Love and Math

Frenkel Edward 2008Talking of his grandfather who had overcome poverty and blindness to become a US Senator, Gore Vidal once wrote that no challenge is finally insurmountable if you mean to prevail.  I was reminded of this in reading Edward Frenkel’s superb memoir, Love and Math.  Frenkel overcame the widespread and systemic anti-semitism in Soviet Mathematics to establish himself as a world-leading mathematician at a very young age.

Denied entry in 1984 because of his ethnicity to Moscow State University’s (MGU’s) Department of Mechanics and Mathematics (Mekh-Mat), the leading undergraduate mathematics programme in the USSR, he entered instead the mathematics program at Kerosinka, the Moscow Institute of Oil and Gas.  Anti-semitism (and anti-Armenianism, anti-Chinese racism, etc) in the admissions process at Mekh-Mat was so widespread, that other Moscow institutions, such as Kerosinka, were able to recruit very good Jewish and minority students.   One theory is that this policy was deliberate, since having all the Jewish mathematicians studying in one or two institutions made their monitoring easier for the KGB.

Frenkel had grown up in Kolomna – only 70 miles from Moscow, but well into the provinces – and had not attended a special mathematics school (as did, for example, Vadim Delone at FizMat #2), nor had an opportunity to participate in the mathematical study circles that were widespread in the larger soviet cities.  He did have the help of a local mathematician, Evgeny Petrov, a professor at a teacher training college in Kolomna.   Frenkel was very fortunate to have such help.   I recall my envy on learning on the first day of lectures in my first year at university that some of my fellow students, who had grown up near to the university, had been meeting our professors for years previously for after-school mentoring and coaching. (On the other hand, even the brightest of my fellow students so mentored ended up winning no Fields Medal, nor even becoming a mathematician.)

Good mathematical undergraduates from Kerosinka and other specialized institutes in Moscow literally scaled the fences at MGU to attend, illegally but often with the encouragement of the teachers, lectures at Mekh-Mat.  Frenkel did this and was again fortunate in being befriended by some very great mentors:  Dmitry Fuchs (now at UC Davis), his student Boris Feigin, and Yakov Khurgin.  Their generous mentoring was unpaid, time-intensive, and often brave, given the society they lived in.   As a result, Frenkel wrote his first research paper in only his second year as an undegraduate, a paper subsequently published in Israel Gelfand’s famous journal, Functional Analysis and Applications.  Gelfand was someone that even my professors, in the 1970s and in faraway Australia, spoke of with awe.

With the opening of perestroika, the Mathematics Department at Harvard University decided to invite some young Soviet mathematicians for research visits, and Frenkel was one of these:  He received his invitation in March 1989, before he had even completed his first degree.  While at Harvard, he had another Russian mentor, Vladimir Drinfeld (now at University of Chicago), and Frenkel completed his PhD there, in 1 year, under the supervision of another Russian, Joseph Bernstein (now at Tel-Aviv).  Frenkel is very generous in his acknowledgement of the support he received from his mentors and from others, and his story warms the heart.  Despite the anti-semitism he experienced, he has prevailed in the end, being now a professor at U-Cal Berkeley (and a film-maker).  Reading his account, I was reminded repeatedly of the ancient spiritual wisdom:  When the disciple is ready, the guru will appear.

Frenkel interleaves his personal story with an account of his changing research focus along the way, a focus which has mostly followed the powerful thread of the Geometric Langlands Programme.   His writing is fluent, wise and witty, and he manages to convey well the excitement and pure, joyous exhilaration that mathematical thinking can provide.  His writing makes most of the underlying mathematical ideas clear to non-experts.  That said, however, the text has a couple of weaknesses, both minor, although both I found irritating.  No one who does not already know something of category theory would understand it, even at a high level, from the single paragraph devoted to it on page 156.   Another minor criticism is that the text does not always adequately explain the diagrams, or what is being done with them.    But then I have particular views about reasoning over diagrams.

In summary, this is a superb book – wise, generous, witty, and heart-warming – and reading it will enlarge your knowledge of mathematics, of the Langlands Program, and of the power of the human spirit.   Everyone in the pure mathematical universe should read it.

An index to posts on the Matherati is here.


Edward Frenkel [2013]:  Love and Math:  The Heart of Hidden Reality. New York, NY:  Basic Books.


Gertrude Stein:

One plunges here and there with energy and misdirection during the storm and stress of the making of a personality until at last we reach the twenty-ninth year the straight and narrow gateway of maturity and life which was all uproar and confusion narrows down to form and purpose and we exchange a great dim possibility for a small hard reality.”

Keeping open a great dim possibility, and thus avoiding a narrowing to a small hard reality, is the main purpose of life.

RIP: Peter Geach

The death has occured of British philosopher and logician Peter Geach (1916-2013).
There is a famous story, perhaps apocryphal, of the logician Alfred Tarski, Polish-born but in American exile from WW II, asking his American City College of New York colleague Emil Post why he, Post, was the only prominent propositional logician who was not Polish.   Post replied that he was not born American, but had come to the USA as a child, and had in fact been born in Poland (although at the time part of the Russian empire).   It has seemed at times that Poland cornered the market in logicians and we find yet another example in Peter Geach.  According to his Guardian obituary, his maternal grandparents were Polish.
Long ago, I wrote an essay, in a logic course taught by Paul Thom and Malcolm Rennie, exploring a system of entailment due to Geach.  Then, as now, pure mathematicians mostly disparaged logic, and my university offered no further courses in the discipline that has since become the single most important to artificial intelligence and automated reasoning.   Universities are very good at preparing their graduates for the past; for the future, not so much.

RIP: Natalia Gorbanevskaya

Natalie Gorbanevska 19677
The death occurred last month of Natalia Gorbanevskaya (1936-2013, pictured in 1967), Russian poet and Soviet dissident, and one of the Moscow Seven, brave opponents of the occupation by forces of the Warsaw Pact of Czechoslovakia in August 1968.  From 1975 she lived in exile, initially in Israel and then in France.  For most of this time she was stateless, and did not have a passport until 2006, when granted Polish citizenship.   As in the 19th century, Russia disowns its best and brightest children.  The Economist has an obituary here.
There was more than this one protest against the invasion, with over 200 people involved in protests elsewhere in the USSR and across the Eastern Bloc.  A list of 160 Soviet protesters against the invasion, prepared by Memorial, is here.  The courage of the Moscow Seven and these others has been recognized by the Czech Republic, but not yet by the Russian Federation.   Indeed, Russia has still to apologize to Czechslovakia for the invasion.
From Gorbanevskaya’s poetry (translation by Daniel Weissbort):

The crime has not yet been expunged,
the hour of truth has not yet struck.
logs in the stove still ticking over,
although the fire’s already out.

Recent Reading 10

The latest in a sequence of lists of recently-read books.
David Eagleman [2010]: Sum: Tales from the Afterlives.  (London, UK:  Canongate).  A superb collection of very short stories, each premised on the assumption that something (our bodies, our souls, our names, our molecules, etc) lives beyond death. Superbly fascinating.  One will blow your mind!  (HT: WPN).
A. C. Grayling [2013]:  Friendship.  (New Haven, CT and London, UK:  Yale University Press).
Andrew Sullivan [1998]:  Love Undetectable:  Reflections on Friendship, Sex and Survival.  (London, UK: Vintage, 1999).
Michael Blakemore [2013]: Stage Blood. (London, UK: Faber & Faber).  A riveting account of Blakemore’s time at the National Theatre in London.
William S. Burroughs and Jack Kerouac [1945/2008]:  And the Hippos were Boiled in their Tanks. (London, UK:  Penguin Classics).   Mostly writing alternate chapters, this is a fictional account of events based on the death of David Kammerer at the hands of Lucien Carr.
Jack Kerouac [1968]:  Vanity of Duluoz.   (London:  Penguin Modern Classics, 2001).
Charles McCarry [1974]:  The Tears of Autumn. (London, UK:  Duckworth Overlook, 2009).   The assassination of JFK as a conspiracy organized by the family of the Diem brothers, involving Cuban military officials, the KGB, and the Mafia.
John Williams [1965]:  Stoner. (London, UK: Vintage, 2012).  Alerted by the enthusiasm of the late Norman Geras, and reinforced by the praise of Julian Barnes,  I starting reading this book with keen anticipation.  I should have known better:  someone who liked the books of Philip Roth clearly had a literary taste to be wary of.     Stoner was a great disappointment, and certainly does not belong in any collection of Great American Novels.
Is the book great literature?  Well, frankly, no.  It is well-written, no question, but not well enough.  We are told the main character William Stoner has no friends while an undergraduate, but nothing in the thin preceeding pages would explain why.   We are told he switches from studying agriculture to literature after an epiphany in a compulsory literature class, but this paragraph (and it is just a paragraph) is very thin indeed.   Why did he have this epiphany?  Where did it come from?  Nothing beforehand (in the book) would justify this event, and the event itself is only barely described.   Do people make such a switch so often, that no explanation is needed?  Not in my experience.
I can see that members of the literati – for instance, Julian Barnes – would like to read about people who come to love literature and who then devote their life to its teaching.  But Williams merely states these attributes of William Stoner as facts, without providing any compelling justification – not psychological, nor social, nor familial, nor cultural, nor literary, not spiritual, nor nothing – for these facts.     Indeed, there is hardly any justification at all, let alone a compelling one.
The narration is by a third-person narrator, and he or she seems to know what is inside Dr Stoner’s head.  Moreover, every other character is a cypher to the narrator, as (presumably) they are to Stoner himself.  One is therefore tempted to read the narration as being in the first-person.  But then, some of it is too vague for either a knowledgeable first-person or an omniscient third:  on pager 109, for instance, we read that Stoner disposed of his $2000 inheritance by giving “a few hundred dollars” to his parents’ black farm worker.    A few hundred?  Surely, Stoner knew at the time exactly how much he gave.  Likewise, surely, an omniscient narrator would also know the amount.   This is sloppy writing, and it undermines the case for the narrator being either first- or an omniscient third-person.
Similarly, we are told several times that Stoner had a deep friendship with Dave Masters, who is killed in the Great War.   But although this friendship is mentioned, it is not described in any depth.  It is certainly not invoked, nor is an invocation even attempted.  So, again, we come away thinking the narrator barely knows about which he speaks.   Just how credible, then, is anything the narrator says?    The book undermines its own case.
Why has the book proven popular?   Well it is more popular in Europe than in America.  I believe the answer to this disparity goes to something the former British Labour MP, Bryan Gould, once said when comparing political life in Europe with that in Australia, New Zealand, or North America:  In the New World, anyone upset by a social problem tries to fix it.  In the Old World, anyone upset by a social problem tries to live with it.   Stoner is a book about a man who lives with every major problem of his life, accommodating himself to an unhappy marriage, to a wife who appears on the edge of madness, to the end of his only happy relationship, to an alcoholic daughter, to not seeing his only grandchild, to an unsatisfying and tedious job, to an unfair assignment of work duties, to no promotions, to a lack of close friendships, to public gossip and innuendo about his marriage and relationships, to the death of his parents and his one apparently-close friend, while only ever once, it seems, standing up for himself.  And the counter-attack he launches is in such a small and picayune way, hurting the very students he is supposed to care for, that it can hardly be worthy of any emulation.
Certainly such people exist (indeed, the Old World is full of them),  but this novel never presents a compelling case that this particular man, William Stoner, should behave in this way.   Indeed, it hardly presents any case at all – the writing is all tell, and no show.    The power of showing is demonstrated by the one scene where the author does invoke the events, rather than merely mentioning them: the PhD upgrade viva of Charles Walker, where we can read the dialog for ourselves, and draw our own conclusions.    If only the author had done this more often, the book would have been much better.


Having created lists of concerts I have attended, bands I have heard, galleries I have visited, etc, I overlooked theatre and dance productions I have seen.  Herewith a list, sometimes annotated, to be updated as and when I remember additional events.

  • The Lieutenant of Inishmore, at the Noel Coward Theatre, St Martin’s Lane, London, August 2018.  Martin McDonagh’s very funny satire on the IRA and the INLA, in a well-acted production.  The production was somewhat gory for my tastes.
  • Lovers Anonymous developed, written and performed by Encompass Theatre Collective, St Pancras Community Association, Camden, as part of the Camden Fringe, 4 August 2018. Audience of about 25 seated in a circle, as if we were all participants in an AA-style meeting of people with relationship problems.  A mix of acting, music, dance & improv, it was energetic and entertaining, but lacked narrative coherence and character development. The long speeches sounded too glib, so they were not convincing as contributions from the floor.  I guess you need a lot of rehearsal in order to truly sound unrehearsed, as Monty Clift showed.
  • Goethe and Christiane performed by One Night Stand Productions and eurus ops theatre company, written and directed by Joseph Prestwich, at the Bread and Roses Theatre, Clapham, South London, on Saturday 26 August 2017. This was an interesting and amusing new play based on Goethe’s life and his engagement with Italy. The staging and acting were both excellent. Webpage here.
  • Henry V by Cyphers Theatre Company at The Proud Achivist, on Sunday 25 October 2015, St. Crispin’s Day, and the 600th Anniversary of the Battle of Agincourt. Directed by Marcus Bazley, and starring Paul Anthony, Carmella Brown, William Holyhead, Dylan Lincoln, Rupert Sadler and Louise Wilcox. As before, this is an exciting and energetic production, and was again superbly acted. One had to fight hard to ignore the leaking sound of the fine ragtime and blues pianist in the bar outside.
  • A Midsummer Night’s Dream, at Tutu’s, King’s College London, 23-25 March 2015, directed by Luke James Boneham, and starring Joe Prestwich, Grace Farrell, Ally McDermott, Rosalia Mythos-Perris, Tom Marsh, Ben Dallyn, Emily Brown, Travis Alabanza, George Collecott, Akshay Sharan, Ioana Andrei, Aurelie Blanc and Jackie Edwards. This was a very good production. I particularly liked the detailed choreography of fast-paced, witty movement in the scene where Lysander (Tom Marsh) and Demetrius (Ben Dallyn) were both besotted with Helena (Emily Brown). Not sure if this choreography was planned and directed or was improvised by the actors – in either case, it was very good.image
  • Proof, a play David Auburn, at Tutu’s, King’s College London, March 2015, directed by Mathew Hodson and supported by the Faculty of Natural and Mathematical Sciences of King’s College London.
  • Great Expectations, at The Proud Achivist, February 2015, in a Cyphers Theatre Company production, directed by Marcus Bazley, and starring Chris Anderton, Victoria Hamblen, William Holyhead, Dylan Lincoln and Rupert Sadler (as Pip). Another superb production from this ensemble – fast, frenetic, fluent, folksy, feisty and fun.
  • Heels of Glory: A Drag Action Musical, by Tricity Vogue (writer) and Richard Link (composer), directed by Stephen Heatley, at Chelsea Theatre, London, January 2015. Some good music, and the henchpersons were choreographed well. But lyrics and words and comedy and plot and singing and acting and lighting could all do with some more work. OTOH, perhaps best to ignore my comments, as I’ve never really got drag.
  • Great Britain, National Theatre production of play by Richard Bean, directed by Nicholas Hytner, at the Theatre Royal, Haymarket, 29 December 2014. I lasted just the first half, and would have left earlier if I could have done so without disturbing anyone. Not at all funny – there were perhaps just three mildly-amusing one-liners, none of them particularly witty or satirical, in the first half. Lots of swearing and explicit sexual innuendo (both verbal and physical), which I assume was intended to be funny. But who laughs at swear words and extreme male chauvinist displays of sexist insults these days? Who ever did, come to that? (In my entire life, I have never met anyone who laughed at Benny Hill, for instance, which may only show what sheltered upbringings modern Australians have.)The script had the feel of something written by someone in late middle age, trying his hardest to be down and dirty with the kids – and missing it completely. As an example: Why was the Police Commissioner’s secret gay lover half-Chinese and half-Welsh? I imagine such specific detail was intended to be funny. But it wasn’t funny, and no one laughed at it. Nothing was done with this detail (at least in the first half), so why was it there at all? It was as funny as saying he was half-Welsh and an architect, ie, not at all. Perhaps it would be funny to people who don’t know any Chinese people or any Welsh people, or people who don’t live in modern Britain. Perhaps Benny Hill would have found it funny.The actors did their best with a script that should have gone straight from paper factory to wrapping fish-and-chips. I have known a dozen people wittier everyday, all the time, than anything I heard here, and encounter similar people frequently. The average stranger in a British post office queue is funnier. And they do not have the luxury of writing their words in advance.Perhaps the play was funnier on another night, the night the critics went. Or perhaps I just wasn’t in the target demographic, since I was expecting to see clever political satire and sharp wit, rather than f-words, unfunny d-jokes, and stale, ham-fisted political commentary. However, no one around me was laughing either, so there must have been a lot of us from that wrong demographic there.
  • King Lear, at the Greenwood Theatre, by the King’s Shakespeare Company, directed by Freddie Fullerton, produced by Aja Garrod and Serena Grasso, and starring Steffan Rizzi (Lear), Lydia Fleming (Goneril), Bex Evans (Regan), Juliet Wallace (Cordelia), Matthew Aldridge (Gloucestor), Rupert Sadler (Edgar), Magnus Gordon (Edmund), Joe Prestwich (Fool), Tom Marsh (Kent), Benjy Cox (Albany), Will Holyhead (Cornwall/Old Man/Captain), George Colecot (Oswald/Burgundy), Andrew Marks (France/Knight/Servant/Messenger), Ally McDermott (Curan/Knight/Servant/Gentleman), and (as Knights) Marcus Bell, Charlotte Downes, Liam Flaherty, Ollie Harrison, Nessa Khurram, Mattho Mandersloot, Zack McGuinness, Holly Nicholls, and Tallulah Smart. This was a monumental production, intelligent, violent, and morally serious. December 2014.
  • Romeo and Juliet, by London Theatre Workshop, The Eel Brook, Fulham. Audience only a few more than cast, sadly. Some inspired performances, but felt like the troupe were still finding their feet with the play. Perhaps would have been better later in the run. Hard to discern what this production was for. Why another production of R&J? Why now? Why this way? A lot of knives, unnerving to those of us awake in the front row.
  • Henry V, at The Proud Achivist, October 2014, in a co-production of Cyphers Theatre Company and King’s Shakespeare Company, directed by Marcus Bazley, and starring Chris Anderton, Victoria Hamblen, William Holyhead, Dylan Lincoln, and Rupert Sadler.  This was a very impressive production, of high professional standard.  Who wouldn’t want to be an actor, when you get to run around in public like this, shouting and fighting? A superb production, fast-paced, clever, and witty. All the sound effects – seagulls, sailing ships, war drums, swells – were produced by the actors themselves, and transported us instantly. The costumes were cleverly and subtly colour-coded so that we could tell French from English characters played by doubling actors. Some nice public participation, such as asking audience members to donate coins for the welfare of incognito Henry’s soldier challenger. And some clever improv by Will Holyhead when an audience member handed him a kangaroo-laden Australian dollar coin. “This seems to be a strange animal . . . A dragon?”  Who wouldn’t want to be an actor, when you get to engage in banter like this?
  • Blackshaw Theatre New Writing Night, 30 September 2014, Horse and Stables Pub, Waterloo, London. Five very good items tonight, especially Luca Vigano’s short play about a hit-man commissioned to kill his client, Slice of Death, directed by Stephen Bailey and starring Annie McKenzie and Oscar Porter Brentford.
  • Teh Internet is Serious Business, play about Anonymous and LulzSec by Tim Price, at the Royal Court Theatre downstairs, Sloane Square, London, 23 September 2014 (press night).   I recommend the play very highly.  As someone remarked afterwards, there can be few plays around that present C++ code through the medium of interpretative dance.   The play is fast, kaleidoscopic, witty, and visceral, and some scenes are very funny.  I think there are many possible explanations for the actions and evolution of Anonymous, and the play essentially presents just one narrative.  The one it presents is plausible, however.   It is also good in capturing the specific personalities and motivations of some of the LulzSec members, particularly Tflow and Topiary, who were in the downstairs bar before the show.
  • Solo for Two, Natalia Osipova and Ivan Vasiliev, London Coliseum, London, August 2014.
  • Blackshaw Theatre New Writing Night, 29 July 2014, Horse and Stables Pub, Waterloo, London.  Of the events featured this night, only Gravy, written by Harold Kimmel and directed by Christian Durham, was worth writing home about:   this presented a very funny NYPD investigation of the crime scene that ends Hamlet, with the Ghost and Horatio called in for questioning over the multiple murders, incest, and various perversions discovered.
  • Gulf, performed by Pivot Theatre Company, written by Jeff Scott and Alister MacQuarrie, directed by Charlie Kenber with music by Patrick Sale, at Camden People’s Theatre, London, July 2014.   The play explored relationships between a mother and her teenage daughter, the daughter and her school headmaster, the mother and her colleagues and a psychiatrist, and issues of pedophilia, teenage sex, and the internet.   I found the play confusing, especially with actors switching roles apparently randomly, and lots of scenes made no clear sense.  Perhaps the play was about too many issues and too many relationships to be adequately covered in the time.   I liked the  music, as music, but not sure it worked with the play.
  • Measure for Measure in Cabaret, by King’s Shakespeare Company, directed by Lauren O’Hara and music by Henry Keynes Carpenter, final dress rehearsal, London, July 2014, prior to participation in the Bristol BardFest.
  • London Student Drama Festival 2014, Teatro Technis, Camden, London, 21 June 2014.  Five short plays: 12″; Honestly (both Imperial College); The Parting Glass (UCL); Lizards (SOAS); Guilty Parties (KCL).  Best by far was the KCL entry, very funny and well acted, written by Alister MacQuarrie, who rightly won Best Writer award for second year running. SOAS entry was workshopped and showed it; could have done with more work.  UCL play was an Oirish drama about The Troubles – oh so serious, so overdone, its conclusions telegraphed ahead of time, with melodramatic acting, cod accents, two anti-minimalist sets leaving nothing to our imaginations, an upright piano, and enough actors for a Cecil B. De Mille epic, including even a 5-person Celtic band on stage:  Holy Mother of Mercy was this awful!    For reasons unknown, this insult to those of us of Irish descent won award for best entry.   And speaking as indeed such a person, why must any Irish drama be accompanied by Celtic folk music, as if Irish people can’t appreciate any other type of music?  Has no one heard of John Field, James Galway, or the Vanbrugh Quartet?   Even The Messiah had its first performance in Dublin!  Five centuries of English condescension towards Ireland embodied in one folk band onstage tonight.
  • Another Country, by Julian Mitchell, directed by Jeremy Herrin, at Trafalgar Studios, Whitehall, London, June 2014.  A superb production of a play which imagines what events in an English public school in the 1920s might have led the Cambridge 5 to betray their country.  Rob Callender superb as the young Guy Burgess:  authentic, spirited, leopardesque, riveting.
  • Blackshaw Theatre New Writing Night, 27 May 2014, Horse and Stables Pub, Waterloo, London.
  • Trojan Barbie, by Christine Evans, by the King’s Players, King’s College London, under Holly Robinson (director) and Dan Bird (producer), in Tutu’s, KCLSU, Temple, London, March 2014.   Without question, one of the worst live performances I have had the misfortune to witness.
  • Copenhagen, by Michael Frayn, performed by Ria Abbott (Margrethe Bohr), Freddie Fullerton (Niels Bohr) and Tom Marsh (Werner Heisenberg), under Alister MacQuarrie (director), Aja Garrod (producer), and William Nash (executive producer) in the Old Anatomy Museum, King’s College London, Strand, March 2014.  Superbly acted and directed, this was theatre of a high professional standard, equal to any I have seen.    Another review is here.
  • Romeo and Juliet, by King’s College London English Literary Society, under W. Nash (director), at the Greenwood Theatre, London, February 2014.  An innovative, witty, and funny treatment, superbly acted.
  • The Tempest, by King’s Shakespeare Company, under Hannah Elsy (director) and Aja Garrod (producer), at The Rag Factory, Heneage Street, Brick Lane, London, December 2013.  Outstanding performances by Imogen Free (Ariel) and Max Funcheon-Dinnen (Stephano).   The modern touches worked very well, and brought the play alive.  Was a full house.
  • The Magic Flute, by English National Opera, directed by Simon McBurney, London, December 2013.  As always with this director, there were some stunning visual effects, for instance, the shoals of actors representing birds, each fluttering folded paper to produce a rustling sound.
  • Marlowe’s Edward II, by The National Theatre, London, October 2013.
  • Richard II, starring Eddie Redmayne and directed by Michael Grandage, at the Donmar Warehouse, London, December 2011.
  • Hamlet, by Schaubuhne Berlin, at the Barbican Theatre, London, December 2011.
  • Marlowe’s Dr Faustus, Liverpool, 2004.
  • The Elephant Vanishes, by Theatre de Complicite, Lincoln Centre, New York, June 2004.
  • Hamlet, by Calixto Bieito, in Birmingham, September 2003.

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