Early morning, but an August morning so it’s hot already. I’m thanking the Acme Building’s air conditioning as I unlock the door to my 12th‑floor office. There’s Vinnie, stretched out on the couch with a book. “What’re you reading there, Vinnie?”
“Morning, Sy. It’s one of Ken Follett‘s books, Pillars of The Earth, about a couple of families battling over a cathedral. One family wants to build it, the other hates whatever the first family wants, and this goes on for generations. Meanwhile, I’m learning more than I want to know about how they made felt in Medieval times.”
“Follett does like to dive down rabbit holes, and he’s proud to show off what he digs up. I just finished another of his books, Code to Zero. It’s a thriller loaded with arcane tidbits. The action’s wrapped around some Soviet plot in the late 1950s to disrupt America’s Explorer satellite program. We get close-ups of rocketship anatomy; we find out why unsymmetrical dimethylhydrazine is a bad bet as a rocket fuel; things like that.”
“Sounds interesting.”
“Yeah, I think you’d like it. Lots of action while the hero’s chasing around trying to figure out what happened to him and why. Spoiler alert — things get frantic toward the end.”
“Thrillers always do, that’s why they’re thrillers.”
“Mm‑hm. But I’m a numbers guy, so what really caught my eye was Follett’s collection of obscure numerical lore. One of the book’s characters, Elspeth, has an ongoing math‑nerd game with another character. Each player names a special number. The other has to explain why that number’s special.”
“Can’t be too hard. Practically every number’s special somehow.”
“True, but Follett found some doozies. For instance, Elspeth plays number 29. It’s special because it’s the root of a whole train of prime numbers: 29, 31, 37, 47,… all united by a common formula. The nth member of the series (counting 29 itself as n=0) is given by 29+2n2. The series breaks at n=29 because 29+2*292=1711, which clearly is divisible by 29.”
“29 days in February, sometimes.”
“That’s not number‑theory special. Another Elspeth gambit involves the abc=a1+b2+c3 formula where each letter is a base‑10 digit on one side and a number raised to a power on the other. She plays 135, special because 11+32+53=1+9+125=135. The other nerd matches her pattern with 11+72+53=1+49+125=175. That got me wondering if any other numbers fit the template. I worked it up on Old Reliable—”
“Of course you would.”
“You know me so well. Turns out that both 518 and 598 qualify, but no others. Elspeth plays with cubes, too. There’s a conversation in the book about 136 and 244 being partners because 13+33+63=244 but 23+43+43=136. Number 8000 is 203 but it’s also 113+123+133+143.”
“How do they even find these things?”
“My guess is heroic mathematicians with time on their hands in a no‑machinery no‑screens environment. Think, these guys were doing arithmetic with an abacus. Four centuries ago Fermat conjectured that numbers of the form 22n+1 are prime. He tried cases n=0 through 4 and they all worked. A century later, Euler showed that 225+1=4 294 967 297 isn’t prime — it’s evenly divisible by 641. Imagine even generating that number on an abacus. Then imagine looking for a zero remainder each time you abacus‑divide by potentially 65000 successive primes. Fortunately Euler struck gold on the 115th test.”
“Rechecked it a couple of times, I bet.”
“Indeed. Those cubes — number theoreticians love sums of powers. There’s one example in Code to Zero that boggles my mind. Up near the book’s frantic finale, Elspeth just happens to know that 168303 is the sum of the 1000 cubes from 11343 through 21333. Why would some hero hit on that combination, and why would they bother to check if the sum is a cube?”
“Dunno, I’m not a numbers theory guy.”
~ Rich Olcott
- Thanks to Lloyd Boyer for pointing me to Code to Zero and the wonders therein.
Hard Science Ain't Hard 
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Very enjoyable post.
I never succeeded in getting too far into “Pillars of the Earth” btw. Might consider looking at it again, though.
Are you familiar with this book: The Cathedral & the Bazaar: Musings on Linux and Open Source by an Accidental Revolutionary https://a.co/d/0az7iMMI. From an influential essay by Eric Raymond in the early days of open source.
Some interesting ideas, of course, but I don’t blindly agree with his conclusions. There is something to building something that lasts, imho.
Seems to me there is a Jose Saramonga novel about a multi-generational cathedral building project that I read at one point.
If your hometown aspired to a certain elevated status, apparently you needed a cathedral to bolster your claim. Karl Marx or Thorstein Veblen might explain the phenomenon in different terms.
But I think it must have had something to do with having a long-term perspective, an attitude which someone with generational wealth might be attracted to, especially in a society with almost zero social/class mobility.
One would expect someone like Stewart Brand, who inherited a sizable fortune from somewhere, might have an interesting perspective on “long time” — I see he has a new book extolling the virtues of “maintenance” — obviously, never a maintenance programmer.
In Venice, where I spent several days during a CMG-Italia meeting in the spring of 1999, I believe. I took advantage of a private, back stage tour of the st mark’s cathedral. It is actually from an architectural perspective a relatively unimposing structure, maybe only two stories high and no vaulted ceiling, if memory serves. It is centuries older than the huge cathedral building project that were built later in late Middle Ages and early Renaissance — quite possibly the engineering and construction wasn’t up to doing much more than that at the time. Lavishly decorated by mosaics created from colored glass beads. Maintenance on the mosaics is pretty much constant, we were told. There is a crypt where the bones of St. Mark reside — I assume that is the Gospel author. Venetians around 800 AD went to Alexandria, stole the remains, and brought them back to the city, where they have remained ever since. They are pretty proud of doing this — somehow Venice became the rightful owner of these bones. (The incident may have something to do with proselytizing armies of Islamic Arabs overrunning Egypt, but I don’t know.)
Stephen Jay Gould got off on the decorated spandrels of St. Marks. Are you familiar with his essay? He criticizes the “Just So Stories” that evolutionary biologists fabricate to explain some attribute of a species that natural selection has polished to an enviable degree.
A few years later I visited Florence and did some research in advance of the trip on Brunelleschi, who was the architect/engineer who designed and built the Duomo. A massive undertaking, it was accomplished within his lifetime. The entire cathedral was a multi generational project, however, each succeeding generation trying to one-up the previous one. Until they ran out of money, of course…
When I visited, you could still take stairways up to the roof and go outside and view the city. Also, an ongoing maintenance nightmare, and a great deal of concern that the whole thing will fall apart and collapse. There are wooden structures, too, supporting the roof, scaffolding everywhere where they were trying to shore it up. They worry about the state of the wood, of course…
When he was working on the design, Brunelleschi travelled to Rome to look at the Pantheon and see how the Romans built that. The Pantheon was the largest free-standing dome surviving in Europe — it is also open at the top ; the interior is all granite so there is no concern about the interior getting damaged by the rain. As something that has survived intact for 2000 years, it is a pretty impressive space. (Go Freemasons.) In constant use, it was re-purposed as a church in the 600s, which also entails constant maintenance.
Brunelleschi‘s dome is much, much bigger. I remember that Brunelleschi had to invent any number of new pieces of equipment to haul huge stones around, etc.
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