I read this play several times when I was a teenager, and saw it at a local repertory theatre, and I was 100% team Catherine. I reread it as an adult and the doubt didn't really occur to me, even though at this stage in my career I have a stronger bias in favor of older established mathematicians vs young upstarts, compared to our culture at large I have not however seen the movie, which I understand does some things differently from the play.
I am willing to go on in detail about the nitpicks I have about this play as a professional mathematician if anyone wants to hear -- but once thing I'll content myself is to point out that Hal's inability, as an early career post-PhD mathematician, to name a woman mathematician off the top of his head, is supposed to come off as "he's a sexist dude from a sexist culture", on reread came off as "dude, do you live under a rock?" And part of that is the increased visibility of women mathematicians -- but even in 1999 I feel like he should be able to name a woman he went to grad school with or met at a conference!
omg wait i would LOVE to hear your nitpicks As A Professional Mathematician, if you're willing to share, haha, that was the thing i was idly wondering about as i was reading...! like i think the framing the *play* was encouraging was "is she not being believed because of history-of-psychiatric-illness/gender stuff/etc," but i was sitting there wondering, like... how common is it for someone, in contemporary times, to have a MAJOR result, working totally without collaboration with anyone else, etc...?
obviously it's HAPPENED before but like. is the assertion that this is The Next Ramanujan and etc and. yeah i'm rambling LOL but i'd love to hear your thoughts!
Solo papers in top journals are still a thing, though very often the author will thank someone else in the acknowledgments for giving them the idea that they followed through on. The capacity to be alone is still valuable: it is still important to have some contact with other mathematicians to be successful, but in cases where there is low-hanging fruit to be picked, it is often picked by people who are not intimidated by the reputation of the problem! The classic example is George Dantzig's "homework problems" that inspired Good Will Hunting, but see the story of Lisa Piccirillo's proof that the Conway knot is not slice for a recent example.
Really what makes the underlying plot credible to me, even if I have many details to nitpick, is that Catherine, unlike most people who believe they are the next Ramanujan, is a second-generation mathematician who was close to her father, a UChicago professor, who would have shaped her mathematical taste in ways that would help her find problems that are both of interest to the research mathematical community and accessible to a relative outsider. (Indeed, very recently UChicago professor Akhil Mathew has been succesful at pointing LLM reasoning models to such problems, though the strengths of LLMs are very different from someone like Catherine's.)
And Catherine would be part of the long tradition of second-generation women mathematicians, going back to Hypatia, Alicia Boole Stott, and Emmy Noether. Her father would also have taught her to be critical of her own work in ways that most people who claim proofs of famous results do -- and I think that tendency to self-criticism is reflected by the depression she's in at the start of the play -- while her father's example would also have inspired the self-confidence in her that allowed her to start in the first place. And she could plausibly have had access to the UChicago library as well as her father's personal mathematical library, though people would assume that she was checking out books on behalf of her father. Also as a mathematician's daughter she'd be more likely to have opportunities to learn college-level math in high school through acceleration/summer programs/etc. Indeed, a friend of mine attended a summer program for women in math where it turned out that almost everyone had a mathematician parent.
Unfortunately David Auburn does not have the mathematical maturity to write the dialogue plausibly for this, so the characters talk mostly number theory trivia. Though something with more mathematical depth would probably go over the head of everyone in the audience except the one person who is so nerdsniped they are distracted for the rest of the play :-D I do think it's good that he doesn't specify the problem that was solved -- he easily could have said that Catherine proved the infinitude of Sophie Germain primes, he already did the exposition for that, but he doesn't. Though it's actually plausible that Catherine's result was in that direction -- Yitang Zhang's result on bounded gaps between primes is remarkable as an example (it built on work of Goldston-Pintz-YÄąldÄąrÄąm from the early 2000s, but one could massage the timeline) -- and one of the most impressive papers I've seen written by a high schooler is the work on the distribution of Carmichael numbers by Daniel Larsen, also from a mathematical family.
I have more thoughts about what we're told of the actual proof (I don't actually think elliptic curves and modular forms are as "hip" as Hal finds them) but I will save them for another post.
Time for the promised nitpicks/speculation regarding the proof in Proof! Most of the mathematical detail we've given on in comes from this line.
HAL. That was last week. I spent this week reading the proof. I think I understand it, more or less. It uses a lot of newer mathematical techniques, things that were developed in the last decade. Elliptic curves. Modular forms. I think I learned more mathematics this week than I did in four years of grad school.
OK, first of all, that last sentence is clearly hyperbole. No matter how brilliant the proof you're reading or what substances you're on, math takes time to digest, and there's only so much you can learn in a week, while on the other hand the UChicago math grad program is pretty demanding. (You do get faster at learning math as you go on, but still.)
The name-dropping of elliptic curves and modular forms is a reference to Andrew Wiles' proof of Fermat's last theorem (announced in 1993 and published in 1995) which was fresh in the public consciousness at the time Proof came out due to the 1997 PBS Nova documentary (linking the website partly just because it is a charming time capsule of the 90's internet).
The basic idea that the proof can't be Robert's because it's using techniques developed after he lost his mind is reasonable -- but elliptic curves and modular forms just aren't that new! In their modern form they date to the early 20th century, though they are grounded in 19th century mathematics (and, for elliptic curves, the work of Diophantus), and there was active research on these topics (and connections between them) throughout the second half of the 20th century -- they may not have been as trendy as it was post-Wiles but they were being studied by good people at top places.
Wiles's proof of Fermat's last theorem proved a conjecture relating elliptic curves to modular forms that dated from the 1950s, which thanks to research done in the early 1980s was known to imply Fermat's last theorem. If you wanted , in the late 90's to talk about the aspects of Wiles's proof that were truly cutting-edge, you'd say something about "modularity lifting of Galois representations" or "patching".
Of course this is a bit unfair of me to ask a playwright to be on top of mathematical trends and buzzwords. But I also think that Catherine (or Robert, for that matter) probably couldn't have written something like Wiles's proof -- it builds on a lot of existing theory, and is in a field where it's particularly hard for newcomers to make progress without extensive mentorship. Wiles was able to do it both because he was brilliant and because he'd spent his whole career working on this sort of thing; I'm not sure that many other people could. A math PhD in a related field who wants to read Wiles's proof might actually need to learn more math than they did in graduate school. There's an ongoing project to formalize the proof of Fermat's Last Theorem (taking some shortcuts) which has been going since 2024 and is still nowhere near done.
When I read the play recently, I came up with the theory that Catherine's proof was actually Maryna Viazovska's proof of optimality of sphere packing in eight dimensions. It's a natural question that Robert might have told Catherine about. The proof uses modular forms (though not elliptic curves) but not in as deep or technical a way as Wiles's proof -- it's a paper that a mathematician who had no previous experience of modular forms could actually check in a week. It also relies on previous work of Cohn and Elkies from 2003 (but first published on the arXiv in 2001) so Hal could conclude that Robert didn't write it because he hadn't read that paper (possibly fudging the timeline here if you still want to have the play set in 1999, but not by much). And her use of modular forms to solve the problem was genuinely surprising -- nobody expected things would work out that way, including her Ph.D. advisor (who is an expect on this type of modular forms). Not to mention that it led to Viazovska getting the Fields Medal as well as job offers from lots of top places, so it would certainly be a vaulable McGuffin.
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I read this play several times when I was a teenager, and saw it at a local repertory theatre, and I was 100% team Catherine. I reread it as an adult and the doubt didn't really occur to me, even though at this stage in my career I have a stronger bias in favor of older established mathematicians vs young upstarts, compared to our culture at large I have not however seen the movie, which I understand does some things differently from the play.
I am willing to go on in detail about the nitpicks I have about this play as a professional mathematician if anyone wants to hear -- but once thing I'll content myself is to point out that Hal's inability, as an early career post-PhD mathematician, to name a woman mathematician off the top of his head, is supposed to come off as "he's a sexist dude from a sexist culture", on reread came off as "dude, do you live under a rock?" And part of that is the increased visibility of women mathematicians -- but even in 1999 I feel like he should be able to name a woman he went to grad school with or met at a conference!
omg wait i would LOVE to hear your nitpicks As A Professional Mathematician, if you're willing to share, haha, that was the thing i was idly wondering about as i was reading...! like i think the framing the *play* was encouraging was "is she not being believed because of history-of-psychiatric-illness/gender stuff/etc," but i was sitting there wondering, like... how common is it for someone, in contemporary times, to have a MAJOR result, working totally without collaboration with anyone else, etc...?
obviously it's HAPPENED before but like. is the assertion that this is The Next Ramanujan and etc and. yeah i'm rambling LOL but i'd love to hear your thoughts!
Solo papers in top journals are still a thing, though very often the author will thank someone else in the acknowledgments for giving them the idea that they followed through on. The capacity to be alone is still valuable: it is still important to have some contact with other mathematicians to be successful, but in cases where there is low-hanging fruit to be picked, it is often picked by people who are not intimidated by the reputation of the problem! The classic example is George Dantzig's "homework problems" that inspired Good Will Hunting, but see the story of Lisa Piccirillo's proof that the Conway knot is not slice for a recent example.
Really what makes the underlying plot credible to me, even if I have many details to nitpick, is that Catherine, unlike most people who believe they are the next Ramanujan, is a second-generation mathematician who was close to her father, a UChicago professor, who would have shaped her mathematical taste in ways that would help her find problems that are both of interest to the research mathematical community and accessible to a relative outsider. (Indeed, very recently UChicago professor Akhil Mathew has been succesful at pointing LLM reasoning models to such problems, though the strengths of LLMs are very different from someone like Catherine's.)
And Catherine would be part of the long tradition of second-generation women mathematicians, going back to Hypatia, Alicia Boole Stott, and Emmy Noether. Her father would also have taught her to be critical of her own work in ways that most people who claim proofs of famous results do -- and I think that tendency to self-criticism is reflected by the depression she's in at the start of the play -- while her father's example would also have inspired the self-confidence in her that allowed her to start in the first place. And she could plausibly have had access to the UChicago library as well as her father's personal mathematical library, though people would assume that she was checking out books on behalf of her father. Also as a mathematician's daughter she'd be more likely to have opportunities to learn college-level math in high school through acceleration/summer programs/etc. Indeed, a friend of mine attended a summer program for women in math where it turned out that almost everyone had a mathematician parent.
Unfortunately David Auburn does not have the mathematical maturity to write the dialogue plausibly for this, so the characters talk mostly number theory trivia. Though something with more mathematical depth would probably go over the head of everyone in the audience except the one person who is so nerdsniped they are distracted for the rest of the play :-D I do think it's good that he doesn't specify the problem that was solved -- he easily could have said that Catherine proved the infinitude of Sophie Germain primes, he already did the exposition for that, but he doesn't. Though it's actually plausible that Catherine's result was in that direction -- Yitang Zhang's result on bounded gaps between primes is remarkable as an example (it built on work of Goldston-Pintz-YÄąldÄąrÄąm from the early 2000s, but one could massage the timeline) -- and one of the most impressive papers I've seen written by a high schooler is the work on the distribution of Carmichael numbers by Daniel Larsen, also from a mathematical family.
I have more thoughts about what we're told of the actual proof (I don't actually think elliptic curves and modular forms are as "hip" as Hal finds them) but I will save them for another post.
I read this play several times when I was a teenager, and saw it at a local repertory theatre, and I was 100% team Catherine. I reread it as an adult and the doubt didn't really occur to me, even though at this stage in my career I have a stronger bias in favor of older established mathematicians vs young upstarts, compared to our culture at large I have not however seen the movie, which I understand does some things differently from the play.
I am willing to go on in detail about the nitpicks I have about this play as a professional mathematician if anyone wants to hear -- but once thing I'll content myself is to point out that Hal's inability, as an early career post-PhD mathematician, to name a woman mathematician off the top of his head, is supposed to come off as "he's a sexist dude from a sexist culture", on reread came off as "dude, do you live under a rock?" And part of that is the increased visibility of women mathematicians -- but even in 1999 I feel like he should be able to name a woman he went to grad school with or met at a conference!
JOKES are against the rules.
A tour of nineties Fantasyland, with stops along the way in California, Minnesota, Shannara, Valdemar, Derkhol
A tour of nineties Fantasyland, with stops along the way in California, Minnesota, Shannara, Valdemar, Derkholm, Dalemark, and the 'Maggots' entry in the Encyclopedia of Fantasy (1997).
Transcript available here, and our next (and last) bonus episode for the season will be our overview/Q&A, which we'll be recording in early July!
"And it's a British comic fantasy writing tradition that was
hugely influential on a style I would call âAnglophone millennial on the internetâ. [Becca laughing] All of Tumblr writes like this and a good chunk of Reddit writes like this. It's not funny unless you're good at it, which most people are not. But the cynical tone, the constant allusion, the mad, slightly forced wordplay."
Important news in the Fanny Mendelssohn Hensel fandom!
There's an oft-quoted line from a letter from Abraham Mendelssohn to his daughter Fanny saying that while her (now more famous) brother Felix may pursue music as a profession, for her it can only be an ornament, never the foundation of her being and doing.
However, recent research has pointed out that this line shas been misquoted for ~150 years, and the original does not have this never. Instead it reads:
Die Musik wird fĂźr ihn vielleicht Beruf, während sie fĂźr dich stets nur Zierde, immer Bildungsmittel, GrundbaĂ deines Seins und Tuns werden kann und soll.Â
translated by HenselPushers into English as:
Music will perhaps become his profession, whilst for you it can and must only be an ornament, always a means for self-cultivation, the root of your being and doing.
It's still very gender essentialist, especially in context, but provides more complexity.
I learned this from this HenselPushers post, which provides a bunch of additional context.
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this is a probably-embarrassingly-banal recurring thought/observation i've had lately, but (artsy commentary below the cut)â
it seems like really great art (in a variety of mediums) only really arises out of a whole ecology supporting that artâe.g.,
-> you don't get great oration the way you did during Frederick Douglass's time because oratory is no longer a âliveâ art in the way it was back then (audiences prefer other options for entertainment/information; audiences donât have the patience for that style of delivery, etc);
-> Mozart's genius for improvisation, while impressive, was an outlier on a spectrum of talent that existed back then, and wasnât categorically different; he was pulling from a massive vocabulary of licks/phrases/etc that he knew by heart because that was How Music Education Worked Back Thenâi saw a video recently that talked about that, and which also claimed the mythopoetic status of âsingular genius composerâ only began to rise and become so socially prominent during the Romantic era specifically because the ecosystem that supported that style of music education (e.g. sacred music and the church and such) was on the wane, which is FASCINATING even if itâs probably more âcomplicatedly trueâ rather than âstraighforwardly trueâ;
-> and also, i enjoyed this Kanakia column that argued that the Western (as in "western/cowboy novels") managed to produce some truly great work, but only when that general *ecosystem* reached its apexâŚ
anyway.
most people, i think, don't think of the arts like this? like, i was into composing music when i was a kid, and i remember my parentsâwho are lovely, just not AT ALL musicalâregarded it with a bit of awe. after i worked really hard writing this one song & performed it at a recital, my mom asked me if there would be more if i only âhad one song in me.â she wasnât asking in a negative âyou should be doing moreâ way! but in a wistful-earnest way, like, âwow, itâs so lucky you had even this one song in you; sometimes thatâs all there is and we just have to be grateful for itâ kind of way. they asked me where my ideas for songs came from. and i, being a kid, was like âuhhh idk they just come to meâ and they were awed all over again.
as an adult i know that wasnât the whole storyâthe real answer is, well, i had piano lessons, so i already had some idea (both intuitive and formal) of common chord/arpeggio/etc patterns; i played a lot of nobuo uematsu and frĂŠdĂŠric chopin so their compositional styles "lived" in me; and so when i started playing with a little melody for fun, i had some âhunchesâ for where to take it, how to develop it, and âit just came to meâ but⌠only because i had this whole vocabulary that i, being a kid, didnât even realize was a learned thing; it just felt like part of the air i breathed.
anyway!
i got to thinking about this recently when reading adam kostko's post about the process of learning to how to better listen & look in order to better appreciate art⌠and he argues that e.g. those with some formal music education may in fact get less out of a music performance because theyâre trying to âdecodeâ the piece rather than really listen. which is interesting, and i think has some truth, but i suspect itâs *specifically* that music education today mostly involves learning some theory âin a vacuumâ (e.g. âlabel these chordsâ-style worksheets) and learning how to precisely replicate prewritten songs, rather than⌠developing that fluency & that access to the wider ecosystem
uhhh hm do i have a thesis here. i guess (1) itâs weird to me i rarely/never hear defenses of canon articulated in these terms: âthis is the working vocabulary of your literary/artistic/musical inheritance (which is well and truly yours by right of being a human being on planet earth), and you need some fluency in it in order to have access to it, and really you need much more fluency than modern primary/secondary education is going to be able to give you on its own, but we should at least give people a fighting chanceâ, and (2) i used to be pretty anti-rote-memorization but iâm now kinda pro-memorization for like. idk. good poetry. some music. sacred texts. anything that gives you some richer basis of expression to fall back on in a pinch
Teaching to develop fluency is hard! I haven't read the Kotsko post yet, but see this post on how I never developed musical fluency, and I've also seen this from the other side when teaching college-level math.
(I think my take on memorization, as someone who has always been both good and motivated when it came to memorizing things, is that memorization is worthwhile both for the mental skills it teaches and for being able to carry things around in your head as touchstones -- but also that it is helpful as a kid to get some *choice* in what sorts of things you choose to memorize, even if this means that you memorize stupid things to start while you figure out what's worth memorizing. I don't actually need the 30? digits of pi that I learned as a kid, but it was one of the things that paved the way for me to start memorizing poetry as a teenager.)
Also the start of your post resonated because right now, in pure mathematics, which has some aspects of art, there's a lot of chatter in about the ways in which our ecosystem is being threatened, both by AI and by funding cuts.
was a real doctor, in the sense of being a practicing physican; on the other hand he only had a master's degree so you could argue that he was not a real doctor.
was not a real worm, per his picture (but he also wrote his name Olaus Wormius, which is pretty cool)
was interested in things, which he collected and catalogued in the Museum WormianumÂ
had a drum in his museum collection, though it is unclear if he liked to play it (and given that it was a SĂĄmi ceremonial drum this is all sort of uncomfortable cultural appropriation).
I have yet to determine if Rabbi Vole also has a historical antecedent.
I missed that Ole Worm actually got a doctorate in physiology from Basel before getting a Master of Arts degree. (He defended a thesis on "a hundred selected medical controversies".) So he was actually a real doctor!
I also found several published volumes of his correspondence, and so I can cofirm that they did, indeed, call him Doktor Worm.
was a real doctor, in the sense of being a practicing physican; on the other hand he only had a master's degree so you could argue that he was not a real doctor.
was not a real worm, per his picture (but he also wrote his name Olaus Wormius, which is pretty cool)
was interested in things, which he collected and catalogued in the Museum WormianumÂ
had a drum in his museum collection, though it is unclear if he liked to play it (and given that it was a SĂĄmi ceremonial drum this is all sort of uncomfortable cultural appropriation).
I have yet to determine if Rabbi Vole also has a historical antecedent.
I not-that-long ago watched the Ian Carmichael BBC Lord Peter Wimsey series, which were great fun, but really my main takeaway is OMG those dressing gowns are glorious, I see where Diana Wynne Jones got Chrestomanci's wardrobe from. I am very sorry that I did not screenshot them all when I got the DVDs out from the library, so you wil have to settle for the only one I could easily Google (from The Nine Tailors):
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OMG, this is fantastic, and Alexandra Ionescu-Tulcea Bellow reminds me of other older mathematicians I know who have taken time to read the classics deeply. I was curious to know more about her mathematical career, and found this interview.
Ruth Slenczynska was a child prodigy who played with five US Presidents and recorded into her 90s.
She met Rachmaninoff in 1934 (at age 9), after substituting for him in a concert.
"Mr Rachmaninov had to cancel due to a problem with his elbow," she later recalled. "The manager did not want to lose money from the ticket sales so he contacted my father to see if I could play the concert."
She was summoned to meet the maestro soon afterwards.
"I was a frightened little girl at the door of his apartment at the Villa Majestic in Paris,"Â Slenczynska told NPR in 2022, "and he pointed this long index finger down at me and he said, 'You mean that plays the piano?'"
from an NPR article linked therein, where they interviewed her upon her releasing a new album at age 97:
With the advantage of the long view of life, Slenczynska enjoys dispensing sage advice. "You don't become a pianist until you're past the age of 60," she states with blunt certainty. "And then you should have something to say that's worthwhile. If you don't, forget it." Never mind that Slenczynska made her debut as a pianist at age 4.
also: this bit from the reddit post where i found the story from (tragically the referenced book seems Out Of Print And Hard To Find so i can't dig up a reference from the source itself!):
There is a wonderful anecdote in her book 'Forbidden Childhood' where she recounts receiving lessons from both Rachmaninoff and Cortot at around the same time (the two did not realise this). It was widely known at the time that these two titans were quite dismissive of each other, Cortot considered Rachmaninoff's music to be passĂŠ whilst Rachmaninoff is on record making some snide remarks about Cortot's technical unreliability.
In the book, Slenczynska discusses how both Rachmaninoff and Cortot were impressed by each other's (unbeknownst to them) musical suggestions and ideas.
An Overly In-depth Analysis of Spinning Silver Many Years Late
`When I first started writing this in 2022, I had recently finished reading Naomi Novikâs Spinning Silver for the first time. I wanted to remember a particular quote in the book, and stumbled upon some reviews from 2019, when the paperback was released.
The quote I was looking for: You will never be a Staryk Queen until you make a hundred winters in one day, seal the crack in the mountain, and make the white tree bloom.
The reviews:Â
âŚread Temeraire and Uprooted at least ten times, but couldnât reread this. The relationships between the two main men and two main women are abusive. Certainly, thereâs trauma involved, but itâs not a womanâs job to heal menâs trauma through sacrificing themselvesâŚ
âŚI adored Uprooted (had some issues, but still loved it completely), however Spinning Silver just felt off â not as magical, terrible âromancesâ, too many POVs, etc. All in all, it just wasnât as gripping. I liked Miryemâs character, but the other two protagonists were very bland âstrong female charactersâŚâ
I hate this. I hate this so much. I hate this enough that Iâm going to write an excessively long post defending Spinning Silver for three years. For everyone that doesnât want to read a masters-student dissertation of an essay or who hasnât read the book yet and wants to go into this spoiler free, hereâs the TL:DR version.
There are no romances in this book. The two reviewers above are trying to apply the enemies to lovers tropes they loved so much in Uprooted to a grimm fairy tale about politics, feminism, and Jewish persecution. There are no romances in this book. This is hard to grasp, because two of the main characters are married, and that marriage is a major part of the plot, but no one in those marriages including the men wanted the marriage in the first place. To call it âabusiveâ is to read modern expectations onto a historical political marriage that, while not inaccurate, fundamentally misunderstands the point and the context in which the story takes place.Â
Also, I would recommend the audio book, if you have trouble with multiple points of view. They are all in first person, and although it starts out with just two, we add more and more POV until thereâs 5 or 6 total. The reader Lisa Flanagan does an excellent job distinguishing POVs which will make this aspect of it easier.
Read the book, particularly the audiobook. But if you are reading this book looking for romance, youâre going to be disappointed. Itâs still one of the best if not the best re-imagined fairy tale Iâve ever read. Hereâs an excessively long post about why.
The Introduction
The very first thing weâre introduced to is Miryem as our narrator explaining that stories arenât about âhow they tell itâ but getting out of paying your debts. So how do âtheyâ tell it? The introductory story is about a girl having sex out of wedlock who is left in the lurch because the âlord, prince, rich manâs sonâ has a duty.Â
Itâs about saving yourself for marriage. Even in how âtheyâ tell it, who the man is doesnât matter and no one is in love. Your duty to your family comes first.Â
This story is not about romance. The story this story is subverting is not about romance. Even in how âtheyâ tell it, romance isnât a good thing.Â
In actual fairy tales, not Disney princess stories, romance often has nothing to do with it. These are stories for little children to get them to obey their parents. Rumpelstilskin is about ingenuity and perseverance. Even in a story like Cinderella, the romance is entirely incidental - the story is about hard work, strength through adversity, and moral superiority. The marriage itself isnât romantic in the sense that the two main characters fall in love. These stories are older than the modern concept of love. For authors with a strong sense of familial duty and nationalism, writing about something as subversive as romantic love would go against their goals.
This is the setting that Spinning Silver takes place in. Itâs a modern fairy tale set in a regency era. The fairy tale Miryem tells in our introduction paints romance as a bad thing. You marry out of duty.Â
But Miryem from the start tells us that filial duty isnât what the stories are really about. Theyâre really about paying your debts. Within the first 2 minutes of this book, itâs already told us three times that this story isnât about romance. Once in the setting of a fairy tale about filial duty, once in the denial of how they tell it, and once in the revelation of the real interpretation.
The Power of Threes
The power of repetition and specifically of threes comes up over and over again in the book. In many cultures across the world, three has special significance.
From the fairy tale side of it, Rumpelstilskin itself contains layers of threes within threes. Rumpelstilskin makes a bargain for the millerâs daughter on the third night. The queen has three days to guess Rumpelstilskinâs name, and guesses three names each day.
Itâs likely that these repetitions of threes in fairy tales come from the Christian backdrop they were written in, which at times focuses on the third path in the middle of two binaries, or the significance of building power, though itâs difficult to make any sweeping, central claims about why three is significant because fairy tales are so widespread across countries, time, and religion. But itâs important that Novik is writing this from a Lithuanian Jewish perspective, so thereâs a subtle shift in the interpretation and meaning of the rule of threes. Iâm not Jewish, so what specifically this is as grounded in Novikâs ancestry is something I canât be clear on.
During my research, one explanation that seems to resonate with the symbolism of this book is a Chabad interpretation. From chabad.org:
The number three symbolizes a harmony that includes and synthesizes two opposites. The unity symbolized by the number three isnât accomplished by getting rid of number two, the entity that caused the discord, and reverting to the unity symbolized by number one. Rather, three merges the two to create a new entity, one that harmoniously includes both opposites.Â
Lithuanian Judaism is majority non-Hasidic, so this is just one tangentially-related explanation of the importance of threes. Iâm sure thereâs other interpretations Iâm missing because I canât possibly begin to know where to look. But I like this explanation for grounding the story because I think it fits well with the symmetry of our protagonists and their husbands (or lack thereof), and the way the story is building to their creating something new.
So when the very first thing we are shown within the first two minutes of the book is a thrice denial of romance, we need to take Naomi Novik seriously when she says that the book is about getting out of paying your debts. Or, at the very least, this is what Miryem thinks the book is about. The way in which the characters grow and change does reveal some of the original cynicism in this thesis, but ultimately this is a story about what we owe each other, and how that debt comes for us if we donât pay it. And on top of that, Miryem describes the love interest of the millerâs daughter as âlord, prince, rich manâs sonâ (3 possibilities). Who this love interest is doesnât matter in the slightest.
All this to say that within the first two minutes of the book, if you are still reading this expecting a romance, you arenât listening to the author.
Jewish Heritage
Also within the first few minutes of the book, we learn that Miryem is a Jewish moneylender in a fantasy version of Russian-occupied Lithuania some time in the Middle Ages. Iâm not going to get too deep into this. I am, as I said, not Jewish, and these characterisations edge very close, on purpose, to deeply anti-Semitic tropes. But understanding what Novik is saying about her heritage and her familyâs persecution is critically important to understanding the book.Â
Naomi Novik is a second-generation American. Sheâs Lithuanian Jewish on her fatherâs side, and Polish Catholic on her motherâs side. In many ways, Spinning Silver has been treated as a spiritual successor to Uprooted. Uprooted is set in a fantasy version of Poland, Spinning Silver is set in a fantasy version of Lithuania. Both stories are about Novikâs heritage, and the stories from her ancestors. Spinning Silver is a lot more obvious about this, but thereâs a non-zero amount of Catholicism in the way the Dragon structures his magic, and in the older folk magic that lives in the trees.
Spinning Silver is much more explicit, and Novik has said as much, that Miryemâs family is supposed to reflect her fatherâs family and his experience as a Lithuanian Jew.
Our book takes place in a fantasy version of Lithuania in 1816. Thatâs a very specific date Iâve picked out for a book that otherwise appears to be âthe ambiguous past.â How did I come to that conclusion?
I did a little bit of research to try and determine when and this is what I came up with: Lithuania didnât exist until the 13th century. Lithuania didnât have a tsar on the throne until Russian imperialism in the late 1700s. Restrictions on Jewsâ ability to work in craft or trade began around 1100 in Europe, and began to wane around 1850. In Lithuania, this fluctuated depending on the specific time period, so we can a little further narrow the timing down to after the mid 1600s but before the 1850s, probably during early Russian imperialism. Leadership is religious, either Eastern Orthodox or Catholic, who at the time believed that charging interest was sinful, so employed members of other religions, specifically Jews, to do their money lending for them. Because of the association with sinful, dirty work, and previous oppression as a religious minority, this led to a significant rise in anti-Semitism, coming to a head with a series of Jewish pogroms in Russia from (officially) 1821-1906, leading millions to flee and thousands of deaths. So we can narrow our estimation down to about 80 years, between 1820-1900.
Then my historian partner started reading it with me and exclaimed, "is that a reference to the Year Without A Summer" so actually 1816, but you can also see how easy it is to narrow that date down even as an amateur just by examining the exact flavor of anti-Semitism in the text. Which is why, even after I learned about the year Without A Summer, I left my aimless searching in.
Most audience members probably donât know this much detail about history, but Spinning Silver is very clearly written with an audience understanding of this history in mind. Weâre supposed to see the rise in anti-Semitism throughout the book which adds a layer of tension because at any moment, the politics in the wider world and rising anti-Semitism might catch up to our protaginists, and Miryem and her entire family could be killed.Â
Thatâs it, book over. Anti-Semitism sweeps through, destroys everything it touches, and none of the clever problem-solving of any of our heroines matters. Itâs over.
This dark possibility looms over the story like a storm cloud the entire time. The most explicit reference is when Miryem uses the tunnel her grandfather dug.
âI pulled it up easily, and there was a ladder there waiting for me to climb down. Waiting for many people to climb down, here close to the synagogue, in case one day men came through the wall of the quarter with torches and axes, the way they had in the west where my grandfatherâs grandmother had been a girl.â
The fear of persecution isnât just something of the past. It is something that people in this community are actively thinking about and planning contingencies for.
Weâre five pages in and Iâve barely gotten through the first five minutes of the book. I could do this for literally the rest of the book if I wanted to - five minutes later, Miryem as narrator starts talking about a festival at the turn of the seasons between Autumn and Winter, which she calls âtheir festivalâ and resents the townspeople for it because theyâre spending money they borrowed from Panov Mandelstam on it. Meanwhile, Panov Mandelstam is lighting a candle for the third day of their own festival, when a cold wind sweeps in and blows the candles out. Her father tells them itâs a sign for bed time instead of relighting them, because theyâre almost out of oil. Panov Mandelstam is reduced to whittling candles out of wood because, âthere isnât going to be any miracle of light in our house.â I didnât catch this the first time around, because Iâm an ignorant goyim I wasnât thinking about this book as an explicitly Jewish fairytale. But Novik is obviously making a reference to Channukkah, and the fact that Panov Mandeltam doesnât relight the candles for Channukkah is powerfully unsettling. And then on the eigth day, Miryem takes up her fatherâs work and collects the money heâs been neglecting, and there is light in their house for Channukkah after all, but the miracle is hard work, not magic. The entire book is like that, layers upon layers of meaning with every sentence. Subtle clues before the curtain is pulled back. I want to teach a seminar using only this book on the definition of âshow, donât tell.â
Good and Evil
But at some point Iâm going to have to move on, and so letâs talk about trauma, poverty, and morals.
Novik introduces the townsfolk as Miryem sees them, but not all the townsfolk. Each person introduced by name winds up coming back later, enacting some kind of harm. But it seems to me that this harm is foreshadowed in each instance.
First, weâre introduced to Oleg. Olegâs wife is described as being Olegâs âsquirrelly, nervous wife.â This isnât the only time it occurs to me to wonder if Oleg beats his wife, but I think the description is intentional. Oleg eventually tries to murder Miryem, for explicitly anti-Semetic reasons, but I think this violence is foreshadowed in the way we see him interact, in brief flashes, with his wife and son, and how theyâre always described as being a little withdrawn, a little afraid of Oleg, and not very sad that heâs gone, except in the part where this is going to be a financial burden on the family.
Next introduced is Kajus. Kajus who had borrowed two gold pieces to establish himself as a krupnik brewer (the krupnik he brews would lead to Daâs alcoholism). His solution to Miryem banging on their doors is to offer her a drink. Clearly getting people hooked and indebted to him is a tactic heâs used to success more than once.Â
The last person introduced in this sequence is Lyudmila. Again, we are given a set of three. Lyudmila is different. Lyudmila never borrowed money. She doesnât have a direct reason for despising the Mandelstams. Or at least, she shouldnât. And yet, her distain jumps off the page. Lyudmila is the quiet, insidious voice spreading lies and rumors about the Jewish family in town. Her violence is not explicit. But it is the same.
The last person weâre introduced to, given an entire separate section to his own, is Gorek.
Good and Evil part 2 - is Wandaâs Da an evil character?
Gorek, whoâs better known for the rest of the book as Wandaâs Da, is also introduced to us first as a borrower trying to get out of paying his debts. Gorek is a violent drunk. This is established repeatedly. Gorek is not a good man.
But is he evil? Certainly he seems to be the antagonist of Wandaâs story, and thereâs no love lost when he dies. But I think itâs interesting that even Gorek, in many respects, is sympathetic. Heâs not very different from any of the other men in this town. Oleg is violent. Kajus profits off the many people in the town that drink their troubles away. Gorek is not uniquely awful even if he is particularly awful. And even for Gorek, the text takes pains to remind us that he buried his wife and five children. His life is hard. Their plot of land is sat next to a tree where nothing will grow. How much rye did they waste before they learned that lesson? And when Mama was alive, they had enough to eat in the winter, but only because she was very, very careful to divide everything up. On his own, Gorek couldnât make that math add up, even before he started drinking his troubles away. Gorek is facing a life where unless something drastic changes, he and his children will slowly starve to death, and thereâs nothing he can do about it.
So he sells his daughter for one jug of krupnik a week. Gorek has made his bed; he doesnât want to keep living. Heâs drinking himself into the grave he dug for his wife. But in the meantime he does still need to take care of his children.
I donât say this to forgive his actions; I do think Gorekâs actions are unforgivable. Some people cannot be redeemed, they can only be defeated, and Gorek is one of those people. But at the end of the book, Wanda and Sergei and Stepon still bury him when they go back to Pavys, next to the rest of their deceased family.
Gorek is a product of his environment, and that environment is cruel and cold. The people it produces are by and large cruel and cold. No one in the town bothers to bury Gorek. No one stops him from hitting his wife and children. Thereâs nothing at all strange, according to the rest of the town, about his selling his daughter for drink.
I wouldnât go so far as to say that Gorek is not evil, but I also think that this book is taking pains to present with sympathy the kind of environment which creates people like Gorek. Like our Staryk king, who was entirely prepared to force himself onto Miryem even though neither one of them wanted it. Like Mirnatius, who did not himself commit any acts of violence, but who was perfectly willing to benefit from the violence being committed with his face. The world is cold and cruel, and it is very, very easy to become cold and cruel from it.
The Power of Threes revisited: Miryemâs magic
Even Miryem says that sheâs had to be cold and cruel to be their familyâs moneylender. We donât see very much of this. But she does after all agree to have someone work in her house for essentially no pay. We donât necessarily realize it, because it comes at our own turning point, but Miryem has to learn empathy just as much as her Staryk king does. When she agrees to allow Flek and Tsop and Shofer to help her with her trials.
I read Novikâs new anthology Buried Deep and Other Stories and in that collection she says itâs a line from the Staryk king about Miryemâs magic that made her want to expand what was originally a short story into a full book. âA power claimed and challenged and thrice carried out is true; the proving makes it so.â
Fairy tales are about hard work. This line from the Staryk king isnât just a way of constructing magic, itâs just literally true. If I get a job as an accountant, despite not knowing anything about accounting, and I donât fail, then by the end I will be an accountant. I love this, that the magic in Spinning Silver is just hard work.
Miryemâs magic is another rule of threes. The Staryk king challenges her to turn silver into gold three times, to make the magic true, and she does it â with mundane means, through ordinary hard work, but itâs done. She barters freedom for a day by turning three storehouses to gold, and she does that too â with wit and hard work, but itâs done. The Staryk king challenges her that sheâll never be a Staryk queen, unless she can do three feats of high magic, and she does each one. Or rather, each one gets done, and Miryem has a hand in it. But the first feat of high magic requires the assistance of one other person. The second â the assistance of three. Much like each trial before it grew in magnitude â first 6 coins, then 60, then 600 â so too do all three stories grow in magnitude. It would stand to reason then that the third test of magic would require at least three upon three people. But Miryem is not the only protagonist in this story.
Circling back to Romance: Arranged Marriage is Bad Thatâs Obviously The Point
In addition to the rule of threes woven repeatedly in Miryemâs story, the entire story itself is a Triptych. One story is the story of the girl who could turn silver into gold. One story is the story of the children who find themselves lost in the woods and stumble onto a witchâs house full of rich food. One story is the story of the dukeâs misfit daughter who marries a prince. They are all of them different fairy tales. And at the end of the story, they all come crashing into each other. The white tree belongs to Wandaâs story, bought with six lives.
Three sets of three people in each story
There are many, many examples of threes woven throughout this story, but it was only three years into writing this essay that I realized that the marriages themselves are a set of three as well. After all, only Irina and Miryem get married, right?
But Wanda is offered a marriage proposal. In a story with less magic, Wanda would have married Lukas, and been yet another generation of poor, miserable women that died in childbirth. But Wanda says no, a thing entirely unheard of in this era. Women didnât say no to marriages arranged by their fathers.
And at the end of the story, Wanda is still unwed, with absolutely no indication that this will ever change. Wandaâs agency, this rejection of marriage, is treated with the same weight as the marriages themselves. Saying no is just as valuable as Irinaâs political marriage, or courting for a year and a day and marrying for love, as Miryem eventually does.
And Miryem does marry for love. She originally has no choice in the matter, but that contract is rendered void when the Staryk king is forced to let her go. We donât see the yearâs worth of courting because itâs not relevant to the story because this is not a romance but I really donât want to lose this point because I think Wandaâs story sometimes gets forgotten precisely because it doesnât have a marriage. But Novik is explicit about this through Wandaâs story. Irina had no choice, not really. So it never occurred to her to say yes or no. She kills the man who sought to marry her â Chernobog wanted to marry Irina, not Mirnatius. Irina murders her would-be husband, Miryem divorces hers, and Wanda says no. Yes, the arranged marriages in this book are abusive â Novik knows that and tears them down one by one and rebuilds them into something with far more agency, that our women protagonists chose.
The Story
So weâve come all this way and learned that Spinning Silver is not a romance, not really. The married couples in the story do come to love each other, after a fashion. But that love blooming was not the point. The point wasâŚ
Well it was about getting out of paying your debts, wasnât it? Novik told us very explicitly that it was about getting out of paying your debts right on the first page. Itâs not how they told it. But she knew.
Miryem spends the entire book making her fortune from nothing. Wanda takes over the work from her. Stepon takes over after Wanda. The debt that the town owed to Josef was a major thread over and over again throughout the whole story. Oleg tries to kill Miryem over it. The Staryk king seeks Miryemâs hand because of it. Raquel had been sick because their dowry had been spent. Wanda comes to their house to pay off the debt. Nearly everything in the book can be traced back to the debt against Josef Mandelstam.
And then, in Chapter 25, Josef sends Wanda with many letters to the people of the town forgiving all the remaining debt that was owed. The people of Pavys get out of paying their debt.
But⌠how do they get out of it? Not through any trickery of their own, not really. There is a stated implication that fear was a big part of it. Sending Wanda with letters of forgiveness would mean that they would not be harried or harmed while they were wrapping up affairs in the town. But Josef also doesnât need the money. They have a home of their own, many hands to make light the work, blessings from the Sunlit Tsar to establish their place in the world, and blessings from the Staryk king that will ensure their safety even through a hard winter. They want for nothing, so they do not seek to reclaim what is theirs.
And in a way they got all those blessings through paying their debts, but in a way they did not. The Staryk way of paying their debts teaches us something very important about what a debt really is. The Staryks donât keep debts. They make fair trade. And if they canât make fair trade, there is no deal. Or at least, they say they make fair trade. They didnât trade for the gold they steal from the Sunlit world, though I suspect they would argue that the pain that is caused to the people of that world is trade for their putting a monster on the throne. And Miryem rightly points out that they had been raiding for gold and raping the people of Lithvas long before Chernobog sat on the throne. They make fair trade. But only with those they view as their equals.
But the Sunlit world is even worse. The Tsar doesnât make fair trade. He spends magic like water and steals the lives of people that didnât bargain with him to pay for it. In the Sunlit world, people take as much as they can with as little return as they can get away with. Not everyone, of course. But it is of particular note here that in this story, Jews are vilified particularly because they ask for fair trade in return. And the people they loan money to donât want to give it to them.
But fair trade can only go so far. The Staryk king is trying to make a road back to his kingdom, and he canât, because there is nothing of winter that they can find in the warm summer day. And he cannot take Steponâs white tree seed, because it was bought with six lives, and given to Stepon alone, and there is nothing that the Staryk king can barter with that would measure against a motherâs love. But Stepon wants to see the white tree grown, so they find a way to plant it. Irina digs hard soil in apology, and the Mandelstams sing a hymn to encourage growth, and although none of this was done for the Staryk king, he still uses the work to create his road.
Sometimes, fair trade isnât enough, and one must trust that it is to the benefit of all to aid each other.
The truest way of getting out of paying your debts⌠is to abolish the concept of debt.
Thatâs right, motherfuckers, eat your kings and burn the banks to the ground, love is the anti-capitalist manifesto we made along the way!
This section was going to be a little bit of a joke, but the more I think about it, the more it really isnât. Miryemâs magic makes wealth meaningless in its magnitude. Wandaâs magic is having food and shelter to spare. And Irinaâs magic is having just leadership that rules for the people, not for power. Novikâs fairytale ending is collectivism. She tells us three times, through three stories of hardship. And it isnât even about becoming a princess, because Wanda marries no one, and lives in a magical house that seems to always have everything they need. So long as they do what they can to take care of it.
The real magic is community. Doing for yourself what you can, and reaching your hand to another when you can spare, so that they might do the same. And so long as we all do that together, the darkness cannot come in to feast.
And the final sonata! When writing up #28 I googled for "beethoven inventing jazz", and the search resullts indicated that this is the sonata where he really anticipates jazz, so that's going to be exciting. Returning to Daniel Barenboim .
Movement 1. Maestoso â Allegro con brio ed appassionato. This is a dramatic start. Some sad two-note phrases with harmony. And now we're going deep and dark. Getting worked up, and now it's starting to sound a bit jazzy. I'm not sure if this is technically a fugue but we're repeating our theme all over the place. More mood, but really this thing is just having constant bipolar mood swings. I'm not sure the camera needs to show us the drops of sweat on Barenboim's forehead but I can understand why they're there . And now we're doing a different harmony, with a sort of march-y thing, this is cool. We had another slow moody bit, and I thought it was going to break into another fast section, but instead we're getting some interesting harmony before slowly stepping up the tempo. Ooooh, I like this rippling harmonic chordy bit that ends the movement.
Movement 2. Arietta: Adagio molto semplice e cantabile. And now we naturally transition into a slow movement. This is a particularly gorgeous slow movement but I assume it's going to build up somewhere as we still have almost 20 minutes to go (and also we haven't really invented jazz yet?). But right now we're just going slow and building up harmony; now we're walking along with a slightly faster tune with some cool rhythm in how it's accompanied. Yes, this is what I've been waiting for, the jazzy theme introducing itself, still slowly, but the overall mood is more cheerful. Now, we're getting into full jazz mode and I'm enjoying myself! Back to slow, low and dark but sounding jazzier now. I like how this bit is atmospheric. Like, Beethoven is still holding a Mood, but it's a much cooler mood. Now the melody emerges again. We get some dark chords that are then echoed in the left hand melody sounding not so dark -- this trembling in the high register is great. More sad chords leading into a return of the slow sad melody. But our left hand crosses over to make some nicer sounding high pitched notes. I think this is a triumphant recapitulation here? but now it's going dark ? back to triumphant. Trilling, and bringing back the melody as left hand accompaniment to the trill. Suddenly we slow down and do this simple elaboration of the theme, ending on some dark chords.
Overall: This was a great way to end, some very cool moods and more jazzy bits. And yay, we made it through the challenge! I may need to take a break from sonatas now for a change of pace -- close listening to one sonata a day is a Bit Much -- but I will be relistening to some of these in time :-D
Wow, we're almost done! Watching this Vladimir Ashkenazy recording.
Movement 1. Moderato cantabile molto espressivo. Yep, that's a lovely cantabile, and we start to ornament it quickly. The harmonies on this are great -- really, everything here is great. We're getting some chances for really impressive piano technique here, but it all fits together naturally rather than being show-off moments. And we get some off-color chords right there at the end.
Movement 2. Allegro molto. More aggression here, and some funkier rhythms. This does feel more like banging the piano to show off, but it still all fits. And again we get an ending with some different chords.
Movement 3. Adagio ma non troppo â Allegro ma non troppo. Oooh, the opening harmony here is great. Then we're softly but dramatically repeatedly hitting a high note. There's just so much tension in all of this. Now we're back to having a melody, which is a pretty typical Beethoven melody, but the harmony is still creating tension. We let the chords resolve for a moment, just to do some lower dark sounding chords. Hey, it's fugue time! (is this the bit that @queenlua is learning?) This melody is so simple, but we're laying it over itself to give some great counterpoint, as it builds up it feels cheery, but we're also adding in some angsty chords sometime. Getting the fugue to fit into the harmonic drama of the piece and not just feel fugue-y for its own sake is a nice trick. Now we're out of the fugue, and lingering in angsty harmony. Escalating the chords, this is pretty metal. Oh hey the fugue is back! I like you, happy fugue! And yet the harmonies start getting darker again. OK, now it's show off piano time. But we've modulated into something triumphant somehow.
Overall: That was excellent, especially the last movement, which had a satisfying emotional arc. I see we're repeating the "two short movements, then a long movement" structure of #30, which I'm not entirely sure how I feel about but appreciate the early movements not wearing out their welcome. I will want to listen to it again to get a better sense of how it all works. (Also, Vladimir Ashkenazy is hot.)
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Returning to Boris Giltburg. I tried to watch this on Naxos but somehow the order of the movements got mixed up the first time, and I didn't realize until the movement I thought was supposed to be prestissimo was slow. Taking this again from the top!
I .Vivace ma non troppo â Adagio espressivo. Nicely walking along here, delicate melodies. Ooooh, these harmonies are getting colorful. Rippling effects, and then some delicate melody.
II. Prestissimo OK, this is actually a fast movement. Now we're slowing down for some dramatic moments. When I thought this was the opening movement I was enjoying the Drama and Mood of it all, but also noticed that it was really short. Which it is!
III. Gesangvoll, mit innigster Empfindung. Andante molto cantabile ed espressivo. And now we're getting our slow movement; which was interesting to listen to the beginning of when I thought it was the prestissimo and was just faking me out with a slow bit. But so far, this is a slow movement, I like these, but also I've gotten a lot of them; what is Beethoven going to do to keep it interesting for the next 10 minutes? We're adding in another layer of harmony now. Now we're elaborating, and it's not feeling like a slow movement so much now. And it really isn't now; what happened to "Gesangvoll"/"cantabile"? But we're back to the main theme, which is actually really singable, and doing some cool counterpoint with it. Oooh, there are some nice harmonies here; I'm not sure we're really getting "innigster Empfindung" here but it's good. Now we're stepping up the mood, and the virtuosity; there's some cool trembling here. Back to a simple statement of the theme, and we end on a held chord, nothing flashy.
Overall: the form is really odd here, with two short fast movements leading to a long movement which starts slow but goes all over the place. It felt more conventional when I accidentally started with movement 2, apart from that movement being really short. Musically this was good, but didn't stand out that much among Beethoven's oeuvre.