#Cayley's theory

[girl-debord]

"A radical monopoly exists where all alternatives have been rendered either inaccessible or unimaginable. An obvious example is an environment in which one simply can't live without a car. What Illich calls 'natural competence' is ruled out. The ability to walk is of no use if your destination is on the other side of a freeway you can't get across; your skill in performing a job is of no consequence if you don't possess the required educational certificate."

- David Cayley, Ivan Illich: An Intellectual Journey

[coming-up-with-usernames-is-hard]

PhD Blog Week 4

Reading

Kac and Raina bombay lectures, read half of chapter 4, it seems to make more sense than Date's book but that might just be because the notation is closer to what my supervisor uses and I've already seen the explanation once now

Courses

Lie theory: Proved Engel's theorem and looked at Lie's theorem, introduced the Killing form

CFT: SO MUCH QFT. Supposedly QFT is not a prerequisite for this course but if I hadn't already spent a whole year studying QFT I'm not sure how I would have followed anything in this lecture. We're taking an axiomatic approach which is essentially "correlators exist and have these nice properties", and then we introduced path integrals and showed they had the same nice properties, so I guess they can be the same thing. Of course path integrals are badly defined and don't make any sense, but it's fine, you just believe that path integrals and functional derivatives work like normal derivatives and it all works out fine. No actual CFT this time, the conformal symmetry should come in the next lecture

Differential Topology: Painfully detailed calculation of the tangent space to S¹, defined a vector field. Really wish we were using derivations as the basis of our definitions, alas I have to deal with equivalence classes of elements of a disjoint union. It's a weird definition of the tangent space because it presupposes that it's a vector space of dimension equal to that of the manifold. Plus, it's so notation heavy. We're explicitly working with equivalence classes of pairs of a label of a chart and a vector in ℝⁿ and everything is just nested brackets. When I've seen this material previously the goal has always been to drop as much notation as possible and forget any equivalence classes that may be taking place and just work with a representative

Talks

Example showcases started this week, we each have to give a 30min talk about an "example" relevant to what we're researching. We saw four this week, all of which were good. The first was on moduli spaces of flowlines, I followed what was happening but I didn't quite get the point of what we were doing. The second was on surgery theory, I think I got the idea but I've got absolutely no clue on any of the details. The third was on dual Artin groups, which are related to Artin groups (although the "dual" is misleading, there's no duality) and Artin groups are related to Coxeter groups, which I know a little about because Coxeter diagrams are related to Dynkin diagrams and Dynkin diagrams are related to Lie algebras which are nice. The fourth was on CAT(0)-spaces and CAT(0)-groups. I went into this with no idea what a CAT(0)-space is and now I feel I have a good idea, and there was a nice way to think of the free group as moving different parts of its own Cayley graph into focus which reminded me of zippers in type theory, where a zipper is the derivative of the type, which feels like some black magic where you start differentiating objects formed from (co)products in a category as if they were normal polynomials.

My example showcase is next week, so I've started planning that. Currently planning to focus on how we can take inspiration from physics to discover things in maths, but that might all change once I write the talk and work out if it fits in 30min

Supervisor Meeting

Met with my supervisors, most of the meeting was spent looking at different ways to represent the Clifford algebra of fermions. One way was as an infinite tensor product of copies of ℂ² on which Pauli matrices act, the other was as the exterior algebra of an infinite dimensional space where the basis consists of single-fermion states and the wedge product gives us all of the required anticommuting properties. Still have some sign ambiguity between different soruces that I've yet to track down. Also did an example of the boson algebra acting on the Maya diagrams which clarified some misconceptions I had from the previous meeting

Reading Groups

Complex Geometry: We finished off the proof of the Bruhat decomposition and I followed most of it, it's just when it comes to putting it all together that I get lost. I decided I wouldn't be able to give the talk next week, I just don't know enough algebraic geometry and don't have the time to learn it

Infinity Categories: Looked at infinity groupoids (I understood these ok) and how they're the same as Kan complexes (don't understand these). So far it's a lot of drawing simplices and then filling them in. Similar to complex geometry, each step follows but putting it all together I get lost in the details

Categories: Normal 1-categories seem easy in comparison, after missing the first week which clashed with infinity categories the second week we looked at duality and functors

Teaching

TA'd two first year tutorials this week. The problem sheet this week was much harder than the first two, mostly because the questions weren't written very clearly.

I was assigned marking from two courses this week. Marked about 40 assessments, which took about 6 hours. I could go faster if I wrote less feedback but I think the feedback is useful while I have the time to give it. That said it would be nice not to have to write "underline vectors" ever again

[anumberofhobbies]

Also today, we teach that the theories of Sir Isaac Newton (1642-1726) and Swiss mathematician Daniel Bernoulli (1700-1782) provide the detailed science that explains lift. They don’t, at least not fully. The basic problem is that neither theory completely explains real-world observations. Bernoulli’s principle—that the faster air on top of the wing experiences reduced pressure—is correct but doesn’t explain why it’s correct. It also doesn’t explain inverted flight. That’s where Newton’s second and third laws (see the sidebar below for details) come into play. Taken together, Newton’s laws describe how we can fly inverted and how angle of attack works. But they don’t have the details we need from Bernoulli. Still, once we put Bernoulli and Newton in the same room, then sprinkle some Cayley throughout, we have a working idea of how to build and fly an airplane. But we still don’t know exactly why the air on top of the wing is at a lower pressure than the air underneath it.

By Ben Iannotta | February 2023 Given how deeply air transportation is woven into modern life, it’s surprising that the precise workings of aerodynamic lift remain a topic of debate among the experts. To sort all this out, I met on a video call last month with Paul Bevilaqua, retired from Lockheed Martin Skunk Works, and Haithem Taha of the University of California, Irvine. I learned about several myths and at least one collapsing theory. Here is our discussion, lightly edited and compressed.

[spectrallysequenced]

as you know some things about the baumslag solitar groups - so by extrapolation about geometric group theory - what is your favourite finitely generated infinte group and why?

I had to think about this for a while, but honestly I don't think I have an answer. I asked my friend Jack who is a geometric group theorist, and his answer was F_2, because it's very beautiful (meaning its standard cayley graph is), he likes trees, and because freeness is a very cool and important property. I'll add that as a tree its Gromov Boundary is a cantor set, which are also very cool. Also, the Nielsen Schreier theorem (Which has a beautiful proof using covering spaces) says it contains a copy of every other finitely generated free group.

[atplblog]

Price: [price_with_discount] (as of [price_update_date] - Details) [ad_1] This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other.  The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects. Publisher ‏ : ‎ Springer Nature Switzerland AG; 1st ed. 2021 edition (2 November 2022) Language ‏ : ‎ English Paperback ‏ : ‎ 538 pages ISBN-10 ‏ : ‎ 3030884120 ISBN-13 ‏ : ‎ 978-3030884123 Item Weight ‏ : ‎ 771 g Dimensions ‏ : ‎ 15.5 x 3.2 x 23.5 cm Country of Origin ‏ : ‎ India Net Quantity ‏ : ‎ 1.0 count Generic Name ‏ : ‎ rug [ad_2]

[thebrilliot]

Rubik's cube solving agent: Road Map

K, haven't done stuff in a little bit; I wasn't sure what to do first. BUT I did do a lot of studying group theory, and I do really appreciate when someone else has already established a vocabulary for a system of thinking. It does apply very well to Rubik's cubes.

So I'm thinking that there is enough that I want to change that I will be better off refactoring right now. The code base isn't even large at this point but I do know some of things that I want to accomplish with this project, and I want to make quick progress on this. I have other projects I want to get to too! Making progress on this problem I first started on 12 years ago will feel sooooo good. Gotta keep moving forward. More iteration = more speed even if that requires rewriting code more often.

That means I'm going to make a new branch for v0.2! Once I have v0.2 where I want it, I'll make the repo public. I think I will be comfortable with that. I have been reading about words and normal form and generating sets and Cayley diagrams and things. If you watch Matthew Macauley's Visual Group Theory lectures on YouTube, he talks about a "Big Book" that contains the shortest solution for every Rubik's cube and I'm borrowing that idea for what I previously called a "Store". Here is the rough road map for the project now:

v0.1 (there is a cube and you can turn it)

completed lol

v0.2 (flexible and (mostly) optimized book generation)

better and alternative notation, position vs. ID relative cube representation, enable flexible book creation via CLI, maximize book size using embedded DB, cube and word normal and compressed serialization

v0.3 (usable for anyone)

Python interface using pyo3, TUI improvement, colored facelet representation, strategic-game-cube dataset compatibility, word reduction and substitution

v0.4 (suitable for training Rubik's cube agents)

books as training datasets, 4 trainable tasks - (valid cube identification, masked cubelet prediction, depth prediction, cube solving RL)

v0.5 (nice-to-haves, idk)

algorithm exploration in TUI?, conjugacy classes (at least I'll give it a try), 3D viewer???, I do think it would be cool to watch the cube as the agent tries to solve the cube

I swear this will all make more sense when you can see the repo! I wish I had stuff to show , you know? Unfortunately, that's not how studying works, and my notes and thoughts are a mess. Hey, let me know if you would want to watch me work! The fun of this for me is that there is literally no point to it, lol. I'm making this for me. It will bother me if I don't finish yet another project and leaving the problem itself unsolved is already bothering me. If you want to join me in the fun, I will gladly show you my mad ravings and rant about how this entire project is just to enable a single experiment see if, when you're training a model to navigate a space that can be represented by permutations, the permutations will show up in the embeddings.

I don't stream much but I have a Twitch account! What do you think?

[gabbycoco-blog]

Can The Aged Keep Up With The Digital Aged?

Activism is the pursuit of social, political, economic, or environmental reform with the aim of affecting societal change for what is believed to be the greater good.Bradley Allsop develops the word "slacktivism" in "Social media and Activism: A Literature Review," which argues that utilizing social media as a tool to raise awareness has minimal effect on problems. On the other hand, according to Malcolm Gladwell, social media is a terrific tool for spreading knowledge widely but is useless since it encourages weak bonds. I partially concur with the writers' viewpoint, however I believe that elderly leaders and elites who retain power but lack the ability to comprehend close relationships with users and stakeholders miss the powerful effects of social media.Social media now has the ability to impact more than just one's profile page, highlighting both weak and powerful trends. I've just become obsessed with true crime, and I've been binge-watching Murdaugh Murders: A Southern Scandal on Netflix. In this show, social media is utilized to highlight the broken judicial system in Hampton County, South Carolina. Alexander Murdaugh's youngest son, Paul Murdaugh, was charged with multiple felonies February 23, 2019 following ramming his fathers boat into a bridge causing the death of 19-year-old Mallory Beach. Later in the series, it was discovered that the Murdaugh's were responsible for a number of local deaths. According to this reading, paradigm shifters have been identified as being involved in this crime because it is thought that social media was used to fundamentally alter people's perceptions and raise public awareness of the eerie influence the Murdaugh family has long enjoyed in Hampton County, South Carolina. In this case, social media was so heavily utilized that Paul Murdaugh suffered several physical assaults from locals. Are we underestimating the awareness people with power have? If not, how do we make elites understand the repercussions of social media activism?

Social media appears to be the main driver while companies experience more and more problems regarding rumors and misinformation. Theories are too abstract and not readily applicable for public relations professionals to put into practice. Role theory indicates an understanding of relationships, locating themselves in the relationships, determining the role appropriate to locate the type of relationship and behaving accordingly. Recognizing the target audience while acknowledging the consumer and their brand perception is critical. To what extent is it appropriate to use informal communication methods to communicate with a target audience when a crisis is evident? In their article "Challenging the dialogic promise: how Ben & Jerry’s support for Black Lives Matter fosters dissensus on social media," Erica Ciszek and Nneka Logan explained how critical discourse analysis (CDA) is used to examine this study and the public's reaction. As the marketing manager at Red Stick Social and throughout my time in college, I've learned that, even though public relations and marketing experts cannot control how an audience will react to change, we can still retain the message we are putting out. According to the report, Ben & Jerry's got criticism for their support of the Black Lives Matter movement. Yet, the study's findings demonstrate that supporters of Ben & Jerry's were strong. In “Effects of Issue Ownership, Perceived Fit, and Authenticity in Corporate Social Advocacy on Corporate Reputation,”Joon Soo Lim and Cayley Young argue that more and more large companies feel the need to speak out on controversial social-political issues. It has created a competitive narrative to gain more consumers and generate unique branding. That's the appeal of being free to voice an opinion online, as opposed to how a business, brand, or organization can only exercise control over its messaging. Can we trust these large brands as they claim to be authentic when speaking out about controversial social-political issues?

Leping You and Linda Hon highlight the difference between two approaches in the communication industry that are used for measurement in the digital world. Corporate social advocacy and corporate political advocacy in the communication industry is very evident— our duty as PR professionals and practitioners is to acknowledge and gain perspective with invisible ethical and intuitive guidelines. The goal is to relay clear messaging in the appropriate language to create a more substantial brand reputation. Although customers produce a brand's narrative, marketing professionals create and control the actual message. Most organizations that depend on antiquated systematic asymmetrical approaches would be better served to institute the two-way symmetrical systematic communication framework. The latter is the most sophisticated, moral and ethical motion. A company or organization will gain credibility, authenticity, and trust in today's society by applying these studied theories and proven strategies.  

The boundary between theory and practice on activism appears to be drawn in all of the assigned articles. Each author has a different perspective on the ramifications, but they all do a decent job of addressing how social media is utilized for activism.

[booleanip]

Leonardo da Vinci made the first real studies of flight in the 1480s. He had over 100 drawings that illustrated his theories on flight. The Ornithopter flying machine was never actually created. It was a design that Leonardo da Vinci created to show how man could fly. The modern-day helicopter is based on this concept. George Cayley worked to discover a way that man could fly. He designed many different versions of gliders that used the movements of the body to control. A young boy, whose name is not known, was the first to fly one of his gliders. The modern age of powered flight began in 1903 after Orville and Wilbur Wright made the first sustained, powered flight on December 17 in a plane. This twelve-second flight led to the development of the first practical airplane in 1905 and launched worldwide efforts to build better flying machines. The human’s feat to flying has seen many small steps in the making. Checkout the document to view some earliest but not so successful invention patents in the development of aircrafts. #aviation #aircrafts #historyofflying #intellectualproperty #IPR #patents #boeing #airbus #lockheedmartin #Leonardo #Bombardier #uac #ipconsulting #booleanipconsulting

[positivelyapunovexponent-good]

Oooh this looks quite fun! I shall partake. I’m also a bit shy about tagging people but anyone who wants to is welcome to join in!

A couple notes on each of my choices because I have much to say about each of them!

Dungeon Meshi is one of the only pieces of media where I cannot pick a favorite character. At all. I love everyone in the main party + Falin and equal amount and agonised over which character to chose for this poll for frankly too long. Finally settled on Senshi because he’s the most iconic

It was also a little difficult to settle on The Archivist as my favorite character in TMA since the supporting characters are so good, but at the end of the day I cannot resist the incompetent asshole academic who is canonically described as a “grubby Jesus”

I have admittedly been somewhat liberal in what I have interpreted a “character” to be, in my inclusion of real life mathematician Paul Erdős in my poll. However, I stand by my decision, as many would describe him as “a character” in the sense he was quite eccentric. If you don’t believe me PLEASE read his Wikipedia page (or at least the ‘Personality’ section). Seriously it’s one of the few Wikipedia pages I’ve ever read that’s made me laugh out loud uncontrollably. Also - quirks aside- his mathematical work is very cool too! Look up the Erdos Distance problem if you want somewhere to start- mathematicians continue to be chipping away at it in the decades after Erdos’ death. My research advisor once attracted the attention of airport cops after he started jumping up and down with joy in the terminal upon receiving the news that his colleagues significantly improved the exponent of the Erdos distance problem bound. (Honestly he’s kinda a “character” too. )

Okay I now proceed to get even more liberal with the definition of “character” for the purposes of this poll. In particular, the Fourier characters of the cyclic group G = (Z_n, +) are the star blorbos of my thesis. This is because they are QUITE useful for computing the eigenvalues of the adjacency matrix of any Cayley graph on generating set S of G (specifically, the eigenvalues are the sums of Fourier characters evaluated at each of generators in S). Because they are such blorbos to me and literally called characters, I maintain they deserve a place in a character poll

Okay I finally return to a slightly more… ahem… traditional interpretation of “character” in a fandom context. The fandom in question here is my girlfriend’s D&D campaign, so not much of a broad audience. Which is a shame, because it’s WICKED good. If it was a piece of published media widely consumed on tumblr, the character of Ubiquity in particular would have a firmly cemented status as a tumblr sexyman in the most traditional possible sense. I hate the tragic grease stain of a man so much, but I hate him so affectionately that he’s also my favorite. Anyways, my girlfriend’s campaign has been going for years now, and it is by far the “fandom” I spend the most of my creative energy on thinking about- I could theorise for hours, it singlehandedly cured my art block, and I have multiple dumb AUs living rent free in my mind. All that is to say my girlfriend is an absolute world-building genius and one of my favorite writers

inspired by @1tbls et al— no one tagged me but it seemed fun and I want in

if you want to partake, make a poll with 5 of your favorite characters & tag 5 people

however I get Very Nervous about tagging folks in things like this so if you see this just consider yourself invited to join in

[coming-up-with-usernames-is-hard]

PhD Blog Week 6

Courses

CFT: Actually more reasonable this week, spent most of the lecture studying the analytic structure of correlators, which just amounts to picking nice conformal transformations to pull out the information needed

Diff Top: The exterior algebra, but in the absolute worst way possible. Now that we're doing something I know about it just makes me wonder how bad the manifolds lectures were. Assessment was released, doesn't look too bad but I think it will take ages

Lie theory: Finished the proof of Weyl's theorem and started on the classification of simple Lie algebras by defining a Cartan subalgebra

Talks

Example showcases: Moduli spaces, started well with a nice example of the moduli space of triangles, then suddenly ramped up and started discussing schemes and I was lost. Hyperbolic groups and their boundaries, nice pictures and impressive drawing on the board of hyperbolic space, the boundary of a group is an interesting concept, it's the boundary of the Cayley graph embedded in hyperbolic space. Knots and finite type invariants, basically defined the Jones polynomial and another type of invariant, impressive live drawings of knots, evaluating the Jones polynomial at e^h and then Taylor expanding the coefficients are these finite type invariants, which is neat, but I'd like to have seen why it's true. Final talk was a physics one, looked at a particular list of conditions that might be desireable for a reasonable spacetime and came up with a contradiction implying that such a reasonable spacetime couldn't exist, it was nice to see someone else doing physics, and fun to think about GR again, which I haven't done for a while.

Supervisor Meeting

Spent half the meeting recapping the previous one for the people who missed it, which was a good test of my understanding, I don't think I did too badly. Then looked at how a simple modification of the rules we had would allow us to achieve equivalent results for other bases than the Schur functions, these rules correspond to adding horizontal and vertical strips (rather than general ribbons) to the Young diagrams, and the resulting lattice has 5 allowed vertices rather than 6, because to block unwanted vertical/horizontal boxes removes one choice

Reading Groups

Complex geometry: Missed it this week, I'll have to read the notes

Infinity categories: Defined limits in an infinity category, spent most of the time defining the join of two simplicial sets, then once you've done this the definition isn't actually that different to a 1-category

Categories: Equivalence of categories

Teaching

Just the two TA sessions this week, we move back to the maths building next week so no more running all over campus

[themathblogofsashanova]

August 25, 2022: Identity, Symmetry and Permutation, and Corollaries Named After My Favorite Black Holes

Upon starting to read the applications of category theory collected here, I was particularly interested in Corollary 2.2.10, (and not just because it is named partially after my favorite black hole).

Any group is isomorphic to a subgroup of a permutation group.

The reason for this being precisely the application discussed yesterday, wherein instead of referencing "truth" we simply state that preservation of form must occur while there is an actual shift in analytical identity.

I have been particularly fond of the following channel, having attempted to incorporate it in my classwork.

Mathemaniac does a great job of visualizing the mathematics in question, while showing procedural excellence in teaching as well. I highly recommend this channel.

Similar to me, I was particularly interested given my last post in the similarity between permutation and symmetry. Interestingly, not all permutations related to symmetries--in fact an uneven distribution of location change of all the original vertices led to a skew or distortion in the shape, leading to corruption of form. So, Mathemaniac says that what is really meant is symmetry of form and not permutation of form unless you qualify that "integrity of form is not corrupted", and the fact that is implied is not at all something that follows from the term "permutation". Which is fascinating, because this terminological issue is itself a bit of a category issue.

What I also found fascinating is that we use the equitable rotation in relation to the identity point to establish if symmetry has occurred. This doesn't in anyway require centralization, however, centralized calculations can make checking for symmetrical distribution more cost efficient computationally, creating a standard segment that can be replicated from a certain position and iterating that process the amount of sides on the shape.

How does this relate to graph theory? I will continue to answer the original question, while not forgetting yesterday's paper in the meantime. Hopefully tomorrow I can link the applications of category theory and the paper in the same post. Such is my brain on mathematics...extremely hyper itself!

[numb3rth30ry]

An order 4 permutohedron.

Quoting Wikipedia, “In mathematics, the permutohedron of order n (also spelled permutahedron) is an (n − 1)-dimensional polytope embedded in an n-dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3, ..., n). More generally, the term describes any polyhedron which is the convex hull of a free orbit of the symmetric group Sn acting naturally on R^n. The edge-graph of any permutohedron is the Cayley graph of Sn with respect to the generating set of adjacent transpositions (1,2), . . . , (n − 1,n).”

Mathematics is beautiful. <3

[functor-reality]

yes it is (one can also view it as the length metric in the cayley graph, withot double edges, if one takes each edge to have length one) the actual metric depends on the (finite!) generating set, but only upto quasi isometry

a quasi isometric embedding f is basically an isometry with some constants added (it does not have to be continous anymore)

there is a quasi isometry between two spaces if there is an qi embedding each way and their compositions have finite distance from the respective identities

A good intuitive view of a quasi isometry is - two spaces are quasi isometric if they look the same if i zoom out enough (an integer alttice and a real vectorspace for example, or a group and it's cayley graph)

(a lot of) geometric group theory then is about studying properties of groups and spaces that are invariant under quasi isometry

i do also like algebraic topology and differential geometry/topology so the coice is difficult

you could also choose algebraic geometry if you want groups (or in many cases algebras) "on" your space (sheaves)

That maths poll was interesting but I'd love to hear from people who chose to study maths at a higher level. No "i hate maths" option.

[lawsofemotion]

Updated Chapter 9: Isomorphisms!

[transgenderer]

i wonder if you could reformulate group theory centered on considering a group primarily in terms of the set (or like, object) that its the automorphism group of rather than thinking of it primarily in terms of its like, cayley table/graph

[thejugheadparadox]

ok i talked abt rossetti + elizabeth siddal’s self portrait as part of my art history final 2 years ago and i am dying to know about christina. please

CHRISTINA ROSSETTI!!! i honestly barely knew anything about the portrait before seeing that post i would love to know more. i am so fascinated by christina georgina rossetti born 1830 died 1894, so she’s like ridiculously quintessentially victorian, she basically never knew another monarch. when she was a child she was angry and had a lot of tantrums, her and her brother the painter one dante gabriel were know as the two storms whilst their others siblings maria and william were known as the two calms (suuch classic irritating twee victorian fake middle class art family shit but i find it faintly endearing). she dropped out of school at the age of 14 due to a religious breakdown, and never went back. during and after that she was really fixated on christianity especially anglo-catholicism and its very specific doctrines. she was REALLY into it in a way the rest of her family werent (except her sister who became a nun i guess). she’d been writing poetry since she was very young, cus she’s from this eccentric art dynasty they played writing games as kids and shit - her maternal uncle was john william polidori who wrote the first published vampire story and was lord byrons doctor if that rings any bells? that relation specifically is sooo interesting to me bc its about legacy and who you are remembered as and whether youre noticed and also maybe youre gay? yk. i love it. 

ANYWAYS. she was so into religion that it stopped her getting married twice. she was engaged to the prb painter james collinson for a bit but broke it off bc he reverted to roman catholicism and she couldnt be doing w that shit. she later got engaged to charles cayley and also broke that off for religious reasons! Or At Least Thats What They Say. she also turned down a possible proposal (ppl dont know if he proposed and the whole affair is a guess) from john brett, which she wrote a fun mean poem about called no thank you john. anyway she never married and she pursued lots of Things but none of them really went anywhere, she wanted to be a nurse w florence nightingale in the crimean war but got rejected, she worked with “fallen women” in her 30s and 40s. shes not one of those tragic figures who never knew fame while they were alive tho, she was pretty successful and released multiple collections. she was publicly antifeminist and declined to sign petitions in support of womens suffrage but wrote this one unpublished poem called from the antique that explicitly expresses her dissatisfaction with her limited life as a woman. 

she got ill lots, as is classic for old timey lady poets, like emily dickinson style. she got depressed lots and after her dad died her family didnt have much money. she wrote a lot about inadequacy, as a woman and as a person and most often as a servant of god (every fucking poem ends up about jesus i swear to god it gets annoying). her brother was more successful and her sister was more devout and she never seemed to get the things she wanted and she never really had any friends, especially female ones. almost every time she was published, it was by her brother, william michael, who also published her works en masse after she died, and we have explicit sources showing both her brothers would tell her not to publish poetry they deemed out of character or unwomanly. i dont mean to entirely demonise them as the Bad Guys of the story but i find it very.... interesting that when u look at her poetry that is available but not officially published there are both feminist poems and a couple of pieces that coiuld be interpreted as love poems towards women. there are (admittedly pretty unfounded as far as i can tell) theories that even more of them existed and were destroyed, but i should say we DO know that there are missing poems and destroyed scraps that pique ones interest i will say!

ive read her collected family letters and what stood out to me is HOW ridiculously fucking boring they are. i think theyre hiding something.. i am fascinated by all of it. she interests me. i have some kind of parasocial relationship with her and i feel like her work is SO easy to translate to modern day and what ppl our age are writing about like she wrote what is essentially lonely notes app poetry about religious guilt and sexual repression and hating herself like. god i sound like those ppl who say dantes inferno is fanfic but i think about it a lot and i think about her a lot and i would recommend a lot of her poetry... if anyone wants specific recs do ask. to me its a story about hiding and repression and wanting to be good. jesus christ okay u did not ask for this but youre getting it. you made me start thinking about her again this is on you.