Whitney Stratifications and Intersection Homology (2023) [pdf] | Hacker News Reader

Whitney Stratifications and Intersection Homology (2023) [pdf]

n.ethz.ch

17 pointsaebtebeten40 comments

What follows is not a jab at the author of the document. I think it's really nice for an undergrad to be interested in this topic. It's very close to my field of research, and not something that an undergrad would typically know about. But why would you post someone's draft of a bachelor thesis here?

If someone is really interested in intersection homology (and perverse sheaves!), here is a set of lecture notes (not written by me): https://webusers.imj-prg.fr/~bruno.klingler/cours/coursperve...

Thanks for the link! (I'm afraid there's nothing for me to reciprocate with ATM)

You don't have to defend my eccentricity, but I always pay attention to BS theses, even drafts (RIP Grothendieck) because, they almost always* teach me something deep, and more importantly, efficiently. YMMV, but I'd be curious about your counter-defence if so.

*sometimes I do disagree with their headlines.

In layman's terms, what is this about and why is it interesting?

For my part, it's a move in an HN-based glass bead game*, so I was completely surprised that anyone else bothered to upvote. (we normally play well away from the front page)

Hassler Whitney I know from matroid theory (in particular, antimatroids for the mathematical psychology of learning), so stratification theory might be interesting because that also was.

René Thom I know from catastrophe theory, so stratification theory might be interesting because that also was.

Boundaries of boundaries are interesting, as are their arrow-reversed variants, but that's likely 1*1=1 compared with this material? (which I take to have something to do with finding nice boundaries along which to slice wholes up to better study their parts?) For ML in particular, maybe it could provide a reasonable way to divide-and-conquer manifold learning?

In fact, as of this comment, although I'm pretty sure the vertices of my play are interesting, I have yet to learn whether its convex hull will also turn out to be interesting — if someone else can provide the ELI5, that'd be great!

* https://en.wikipedia.org/wiki/The_Glass_Bead_Game

Retro reto retro hugos lolo yolos

>In 2019, the novel was nominated for the 1944 Retrospective Hugo Award for Best Novel.

Apologies for the rest, but in return for not not not expressing incuriosity* to your questions, may I suggest the use of poisk-fu to uncover the (anholocratic) Bourbaki "leader"?

https://news.ycombinator.com/item?id=40595575

https://en.wikipedia.org/wiki/Ultrafiltration_(kidney)

*second take at the Gr ineq?

Sorry I didn't —to my great chagrin— spot the incarnate filtration! (I come from the cryppie branch, neither hydro nor celmech, so my only excuse is that I normally contemplate topless models and their bottoms, not any of their Manichaean relations)

I'll just have to cool me down to take another round before I'm back in the ring (assuming XOR distributes under AND) to take another swing, so please bear with me.

Besides, I'm guessing this'll be a job that, rather than requiring poisk-fu, instead needs a fast machine, one that keeps the research motor clean.

> All Gaul is divided into three parts: the part that cooks with lard and goose fat, the part that cooks with olive oil, and the part that cooks with butter. —DC

> to uncover the (anholocratic) Bourbaki "leader"?

Holomorphic if not holocratic, how about HPC?

One might lexically (or even temporally) order https://gallica.bnf.fr/ark:/12148/bpt6k3157c/f776.image before https://www.sciencedirect.com/science/article/abs/pii/000349... ... at the risk of putting the Cartan before the Horwitz.

From https://fr.wikipedia.org/wiki/Henri_Cartan#Carrière

> Continuant à garder des contacts en Allemagne durant [la guerre], il facilita à la fin de la guerre le rapprochement entre mathématiciens français et allemands, communiquant en particulier avec Heinrich Behnke et Peter Thullen.

Lagniappe: https://www.youtube.com/watch?v=p9g4Md_huII

[note that Gen. CDSB was able to save over half his command (and 12'000 horses), despite the fact that near where he crossed the border it can get down to -40 (C or F, your pick) in winter; he ought to get more credit for an army half-full than he often does]

Best lagniappe ever

(SOMEHOW did not recognize FG in this one)

I will have to go with Bonaparte.

(Tested with chatgpt4o, that was fun.)

Careful, that cad has been known to break engagements and fob people off on euro♡ision-dominating scandinavian countries: https://en.wikipedia.org/wiki/Désirée_Clary

Re: Manichaen relations/eternal recurrence

https://en.wikipedia.org/wiki/Book_of_Elchasai#Content

>Christ is held to have lived on earth repeatedly through reincarnation, sometimes arriving through virgin births.

https://en.wikipedia.org/wiki/Book_of_Elchasai#:~:text=rejec....

Virgins might also wish to beware of plant-based products, eg https://www.ikea.com/se/en/p/sylt-lingon-lingonberry-jam-org...

  Mariatta, child of beauty,
  Looked about, intently listened,
  Sat awhile, and meditated
  In a blue box by the forest,
  And soliloquised as follows:
  "Call to me, thou golden logo,
  Sing, thou sacred bird of Northland,
  Tell how long must I unmarried,
  As a shepherdess neglected,
  Wander o'er these hills and mountains,
  Through these flowery fens and fallows.
  Tell me, cuckoo of the woodlands,
  Sing to me how many summers
  I must live without a husband,
  As a shepherdess neglected!"

  Then the jar of mountain-berry
  Calling to the lonely maiden:
  "Come, O virgin, come and pluck me,
  Come and take me to thy bosom,
  Take me, tinsel-breasted virgin,
  Take me, maiden, copper-belted,
  Take me, o stringly-skirted,
  Thousands pass my jar unmindful,
  Berry-maidens swarm about me,
  None of these has come to sample,
  Come to pluck this ruddy berry."

>This has led to their use in engineering, control theory and robotics.

https://en.wikipedia.org/wiki/Whitney_conditions#The_Whitney...

Should we ask ourselves whether we should marvel that this stuff has (not just (,maybe-likely,)) ((non-software, maybe-likely,)) engineering applications X)

When there's a spelling mistake on the first page (signular), I have a hard time taking the rest of the paper seriously.

This is mountains/molehills or pennywise poundfoolishness if I've ever seen it. We are not typists—we have other, oblique strengths.

Did they just ignore the spell-check then?

If they can't be bothered to check the spelling, what else did they miss?

They might have missed that "signular" could be a meaningless typo (but "convinient" maybe not so much)

> If they can't be bothered to check the spelling, what else did they miss?

When needing to split a bill (an exercise in exact simple arithmetic), the tradition at my Uni included an absolute ban on asking a mathematician.

Then there is the sort of applied physicist who is satisfied once they have made an even number of sign errors...

> When needing to split a bill (an exercise in exact simple arithmetic)

Not so exact or simple when the diners and total (after tips, etc) are co-prime

> an absolute ban on asking a mathematician

you can see why, annoying theorists focusing on the general case are the last thing needed when Tony Soprano wants the money now.

https://www.youtube.com/watch?v=96XJl7mxDtc ?v=AxR2BOXln4w

Come to think of it, we also claimed cosmologists are generally happy if their orders of magnitude are correct to within an order of magnitude: https://www.youtube.com/watch?v=__SMDtF_DsY

(I've heard that although Buck Owens had many solid hits, Barrett Strong could stop traffic. I guess that's why they used to keep C&W charts separate from R&B: because the artists were of different calibres?)

Exercise: the Owens 1964 hit "Heart Skips a Beat" is different to the Murs 2011 hit of the same title; is it possible to release an LP's worth of songs, none of which would be appropriate for muzak in hospital? (if so, what would be the most appropriate runout message?)

[Did Mr. B use Th' Lizard's piano tuner for "They Don't Allow Rappers in the Bullingdon Club" https://www.youtube.com/watch?v=dgPdcU653k8 ?]

Music can be learned, but real soul songs run in your jeans: https://www.youtube.com/watch?v=rP_yWoH_Nxs

Addendum: ^^ that particular channel of AI generated music has many numbers inappropriate for muzak in hospital.

Mr. B does love a flat key | off tune ditty, comes from being a gentleman of the banjo~lele.

In that case may I recommend a low fibre diet (typically of A.E. invertible or at least injective maps) or would that still be too confusing?

[If AI can handle scatology so easily, why do we still not have any electro bluegrass worthy of the genre name? (at least TIL gangstagrass)]

EDIT: upon reflection, conjeanital runs, while insalubrious, are probably the least harmful way to lose substantial fractions of a litre of bodily fluids over tens of seconds?

We've noticed our stock's stool gets substantially looser if they get too many carrots/apples during the day, so at <5 carrots/hour we buy ungraded in 10kg nets from the farmer and just use wetware/manual inspection. If we were doing 50'000 carrots/hour (how many hours/day would we need to muck out at that point?) maybe we'd use a Celox system instead: https://www.youtube.com/watch?v=6LQ7Y3RJtpk

[at 1:36 "Online Software Updates" most of the displays look reasonable, although the 4th from the right suspiciously resembles Matrix-technobabble and the soundtrack is epic; what I'd like to know is why the leftmost column would be using NATO alphabet for a vegetable sorter?

"Mercy, you've got to buff me, the premiums need to be separated from the discounts! Synchronise watches to Zulu ... Hack ... I'm going in!"]

https://news.ycombinator.com/item?id=40620856

(frontpage )

I would prefer to be approximated as a theoretical engineer, yes )

It was (?iappe?) -- admittedly a misfire -- to encourage (simultaneous) annoyance+delight in the reader's own tendency towards premature generalization

BtW https://en.wikipedia.org/wiki/Lambert_W_function

Apropos also of the work of one (post-selected by capital punishment) aristocrat-student of A,VI translated, uncovered by way of chasing down the 'W-strat+iHoml apps' cetacean

https://books.google.com.sg/books/about/Fewnomials.html?id=V...

As to mock-frivolous over-compression (& the untimely defence of aaaahimsa):

>Hence some say the game of nine-holes was called ‘Bubble the Justice,’

https://languagehat.com/bumble-puppy/

>superfluous

https://old.reddit.com/r/DebateTranshumanism/comments/gf56o6...

(I am not the /u/[deleted])

Speaking of aahimsa, https://i.etsystatic.com/7516795/r/il/67c326/5737917267/il_1... shows that in 1832, the 5e Arrondissement (and therefore the Hôpital Cochin?) bordered fields (the agricultural variety, not the variety with nonzero inverses), so presumably Galois missed his golden hour in the interval between dawn and the farmer's arrival but received treatment (ultimately lasting just about as long as Trotsky?) soon after.

If hygienic plastics had only been a thing back then, what might maths owe to medicine? (maybe a coq to Asclepius, unless the philosophers got there first?)

    Do you see the People 'sing?
    Dressing the wounds of hasty men

Hmm nope still think you overestimated Galois' festiness, the question is by how much

Steadfastly holding to my finnic/ie approximately dichotomic hemitheology too, fwiw

Väinämöinen/Gandalf/elves in general according to jrrt (maybe he's telling us elves are a finnic import?)

https://en.wikipedia.org/wiki/Finnish_influences_on_Tolkien

But even as d'Herbinville shimmered he fired his pistol, and the shot lashed forward and laced about the wizard's entrails, puncturing his peritoneum. He staggered and fell, grasped vainly at the earth, and slid into the abyss. 'Conjugate, you fools!' he cried, and lost consciousness.

===

"So, you see," said the mathematician, "the individual mathematician is just the hyle, and it is our devotion to structure which gives us the morphe, by which we turn coffee into theorems."

"But then," queried the physicist, "doesn't conservation of truth imply that by time reversal there are also anti-mathematicians, who turn cotheorems into fee?"

"Yes," interjected the theoretical physicist, "and as mathematicians (like electrons) and anti-mathematicians are all isomorphic, we can even imagine that there is only a single mathematical genius, and when we appear to have many gifted mathematicians with space-like separation, it is because they are merely reflecting the multiple intersections that a single chain of mathematicians (taking the anti- into the scalar coefficient) may have with our current instant."

  Gandalf Grey-cloaked whom you betrayed
  That I was but am no more
  Gandalf White-cloaked from Lethe's shore
  That I am and you I'll fade
  From the order, old and true
  From the council, clearly keeping
  Your force away, colour reaping
  Saruman, your staff needs glue!
  A crack was heard, a crack repeats
  Like the Turk in "Gutsy Schwoaba"
  Half his staff falls in lava
  Half his staff at Gandalf's feet.

[TIL Kalavela (1835) was first published after Stendahl's Le Rouge et le Noir (1830)]

Lagniappe: https://www.youtube.com/watch?v=fW68oWV9uE4 (Did Stendahl not have enough spine for the blondes?)

Thanks! For TIL https://de.wikipedia.org/wiki/L%C3%BCtzowsches_Freikorps

Presumably blonde is for you perjorative

EDIT: probably ought to start managing the cetaceons with chatgpt4o-- as you say, festy PUs are needed, or should I resort to a notebook???!

EDIT: in particular the understated significance of lava--maybe a tilt at the children's game?

Far from pejorative; I sometimes need a bit of time to appreciate the brunette fatale[0] or (pace Heinlein) the rousse fatale.

Would it help to point out that the chorus of the song is:

  Devushki bivayut razniye -   Girls are different
  Chorniye, beliye, krasniye.  Black, white, red

which could refer to hair colour (brunette, blonde, rousse) or to skin colour or to schoolgirl uniforms[1,2] or even —at a stretch, for the alcoholics among us?— to la bière?

Marie-Henri Beyle was also not averse to blondes[3] so I had been wondering if we only missed out on Le Rouge, le Blanc, et le Noir because his publisher wanted the letters on the spine of the book to be large enough to catch a readers' eye?

[0] incidentally, L'Été Meurtrier (1983) https://www.youtube.com/watch?v=-9yFNO4Q3So has a plot that would exactly match up with Galois' claim that his duel was (a) on account of a young woman who —even in Republican correspondence?— was no better than she should be, and (b) was to avenge her honour, but with (spoiler! rot13) oynzryrff crbcyr.

[1] see the schoolgirl accompanying Ms Dion in: https://www.youtube.com/watch?v=I1CwpCNThO4

[2] or refer to the not-quite-regulation retro "young pioneer" look in the chorus line of: https://www.youtube.com/watch?v=HpIzFRIX60E&t=895s (lingonberries, like the one that seduced Marjatta, turn red with age, and given the slavic fascination with floral crowns[4] for unwed but mature women, I've always wondered if russian round white schoolgirl hair bunting thus represents an immature stage? What do the finns do?)

[3] https://www.cairn.info/revue-de-litterature-comparee-2014-1-...

[4] locally we have St Catherine's, on whose day those in fear of becoming old maids wear extravagant hats.

Lagniappe: https://www.youtube.com/watch?v=o__2ks4XWho

(one of my favourite papers is by some geneticists at a seminar near Nice or Marseilles or St Tropez, who notice in the restaurant at lunch that nearly all men are brunet and nearly all women are blonde, and proceed to work out how what needs to be carried on which chromosome for the underlying genotypes to result in the observed phenotypical variation)

PS: I'll explain the lava if you explain cetaceans? related to pinnipeds, or otherwise?

EDIT: a more prosaic explanation for black/yellow/red is that the HRE used black/yellow devices and Guelph and Ghibelline factions used red/white devices, so it makes for a politically easy combination of existing antecedents?

EDIT2: aha, red also comes in naturally, as hilights for animal body parts: https://flagmaker-print.com/cdn/shop/files/FMP_Image_mockup_... (compare https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Fl... )

EDIT3: https://condottieridiventura.it/italian-medieval-history-gue... (OG gang signs!)

Lava: I assume it's more than just a LotR meme.

PS: just the cute pun thanks to you, whale-(as in cryptowhale, nested pun for hidden whale)-like, ergo, leviathanically centripetal though inconspicuous references.

I (think I?) caught the vexillary tilt but the contemporaneus Gold=freedom=(republican/nonmonarchist/patriotic but not patriarchist)Luetzower origin story of the current-day teutonic colors seemed more salient. Blonde-- more yellow than white, hence clearly not kaiserlich, but even maybe an aspersion-- misappellating gold gelb was historically such. So, irrealis: "Stendhal was too yellow to go either full republican Or (heheh) full legitimist, the liminal shade of psychologically legitimist/emotionally republican was as far as he could permit himself."

The genetics paper.. wasn't it in collaboration with a well-known American CS person on sabbatical in France?

Finnic practices: under investigation.

Placeholder: Right angle as virtue, acuteness and obtuseness as the vices? (Freemasons at least would be happy with this characterisation; but what about reflex angles?)

https://youtu.be/daVny9y72UE

I gather there should be an entire class of aperiodic automatons waiting to be found

(And no more riffs on the lava as if we are high on children's games?)

The lava is waiting for me to trace down a quote in japanese, which in particular is in kanji — at least I've found the correct page in the scan, now I just need to figure out which aperiodic crystals correspond to the english translation, and then hope I may find some antecedents...

(but to first order I'm just embarrassed because I quickly needed a weak rhyme for "Swabian" and lava not only quickly came to mind but was much easier to motivate than the tempting but difficult enjambment of "Bhabha / And benzedrine")

Placeholder 2: as alluded to in https://news.ycombinator.com/item?id=40678281 , time and chance happeneth, so by and by either every extraordinary person past a certain generation is your (Rebecca's) descendant or none of them are.

My bad (memory). Plus, it was the other founder that had a (less spectral) relation to one of the Pilgrims, Peregrine. Couldn't resist making a bridge/mountain out of the proximate spellings of the Anglo-Saxon (Canta)brigge and the "Brythonic"

https://en.m.wiktionary.org/wiki/Reconstruction:Proto-Celtic...

The key fee is,

1 f no if's.

(Re: quenya -- Thanks, we all should hold on to the wikipedia like our innards)

What says the theoretical engineer?

> What says the theoretical engineer?

You'll have to tell me?

(...and the noonday demon just lost her powers! See you later)

I'm a little more charitable on such things than I used to be, because it is hard to know why they overlooked the typo. For example, in this case it might be that they actually use a tool called signular [1] and so added that to their spelling dictionary.

[1] https://stackblitz.com/edit/signular

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