Saint Michael Sword: Are the cathedrals really on a straight line?
geospatial.netlify.app
geospatial.netlify.app
Here a few of the salient points:
> They are not cathedrals!
True! As I learned after writing the blog post, a Cathedral is not simply a large church. As written in several comments there has to be a bishop.
> Fallacy of using other projection than the Mercator one.
It was known that they are "visually" aligned on the Mercator projection. The question is: does it mean that they are aligned on the surface of the earth? That question was the crucial one underpinned the post.
> Birthday paradox and Texas sharpshooter fallacy.
These are two really interesting take on the problem that I did not considered or knew about. Certainly worth exploring in a next blog post.
Also I have to inform you that the blog is temporarily suspended. This decision is after an unfortunate billing policy from the provider netlify. It has nothing to do with the comments received here. On the contrary the comments received here had encouraged me to write more (and to document myself better beforehand).
I hope to be able to bring it up back soon with a different provider, that would not add extra costs with no capping for going "viral" and exceeding the allowed free bandwidth.
https://sebastianof.github.io/GeoDsBlog/posts/gds-2024-04-20...
Sorry for the temporary disruption.
I just wrote another comment that may interest you to some degree: https://news.ycombinator.com/item?id=40607523
It's probably best to reply to each person's comment, letting them know first also know you're author of the article/project.
When you say "strait line" is it globe based curved path like the flight of a bird? Why was it called a sword?
Edit: found a working link! still extra extra curious!
Cyprus: https://www.google.com/maps/search/st.+michael/@34.8439762,3...
Rhodos: https://www.google.com/maps/search/st.+michael/@36.5898973,2...
Thessaloniki: https://www.google.com/maps/search/st.+michael/@40.9052893,2...
Croatia: https://www.google.com/maps/search/st.+michael/@44.8895084,1...
Switzerland: https://www.google.com/maps/search/st.+michael/@47.0545837,8...
France, almost right through Paris notably: https://www.google.com/maps/search/st.+michael/@48.823467,2....
England, Exeter area (bunch of Michael churches): https://www.google.com/maps/search/st.+michael/@50.7123109,-...
Many are actually kind of notable in that they bunch fairly near the geodesic like in Croatia. They might be the birthday paradox, definitely a possibility. Yet quite a bit of clustering along that route.
you missed a chance to say "only under a bishopric"
Who first wrote about this? Who picked those seven sites? The earliest source mentioned is from 1969, and it's not even about this particular line.
There's no shortage of writing about esoteric Christian topics throughout the centuries, but this one seems really thin and really modern.
For example, the Santo Daime church originating in Brazil - and who drink Ayahuasca at the beginning of and throughout what they call works [Ayahuasca is in Brazil's constitution as a right, and Canada also has it legalized for the church to import legally] - and then sing from hymns depending on the type of work and time of the year, their hymns containing the teachings, sung mostly in Portuguese; arguably those teachings will have been divinely transmitted to the people, mostly the founder to begin, while in the altered-connected state; the biologic pathway for part of this experience is the concept of ego death-dissolution, where your ego temporarily is out of the way to allow your senses to be more aligned with the more holistic - your senses not "calcified" away from feeling more than just your strongest stimuli of your own senses and the signals of your ego mind - both that can mask the more subtle - and can be repressed if disconnected from it at a young age due to various reasons.
Furthermore, if you read the book The Immortality Key, there is the belief circulating that wine - "the blood of Christ" - historically wasn't alcohol but wine was a mix, and arguably an entheogen-psychdelic that then connected people to an altered state to help open the mind and heart, and heal vs. alcohol which is a depressant and poison; where the knowledge that Jesus taught/shared was supposedly from 300 years prior from the Greece region, where millions of people would pilgrimage to annually arguably to partake in drinking the "wine."
Part of the misunderstanding is that it's believed that Christ has already resurrected but in energetic form, where he joined the divine celestial order, along with St. Michael and other energetic-conscious beings.
I've thought it's an interesting idea, whether it was oppressors who wanted to prevent this healing and weaken people's connection to God - which arguably gives people strength when they have a faith in something invisible [and unengaged most of the time], and/or if it was authoritarians incidentally working with or benefitting from industrial complexes - producers and merchants of alcohol who decided to claim their alcohol was the "wine" that "everyone was talking about and pilgrimaging for" - and in high demand, for the sake of profits; which would have also caused people to not ride the wave of word of mouth transmission toward drinking Ayahuasca et al; it makes me think partly of the more recent "war on drugs" that happened to suppress-control and prevent access to arguably highly effective non-patentable and relatively natural medicines, that are now coming to light again - Ayahuasca, mushrooms, ketamine, MDMA, etc.
In conclusion, St. Michael or anyone in the divine order - conscious energetic beings who can influence at least in so much as giving guidance - could have guided each builder or person picking the build site independently, potentially leading to such a phenomenon - whether the St. Michael's Sword line was simply coincidence or happenstance, or perhaps could simply be decided to be human-made and simply a recognition to honour St. Michael; to me it boils down to a fun-playful thought exercise, but where it could be dangerous in that an ideological mob could use it to demonize people who let's say are needing or desperate for hope or truth of the divine - and haven't yet reached a faith state.
[1]: https://www.philipkosloski.com/who-discovered-the-sword-of-s...
Agree so, there is no line besides the one people make up.
https://en.wikipedia.org/wiki/St_Michael's_Mount
p.s. It's a cool place to visit btw. You can walk over to the house at low tide and then the house is on a steep hill surrounded by a lovely garden which you are compelled to enjoy until the next low tide at which point you can walk back to the mainland. Nearby is a heliport where you can get a passenger helicopter to the Scilly Isles which are also worth a visit.
[1] https://epicpew.com/hail-bright-star-ocean-ave-stella-maris/ (worth noting that this source is some sort of Catholic thing and is written in what the Wikipedia banners on some articles used to refer to as an "in-universe style")
This makes more sense, as castles tend to move in straight lines. As another comment mentions, if these were cathedrals that would mean a bishop in residence, and we all know bishops prefer to move diagonally.
(i. e. Mont Saint Michele the bishop who saw St. Michael originally refused to construct the shrine because he wasn't sure of the veracity of the vision. It was only after he was wounded by St. Michael's sword and the wound refused to heal that he went to establish the shrine. And only then did the wound closed up.)
Make of that what you will.
Second, is this a post-hoc story we told about the shrines (perhaps to avoid destruction / re-purposing by a greedy local lord?)
...According to the guy trying to sell you a big mac or whatever they are called there.
https://www.irishtimes.com/life-and-style/food-and-drink/lik...
but just to back that up:
https://en.wikipedia.org/wiki/Skellig_Michael#History
Not a cathedral, No mention of an appearance of St Michael, and the monastery predates the dedication to him (it?) by several centuries.
https://en.wikipedia.org/wiki/St_Michael%27s_Mount
Not a cathedral, site predates dedication to michael. No mention of an appearance of michael.
https://en.wikipedia.org/wiki/Mont-Saint-Michel
This one has a story of an appearance, still not a cathedral
https://en.wikipedia.org/wiki/Sacra_di_San_Michele
Not a cathedral, does have a story about an appearance, but that site significantly predates that appearance.
https://en.wikipedia.org/wiki/San_Michele_Arcangelo,_Perugia
Pre christian temple that was converted, not a cathedral
Taxiarchi Michail
Monastary, not a cathedral
https://en.wikipedia.org/wiki/Stella_Maris_Monastery
Not even dedicated to michael.
2. https://en.wikipedia.org/wiki/St_Michael%27s_Mount#Folklore - "There are popular claims of a tradition that the Archangel Michael appeared before local fishermen on the mount in the 5th century AD.[44] But in fact this is a modern myth. The earliest appearance of it is in a version by John Mirk, copying details of the medieval legend for Mont-Saint-Michel from the Golden Legend.[45] The folk-story was examined and found to be based on a 15th-century misunderstanding by Max Muller."
> an appearance of the Burger King himself explicitly asking for a shrine in the location
The word cathedral comes from a Latin word meaning “seat.” The seat referred to is the seat of the bishop, who is the leader of a group of churches related to the cathedral. The bishop's seat is both a metaphor for the cathedral as the bishop's “seat of power” and his actual chair, the "cathedra," inside the cathedral.
It's not a possible word in Latin; it would have to be a loan from Greek.
Source: not religious at all but my brother is a dominican friar so has explained this stuff to me. Also confirmed by this for example https://catholicsay.com/differences-between-a-bishop-archbis...
- St Michael's Mount: monastery, 9th century
- Mont Saint-Michel: monastery & sanctuary, 708
- Sacra di San Michele: monastery, circa 983-987
- San Michele Arcangelo: sanctuary, 490 (St. Michael, supposedly did appear here)
- Taxiarchi Michail: monastery, 18th century (the younger one)
- Stella Maris: monastery, 1185 for the latin monastery (but in fact 15th century BCE as part of Mount Carmel)
So, none of them are a proper cathedrals but monasteries and sanctuaries. With San Michele Arcangelo & Mont Saint-Michel the only two important ones as pilgrimage destinations.
For a partial map of St. Michael churches or alike see: https://www.reseausaintmichel.eu/carte-des-sites/
The "line" could easily be "broken", if we add for example, the Castel Sant'Angelo in Roma (Mausoleum of Hadrian) or Saint-Michel de Cuxà. Both are far more prestigious than... Skellig Michael than nobody would know about if if was not on this "line".
Also worth noting: "[Michael's] churches were often located in elevated spots", says the page on San Michele Arcangelo, Perugia.
The obvious next step here is gathering a database of every spot claimed to be sacred to Michael, plotting them on a map, and seeing if this particular set of seven places leaps out of the data. But that sure sounds like work.
(Well, that's the obvious next data scientist step, there's also the obvious next step for the magician or priest, which is to go to or create a sacred space suitable for summoning archangels, call down Michael, and say "hey thanks for coming, so what's up with this line we call your sword?".)
Pondered the estimation a bit more. The first two points of a group of 7 define a line. The probability of the remaining five being close enough to the line is just the probability of each being close enough, to the power of five. We can roughly estimate that probability as the "close enough" distance divided by the total area. Let's just normalize. Let's assume distribution within a unit square Some of the lines would not cut in a way that most of the "close enough" area is inside the box, but that's a constant factor and not to big.
Given n points and the probability p7 that seven points lie close enough to a line, we take the number of different sets of seven points, N7 = (n choose 7). The likelihood of a match is (1-(1-p7)^N7).
This is a very rough estimation, of course, but it gives some idea of the likelihood.
If you filter to monasteries, it trims it down a lot https://overpass-turbo.eu/s/1MyP
With the number of cathedrals in Europe I don't really think this is supported.
https://en.wikipedia.org/wiki/Dedications_in_the_Church_of_E...
And if we extend the search to all placenames dedicated to St Michael quite a bit more!
It's not pure coincidence but it is a kind of observation error as highlighted in other comment. Increasing and decreasing the variables and measurements effects the odds.
Basically you can get a line between many things on earth, but 1) the dimensions of that line cannot be chosen if you also want to choose the things that define it or 2) the dimensions can be chosen but the things that make it up cannot.
Also compare star maps.
If they really were cathedrals, a coincidence would have been extraordinary.
Traditionally, it had been mostly exposed locations that were dedicated to St Michael, e.g., locations that had been alleged entrances to the underworld in antiquity. 6 out 7 of these locations are in costal areas, with corresponding erosion features. So this shouldn't be of much surprise, as the line crosses several costal regions – of which there are plenty.
(In other words, the line crosses 6 costal areas with a St Micheal nearby and 6 without. The second fact may be as remarkable as the first one.)
Edit: Challenge, can we identify a "St Michael's Serpent", approximating a sine wave?
- St Michael's Church in Bengaluru, India
- Gereja Katolik Santo Mikael in Surabaya, Indonesia
- St Michael's Catholic Church in Kilcoy, Australia
- St Michael's Church in Auckland, New Zealand
Perhaps the real data challenge here is to find the straight line with the most St Michael'ses globally.
The steps of the stairs are just cut and shaped stone, the walls are just stone. It can be summer and 90degrees in Turin, and inside the cathedral is 30 degrees and so chill.
If you ever find yourself close, go visit it, it's a very humbling experience.
Which temperature scale are you using here?
C->F: multiply by 2, then add 30
F->C: subtract 30, then divide by 2.
Going the other way
86-30 / 2 = 28 which is close to 30.
Alternatively, Fahrenheit, and 90 is realistic for outdoors mid-summer in Italy and 30 is a poetic exaggeration for ~80 inside a stone-building. If meant literally, the holy water would freeze inside the cathedral. Besides, nobody uses Fahrenheit in Europe, but poetic exaggeration is common.
But then again, I am sensitive to heat.
https://en.wikipedia.org/wiki/Glen_Roy#The_Parallel_Roads_of...
Edit: Also have a look at the Lochaber Geopark:
5. (Miller's Law) Three points determine a curve.
6. (Mar's Law) Everything is linear if plotted log-log with a fat magic marker.
In fact, as an architect of a cathedral, you pretty much had to make 22 or more of anything to avoid having a meaning ascribed.
What I'm saying is that it didn't matter what the architect did. Someone, well after the fact, would have found a tenuous connection between their work and the Bible and claimed they were divinely inspired.
https://en.m.wikipedia.org/wiki/Pythagoreanism
The practice of wonder surrounding numbers and their role in existence has been practiced by nearly every ancient civilization for many millennia.
Definitely not unique to Christianity. Definitely as natural as religious practice itself.
> The Pythagoreans also thought that animals were sentient and minimally rational. The arguments advanced by Pythagoreans convinced numerous of their philosopher contemporaries to adopt a vegetarian diet. The Pythagorean sense of kinship with non-humans positioned them as a counterculture in the dominant meat-eating culture.
The beings who built the cathedrals had methods and technologies of amazing power that we know virtually nothing about. They are artifacts of something that is now, presumably, gone.
It's a UNESCO world heritage site and a huge tourist attraction long before Star Wars, but it is definitely not a Cathedral.
CGI'ing over them is a genius solution that makes me absurdly happy.
Another thing that would be interesting is to look at the effect of non-uniformly distributed birthdays. For example, the day that's nine months after valentine's day or christmas might (?) have a slightly higher number of births than an average day. Then you could look at what kind of an effect this would have on the probability of a common birthday as a function of group size.
He gave example from some text taken out of bible with spaces removed. That's lots of letters on one screen, and from those letters he was able find his name, date and topic of the talk, when joining letters at equal distance.
Finding unbelievable patterns is not as amazing as we think.
A very far-fetched claim without any proof. Simple answer: selection bias
> Did the builders knew the earth was round?
If he had just googled that he would have gotten the answer, which is, of course, "yes"
From wikipedia, the list of St Michael churches:
St. Michael's Church (disambiguation)
Parroquia de San Miguel Arcángel (es), San Miguel de Allende, Guanajuato Mexico World Heritage Site
Sacra di San Michele (Saint Michael's Abbey), near Turin, Italy
Pfarrei Brixen St. Michael with the White Tower, Brixen, Italy
Cathedral of St. Michael and St. Gudula, in Brussels, Belgium
Mont Saint-Michel, Normandy, France – a World Heritage Site
St. Michael's Cathedral Basilica (Toronto), Canada
St. Michael's Cathedral (Izhevsk), Russia
St. Michael's Cathedral, Qingdao, China
Chudov Monastery in the Moscow Kremlin
Cathedral of the Archangel in the Moscow Kremlin – a World Heritage Site
Sanctuary of Monte Sant'Angelo, Gargano, Italy – a World Heritage Site
St Michael's Mount, Cornwall, UK
St. Michael, Minnesota
St. Michael's Basilica, Miramichi, Canada
Skellig Michael, off the Irish west coast – a World Heritage Site
St Michael's Cathedral, Coventry, UK
St. Michael's Golden-Domed Monastery, Kyiv, Ukraine
St. Michael's Church, Vienna in Vienna, Austria
Tayabas Basilica, Tayabas, Quezon, Philippines
St. Michael's Church, Berlin, Germany
San Miguel Church (Manila), Philippines
St. Michael's Jesuit church, Munich, Germany
St. Michael's Cathedral, Belgrade in Belgrade, Serbia
Cathedral of St. Michael the Archangel in Gamu, Isabela, Philippines
Mission San Miguel Arcángel, San Miguel, California, United States, one of the California Missions
St Michael at the North Gate, Oxford, UK
St. Michael's Roman Catholic church, Cluj-Napoca, Romania
St. Michael's Church, Mumbai, India
Church of St. Michael, Štip, Republic of North Macedonia
St Michael and All Angels Church, Polwatte
St Michael's Church, Churchill, UK
San Miguel Arcangel Church, Marilao, Bulacan, Philippines
San Miguel Arcangel Church, San Miguel, Bulacan, Philippines
St Michael the Archangel, Llanyblodwel, EnglandIt's far more interesting to me that Perkin Warbeck occupied it!
Only on Mercator projection that is younger than many of the sites on the line.
Oder of things:
1. There were bunch of monasteries (not cathedrals), not aligned on any direct line.
2. Mercator invented a projection.
3. Someone looked at map using Mercator a projection and invented story about ley lines.
So there are a lot of magnificent churches that aren't cathedrals (Sagrada Familia, Westminster Abbey, St. Peter's in the Vatican), and a lot of cathedrals that are actually rather dull architecturally.
There is no reason to assume that the lines align in other projections.
People have been specifying locations in terms of NS/EW coordinates since the greeks. Celestial navigation ensures we always have a clear idea where north is, and when two locations are at the same latitude. It's the most natural way we've understood and discussed far-away places.
I don't think it's fair to say mercator invented this projection so much as he famously published maps which used it.
(btw, I agree this line is a complete retrospective coincidence, just not with this particular argument)
Mercator is special projection that was not used before him. Different projections give different distortions.
(hiking in straight line and jumping into boat at the point where land ends is not how people travel)
https://en.wikipedia.org/wiki/Dedications_in_the_Church_of_E...
https://en.wikipedia.org/wiki/St._Michael%27s_Church
Around 150 in Europe alone.
For the next hackaton: Write a programme to find all possible approximately straight lines between any 7 of these churches.
https://en.wikipedia.org/wiki/Church_of_St_Michael_and_All_A...
https://en.wikipedia.org/wiki/Burrow_Mump
https://en.wikipedia.org/wiki/Glastonbury_Tor
Churches were often dedicated to St. Michael when they were built over pagan sanctuaries, because St. Michael could fight the old heathen devil. Another example would be in Brent Knoll, next to the iron age hill fort:
https://en.wikipedia.org/wiki/St_Michael%27s_Church,_Brent_K...
https://en.wikipedia.org/wiki/Brent_Knoll_Camp
That is undoubtedly the case for both St. Michael's Mount (Cornwall) and Mont Saint Michel (Normandy) in the list of 7. They are both perfect defensive sites, on islands close to the shore, but accessible by causeways at low tide, and hence certainly occupied from prehistoric times.
https://en.wikipedia.org/wiki/St_Michael_and_All_Angels_Chur...
Multiple churches in the Philippines presumably due to Spanish Catholicism.
I didn't grow up in California so I don't know the Spanish missions very well (standard elementary school fare). I had never heard of San Miguel.
I've also never heard of Polwatte or Miramichi.
Two churches in the "Moscow Kremlin?" What's that about? And what's the story about Qingdao?
And why just the name of a state, Minnesota, instead of a more precise location?
Then I go to https://en.wikipedia.org/wiki/St._Michael%27s_Church and it disambiguates from https://en.wikipedia.org/wiki/St_Michael_and_All_Angels_Chur.... Finally, yet another long list in https://en.wikipedia.org/wiki/Cathedral_of_Saint_Michael
Aha, but two of them will always be on a straight line. It’s only the other five that are the coincidences.
So, let's just look at the churches as they line up on the Mercator projection. If you google the churches one by one, you start to notice a pattern. They all predate the invention of the Mercator projection. You also notice, as someone else pointed out, there's a hell of a lot of Churches called St Micheals.
Let's consider Europe as roughly a 10 million square km area. The probability of a single point falling within a 50 km wide band (assuming the band runs the full length of Europe) is about 0.01581 (1.581%). The probability of seven points aligning within a 50 km wide band across Europe is approximately: 10^-14
To remove that constraint, so it's just any band, I think it should be more like: given a cathedral is in a particular place, how likely is it that six other cathedrals fall in a 50km wide band aross Europe.
I think if you set the probability of the first one at 1, then the rest works perfectly at any angle of band. I could be wrong, but intuitively that seems correct.
Also, the probability of the first 2 points will always be 100% because they define the line.
Also, it's not 7 random points, it's 7 of thousands of random points.
Ah - I missed this one.
But it turns out that we don't even have to go that far. The line found in TFA is about ~50km wide. Any given 50km wide line covers approximately 1% of europe's area. There are allegedly 800+ locations dedicated to st michael in the UK, so let's make a conservative estimate and say there are ~1000 in all of europe. This means that in any given 1% of europe's area, there are on average 10. Therefore literally any 50km wide line that crosses a substantial portion of europe has a solid chance at having 7 or more st michael dedications in it.
Edit: actually via a generalization of the pigeonhole principle, if we assume that europe is 3000km tall and contains 1000 sites dedicated to st michael, there must exist at least one 50km band that contains at least 17 sites.
(600 was for rough number of cathedrals, but apparently these 7 sites are not even all cathedrals? That would make that factorial much bigger, then...)
They would have to be near enough to water to maintain life, or have access to freshwater for the religious communities there, they would have to be near building materials, they would have to be near population centers, etc.
800 shots. Pick 7.
[0] https://en.wikipedia.org/wiki/Texas_sharpshooter_fallacy
Meaning that the points are not on the shortest path, but are close to being at the same azimuth one to another?
I'm surprised no one has mentioned From Hell here, which plays with the concept of drawing symbols using lines between landmarks. Alan Moore got a lot of his ideas for that from Iain Sinclair, whose books are well worth a read as well. Specifically, the material Moore references is from Lud Heat iirc.
That is: TFA seems to be ignoring the null hypothesis.
I would not say that the method is today lost; while not aligned on a geodesic, the cathedrals are aligned on a spiral starting at the North Pole and ending at the South Pole which always travels at a constant bearing. It’s totally possible to recreate a line like this with a compass by walking such that the compass has a constant reading. Doing so over the Mediterranean, multiple mountain ranges, and bits of the Atlantic would be a bit difficult, though.
Of course it's going to be off with any other method than that of the map itself.
It'd be surprising if these buildings were exactly aligned. Presumably people could easily say that the respective diocese(s) are aligned though.
Local myth has it that the second spire wasn't build because it would topple over.
Probably many more examples like this one exist. "I don't care. Figure it out. You're the expert."
https://salisburycathedral.wordpress.com/the-spire/ is a glorious essay on the architecture of that spire.
Maybe not exactly aligned, but looking at that image of the geodesic line and the location of the churches, they all seem close enough to make me think their locations are not random chance (especially since they were laid out in the days before satellites and airplanes). I presume these are all Catholic churches? Could the medieval Catholic Church have had a plan to do this?
(I actually remember in 7th grade that our math teacher had to repeat time and again that a line of best fit does not necessarily need to join the first and last dot. For some reason it's a very instinctual thing to do.)
I wonder if the line is bang on in that projection.
Long before St. Michael was born, yes.
I'm surprised I can't find a "short" (no longer than the largest distance between points) geodesic fitter anywhere. Sounds like a fun hour-long project using GeographicLib.
Huh?
Yes. This has been known since ancient greek times, and Aristotle calculated the size reasonably well. Maybe not every labourer knew or cared but the architects almost certainly did
Even knowing the earth is round, if I were going to put things in a "straight line" geographically, I'd do it with the reference most people would actually use and see: a 2D map.
These places are old. Skellig Michael goes back past 823AD, Mont-Saint-Michel is about the same sort of age, and the Sanctuary of Monte Sant'Angelo goes back to 490AD(ish). San Michele Arcangelo is on top of a pre-Christian pagan temple. Stella Maris is on an Old Testament Biblical site. None of them is less than a thousand years old.
The bar for finding a map that happens to align, and then explaining how it was made, is not a low one.
There is a projection that might fit, though: Plate Carrée is definitely old enough, and a brief visual sanity check doesn't make it look totally off.
Virtually everything in church design is meant to communicate truths of the faith to illiterate laypeople. That's part of why pictures feature so prominently. They're telling stories to people who can't read. The sense of space, and the drawing of the attention upward, they're also communicating to people on purpose.
If the argument is that the sites were not intentionally built in a line, that it just happened this way, that there just happen to be seven prominent hills with churches built on them that refer to St. Michael (or 6 and Mt. Carmel, which is associated with him in another way), I guess that's a different conversation, but I thought the idea here was that these were lined up somehow on purpose, at least for the latter built ones, and were intentionally built to be "in a line" by some meaning of the term.
What I'd want to know is how old the story of St Michael's Sword actually is. Not the churches, but what's the earliest reference to them being in a line. My bet is that it's well after Mercator, and probably safely after the 18th century, when chunks of Europe got geodetic surveys done.
The expert used spherical mathematics. This was quite widespread knowledge required to build proper sun dials and in the Late Medieval period for long distance navigation. Some were able to use analog computers, called "armillary spheres", for the calculations, which were known since Antiquity.[1]
I'll try to look up an exact quote later. But the gist of several passages was that there was an elite or expert community- obviously, or nobody would have been designing buildings like this!
Let's assume for the sake of this discussion that the 7 sites are deliberately aligned by somebody. They would presumably be a powerful elite, and would be doing it to impress other powerful elites.
"Die Entdeckung der mittelalterlichen Stadtplanung" (2004): https://www.youtube.com/watch?v=-ZzEzhIGnwM
"Mittelalterliche Baukunst – Schönheit ist planbar" (2009) https://www.youtube.com/watch?v=MQcKOkbagDc
Both documentaries are in German, but are well worth watching, even if the automatic English subtitles are sometimes a little inaccurate.
Locations are chosen for the sake of the people who are expected to come to them.
Eratosthenes.
https://en.wikipedia.org/wiki/Earth%27s_circumference#Eratos... https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_Ea...
Mercator exists because it’s easy to navigate with. It’s easy to navigate with because it preserves bearings. Lines of constant bearing are, when you’re navigating on the ground, much more meaningfully ‘straight’ than geodesics.
‘Keep heading North West’ sounds like a pretty straight line.
Wait, you want to know if I'm a Saint?
Are they pointing to anything though?
Indeed, having a cathedral is a thing that can define a settlement as "a city".
Source: https://commonslibrary.parliament.uk/what-makes-a-city/
Given a preferred predetermined position, navigating to the desired latitude would have been easy enough for the time, getting to a spot with the correct longitude is a tricky feat prior to accurate clocks.
Having found such a location there's no apriori guarantee that site is ideal for a large stone building which would lead to some fudging about to find a near althernative site along a corridor.
There's some work to be done upon the order in which these buildings went up and on the locations themselves; for example:
https://en.wikipedia.org/wiki/St_Michael's_Mount
dates as a monastic site back to the 8th Century or so and has very little (almost none) play in position .. it's situated on a rocky outcrop in a strong tidal zone.
All of which leaves questions such as when a decision might first have been made to infill later buildings to match a line through which earlier buildings on which projection.