the invading Roman troops.  Leonardo da Vinci (whom Girolamo Cardano knew) sketched such mirrors as well.  And one of "my mathematicians," John Napier wrote of plans for creating such a device at a time when a second Spanish Aramada attack on England and Scotland was feared.
If this has been known about for so long, why did the architect design the building in such a way?  Was he not aware of the implications?  Well, actually he was aware of this, but he also knew that the sun would only be in the proper position for such concentrations of its rays to take place for 2 to 3 weeks of the year and then only for a couple of hours per day during those weeks.  From what I understand, he was also counting on London's notoriously cloudy, foggy, rainy weather to keep this from being an issue.  (I've heard he's blaming global warming, but that may just be a rumor.)   Responsibility for the issues I've mentioned above has been taken, and those whose vehicles were damaged were reimbursed for repairs.
If you are reading this and have a great deal of familiarity with the building you may have noticed something about the pictures I've posted above that is bothering you.  I went on this photo-jaunt not long after arriving in London, and I was not yet oriented to directions here that early on in my trip.  As some of you may have noticed, I actually ended up on the wrong side, the north side, which is where all of the pictures above (except the first two) are taken.  In my defense, I think my mistake is understandable, not only because of my lack of orientation to the city but because if you look at the two pictures at the top of this post, this building seems to be concave in only one direction.  Because what I could see of the building showed it to be concave on the side I was on I thought I was in the right place.  But then I walked a bit further and noticed that it is actually concave on both sides.  It is more concave to the south, and, of course the south is the side where the sun is going to be more of a problem.  The four pictures below show the south side of the building.  If the glass looks a bit different it's because they have now fixed the issue by installing aluminum (or, as the British would say, "aluminium") fins.  Problem solved!


These two pictures (just above and just below) were taken from the Tower of London.  This city has quite a mix of the old and the new, which I find very enjoyable.
I've included two YouTube videos on this topic below.  The first is just under 2 minutes long, and the second is just over 4 minutes long.  I wanted to share visuals of some of the damage that was done, along with some additional explanation.


Wednesday, March 25, 2020

John Dee - Early Life

Tower of London
John Dee was born in the Tower Ward of London on July 13, 1527 to Roland Dee and Jane Wilde Dee.  John's father Roland was in the textile business, and his mother had an inheritance from her father, William Wilde of Milton-next-Gravesend in Kent.  John was born into a world that was being shaken by unprecedented change:

1492 Christopher Columbus discovers the "New World"
1514 Copernicus drafts (though doesn't yet publish) his heliocentric model of the universe
1517 Martin Luther's 95 Theses set in motion the Protestant Reformation
1519-1522 First circumnavigation of the globe (Magellan-Elcano Expedition)
1527 King Henry VIII begins to seek annulment from Katherine of Aragon, leading eventually to England's break with Rome.

All of these events shaped the world into which John Dee was born and hence the course of his life.
The White Tower, built by William the Conqueror in the early 1080s
John Dee was baptized into the Roman Catholic faith at the church of St. Dunstan's in the East, which at the time would have been an imposing parish church, richly decorated by the members of the wealthy guilds in that area of London.  Now it is a ruin, but it has been preserved by the city of London and now serves as a park, as shown in the five pictures below.
The namesake of the church, St. Dunstan, lived from 909 to 988 and was an abbot of Glastonbury, a bishop of London, and an archbishop of Canterbury.  He was later canonized and was considered a patron saint of goldsmiths and, thus, alchemists.  Given Dee's later associations with Arthurian lore (which involves Glastonbury) and with alchemy, it seems somehow appropriate that the church in which he was baptized and raised was named for this particular saint.
 The area of London in which John Dee grew up was a busy center of commerce.  The quays near the Billingsgate Docks bustled with ships bringing goods into the capital city.  Nearby streets were Cheapside, the thoroughfare for London's main market, known as a "cheap," and Lombard Street named for the northern Italian merchants who had settled there in the twelfth century.   Dee's father was a mercer, and the family was of middling income, but Roland worked hard to improve his lot in order to be able to provide connections and an education for his son.  Eventually Roland Dee became a "gentleman sewer" to the king (which doesn't necessarily mean he sewed the king's clothing, but he was probably involved with buying and maintaining fabrics for the king's palaces and garments).  This put Roland into contact with the king, and thus in position for reward for good services.  In 1544, King Henry VIII appointed Roland Dee to the position of "Packer to the Strangers" - a position in which he assessed customs on exports by foreigners and charged fees for packing them.  By 1541, Roland Dee was one of the wealthiest merchants in St. Dunstan's.  The rise in the Dee fortunes allowed Roland to provide his son John with an education.  After his grammar school training, John Dee entered St. John's College, Cambridge in 1542.
The pictures above and below are of St. John's College as it looked in 2016 on my first sabbatical.  It would have looked different in Dee's time.  It was a small college then and had only been founded 30 years previously.  Dee was tutored by John Cheke, one of the foremost teachers of the day and the first Regius Professor of Greek at Cambridge.  Cheke was also a tutor to Prince Edward and Princess Elizabeth, both future monarchs.
Dee was very serious about his education.  He claims to have studied 18 hours a day, allowing 4 hours for sleep and 2 hours for meals.  Dee showed aptitude for mathematics at an early age.  Certainly, he had learned 'vulgar' numbers of trade in his growing-up years due to his father's business.  Dee was drawn to the geometry of Euclid, but this was not looked on favorably at Cambridge.  In fact, a fellow of the college just before Dee's time there had, in his lectures on mathematics, dismissed such manual studies as geometry as being unfit for gentlemen and unable to provide them the judgement and eloquence that could be gained by literary studies. But Dee remained devoted to geometry, eventually writing the preface to the first English edition of Euclid (1570); this preface has now become famous in its own right.
First English Edition of Euclid's Elements as displayed at RCP London 2016
Dee learned something else at Cambridge that we today might not look favorably on.  It was something that was not part of the curriculum, and this was his occult work, particularly in alchemy which seems to have been a natural outgrowth of Aristotelian philosophy.  This study served him well in his later life consulting for Queen Elizabeth I who herself was a practitioner of alchemy.
De humani corporis fabrica libri septem by Vesalius (RCP London)
 For the reasons stated at the beginning of this post, the world had turned on its head just before the time of Dee's birth, and the changes just kept coming.  It was during Dee's student days at Cambridge that two of the most important books in the scientific revolution were published a book on human anatomy by Andreas Vesalius, De humani corporis fabrica libri septem, and the book on the cosmos that Copernicus had drafted so many years before (but wisely waited to have published after his death), De revolutionibus orbium coelestium.  The book of Vesalius opened up the inner spaces of the human body for study, and the book of Copernicus opened up the outer spaces of the cosmos for study.  These were both published in 1543, and a foundational book on algebra, Girolamo Cardano's Ars Magna was published two years later in 1545.
De humani corporis fabrica libri septem by Vesalius (RCP London)
John Dee's serious approach to his studies paid off, and in 1546 King Henry VIII appointed him as a Junior Founding Fellow of the newly opened Trinity College, Cambridge.  There Dee was a Reader in Greek and also taught logic and sophistry.
Above the Great Gate is Trinity's founder, Henry VIII, with a rather interesting scepter.

Trinity College, Cambridge, Great Court (2016)
The college, of course, looks different now than it would have in Dee's day.  For example, the chapel, which is the building containing the clock, was not finished until 1567, which is during Dee's lifetime but after his time as a fellow there.  The fountain in the center was built in the early years of the 17th century.  A building that Dee would have been familiar with is that of the chapel of King's College, Cambridge, which was built between 1446 and 1515.  King's College is just to the south of Trinity, and St. John's is just to the north.  The chapel was begun by Henry VI of the House of Lancaster, but there is much in the details of the chapel that relate to the Tudor Dynasty that Dee is closely associated with.



Do you see the intertwined H and A in the picture below?  This was carved at the time of Henry VIII's wedding to Anne Boleyn and is part of the ceiling just below the organ.
The Tudor Rose also makes and appearance in many places inside and outside the chapel.

And so, with some digressions and tangents, I give you the early life of John Dee and the world that he was born into.  Future posts will trace more of the course of his life.

Monday, March 23, 2020

Ch-ch-changes

First: A Challenge: Before reading on try to guess what the object pictured above is and how it relates to this sabbatical study.

Second: A Personal Update: It will come as no surprise to anyone in the world right now for me to say that we are living through very unsettled times in this midst of the COVID-19 pandemic.  It's impacting us all in various ways - some in very critical ways.  The impact on me, so far, is less critical, but it has impacted the entire trajectory of this trip and these studies, and therefore of this blog.  The rest of my post will be about how things changed over time and what the plan is from here, and I'm sure my personal feelings during this chaotic time will come out as well.
Italy
Initially, mathematician Girolamo Cardano was to receive the lion's share of my focus.  I was to have spent 5 of my 8 weeks in Italy focusing on this one mathematician and then the remaining 3 weeks in the UK studying the two others: John Napier and John Dee.  This trip had been meticulously planned over the course of two years.  Then a mere two weeks before I was to leave, Italy began to shut down due to COVID-19.  It became obvious  at that point that I would not be able to travel to Italy, not only for health reasons but also because the universities, library archives and museum archives that I needed to connect with were shutting down indefinitely.

A sabbatical isn't just a vacation that can be put off to another time.  I've been given time away from teaching now in order to carry out other work at this time.  It involves an obligation to my college to follow through on plans that had been approved at multiple levels and to follow through on promises I had made regarding outcomes.  There is allowance for changes due to extenuating circumstances (and a pandemic is certainly an extenuating circumstance!!), but the obligation to benefit the college through the work done during this time remains.  Also, my desire to follow through on my studies remained deeply motivating to me.

After canceling five weeks worth of accommodations and tours in Italy, and contacting professors there whom I'd made arrangements to meet and letting them know I was not now coming, I spent a sleepless night mentally running through ideas for a proper substitution for what had been lost.  After seriously considering and casting aside three ideas that would have taken me on a very different trajectory I settled on the fourth, which was to extend my time in the UK - focusing more heavily on Dee and Napier but with Cardano (who had spent time in Edinburgh and London) as a continuing, though smaller, focus.  That was the first change.
UK

As far as this shift to more of a focus on Dee, I'd been reading about all three of these mathematicians for years leading up to this, and something I had read about Dee tickled my brain on that sleepless night as a possible direction of study.  It had never been a major part of my focus on him, but what I remembered is that one thing John Dee did in his "role" under Queen Elizabeth I was to have traced her genealogy (and his own) back to King Arthur.

Yes, I'm aware that that doesn't sound like a very scholarly pursuit, or at least not mainstream.

Remembering, however, that the goal of this sabbatical is to help students in the math classes for my liberal arts majors to enjoy mathematics more, I realized that delving into Arthurian lore and it's connections to Dee and the Tudor monarchs could be a very engaging topic.  So I scrambled to find items I could study and places I could visit in the UK that could connect John Dee, the Tudor Dynasty and King Arthur.

One thing I could do was to travel into the west of England, hitting up such places as Winchester (for the round table), Glastonbury (for Avalon and the grave of Arthur and Guinevere), and Wales (for Caerleon Amphitheater).  In terms of physical items to study, I dug through the footnotes and endnotes of scholarly works on Dee, and I searched archival holdings, and one thing I found was a genealogical scroll that Dee drew up for Queen Elizabeth I, establishing her descent from King Arthur.  This 16th-century scroll can be found in the manuscripts collection of the British Library.

Please note: Yes, I realize that in our day and age we are rightly skeptical about anything that is written about a figure such as King Arthur, and that though a person certainly existed upon whom the legend was centered, he almost certainly was not a king, and we don't even know for sure when that person lived.  But my studies aren't about our day and age, they are about the 16th century, a time in which beliefs were different and in which the new Tudor dynasty had just taken the crown by conquest at the end of a time of civil war and successional uncertainty.  Henry VII had only the most tenuous of claims to the throne, and so he and his progeny felt a need to establish their legitimacy.  One way to do this was to be able to claim descent from King Arthur  .  .  .  but, I digress  .  .  .
On my first full day in the UK I went to the British Library and got my reader's card.  I went to the manuscripts reading room to request this item - fully expecting the answer to be "no."  After all, this is a 16th-century scroll hand drawn by the famous (and in some circle infamous) John Dee.  I imagined it would be too popular and too fragile and therefore not available except perhaps to someone like Roger Penrose or Andrew Wiles or some other famous professor.  But no, it was absolutely available to me to handle and to take pictures of.  The scroll is over 6 feet in length, and it is one of the most astonishing things I have ever seen.  I'm sorry that the pictures I've included are only just a teaser for now, as I have not yet had a chance to request permission to post pictures of the content here.  But hopefully this at least gives an idea of what I was working with and anticipation of pictures yet to come.  Once I have permission to do so, I'll do a full post just on this.

So  .  .  .  so far so good.  I also requested some books relating to these matters at the archives of the Royal College of Physicians in London, a visit I've already written a bit about in a previous post.

But this post is supposed to be about changes  .  .  .  as you can see, though, I became very excited about the new direction.

I had hoped to continue reading at the RCP and the British Library and also at Lambeth Palace Library, but after my first 5 full days in London all libraries and museums had shut down because of the pandemic.  Even Westminster Abbey was closed both to visitors and to worshipers.  Restaurant and hotel staff were talking in undertones about the possibility of having to close soon.  Though I'd been supposed to stay in London another nine days, the places I needed to visit were no longer open, and I wasn't entirely sure what the food and shelter situation would be for me in London in the near future, so I changed my accommodation dates and began my travels out into the West Country, which is lesser populated and therefore, or so I thought, less impacted.

This new destination was Winchester, which has a lovely and very important cathedral.  The first thing I did after checking into my hotel was to tour the cathedral which was right next to my hotel, but that wasn't the draw in terms of my studies.  Winchester is famous for it's round table that for some centuries was believed to have been that of King Arthur, so after a too-quick tour of the cathedral I headed to Winchester's Great Hall so as not to miss out in case closures were coming here soon as well.
But though the cathedral had been open, the Great Hall was not; it had just been closed that day.  I missed it by one day.  While I was standing outside, dejected, a docent crossed the square heading to another door nearby, so I asked her about it, and she shared a lot of wonderful information.  While we were talking, a young man came running across the square and asked about the round table, expressing that he had a guest with him from Australia who had come to the UK just to see this.  He asked if she could open the door just for one minute for them to take a picture, since his guest was all the way from Australia and wouldn't be back.  She didn't back down despite the pleading.  She suggested that perhaps a return trip from Australia might be possible in 10 to 15 years even if they couldn't manage sooner, and that the table would certainly still be here as it had been here for 800 years already and would most likely be here for another 800.
No point hanging around there since seeing the round table was not going to happen, so I went back through the city gate and onto the High Street.  I needed dinner at this point, but what I was seeing was restaurants with blinds drawn or with black plastic in the windows.  I finally found one restaurant that was serving customers, but when I showed up at the hostess podium I was told that they'd had a call from "corporate" 15 minutes before instructing them not to let any other customers in and that this was their last night.  I missed the round table by a day, and I missed the restaurant deadline by 15 minutes.
I turned a corner and saw a bobby, so I went up to him thinking he might have information or suggestions. I told him I had booked into a hotel that day for the next 15 days and I wondered where I was going to get food.  He basically said, "Good luck with that."  I said, "I feel like I'm dreaming and that this can't be real."  He said, "Me too.  I think we all feel that way."  It's a little unsettling when even the police force is freaked out and uncertain!
He did point out that there were a couple of take-away only places around the corner, a Papa John's and a McDonald's, so I got a burger and fries. Not a bad view for a McDonald's take out dinner!  (When I said the cathedral was "right next to" to my hotel, I was not kidding.)

Aside: This is getting long and chatty because I am home from an 11 hour plane flight with no sleep and am 7 hours off the time zone I was recently used to.  I may come back and rewrite this post later, but I wanted to get something up, since I know I left my readers hanging for many days with no news.  This isn't the sort of post I was expecting to write, but then again a pandemic is something none of us were expecting to experience!

After finishing dinner I figured I'd better get to the grocery store and get some food if I wanted to keep eating during my 15-day stay, which was still absolutely the plan at that point.  After purchasing some food and returning to the hotel I thought to ask at the desk if they were going to be staying open.  Long story short: "Probably not."  I followed up with, "So I actually can't really stay here for 15 days then, right?" To which I got the response, "Certainly not."  Hmm   .  .  .  .  funny, they charged me up front for 15 days!  (I'll get a refund, no problem, but still  .  .  .)
Daytime View of Winchester Cathedral from my Hotel Room Window
Nighttime view of Winchester Cathedral from my Hotel Room Window
The plan at that point was still to persevere - 15 day stay here (if they close early, then move on early) - then on to Glastonbury for its associations with King Arthur and so on.

Since I travel frugally, it turned out the both of my hotel rooms had non-functioning televisions.  I wasn't getting a newspaper.  And, though I had registered on my computer for the BBC so I could stream the news, a box popped up saying it was illegal to watch it without a television permit (whatever that is), so I was without news and flying blind.  I didn't try harder to get news because I was very busy with my study, travel and writing.  But then messages started coming in through email and facebook from friends back home who did have access to news:

"Are you getting out?"

"Do you know the US State Department has us at Travel Advisory Level 3?  Oh, no wait, it just now changed to Level 4, the highest possible, rarely used and generally for war zones!"

"The president says flights into the US will be stopped 'very soon.'"

Then I saw an email from my hotel 3 cities down the line letting me know that they were closing and canceling my stay.

OK, evidence was mounting that I was in danger of not having food or shelter (at least not readily available) and that if I didn't get out soon I might be stuck there, which would normally be my dream - STUCK IN ENGLAND!?!?  YES, PLEASE!!!  But without guaranteed food and shelter  .  .  .  hmm  .  .  .  and though I didn't really fear that I'd get the virus, the thought of possibly getting very sick while traveling alone so far from home was starting to weigh on my mind as well, which I think was at least partly due to the panic in others around me which was becoming more contagious than the virus itself.

I had already canceled Italy - had checked out of my London hotel 9 days earlier than expected - taken a train to Winchester and checked in for 15 days still set on completing my travels and studies - and now I was checking out the very next day and heading back to London in order to catch a flight home the day after (though some friends and family members were pleading with me to fly out THAT day and not to wait even one more day!).  Since I wasn't getting news in the UK, I had to rely on what I was hearing from friends in the US, and I was getting somewhat differing messages.  My whole trip involved some degree of heightened stress, but those last few days were stressful in the extreme.

Though I had the privilege of seeing and accessing some beautiful and amazing things during the short time I was there, I don't recommend traveling in the midst of a pandemic!  (When I left home for these travels, by the way, the situation was not yet labeled a pandemic.)
Train from Winchester to London
So, two trains, a walk, a taxi, a flight, and a car ride stood between me and home.  I was already completely exhausted from all the changes of plan in the previous 48 hours, and I was having difficulty sleeping because of the mixed messages I was getting online - many of which were very distressing - and, again, I didn't really have any decent access to news in my situation in the UK.  The situation was changing so rapidly that I did not have time to think things through and weigh my options.  For instance, though hotels were closing, airbnbs were not, and my tour guide for a month from now had offered to pick me up at any point if I ended up getting stuck.  So there may have been other options for me, but it didn't feel like I had the luxury of time in order to think clearly and carefully.
I was so freaked out from the contagious panic by the time I got to my hotel in London that I almost didn't want to eat dinner that night, because it meant eating out.  But I finally got hungry enough to venture out despite growing fear of having someone else prepare my food and serve my food in this pandemic-ridden world.  I had noticed an Italian restaurant on my walk from Paddington Station to my hotel earlier in the day, so off I went.

There were hardly any diners - only 3 tables occupied - widely separated.  With so few people in the restaurant, conversations were easy to overhear.  These two gentlemen, pictured above, were having such an interesting and intelligent conversation, that I couldn't help myself from eavesdropping.  Apparently they were doing the same and heard me tell my waiter that I was a professor on sabbatical and was supposed to have been in the UK for 8 weeks but was leave the next day after only 10 days due to the pandemic.  After I finished and was walking out, these two gentlemen invited me for conversation and offered to buy me a drink.  I tried to keep moving, making an excuse about needing to pack, but they were a little bit insistent, and I was pretty lonely and stressed (and I'd been very interested in their conversation!), so I accepted.

The conversation that ensued was a highlight of my trip!  These guys were amazing and bright and funny.  The conversation ranged from high level talk about mathematical and computer science topics such as set theory, AI, cyber security, and first order predicate calculus, data modeling and extensional definitions for sets, to discussion of the location of Atlantis, the authorship of Shakespeare's plays, Freemasonry and Rosicrucianism.

I love conversations like that anyway, BUT it really fit into my studies.  I've mentioned in previous posts how hard it is to get into the minds of my 16th-century mathematicians because their world was more like a different universe than a different time period.  For Cardano, Dee, and Napier all knowledge was of a piece.  As I've shared before, there was no separation between astrology and astronomy or between alchemy and chemistry.  Religion was a driving force behind natural philosophy (including mathematics), and astrology was a tool for use in medicine.  In some sense, studying anything required studying everything, and it was all legitimately open for study.  This chance conversation where it was "anything goes" brought me closer to the world of my mathematicians in that way.  It was also simply a blessing to get my mind off of yet again packing and traveling.  I do believe that in this trip God sent angels to prepare a path for me, and though I didn't know what the next step was going to be most days, I found that the path was smoothed ahead of me.  I also believe that in some way these two men that I conversed with on Friday night were "angels" too who took my mind off of the stress and drew me into amazing conversation.
Ceiling of the Angel Chapel, Winchester Cathedral
I'll probably feel silly and embarrassed about this post tomorrow because it is so long and scattered and personal and emotional, but with all the quick changes and necessary decision-making and stress of the pandemic situation and lengthy travel, I'm so far beyond exhausted that I don't have a word for for how exhausted I am.  Given the last few days and given how I'm feeling, maybe "scattered" is a good way to leave this post.
Goodbye London!
And now, speaking of changes, another one needs to happen. I need to write a revised sabbatical proposal in order to fulfill my obligations to the college.

In the few days in England I did take 1410 pictures, and I do have material for at least 3 or 4 more blog posts, each of which will be focused on mathematicians and not my stress, so I hope you'll tune in for those.  I also have in mind for my proposal revision to see if I can get an extension on my sabbatical so as to travel next May (after spring semester) in order to finish this up - rather than just putting time into some other work this summer in order to make up the required unit value.  I did find amazing things in my archival readings that have deepened my understanding and also have sent me in new directions - some of which will be very engaging to my students - and one of which might result in a journal article.  I really hope to get back out there as soon as possible to follow up with these, and, certainly, if the goal is to engage my students I also want to follow up on the King Arthur connection!

Speaking of which  .  .  .

Answer to the Challenge: This is known at the London Stone.  It's displayed on the side of a building in the financial district of London, and most people just walk right by it, but it is a very storied stone.  The reason I went looking for it is that it is said to be the stone from which Arthur removed the sword, AND it is said that John Dee shaved off bits of the corners of the stone for use in his alchemical experiments.  There are MANY other stories as well about this stone.  Records show that it was definitely a London landmark at least as far back as medieval times and is said to go back to Roman times, and there are legends about it having been brought to London from Troy.  I'll leave it at that for now.

GOOD NIGHT!