#its simply not applicable to modern society | Explore Tumblr posts and blogs

thatsonemorbidcorvid · 8 months ago

Text

“Many of the women in Heterodoxy moved in corresponding circles and maintained similar beliefs. They were “veterans of social reform efforts,” writes Scutts in Hotbed, and they belonged to “leagues, associations, societies and organizations of all stripes.” A large number were public figures—influential lawyers, journalists, playwrights or physicians, some of whom were the only women in their fields—and often had their names in the papers for the work they were performing. Many members were also involved in a wide variety of women’s rights issues, from promoting the use of birth control to advocating for immigrant mothers.

In the early 20th century, New York City’s Greenwich Village earned a reputation as America’s bohemia, a neighborhood where everyone from artists and poets to activists and organizers came to pursue their dreams.

“In the Village, it was so easy to bump into great minds, to go from one restaurant to another, to a meeting house, to work for a meeting or to a gallery,” says Joanna Scutts, author of Hotbed: Bohemian Greenwich Village and the Secret Club That Sparked Modern Feminism. Here was a community where rents were still affordable, creative individuality thrived, urban diversity and radical experiments were the norm, and bohemian dissenters could come and go as they pleased.

Such a neighborhood was the ideal breeding ground for Heterodoxy, a secret society that paved the way for modern feminism. The female debating club’s name referred to the many unorthodox women among its members. These individuals “questioned forms of orthodoxy in culture, in politics, in philosophy—and in sexuality,” noted ThoughtCo. in 2017.

Born as part of the initial wave of modern feminism that emerged during the 19th and early 20th centuries with suffrage at its center, the radical ideologies debated at Heterodoxy gatherings extended well beyond the scope of a women’s right to vote. In fact, Heterodoxy had only one requirement for membership: that a woman “not be orthodox in her opinion.”

“The Heterodoxy club and the work that it did was very much interconnected with what was going on in the neighborhood,” says Andrew Berman, executive director of Village Preservation, a nonprofit dedicated to documenting and preserving the distinct heritage of Greenwich Village. “With the suffrage movement already beginning to crest, women had started considering how they could free themselves from the generations and generations of structures that had been placed upon them.”

Unitarian minister Marie Jenney Howe founded Heterodoxy in 1912, two years after she and her husband, progressive reformer Frederic C. Howe, moved to the Village. “Howe was already in her 40s,” says Scutts, “and just got to know people through her husband’s professional connections, and during meetings and networks where progressive groups were very active at the time.”

Howe’s mindset on feminism was clear: “We intend simply to be ourselves,” she once said, “not just our little female selves, but our whole big human selves.”

Many of the women in Heterodoxy moved in corresponding circles and maintained similar beliefs. They were “veterans of social reform efforts,” writes Scutts in Hotbed, and they belonged to “leagues, associations, societies and organizations of all stripes.” A large number were public figures—influential lawyers, journalists, playwrights or physicians, some of whom were the only women in their fields—and often had their names in the papers for the work they were performing. Many members were also involved in a wide variety of women’s rights issues, from promoting the use of birth control to advocating for immigrant mothers.

Heterodoxy met every other Saturday to discuss such issues and see how members might collaborate and cultivate networks of reform. Gatherings were considered a safe space for women to talk, exchange ideas and take action. Jessica Campbell, a visual artist whose exhibition on Heterodoxy is currently on display at Philadelphia’s Fabric Workshop and Museum, says, “Their meetings were taking place without any kind of recording or public record. It was this privacy that allowed the women to speak freely.”

Scutts adds, “The freedom to disagree was very important to them.”

With 25 charter members, Heterodoxy included individuals of diverse backgrounds, including lesbian and bisexual women, labor radicals and socialites, and artists and nurses. Meetings were often held in the basement of Polly’s, a MacDougal Street hangout established by anarchist Polly Holladay. Here, at what Berman calls a “sort of nexus for progressive, artistic, intellectual and political thought,” the women would gather at wooden tables to discuss issues like fair employment and fair wages, reproductive rights, and the antiwar movement. The meetings often went on for hours, with each typically revolving around a specific subject determined in advance.

Reflecting on these get-togethers later in life, memoirist Mabel Dodge Luhan described them as gatherings of “fine, daring, rather joyous and independent women, … women who did things and did them openly.”

Occasionally, Heterodoxy hosted guest speakers, like modern birth control pioneer Margaret Sanger, who later became president of the International Planned Parenthood Federation, and anarchist Emma Goldman, known for championing everything from free love to the right of labor to organize.

While the topics discussed at each meeting remained confidential, many of Heterodoxy’s members were quite open about their involvement with the club. “Before I’d even heard of Heterodoxy,” says Scutts, “I had been working in the New-York Historical Society, researching for an [exhibition on] how radical politics had influenced a branch of the suffrage movement. That’s when I began noticing many of the same women’s names in overlapping causes. I then realized that they were all associated with this particular club.”

These women included labor lawyer, suffragist, socialist and journalist Crystal Eastman, who in 1920 co-founded the American Civil Liberties Union to defend the rights of all people nationwide, and playwright Susan Glaspell, a key player in the development of modern American theater.

Other notable alumni were feminist icon Charlotte Perkins Gilman, whose 1892 short story, “The Yellow Wallpaper,” illustrates the mental and physical struggles associated with postpartum depression, and feminist psychoanalyst Beatrice M. Hinkle, the first woman physician in the United States to hold a public health position. Lou Rogers, the suffrage cartoonist whose work was used as a basis for the design of Wonder Woman, was a member of Heterodoxy, as was Jewish socialist activist Rose Pastor Stokes.

Grace Nail Johnson, an advocate for civil rights and an influential figure in the Harlem Renaissance, was Heterodoxy’s only Black member. Howe “had personally written to and invited her,” says Scutts, “as sort of a representation of her race. It’s an unusual case, because racial integration was quite uncommon at the time.”

While exceptions did exist, the majority of Heterodoxy’s members were middle class or wealthy, and the bulk of them had obtained undergraduate degrees—still very much a rarity for women in the early 20th century. Some even held graduate degrees in fields like medicine, law and the social sciences. These were women with the leisure time to participate in political causes, says Scutts, and who could afford to take risks, both literally and figuratively. But while political activism and the ability to discuss topics overtly were both part of Heterodoxy’s overall ethos, most of its members were decidedly left-leaning, and almost all were radical in their ideologies. “Even if the meetings promoted an openness to disagree,” says Scutts, “it wasn’t like these were women from across the political spectrum.”

Rather, they were women who inspired and spurred each other on. For example, about one-third of the club’s members were divorced—a process that was still “incredibly difficult, expensive and even scandalous” at the time, says Scutts. The club acted as somewhat of a support network for them, “just by the virtue of having people around you that are saying, ‘I’ve gone through the process. You can, too, and survive.’”

According to Campbell, Heterodoxy’s new inductees were often asked to share a story about their upbringing with the club’s other members. This approach “helped to break down barriers that might otherwise be there due to their ranging political views and professional allegiances,” the artist says.

The Heterodoxy club usually went on hiatus during the summer months, when members relocated to places like Provincetown, Massachusetts, a seasonal outpost for Greenwich Village residents. As the years progressed, meetings eventually moved to Tuesdays, and the club began changing shape, becoming less radical in tandem with the Village’s own shifting energy. Women secured the right to vote with the ratification of the 19th Amendment in 1920, displacing the momentum that fueled the suffrage movement; around this same time, the Red Scare saw the arrests and deportations of unionists and immigrants. Rent prices in the neighborhood also increased dramatically, driving out the Village’s bohemian spirit. As the club’s core members continued aging, Heterodoxy became more about continuing friendships than debating radical ideologies.

“These women were not all young when they started to meet,” says Scutts in the “Lost Ladies of Lit” podcast. “You know, it’s 20, 30 years later, and so they stayed in touch, but they never really found the second generation or third generation to keep it going in a new form.”

By the early 1940s, the biweekly meetings of Heterodoxy were no more. Still, the club’s legacy lives on, even beyond the scope of modern feminism.

“These days, it’s so easy to dehumanize people when you’re only hearing one facet of their belief system,” says Campbell. “But the ability to change your mind and debate freely like the women of Heterodoxy, without any public record? It’s an interesting model for rethinking the way we talk about problems and interact with other people today.”

97 notes · View notes

creatingblackcharacters2 · 2 months ago

Text

How to spot a Stereotype: An Example

Okay, so I talked about this in my Lesson 6 Stereotypes series, but I feel like people haven't quite... Understood what I meant. So I'm doing a mini lesson/application. First, I'd really appreciate it if you take the time to read the links in my posts, because that will provide you the historical and social context necessary. If you lack it, you will never be fully able to understand this. Remember, all I do here is provide the beginning steps. You have to be willing to do the rest!

One thing I constantly emphasize is that it's not the description of a character that (always) reveals an existing stereotype, but the writing! And again, until you grasp why anti-Black stereotypes are what they are, you will continue to be frustrated with how to avoid incorporating them, both in your writing and in your mindset. I'm going to use one stereotype as an example.

The Mammy Stereotype

"[Black woman character] is very fond, doting, and protective. She's like the team mom of the group."

On the surface, people who are worried about this stereotype will worry, because Black readers have long rolled their eyes and said we're tired of seeing this as one of the Only Options for Black women characters. And we are. Here's the disconnect: the attributes are not what we're tired of, but how they were utilized in the writing- often by non-Black writers!

Mammy: put simply, the caricature of the Mammy is the Black nursemaid that would take care of the Master's white children and the Mistress, prioritizing them above the well-being of herself, her own children, and her own community. She is fat and homely (so as not to attract the Master from the Mistress), unthreatening, sweet and subservient.

In other words, the only value she held was to serve white people's needs (and quench their guilt).

While the image of the Mammy herself is a strong imagery that has faded from its specific origin, I would say the modern day fan archetypes that ring of the Mammy stereotype are the Black woman character that "holds the Braincell", the "begrudgingly fond mother of the group", the canon love interest now relegated to the "mommy/mean lesbian" whose feelings are erased altogether, her new role to help the two white characters get together without acknowledgment of her own potential. She has no real story of her own, or as mentioned, has her own story stolen because "it doesn't look good with her in it" (which is its own bag of worms).

Now, people often give these characters motherly (or what society deems motherly) traits: caring, sweet, protective, loving, self sacrificial. Because they want to defensively show that "they're a great person! Nothing bad! I still think they're good! I'm not racist!"

But upon learning of the stereotype, there appears this insecurity- "oh, my Black woman character has these traits, is she playing into this stereotype?" When you get to this question, what you really need to be asking yourself is:

What makes the Mammy a Mammy?

They are a tool, a utility to white people with more power.

They lack autonomy. How they feel is irrelevant, if it does not serve the white person.

Nonthreatening so as to feel "harmless" to white people who bask in her "selfless" care.

They are not allowed to show frustration or upset at their lot or at life; it is seen as a negative attribute because if they are not caring, they have no use (and may now even be considered a threat).

They will also disagree with anyone else, even to the detriment of themselves, to the benefit of the white person. This is considered "selfless", rather than sacrifice (consider that "real" Mammies were originally slaves. They probably hated every single day with the people they "cared" for, but God forbid they speak on it. To white people, they were supposedly so happy and grateful! Smile and nod!)

Notice, out of the things I listed, "strong", "protective", "intelligent", and "caring" (on its own) weren't there! Because those aren't bad attributes for a Black character to have! Why would we ever suggest that?? Why would I be mad that a Black woman was any of those wonderful things to her peers? That's not the issue. The issue is that they are often used in service of usually white characters and their stories. They're a tool of the writer to coddle their white characters, versus a character that has their own inner workings and existence.

Knowing what you know now; things that would make your strong, protective, and caring Black woman character fit the Mammy stereotype can include:

If she is pushed to the side with no autonomy or inner life of her own, as the narrative centers the white characters and their needs.

If she is never shown to have any reason for acting outside of to the benefit of the white characters around her. That's the only time her presence counts.

If her disagreeing with, getting upset with, or refusing (or really, just not being "motherly") the white characters is deemed trashy by the narrative (whereas anyone else receives nuance or reason for their behavior).

If the white characters in the story treat her poorly, and it is treated as a good thing that she "stays calm" without any sort of reflection on her feelings.

You can come up with any sort of setting, plot scenario, and description of your Black woman character. But at the end of the day, what's going to make it the stereotype is how the narrative treats her, which you will only find out by writing it, and then reviewing your own work!

You're going to have to approach any stereotype this way. It's part of the *intent* thing I keep pushing 😅 if you don't intend to write a stereotype, you're going to have to actively understand what it is, which will help you actively avoid it.

#creatingblackcharacters #antiblackness #stereotypes #black character design

36 notes · View notes

dailycharacteroption · 2 days ago

Text

Pathfinder Agent (Pathfinder Second Edition Archetype)

(art by Sucdeportocale on DeviantArt)

With how vast the Pathfinder setting is, it can sometimes be hard to remember that an important detail of it is the titular Pathfinder Society from which the system gets it’s name.

Focused on archeological and heroic motivations over desires for wealth, the society seeks to recover the secrets and relics of the past and make sure that the more dangerous entities and artifacts are dealt with properly and responsibly. They might not always succeed, but by and large their hearts are in the right place.

It only makes sense then that there would be training regimen to help the agents of the society survive and do well in the ancient wonders and ruins they seek and explore.

Indeed, this archetype is a nod and draws plenty of inspiration from the various Pathfinder prestige classes of the previous edition, such as chroniclers, field agents, delvers, and savants, with the majority of its focus being on the middle two of those. This makes sense given the role this modern archetype is meant to embody.

So let’s take a moment and look at what these agents have to offer, shall we?

The base dedication of the archetype improves the agent’s skills as they learn multiple things to help diversify their abilities, including bolstering their otherwise untrained skills. Additionally, they gain access to the signature wayfinders carried by all agents.

Tombs and ruins are often laden with traps, and many agents train to notice them even when performing other activities.

Said complexes are often very complicated, and some learn to keep careful track of their own movements in order to keep track of their sense of direction.

Teamwork keeps the whole expedition alive, and so many train to aid their allies so well that they gain some of the same benefits too, improving their own aim, defensive ability, or follow-up actions as a result.

Some also learn to reflexively look out for more broad environmental hazards, not just actively malicious traps.

This can also be trained to apply to hidden creatures as well, helping them notice ambushes before they happen.

They are also often trained in bestiary studies, to better know what they are up against when facing down various monsters.

Haunts too are not safe from their perceptive notice.

Thorough note-taking comes in handy, especially when facing certain types of monsters repeatedly, allowing them to notice or recall additional facts later.

Seeing an expert in action is a very useful skill to have in dangerous situations, and these explorers often learn to perfectly imitate the actions of a more skilled individual when performing the same task, such as where to step while moving over narrow ledges, and so on.

Some of the more mystical and curious among them tinker with their wayfinder, unlocking a bit of magic in the form of a cantrip of their choice and the ability to disguise their wayfinder as an unassuming accessory.

When danger is imminent, many reflexively act to warn others, getting them ready for the impending conflict.

Sometimes the work of acquiring a lost relic means making a quick replacement to fool casual inspection. Stealing an item from a treasure vault, tossing the fake somewhere where the bad guy will be fully occupied trying to get it, or simply handing it over to the bad guy to buy time to get the real way safely away. However, these fakes rarely stand up to close examination.

Many also learn not just the nature of many monsters but also their vital areas, letting them strike with the intent of bleeding said foes.

While any brute can force a door open, stronger pathfinder agents often learn to break open doors with precise application of force to just the right area.

Some learn to use their wayfinders to store a little extra magic, giving them an extra casting of one of their minor spells.

Honing their powers of recollection and information processing, some can recall information about multiple foes at once.

They can even recall information in the blink of an eye, which can mean life or death against certain foes.

There are many dangerous effects that can leave allies reeling and unable to act at their fullest when it’s needed most, so some learn to quickly refocus their allies to bring them back to their senses.

The more magical often learn to use the magic of their wayfinders to change their appearance and disguise the item itself as another badge of office.

Whether it’s an ancient text while monsters batter down the door, a bas relief threatening to crumble into the sea, or a similar situation, sometimes an archaeologist needs to memorize a lot of information quickly. So, some agents learn to hone their recollection to replicate the information later in a more portable medium.

When they realize they’re about to accidentally set off a trap, many Pathfinders have the wherewithal to warn their allies so that they can better avoid or resist the effects.

More battle-savvy members learn how to analyze their foes to pinpoint their greatest vulnerabilities and resistances.

Inevitably, most Pathfinders acquire a lot of different magical items, but the nature of magical investure means that one can normally only make use of so many at once. However, in an emergency, some of these agents can quickly swap out and re-invest a new item on the fly, giving them some more flexibility.

There are a lot of abilities to choose from here, so there’s something for everyone. Everything from improving knowledge checks against enemies to trap utility to some bonus magic and trickery. You definitely won’t be able to take it all, but if any of these abilities appeal to you and you want to play up your character’s connection to the society, this archetype may be for you. Be warned though, if you’re looking to view this archetype in it’s original written form, all of these abilities are split between three books, with two of them adding to the original. The drawbacks of adding to pre-existing content.

With such diverse abilities ranging from scholarly to practical, it’s clear that the Pathfinder Society actively encourages it’s members to pursue their own individual paths to mastery at their own pace and goal, which is pretty neat. Of course, you can use this archetype for any sort of adventuring or archaeological organization just fine with some tweaking.

After being refused access to the magistrate’s vault to reference a tablet within, the party is forced to use their talents to break in and study it directly. However, the party ends up encountering a group of ninja while on the heist. Are they guardians hired to protect the vault, or assassins with a mission of their own? There is little time to ponder such questions, as the fight threatens to alert the other guardians.

Normally content to explore alone, the android scholar Analysis-707 occassionally returns to civilization to recruit adventurers for larger expeditions. This time, however, he seems even more withdrawn than usual about what it is that he’s discovered and wants to explore, putting the rest of the crew on edge.

The mystery of what happened to the mighty angelic general Monvial has been lost to time, but it is said that the ruins of is last known location, the forgotten city of Gussk, may hold the answer… Those who dare to seek it discover the horrifying truth in a mural that reveals Monvial’s fall from grace and transformation into the entity Laivnom, a mighty Rhevanna and enemy to all celestials and goodness.

#pathfinder second edition #archetype #pathfinder agent #android #rhevanna #World Guide #PFS Guide #Character Guide

8 notes · View notes

hummussexual · 1 year ago

Text

Excerpt:

Pinkwashing’s relationship with homonationalism and Orientalism

The pinkwashing carried out by Israeli authorities is based on an Orientalist view that Palestinians remain “backwards” in their stance on homosexuality because apparently, we refuse to emulate the progressiveness of the west.

To be “gay friendly,” as gender studies academic Jasbir Puar explains, is to be modern, cosmopolitan, developed, first-world, Global North, and, most significantly, democratic – something that Palestinians supposedly do not have the capability of ever achieving.

This erases the agency of Palestinians, especially the progressive forces inside Palestine – including the achievements of queer Palestinian movements. The Orientalist tropes found in pinkwashing also completely disregards the history and legacies of colonialism and modern-day imperialism in the region. It is an example of euro-centric, western exceptionalism – and a pillar of anti-Arab racism.

Pinkwashing and homonationalism also go hand in hand. First coined by Puar in 2007, the concept of homonationalism argues that western LGBTQI+ movements are often bound up with upholding the racist sovereignty of the nation state. Puar argued that neoliberal and capitalist power structures line up with the queer liberation movement by using sexual diversity and LGBTQI+ rights to peddle or maintain nationalist stances – such as anti-immigration policies which are based on prejudices that the “other” are homophobic and that western society is egalitarian.

For Israel, homonationalism is deployed to justify its own exceptionalism and violent oppression of the “other” – in this case, Palestinians.

Israel flaunts its liberal openness to homosexuality while contrasting it to the sexual oppression among Palestinian society and neighbouring Arab countries. It therefore serves as an excuse for Israel to rationalise its occupation of Palestinians, and to “liberate” oppressed Palestinian queers. The latter is seen through Israel’s myths about “saving” Palestinian queers by “regularly” approving their asylum seeker applications to escape their homophobic and oppressive families or communities in the West Bank or Gaza.

While it’s hard to verify how often these asylum seeker approvals occur, waxing lyrical about their supposed humanitarian work plays into the homonationalist narrative. Since when are immigration authorities – not just in Israel, but any immigration (or border) authority globally – benevolent, progressive entities full of empathy and care? Let alone towards Arabs?

As Queers Against Israeli Apartheid once pointed out, “there is no pink door in the apartheid wall.” This means that like every other Palestinian, LGBTQI+ Palestinians are also at the mercy of Israel’s violent, racist settler-colonial project. This is because queer Palestinians simply do not fit into Israel’s homonationalist quest to uphold the racist sovereignty of its nation state – one where a legally-enforced apartheid system puts only Jewish people at the top of the pyramid.

#pinkwashing #israel #zionism #zionist entity #zionism is racism #lgbt #queer #politics #settler colonialism #palestine #elias jahshan #Hayfaa Chalabi #jasbir puar

98 notes · View notes

regencyama · 6 months ago

Text

The 4 Realities of Writing for a Historical Fandom

The example I use for this is Bridgerton but it's applicable for any fandom where the canon era is in the past.

When you write canon-era fic for a historical fandom, there are 4 things to keep in mind:

The Canon

Actual History

Your Plot

Readers' Expectations

The Canon

Unless you're going against canon, the way the original media depicts the era it's set in is your best guide to writing for that era (and the easiest to research). Bridgerton's laudable racial integration and inaccurate but still beautiful dresses have little to do with actual Regency Era England, but for the most part, the show is correct about the ton and its social mores.

***

Actual History

Knowing what actually happened in the original media's canon era gives you a deeper understanding of that era and helps you write a better fic. I was fortunate to have gone through a Regency Era phase long before Bridgerton started, so I already had resource books about the era at hand. (I highly recommend What Jane Austen Ate and Charles Dickens Knew: From Fox-Hunting to Whist -- the Facts of Daily Life in 19th-Century England by Daniel Pool and An Elegant Madness: High Society in Regency England by Venetia Murray, both available at Amazon.)

Wikipedia is also invaluable, especially if you're on a tight budget -- start with the name of the era you're researching and have fun falling down the rabbit hole. Bookmark any pages that are appropriate and you'll end up with your own personalized wiki.

***

Your Plot

Most of the time, your story's plot will be the deciding factor in what you chose to include or ignore, but sometimes changing the plot even slightly in favor of historical accuracy can improve it. Your leads aren't married yet but need to have a private conversation? Put a chaperone in the room, thus forcing your leads to either say what need to say in an oblique way or find another creative solution to their sudden lack of privacy.

***

Readers' Expectations

There are times when you may need to sacrifice accuracy in order to make your story more appealing or better understood. One example of this comes from Bridgerton itself. Before Queen Victoria wore a white gown in her 1840 wedding, white wedding gowns were not the norm. Daphne's 1813 wedding gown in S1 could have been one of several other colors but because modern audiences expect to see a Western bride in white, that's the color the costume designer gave her.

***

Ideally, all four would work together but in many cases, that simply cannot happen, so you must decide which of the four you're going to sacrifice, and that decision will likely be made several times over the course of writing your fic.

Most of all, have fun. If something simply isn't working for you, change it. Knowing the history, the canon, and the expectations gives you options, it's up to you to decide what works best.

#bridgerton #regency era #regency era ama #writing #writing resources

8 notes · View notes

thelioncourts · 4 months ago

Note

i read the thing in the original pilot script, he saying he was his mother's man etc and since they eventually dropped that (or were they stopped idk) i hope it'll be like u said, but i dont even want to see a kiss shdgfjkd. yeah all these jokes by the cast and the official account make me uncomfortable tho. not everything need to be the same in the amc adaption

I get it being uncomfortable and, unfortunately for a lot of people, gothic storytelling often depicts some kind of incest. gabrielle in particular really showcases almost every trait seen in traditional female gothic lit

Female Gothic novels also address women's discontent with patriarchal society, their difficult and unsatisfying maternal position, and their role within that society. Women's fears of entrapment in the domestic, their bodies, marriage, childbirth, or domestic abuse commonly appear in the genre.

there's also this interest in the gabrielle/lestat thing because incest - while always taboo - is almost always fathers/daughters or siblings in commonality. mother/son or father/son or mother/daughter, etc. are rarer. we do see it in media, look at the classic oedipus rex or bates motel (and i think house of the dragon just did some too (??), but it's still rarer and definitely causes a different kind of stir among watchers.

I think part of why it will be discussed in the show, beyond what I've already said, is that part of the horror of it all is how mother/son incest subverts the traditional maternal instinct. there's this really great read by diplacadi where she states

...mothers are assumed incapable of assaulting their sons because ‘they lack the sexual equipment necessary for direct sexual agency or assault. Without a penis women are assumed to be the acquiescent objects, not the active agents, of sexual acts. The idea of women as actively assaulting men sexually is such a troubling idea to normative definitions of female agency that the existence of such acts is often dismissed. Though McKinnon refers to the way modern Americans view the role of the mother, its applicability to the British eighteenth- and nineteenth- century Gothic is aptly demonstrated in her assertion that: ‘the only way to account for the contravention of the “natural” is by conjuring the “unnatural” – a woman whose intellectual deficiency or psychological pathology completely undermines her maternal nature

now, it's important for us to note that in the books gabrielle and lestat do not have sex and, again, I don't see them doing that. but gabrielle crosses boundaries with lestat - heavily because of her lack of maternal feeling and also because of how she is lestat, she is him in her head, they are the same as she does not relate to her feminine side at all but thrives in her masculinity that she envies lestat for being and having. to her, he is not quite a son as much as the person she was supposed to be, so sharing about how she wants to murder her husband and other sons and sharing how she wants to have the village men do things to her simply for the thrill of causing a scene isn't her sharing with her son - to her - but sharing with a friend, with herself.

I think a kiss between lestat and gabrielle, something that happens in the book, can be expected in the show. and yeah, it sucks, but I think it's going to be how we're also, at some point, going to see armand in his worship of marius, something that will make us all sick to witness but will add to the horror.

in an ideal, lestat is going to realize his worth outside of his mother in the show and maybe not be quite so invested in her. not saying I don't think she's important or that he should have no relationship of any kind with her, but I think if we're going to acknowledge marius' abuse we have to acknowledge gabrielle's. and I think the show has the potential to do all of that while staying true to the story but being. better than it. something the show does with 99% of AR material.

and this isn't even getting into covert incest and the way lestat becomes the father/provider of his house because of his own father's abuse and failure and so, in turn, his father makes him his mother's husband in a lot of ways but !

#i am sorry it makes you uncomfortable though!#i read too much gothic shit and have read and seen too many things with the horror of incest so #i'm fairly numb to it in terms of shock

4 notes · View notes

nicklloydnow · 1 year ago

Text

“Against the World, Against Life

More so today than ever before, Lovecraft would have been a misfit and a recluse. Born in 1890, he already appeared to his contemporaries, in the years of his youth, to be an obsolete reactionary. It's not hard to imagine what he would have thought of our society today. Since his death, it has not ceased evolving in a direction which could only have led him to hate it more. Mechanization and modernization have ineluctably destroyed the lifestyle he was attached to with his every fiber (it is not as if he harbored any delusions about humanity's ability to influence events; as he wrote in a letter, "Everything in modern existence is a direct & absolute corollary of the discoveries of applied steam power & of large-scale applications of electrical energy"). The ideals of liberty and of democracy that he so abhorred have spread all over the planet. The man who declared: "What we detest is simply change itself" could only have bristled at the degree to which the idea of progress has come to be an indisputable and almost unconscious credo. The reach of liberal capitalism has extended over minds; in step and hand in hand with it are mercantilism, publicity, the absurd and sneering cult of economic efficiency, the exclusive and immoderate appetite for material riches. Worse still, liberalism has spread from the domain of economics to the domain of sexuality. Every sentimental fiction has been eradicated. Purity, chastity, fidelity, and decency are ridiculous stigmas. The value of a human being today is measured in terms of his economic efficiency and his erotic potential — that is to say, in terms of the two things that Lovecraft most despised.

Horror writers are reactionaries in general simply because they are particularly, one might even say professionally, aware of the existence of Evil. It is somewhat curious that among Lovecraft's numerous disciples, none has been struck by this simple fact: the evolution of the modern world has made Lovecraftian phobias ever more present, ever more alive.

(…)

True, this is a treacherous path that only leads to narrow straits. Not because of censorship or litigation. Horror writers probably feel that marked hostility toward any form of freedom in the end breeds hostility to life itself. Lovecraft felt the same way, but he did not stop halfway; he was an extremist. That the world was evil, intrinsically evil, evil by its very essence, was a conclusion he had no trouble reaching, and this was also the most profound meaning of his admiration for Puritans. What amazed him about them was that they "hated life and scorned the platitude that it is worth living." We shall traverse this vale of tears that separates birth from death, but we must remain pure. HPL in no way shared the hopes of Puritans; but he shared their refusal. He explained his point of view in a letter to Belknap Long (written, moreover, only a few days before his marriage):

"And as for Puritan inhibitions—I admire them more every day. They are attempts to make of life a work of art—to fashion a pattern of beauty in the hog-wallow that is animal existence— and they spring out of that divine hatred of life which marks the deepest and most sensitive soul."

Toward the end of his days, he did come to, at times, express poignant regrets in the face of the solitude and perceived failure of his existence. But his regrets remained, if one might express them thus, theoretical. He remembered the periods in his life (the end of adolescence, the brief and decisive interval of marriage) where his path might clearly have bifurcated toward what is called happiness. But he understood that he was probably incapable of behaving any other way. And in the end, like Schopenhauer, he concluded that he hadn't fared too badly.

He faced death with courage. Struck by intestinal cancer that spread to his entire upper body, he was transported on March 10, 1937, to the Jane Brown Memorial Hospital. He was an exemplary patient, polite, affable, whose stoicism and courtesy impressed all the nurses, in spite of his very intense physical suffering (thankfully attenuated by morphine). He underwent the pangs of death with resignation and perhaps with a certain secret satisfaction. This life that was leaving behind its carnal envelope was his old enemy; he had denigrated it, fought it, he would not utter a single word of regret. And he passed away, without further incident, on March 15, 1937.

As biographers have said, "Lovecraft died, his work was born." And indeed, we have just begun to put him in his true place, equal or superior to that of Edgar Poe—in any event, resolutely unique. In the face of the repeated failure of his literary creations, he at times felt the sacrifice of his life had actually been in vain. Today we can pronounce a different judgment; we can, for he has been our essential guide, taking us on initiatory journeys to different universes that lie somewhere well beyond the limits of human experience, but that provoke in us a precise and terrible emotional impact.

This man, who did not succeed at life, did indeed succeed at writing. It was hard for him. It took him years. New York helped him. He who was so gentle, so courteous, discovered hatred there. Returning to Providence, he composed the magnificent tales that vibrate like incantations, that are as precise as a dissection. The dramatic structure of the "great texts" is impressively complex; the narrative procedures are precise, new and bold. Perhaps all this would not suffice were it not that at the center of the ensemble, one feels the power of a consuming interior force.

Every great passion, be it love or hate, will in the end generate an authentic work. One may deplore it, but one must recognize it: Lovecraft was more on the side of hate; of hate and fear. The universe, which intellectually he perceived as being indifferent, became hostile aesthetically. His own existence, which might have been nothing but the sum of banal disappointments, turned into a surgical operation, and an inverted celebration.

The work of his mature years remains faithful to the physical prostration of his youth, transfiguring it. This is the profound secret of Lovecraft's genius, and the pure source of his poetry: he succeeded in transforming his aversion for life into an effective hostility.

To offer an alternative to life in all its forms constitutes a permanent opposition, a permanent recourse to life—this is the poet's highest mission on this earth. Howard Phillips Lovecraft fulfilled this mission.” - Michel Houellebecq, ‘H. P. Lovecraft: Against the World, Against Life’ (1991) [p. 135 - 140]

#lovecraft #hp lovecraft #houellebecq #michel houellebecq #efilism #cosmicism #horror #puritans #puritanism

7 notes · View notes

hunting-songs · 8 months ago

Text

BOLD THE FACTS for Senritsu Döne

The Rules are simple! Tag people and name a character you want to know more about! If you want to let the person you tagged decide who to showcase, then don’t name a character and they can pick somebody. Easy! The person who is tagged will then bold the remarks below which apply to their character &, if they want to, include a picture with their reply! Tagged By: A little birdie! Tagging: YOU!

[ PERSONAL] $ Financial: wealthy/ moderate / poor / in poverty While Senritsus paycheck literally is a Hunters Mafiamoney, there are a few art-organisations and Music-Schools that are on her donation-list. So she falls in the usual hunter-category: She earns a lot of money but rarely uses it for herself, because she is too busy risking her life for her passion.

✚ Medical: fit / moderate / sickly / disabled / disadvantaged / non applicable If Senritsu would be dragged back to an actual doctor she would probably asked how it comes that she is still alive, since not even her organs are on the right place/ in the right shape anymore.

✪ Class or Caste: upper /middle / working / unsure / other Senritsu specifically hails from a group of people that would be best described as "Fahrendes Volk"= "Travelling People", who specifically consist of everyone society would not like to have around and are therefor chosing to wander to avoid prosecution/ because as said, noone wants them to stay: Thiefs, (grave)robbers, prostitutes, vagrant Minstrels, Criminals, Vagabonds .... To put her in a class would be therefor against anything she grew up with, because the group specifically is outside of society and therefor also outside of its protection.

✔ Education: qualified/ unqualified / studying /other ✖ Criminal Record: yes, for major crimes / yes, for minor crimes / no/ hascommitted crimes, but not caught yet /yes, but charges were dismissed

[ FAMILY] ◒ Children: had a child or children /has no children / wants children

◑ Relationship with Family: close with sibling(s) / not close with sibling(s) / has no siblings / sibling(s) is deceased

◔ Affiliation: orphaned / adopted/ disowned / raised by birth parent / not applicable

[ TRAITS + TENDENCIES] ♦ extroverted / introverted /in between ♦ disorganized / organized / in between ♦ close minded /open-minded/ in between ♦ calm/ anxious / in between ♦ disagreeable /agreeable/ in between ♦ cautious/ reckless/ in between ♦ patient/ impatient/ in between ♦ outspoken / reserved / in between ♦ leader/ follower / in between ♦ empathetic / vicious bastard / in between ♦ optimistic / pessimistic / in between ♦ traditional / modern/in between ♦ hard-working / lazy / in between ♦ cultured /uncultured / in between/ unknown ♦ loyal/ disloyal / unknown ♦ faithful/ unfaithful / unknown

[ BELIEFS] ★ Faith: monotheist / polytheist / atheist / agnostic

☆ Belief in Ghosts or Spirits: yes/ no / don’t know / don’t care

✮ Belief in an Afterlife: yes /no/ don’t know/don’t care Not religious as she is, Senritsu thinks that everything paranormal can be explained with Nen. And as Nen does not always disappears after death, she thinks that when someone dies they just disappear, but their Aura stays depending on their strongest emotions. What is left behind is of course not the person, but simply a echo of their strongest emotions.

✯ Belief in Reincarnation: yes / no / don’t know /don’t care

❃ Belief in Aliens: yes / no / don’t know/ don’t care

✧ Religious: orthodox / liberal / in between / not religious

❀ Philosophical: yes/ no

[ SEXUALITY & ROMANTIC INCLINATION ] ❤ Sexuality:heterosexual / homosexual / bisexual/ asexual / pansexual

❥ Sex: sex repulsed / sex neutral / sex favorable / naive and clueless

♥ Romance: romance repulsed / romance neutral / romance favorable /naive and clueless / romance suspicious

❣ Sexually: adventurous / experienced / naive / inexperienced / curious

⚧ Potential Sexual Partners: male / female / agender / other / none / all

⚧ Potential Romantic Partners: male / female / agender / other / none / all

[ ABILITIES ] ☠ Combat Skills: excellent / good/ moderate / poor/ none

≡ Literacy Skills: excellent/good / moderate / poor / none

✍ Artistic Skills: excellent / good / moderate / poor/ none

✂ Technical Skills: excellent / good/ moderate / poor / none

[ HABITS ] ☕ Drinking Alcohol: never / special occasions/ sometimes / frequently / Alcoholic Since that night Senritsu had never been drunk. She however would indulge in a after-work-beer with her colleagues frequently and drink a glass of wine for special occasions. She would never go above that one wineglass or that one beerbottle.

☁ Smoking: tried it / trying to quit / quit / never/ rarely / sometimes / frequently / Chain-smoker

✿ Recreational Drugs: never/ special occasions / sometimes / frequently / addict

✌ Medicinal Drugs: never / no longer needs medication /some medication needed/ frequently / to excess *Senritsu frequently takes painkillers. She dos not like to think about the state of her kidneys.

☻ Unhealthy Food: never / special occasions / sometimes /frequently / binge eater

$ Splurge Spending: never / sometimes/ frequently / shopaholic

♣ Gambling: never / rarely /sometimes / frequently / compulsive gamble

#hunting-songs: headcanon #hunting-songs #there IS a reaon that Senritsu always has a yellow detail on her clothes #its the colour of the Fahrendes Volk in medieval age. For example prostitues needed to wear yellow bracelet /yellow bow on their cloth #Now senritsu is not living in medieval age. but its still straightforward symbol to use

4 notes · View notes

lingshanhermit · 11 months ago

Text

Lingshan Hermit: On the Difference Between Eastern and Western Cultures

Max Weber said, "Confucian culture is not a practical study, but only a set of value systems for maintaining social order. Schools did not teach mathematics, natural science or geography, and the people they cultivated had no logical creativity." As you know, this is not the first time I have brought out Max Weber to criticize, and certainly it won't be the last. As far as I know, Weber's view is no longer solely his own today, and this understanding has already become the consensus of many in academia. As for the general public, although they know almost nothing about Confucianism, this does not prevent them from holding similar views.

In my last discussion about Max Weber, I talked about what constitutes useful knowledge. This time I intend to talk about the origins, differences and foundations of Chinese and Western cultures. For a long time, I have always wanted to write an article on the differences between Chinese and Western cultures. To be blunt, in my range of reading over the years, I have hardly seen anyone who could really articulate Chinese culture clearly. In recent years, I have been observing the culture left behind by the Eastern sages and observing its effects on the Chinese people, observing its application in East Asian life. I have also been observing Western society and Western culture. This kind of observation has sometimes provoked in me a strong sadness - especially when I see many Orientals who completely misunderstand and strongly reject Eastern culture. This also gives me a stronger motivation to write this article.

From the perspective of modern utilitarianism, traditional Chinese culture seems to be completely useless - or more precisely, useless. According to modern definitions of "usefulness", Eastern traditional culture has hardly invented anything that you would consider useful. It has no irons, no Uber software, no instant coffee or mechanical keyboards. Chinese society has also not nurtured a Faraday or a Rutherford. From an empiricist point of view, you do not see anyone becoming a Buddha or gaining immortality, nor do you see the gentleman advocated by Confucianism. On the contrary, you do tend to see many hypocrites. Therefore, many people come to the preposterous conclusion that traditional culture is completely fraudulent. For most ordinary people, these traditional cultures are of almost no help at all to their daily lives - most people believe that they are just a bunch of big, empty and useless words. The states described in traditional culture are like living in the clouds, completely disconnected from people's real lives. They require people to do things that are simply impossible. They are not like the Talmud, which points out every aspect of life, even telling you what time you should get up, what kind of wife you should marry, and whose money you should earn. When you encounter specific problems, you go to a psychologist or lawyer, not to Confucius or Mencius, because for the masses, their words are too vague and of no practical help in real life. Because they cannot be applied or connected concretely with one’s own life, most humans living in 2023 do not feel that the teachings of Confucianism (or Buddhism and Taoism) are of any help to their lives. Compared with the words of Confucius, they feel that capsule coffee machines and KFC discount coupons are somewhat more useful.

It is not surprising that this is the result. And the reason this result occurs is because these teachings were not written for the general public - they were not written for housewives or undergraduate business students. Whether it is the Daodejing or the Analects, they were written for people who truly want to explore the truth. So if you try to use them to solve your specific life problems, you will probably only end up disappointed. For most ordinary people, it is very difficult to directly apply these teachings to solve your problems, because they are too profound. Whether it is the Nanhua Jing or The Great Learning, the words recorded in them all come from enlightened beings of varying degrees - they are the experiences and insights of the enlightened. For ordinary people, it is impossible to correctly understand these words, let alone apply them. These words need to be decoded by people with corresponding spiritual accomplishments and wisdom, who can then refer to your specific situation and tell you what to do - only by going through this process can you possibly apply them to your own life and benefit from them, and only then can you slowly understand what these books are actually talking about. Unfortunately, this process has not been systematically established in East Asian societies. Only a very small number of fortunate individuals have the opportunity to glimpse the essence of Chinese culture in this way. Because of the lack of this system, when the masses are faced with the teachings of the sages, they can only attempt to approach the thoughts of the sages through their own way of thinking - it's like guessing riddles. In traditional Chinese society, you are required to repeatedly read the works of the sages until you know them by heart. Those teachers probably assumed that just by becoming thoroughly familiar with Confucius' books, people could slowly understand his state of mind. But obviously, this is just wishful thinking by amateurs. In the systems of Buddhism, Taoism and Confucianism, even Confucius' relatively basic words cannot be understood without the corresponding cultivation state, especially when nothing but a goal is provided. So hypocrisy became the only choice for most people.

In the eyes of modern intellectuals, traditional culture is completely deceptive and useless, because traditional culture did not invent computers or Thompson submachine guns - it just puts forward a whole set of moral norms that they see as completely useless. In their opinion, these moral norms also did not work, they did not make everyone better, but rather turned everyone into hypocrites, teaching everyone to lie and pretend. So from their point of view, Confucian teachings are simply fraudulent things, a set of shackles that restrict human nature and freedom, completely contrary to human nature.

If I were not a spiritual cultivator, if I did not know the relationship between the whole Confucian system and spiritual cultivation, if I had received systematic modern academic education, if I could not break free from the shackles of modern civilization, I would probably agree with their thinking and also believe that traditional culture is completely worthless.

Judging from the practical results of Confucianism in Eastern societies, it is not suitable for large-scale popularization. I have always believed that for ordinary people, it is better not to provide them with incomplete, hierarchical teachings, but to let them construct their secular lives perfectly. One day, when they find that secular life cannot provide what they want, when they become weary of secular life, it will not be too late to start spiritual exploration. I think this would be better, rather than forcing teachings onto everyone's lives as Confucianism did by means of power. Telling everyone how they should be, what kind of people they should be, what they should do, but not providing the corresponding logical systems and concrete steps to become such a person. This makes their requirements seem extremely unreasonable. But because of the intervention of power, the public has no choice but to accept it. However, they do not understand the logic and benefits of doing so. They are simply required to do so, but cannot achieve it, so they can only pretend to be such people, resulting in widespread hypocrisy. (Confucian scholars after Confucius did not realize that what Confucius demonstrated was the result of his own cultivation - those states are by no means accessible to ordinary people simply by reading the Analects repeatedly. You cannot require a person to read Confucius' teachings and immediately achieve Confucius' level of understanding attained after decades of cultivation, especially when nothing but a goal is provided.)

I seem to be criticizing Confucianism for not providing comprehensive services for its theories, but I am actually very clear that it would be completely impossible to provide specific and comprehensive education for everyone - no one could possibly do that.

Few people know how much wisdom it takes to teach the Dharma in a way that makes it comprehensible to everyone, and few people know what kind of enlightenment and skill a person must possess in order to teach according to the disposition of the student. Even in Buddhism, such people are extremely rare. Therefore, it is too much to ask those Confucian scholars who simply read books to do these things. In China's long history, there has always been a lack of people who could link traditional culture with real-life situations - this requires a high degree of enlightenment and skillfulness. Therefore, even if it was Confucianism's wish, it would have been completely impossible for them to achieve. Even in Buddhism, people of such talent are extremely scarce, so most practitioners neither receive suitable teachings for themselves, nor sufficient explanation. Most of the time, they can only arbitrarily understand the teacher's words based on their own state of mind. This gives demons ample room to distort everything they hear.

We just said that Chinese sages had no interest in building a sound secular society. Chinese traditional culture does not aim to establish a perfect secular society. Those systems dedicated to building a perfect secular society live under one assumption: that we only have this one life; that the more we gain, the happier we become; that if we establish a perfect secular society, we will be happy; that if supervision is in place, crime will know difficulties and retreat; that if we improve all our laws, our suffering will decrease or disappear; that if we can manufacture a drug that can treat all diseases, we will no longer suffer from illness. Judging from the huge changes that have taken place in American society in just the past few years, their assumptions are collapsing one by one. These assumptions made by Westerners seem extremely naive from the perspective of Chinese sages. Chinese sages do not agree with their way of thinking. So they did not try to create artificial intelligence, did not try to contact aliens, did not strive to develop AIDS medications, and did not design systems to contain human greed either. They just taught us ways to improve ourselves, starting by observing the problems inherent within us, slowly understanding the root causes of suffering, understanding the composition of suffering, understanding which behaviors and speech lead to suffering, which notions lead to suffering, and then slowly correcting past notions and slowly arriving at the state of liberation.

A true spiritual practitioner, most of his or her cultivation occurs internally, which means that true cultivation involves storms occurring internally - externally, it is almost impossible for outsiders to discern the internal changes happening within a practitioner. What you would probably see is that the person doesn't seem to do anything, just sitting there all day, or chanting some "useless" mantras. Therefore, for the general public, it is almost an impossible task to verify the results of their cultivation. The public does not know what they have attained, what experiences they have had, what feelings they have experienced. Those ascetics by the Ganges River in India and those meditating in the Himalayan mountains seem to modern civilization’s slaves to be doing completely meaningless things - they might even be considered cunning lazybones. But from the perspective of those practitioners, the elites who show up in office buildings every day in neatly dressed suits live meaningless lives: they are about to die, yet still working hard to accumulate things that will soon no longer belong to them.

Just like Indian culture, Chinese culture also largely transcends the sphere of comprehension of modern civilization. From the perspective of the general public, they can hardly see any useful results. Most people cannot see the achievements of those who truly practice Eastern traditional culture - after all, their accomplishments are not as self-evident as those of Elon Musk. Even if you sit face to face with an enlightened being, you cannot experience their state; you have no way of knowing what they have realized. You might even feel that they look no different from your average middle-aged neighbor. Therefore, for the masses, traditional cultural practitioners are far less attractive than Musk. After all, the latter's achievements are embodied in piles of dollars. And among those who claim to be practitioners, there may also be a large number of imposters mixed in. Do not expect the masses to be able to distinguish between imposters and true practitioners - they will simply lump them together.

For the general public, it is almost impossible to verify the efficacy of traditional culture. On the one hand, few people can persist for long periods of time doing something when they cannot see results. On the other hand, most people also fail to receive proper guidance. For example, there is a saying in Chinese traditional culture that "relinquishing is obtaining". Chinese traditional culture also says that "taking losses is good fortune." But most ordinary people neither know the correct things to relinquish nor how to relinquish them, let alone having enough patience to keep doing it. For the masses, lacking proper guidance and a complete and thorough understanding of the theory, what they do is like throwing fish food into a river and expecting the fish to spontaneously leap in swarms to their feet. Therefore, they can hardly see results - all they see is losses as losses, relinquishing as relinquishing, no gains whatsoever. When they see results like these, they will naturally feel that it was all just a scam. Compared with the efficient, fast-acting and verifiable systems established by the West in secular society, they will naturally feel that this represents a superior civilization.

Someone once asked me: Why does Chinese traditional culture seem to go against people's normal desires in almost every way? In their attitudes toward greed, hatred and ignorance, they unanimously display harsh attitudes. Many modern people see this as a major defect of traditional culture. Western culture, on the other hand, is very tolerant about this, so people feel that kind of culture is more in line with human nature. The reason why Western culture is tolerant in this regard is that Western culture is based on the idea that you are an individual, so you will have various desires and demands that a human being should have, and satisfying these desires is not seen as a sin in modern Western culture. Therefore, going on sea voyages to seek treasures and then leisurely enjoying the yields for a lifetime is a topic that Hollywood never tires of. Hollywood movies have influenced generations of people. Today, the world generally believes that the more you get, the happier you become. They are also willing to take risks in order to gain more. But Eastern traditional culture completely disagrees with this way of thinking. They do not believe that the more you get, the happier you become. They believe that if people do not restrain their desires and are led around by their desires, it will ultimately lead to disaster. Over the years, I have seen many people who do not know how to restrain their desires bring tremendous disasters upon themselves and others. In a sense, they are victims of Hollywood movies. Eastern sages believe that desire is endless. If you open this breach, you will be unable to stop it. The more you want, the more you will be out of control until you eventually destroy yourself. In today's world where Western culture has captivated almost everyone, you can see that the wealth some livestreamers accumulate in a single day is equal to what others earn in decades - they believe they are the lucky ones of the times. From my perspective, I don't think it's a good thing to exhaust all of one’s blessings in a day.

Western culture is based on the existence of a real individual “self”, while Eastern traditional culture, as we have just said - it is a spiritual cultivation culture. This kind of culture is based on the fact that there is no real existence of a “self”. It is based on “satisfying one’s desires does not lead to happiness” (desire only gives rise to more desire, thereby inducing more sin and chaos). It is based on conventional and ultimate truth. Eastern traditional culture is based on these things, so much of the time it looks completely contrary to human nature. (Another reason why it appears contrary to human nature is that most executors lack skillfulness - unwise people will execute everything in a very rigid manner.) Confucianism tries to compress our desires to a certain range in preparation for higher levels of cultivation afterwards. However, since most people living in such a society completely don’t understand this system and the purpose of doing so, they just live in such a society very grudgingly, required to comply with various standards. Like when you require a bunch of ordinary people to do things contrary to their temperament but do not tell them the reasons and benefits of doing so, it is not hard to imagine what would eventually happen - this is the cause of many tragedies. I have always believed that things like the Indian caste system and Confucianism are very good things - if used correctly. Unfortunately, they have not been correctly utilized. They were crudely and excessively applied to the whole of society by people lacking wisdom, causing considerable problems. However, from a technical level, it would also have been very difficult for them to be used correctly - both because of the lack of people capable of using these things properly, and also because demons spare no effort trying to sabotage their implementation. (Just like how some religions started out with the intention of severing the conditions that lead to desire by covering women’s faces, but this method has similarly been condemned because it was applied very foolishly. Demons will not miss any opportunity for sabotage.) When the masses do not know the meaning of the Confucian (or Indian caste) demands placed on them but are still required to implement them, they will only carry them out mechanically. Add to that the demons’ tireless efforts to distort any positive endeavor, various problems will naturally arise over time and surface. When these problems emerge, people will blame them on that culture and it will inevitably have to face accusations from all sides. The tragedy is that people who live in such societies for a long time can only see the downsides while being completely oblivious to the benefits. So they naturally believe that this is a completely useless culture that suppresses human nature and has caused countless tragedies.

If our existence were real, if we would be happier the more we possessed, if we could truly achieve happiness by defeating others, then the whole set of Western logic, values, lifestyles and paths to happiness designed accordingly would be correct. But unfortunately, this is not the case. You only need to understand a little bit of quantum mechanics to know that the way we exist is not as we imagine. However, given that quantum mechanics only emerged in the early 20th century, the West's understanding of ultimate truth has only just begun, so you cannot expect them to immediately produce new ideas for life practices.

After all, their value systems and lifestyles arising from the presumption of a real, independently existing self and the independent existence of all phenomena had already lasted over a thousand years.

So Eastern culture is a spiritual cultivation culture system based on "no-self". Because it is too profound, much of its ideology is not suitable for public dissemination, only an extremely small portion is suitable for the masses. That said, it remains an indispensable part of our lives (I have seen too many tragedies that were caused precisely because the protagonists lacked this kind of culture). Perhaps what we should explore is how to apply these cultures in the most harmless way. Any culture or teaching method, in the hands of people who do not know how to use them properly, will become a disaster. Chinese traditional culture has many different levels and angles, these different levels and angles are methods aimed at different levels of people. For wise and skillful people, these methods can be extremely flexible and humane, they are not absolutely unadjustable. But for people lacking wisdom and skill, it is very easy for them to become a whole set of rigid rules and weapons that harm everyone - this is how many tragedies arise. In the hands of a wise person, it can be used to benefit living beings and guide them to realize ultimate truth; but in the hands of an unwise person, it will only be a weapon to harm others. Confucianism, Taoism and Buddhism, some only provided concepts, some provided complete concepts and methods. These concepts and methods have many different levels and angles. Unfortunately, nowadays these methods of different levels have been jumbled up by people who do not understand them and chaotically interpreted by the masses, which has also caused many problems. Therefore, the tools themselves are not the issue, it is a group of unknowing people operating them haphazardly that has caused problems.

Chinese traditional sages had no intention to establish a sound secular society. They did not want to build vacuum tube trains or migrate to Mars. Similarly, they also lacked interest in making perfect sushi or medical security systems. Compared to these things, they prefer to observe their own minds. Compared with the conquering and defeating of others in Western culture, they prefer to conquer themselves and do battle with their own greed, hatred, ignorance, arrogance and doubt. They achieve ultimate happiness in this way. But from an amateur’s point of view, it may look like they have done nothing, just sitting there and expecting you to serve them meals. Even after attaining accomplishment, they do not produce piles of dollars, so they appear to be quite useless.

Written by the Lingshan Hermit on December 18, 2023. First published December 21, 2023. Revised December 22, 2023.

Copyright Notice：All copyrights of Ling Shan Hermit's articles in Simplified and Traditional Chinese, English, and other languages belong to the natural person who owns "Ling Shan Hermit". Please respect copyright. Publishers, media, or individuals (including but not limited to internet media, websites, personal spaces, Weibo, WeChat public accounts, print media) must obtain authorization from Ling Shan Hermit before use. No modifications to the articles are allowed (including: author's name, title, main text content, and punctuation marks). We reserve all legal rights.

灵山居士：东西文化之辨（修订）

2 notes · View notes

aboutanancientenquiry · 2 years ago

Text

Herodotus’ Scythian Logos viewed from a Central Asian Perspective

Hyun Jin Kim “Herodotus’ Scythians Viewed from a Central Asian Perspective: its Historicity and Significance”, Ancient West and East 9 (2010), pp 115-135 (abstract, introductory, and concluding paragraphs):

“Abstract

The literary interpretation of Herodotus in classical scholarship has arguably abandoned the fixation with the historical veracity of Herodotus’ account that characterised earlier Herodotean scholarship. The critical analyses of Detlev Fehling and François Hartog on the historian’s Scythian logos (singled out for criticism) in different ways acted as catalysts fort his development which heralded a generation of more sophisticated critique of the text as essentially a work of literature rather than history. Such an approach has had some positiver esults, especially in identifying the various levels of literary colouring that characterise the historian’s work. However, this article argues that the historical element simply cannot be removed from its former position of centrality in literary interpretation. It calls for a greater appreciation of the historicity of the Scythian logos by challenging the arguments through which Hartog and Fehling triggered the movement away from ‘history’ to ‘literature’. The article shows that a more intensive application of comparative, Central Asian historical and archaeological material in literary analysis, reveals that the logos as a whole is far more deeply immersed in the world of steppe nomadism than is often thought possible in classical scholarship.

The Scythian logos of Herodotus with its strange and wondrous tales about the far north has attracted much attention and critique in recent Herodotean scholarship. In the plethora of scholarship on the logos the critical analyses of Fehling 1 and Hartog 2 have been particularly influential or notorious. Fehling inherited a tradition of empirical, nearly positivistic textual analysis, which was focused primarily on proving Herodotus right or wrong. Hartog’s famous work marked a movement away from this approach to a more sophisticated appreciation of the literary and artistic dimension of Herodotus. The historian’s work, through the lens of late 20th-century neo-historicism, was seen in the context of cultural history and was appreciated as literature, not just history. Moreover, quite remarkably, despite significant differences in approach, both critics agreed that Herodotus’ account of the Scythians is largely, if not entirely, fictitious. Both works, therefore, in different ways contributed to the removal of the element of historicity from its former position of centrality to a peripheral role in all literary discussions on Herodotus.

This article, however, argues that historicity simply cannot be removed from any literary interpretation of Herodotus’ Scythian logos. It shows that both analyses mentioned above have serious limitations that result largely from their almost complete neglect of comparative, Central Asian historical material, a feature that is sadly far too common in literary, theoretical interpretations of Herodotus. The limited use of Central Asian historical or archaeological material to examine the veracity or falsity of various portions of the Scythian logos is indeed nothing new. However, this article, by subjecting the entirety of the Scythian logos to a more intensive comparative analysis, shows that the logos as a whole is far more deeply immersed in the traditions and culture of the Pontic steppe nomads than has previously been thought possible by both Fehling and Hartog and indeed classical scholarship in general.”

“ Thus Herodotus or his sources evidently did possess a greater understanding of steppe society and its military practices than modern critics such as Hartog give him credit for. The oddities and extremes that he mentions in his account of Scythian life and history are mostly historical realities, not make-believe...

As Hinge suggests, in the case of the Scythians at least, the analogies and patternsthat arise occasionally between Greeks and Scythians are not necessarily due to the ‘interpolation of Greek categories into a Scythian context’. They are rather ‘the result of the formulation of Scythian customs and beliefs in a Greek discourse’;115 i.e. they should rather be regarded as indicators of Herodotus’ attempt to Hellenise the Scythians to the extent that their behaviour and history would become intelligible to a Greek audience.

The uniquely Scythian elements in the account of the Scythian war and the description of Scythian customs show that Herodotus understands and appreciates the distinctive features of Scythian society and are a telling proof that he does nottry to make unnecessary analogies or create non-existent polarities. They also indicate clearly that genuine steppe customs and traditions are central to his overall representation of the Scythians in the Scythian logos. However, this by no means suggests that there is no validity in the doubts raised by a number of critics concerning Herodotus’ accuracy nor is it a denial of the reality of the limited application of both past and contemporary Greek theoretical constructs on the Scythians in the Histories by Herodotus.

Most of the steppe customs and historical details that we have presented in this article would be known to scholars engaged in the research of Central Asian history and nomad customs. He or she would be highly amused and perplexed by the fact that anyone could possibly consider them to be make-believe. Yet this is exactly what is asserted by arguably the two most prominent Herodotean scholars of the past five decades! Such an embarrassing situation arises, as has been shown throughout this article, from the tendency in current literary scholarship on the Scythian logos to largely neglect or treat as peripheral non-Greek and non-European historical and comparative material even when analysing the account of a people beyond this geographical or conceptual boundary. Hartog and Fehling, though approaching the text from radically different perspectives, nonetheless arrive at the same erroneous conclusions precisely because neither a solely text-based, empirical analysis as in the case of Fehling or a strictly theoretical and literary interpretation (Hartog), though both are valuable in their own right and have contributed to the development of Hero-dotean scholarship, can adequately grasp the full breadth of Herodotean inquiry.

Fixation with the ‘truth’ had clouded earlier scholarship on Herodotus and Hartog’s innovative, neo-historicist analysis marked a fresh break away from this cycle. However, his approach fails in the sense that it creates a too rigid a barrier between history and literature (extremely odd) and restricts the Histories to an arguably post-structuralist, European, cultural framework. In short a more balanced approach that is more comprehensive, interdisciplinary and comparative must be adopted in the future literary interpretation of Herodotus.”

The whole article can be found on https://href.li/?https://www.academia.edu/10885180/HERODOTUS_SCYTHIANS_VIEWED_FROM_A_CENTRAL_ASIAN_PERSPECTIVE_ITS_HISTORICITY_AND_SIGNIFICANCE

Hyun Jin Kim is Associate Professor in Classics, Historical and Philosophical Studies, University of Melbourne and a Fellow of the Australian Academy ogf Humanities. Many of his books, including his first monograph Ethnicity and Foreigners in Ancient Greece and China (2009; Duckworth), are comparative studies of Ancient Greece, Rome and China. His other monographs, most notably The Huns, Rome and the Birth of Europe (2013; Cambridge University Press), and edited books are studies of the Inner Asian Huns, Geopolitics and Eurasian Empires in Late Antiquity.

Very informative article, although I think that it rather gives too much to Fehling and Hartog, who certainly are not the two most prominent Herodotean scholars of the past five decades. Moreover, it is undeniable that the Herodotean scholarship of the last decades has moved away from Fehling’s and Hartog’s approaches to Herodotus’ work because these approaches had serious flaws, a thing that Pr. Hyun Jim Kim establishes very well in the case of the Scythians in Herodotus’ Histories.

#herodotus #classics #scythians #central asia #hyun jin kim

4 notes · View notes

aitechnologies · 2 years ago

Text

Latest Artificial Intelligence Technologies

AI has taken a tempest in each industry and significantly affects each area of society. The term Artificial intelligence terms were first begun in 1956 at a meeting. The discussion of the gathering prompted interdisciplinary data tech natural language generationnology. The presence of the web helped development with progressing decisively. Artificial intelligence technology was an independent technology quite a while back(30 years), however presently the applications are boundless in each circle of life. Artificial intelligence is known by the AL abbreviation and is the most common way of reproducing human intelligence in machines.

Let us see a few more Artificial Intelligence Technologies…

1. Natural language generation

Machines process and convey another way than the human cerebrum. Normal language age is an in vogue innovation that converts organized information into the native language. The machines are modified with algorithms to change over the data into a desirable format for the client. Natural language is a subset of man-made artificial intelligence that assists content designers with computerizing content and conveying the desirable format . The content developers can utilize the automated content to advance on different social media entertainment stages, and different media stages to reach the targeted audience. Human intercession will essentially lessen as information will be changed over into desired formats. The information can be envisioned as charts, graphs, and so forth.

2. Speech recognition

Speech recognition is one more significant subset of artificial intelligence that changes over human speech into a helpful and justifiable format by PCs. Speech recognition is an extension among human and PC connections. The innovation perceives and changes over human speech in a few languages. Siri on the iPhone is a commendable outline of speech recognition.

3. Virtual agents

Virtual agents have become significant apparatuses for instructional designers. A virtual agent is a computer application that collaborates with humans. Web and mobile applications give chatbots as their client support specialists to communicate with humans to answer their questions. Google Assistant assists with arranging meetings, and Alexia from Amazon assists with making your shopping simple & easy. A virtual assistant additionally behaves like a language partner, which picks prompts from your choice and preference. The IBM Watson comprehends the average customer service questions which are asked in more ways than one. Virtual agents go about as software-as-a-service too.

4. Decision management

Modern organizations are executing decision management systems for data transformation and understanding into prescient models. Enterprise-level applications execute decision management systems to get modern data to perform business data analysis to support authoritative independent decision-making. Decision management helps in settling on fast decisions, evasion of dangers, and in the automation of the process. The decision management system is generally carried out in the monetary area, the medical services area, trading, insurance sector, web based business, and so on.

5. Biometrics

Deep learning is one more part of artificial intelligence that capabilities in view of artificial neural networks. This method helps PCs and machines to advance as a visual demonstration simply of the manner in which humans do. The expression "deep" is begat in light of the fact that it has stowed away layers in neural networks. Ordinarily, a neural network has 2-3 secret layers and can have a limit of 150 secret layers. Deep learning is viable on enormous information to prepare a model and a realistic handling unit. The algorithms work in an order to automate predictive analytics. Deep learning has spread its wings in numerous domains like aviation and military to distinguish objects from satellites, helps in further developing specialist security by recognizing risk occurrences when a labourer draws near to a machine, assists with identifying malignant growth cells, and so forth.

6. Machine learning

Machine learning is a division of artificial intelligence which enables machines to check out data collections without being actually programmed. Machine learning strategy assists businesses to pursue informed decisions with data analytics performed utilizing algorithms and statistical models. Endeavours are putting vigorously in machine learning to receive the rewards of its application in different domains. Medical services and the clinical calling need machine learning methods to examine patient information for the prediction of diseases and viable treatment. The banking and monetary area needs machine learning for customer data analysis to recognize and propose venture choices to clients and for risk and fraud prevention. Retailers use machine learning for predicting changing client preferences, consumer conduct, by breaking down customer data.

7. Robotic process automation

Robotic process automation is a use of artificial intelligence that designs a robot (programming application) to decipher, convey and analyze information. This discipline of artificial intelligence assists with automating to some degree or completely manual operations that are repetitive and rule-based.

8. Peer-to-peer network

The peer-to-peer network assists with associating between various systems and computers for data sharing without the data transmitting via server. Peer-to-peer networks can take care of the most intricate issues. This technology is utilized in digital forms of money(cryptocurrencies). The implementation is financially savvy as individual workstations are connected and servers are not installed.

9. Deep learning platforms

10. AL optimized hardware

Artificial intelligence software has a popularity in the business world. As the consideration for the software expanded, a requirement for the equipment that upholds the software likewise emerged. A regular chip can't uphold artificial intelligence models. Another age of artificial intelligence chips is developed for neural networks, deep learning, and PC vision. The AL hardware incorporates central processors to deal with versatile responsibilities, unique reason worked in silicon for neural networks, neuromorphic chips, and so on. Organizations like Nvidia, Qualcomm. AMD is creating chips that can perform complex artificial intelligence estimations. Medical services and automobile might be the industries that will profit from these chips.

Conclusion

To close, Artificial Intelligence addresses computational models of intelligence. Intelligence can be depicted as designs, models, and functional capabilities that can be programmed for critical thinking, inductions, language processing, and so on. The advantages of utilizing artificial intelligence are now procured in numerous areas. Organizations taking on artificial intelligence ought to run pre-release preliminaries to dispense with inclinations and blunders. The design, models, ought to be robust. In the wake of delivering artificial systems, enterprises ought to screen constantly in various situations. Organizations ought to make and keep up with principles and recruit specialists from different disciplines for better decision-making. The goal and future objectives of artificial intelligence are to automate all complex human activities and take out mistakes and inclinations.

#artificial intelligence companies #artificial intelligence services #emerging technology companies #cutting edge technology companies

4 notes · View notes

battybiologist · 4 months ago

Text

There are a few assumptions at play here that sort of explain why someone could logically arrive to that conclusion.

A violent revolution aims to destroy the state apparatus

A violent revolution consists of nothing but undiscriminating domestic terrorism

The bourgeoisie is essential for the chains of supply to work

We have no idea what a modern violent revolution looks like

The first assumption is actually partially correct (and that's as correct as they're gonna get). Anarchists do want to destroy the state apparatus entirely because they believe it to be inherently oppressive. This destruction would inevitably lead to the breakdown of national infrastructure, and thus the disruption to health services described here. That's why there are other leftist ideologies: Marxism-Leninism (the most popular leftist ideology with its offshoots) is about as far as you can get from anarchy in leftism, in that the state is to be left as it is at worst and strengthened to service the needs of the population at best.

Second assumption is completely false. Did the Soviets burn agricultural fields and poison the Russian water supply when they revolted ? No, they just seized strategic points before moving on to the Winter Palace. The comparison with a hurricane is telling: the post pictures a violent revolution as a horde of bloodthirsty thoughtless terrorists destroying everything in sight (why would revolutionaries target the power grid otherwise ?), a caricature of the common people so reactionary that even Montesquieu would find it unrealistic

Speaking of reactionary, the third assumption is the worst. The entirety of socialism is founded upon the existence of the bourgeoisie, the dominant class who owns the means of production, and of the proletariat, the oppressed class who produces the labor that makes society function. Removing the bourgeoisie by seizing the means of production (what's actually at stake in a violent revolution) doesn't actually change industry at its core, just who's in charge and who gets to benefit from the labor of the proletariat.

Finally, the last assumption is simply a case of a lack of education about world news and of understanding of capitalist imperialism. Burkina Faso had a "socialist" (I hesitate to qualify it as that since it's so early to tell) coup d'état in 2022. Coups d'état are exactly similar to popular revolutions when it comes to violence, and yet, the only reaction from the imperial core was a condemnation by one of their puppets, the ECOWAS. The reason they didn't invade the country and restore their collaborators to power is because the supply chains haven't actually been disrupted. Gold, copper, cotton, all of Burkina Faso's major imports are still flowing to the imperial core. Hell, Endeavour Mining, a London-based Canadian company, still owns 4 mines there, despite Ibrahim Traoré's desire to nationalize the country's gold industry. We've seen a violent revolution at play, and evidently the nightmare scenario invoked in the previous reblogs has not happened, because communism has nothing to gain from wanton destruction

In conclusion, I think I know what types of posts (because it's always about posts when liberals bring up this argument) this is a reaction to, but teenagers with a bad political and historical education venting their anger at the system on Tumblr is not a serious source of information as to how a violent revolution would happen. If you want a good starting point, take a look at the works of Marx and Engels, and from there, read more communist theory to deepen your understanding of the subjects they bring up and explore applications of their principles to other subjects

I think a lot about how, if the glorious violent revolution happens, every kid with significant medical needs in a hospital where power gets cut will die.

You can decide you're willing to sacrifice your own life, but you don't get to tell everybody else on the planet that they're acceptable collateral damage.

#i could talk more about how reformism and violent revolution arent as mutually exclusive as people seem to think #but this post is already long enough #if im asked though i will expand on that

28K notes · View notes

i-edu0services · 8 days ago

Text

Soundarya Institute of Management and Science: Path to Excellence

Soundarya Institute of Management and Science (SIMS) is a renowned educational institute based in Bangalore, Karnataka. Known for its commitment to excellence in education and all-round development, Soundarya Institute of Management and Science has carved a niche for itself in the field of management and scientific research. The institute stands out for its modern infrastructure, experienced faculty, and dynamic approach to education, making it a popular choice for students seeking academic and professional success.

About SIMS:

Founded with a vision to develop leaders and innovators, SIMS offers a wide range of bachelor's and master's degree programs in management, commerce, science, and other disciplines. Our partnership with Bangalore University ensures that our curriculum meets industry standards and equips students with the skills and knowledge they need in today's competitive world.

State-of-the-art Infrastructure:

One of the key highlights of SIMS is its modern campus which provides an ideal learning environment. The institute has spacious classrooms, well-equipped laboratories, and a library with a vast collection of books, magazines, and digital resources. The campus also features facilities like seminar halls, auditoriums, and recreational areas to ensure comprehensive academic and extracurricular activities for students.

Qualified Teachers and Excellent Quality of Education:

SIMS takes pride in its team of qualified and experienced teachers. They are not only educators but also mentors who inspire students to achieve academic excellence and develop critical thinking skills. SIMS' teaching methodology emphasizes interactive learning, case studies, and practical projects to ensure that students gain practical insights along with theoretical knowledge.

Focus on Holistic Development:

At SIMS, training goes beyond textbooks. The institute emphasizes holistic development and encourages students to participate in sports, cultural events, and social initiatives. Through various clubs and societies, students are allowed to showcase their talents, develop leadership skills, and build lasting relationships.

Placement and Career Support:

SIMS is committed to preparing students for successful careers. Its recruitment agency actively collaborates with leading companies and organizations to support campus recruitment campaigns and internships. The institute regularly conducts workshops, training, and career counseling to ensure that students are career-ready. Former SIMS students have secured positions in prestigious organizations, a testimony of the institute's focus on employability.

Why SIMS?

Comprehensive Programmes: A wide variety of courses tailored to the needs of various industries.

Industry Integration: Regular guest lectures, workshops, and industry visits to bridge the gap between academic learning and real-world application.

Student-centered Approach: An inclusive environment that values the development and potential of every student.

Supportive environment: Focus on providing guidance, advice, and resources for personal and professional development.

Final Thoughts:

Soundarya Institute of Management and Science is greater than simply an educational institution—it`s a platform for transformation. With its emphasis on nice education, talent development, and value-primarily based learning, SIMS prepares college students now no longer for careers but additionally for life. Whether you intend to pursue management, science, or commerce, SIMS gives the proper blend of knowledge, opportunities, and steerage that will help you acquire your goals.

For potential college students seeking out a mix of instructional rigor and private growth, Soundarya Institute of Management and Science is surely a worthy choice. Visit the campus, discover its offerings, and take step one in the direction of a vibrant future.

#Soundarya Institute of Management and Science #SIMS Bangalore

0 notes

jcmarchi · 14 days ago

Text

Shape, Symmetries, and Structure: The Changing Role of Mathematics in Machine Learning Research

New Post has been published on https://thedigitalinsider.com/shape-symmetries-and-structure-the-changing-role-of-mathematics-in-machine-learning-research/

Shape, Symmetries, and Structure: The Changing Role of Mathematics in Machine Learning Research

What is the Role of Mathematics in Modern Machine Learning?

The past decade has witnessed a shift in how progress is made in machine learning. Research involving carefully designed and mathematically principled architectures result in only marginal improvements while compute-intensive and engineering-first efforts that scale to ever larger training sets and model parameter counts result in remarkable new capabilities unpredicted by existing theory. Mathematics and statistics, once the primary guides of machine learning research, now struggle to provide immediate insight into the latest breakthroughs. This is not the first time that empirical progress in machine learning has outpaced more theory-motivated approaches, yet the magnitude of recent advances has forced us to swallow the bitter pill of the “Bitter Lesson” yet again [1].

This shift has prompted speculation about mathematics’ diminished role in machine learning research moving forward. It is already evident that mathematics will have to share the stage with a broader range of perspectives (for instance, biology which has deep experience drawing conclusions about irreducibly complex systems or the social sciences as AI is integrated ever more deeply into society). The increasingly interdisciplinary nature of machine learning should be welcomed as a positive development by all researchers.

However, we argue that mathematics remains as relevant as ever; its role is simply evolving. For example, whereas mathematics might once have primarily provided theoretical guarantees on model performance, it may soon be more commonly used for post-hoc explanations of empirical phenomena observed in model training and performance–a role analogous to one that it plays in physics. Similarly, while mathematical intuition might once have guided the design of handcrafted features or architectural details at a granular level, its use may shift to higher-level design choices such as matching architecture to underlying task structure or data symmetries.

None of this is completely new. Mathematics has always served multiple purposes in machine learning. After all, the translation equivariant convolutional neural network, which exemplifies the idea of architecture matching data symmetries mentioned above is now over 40 years old. What’s changing are the kinds of problems where mathematics will have the greatest impact and the ways it will most commonly be applied.

An intriguing consequence of the shift towards scale is that it has broadened the scope of the fields of mathematics applicable to machine learning. “Pure” mathematical domains such as topology, algebra, and geometry, are now joining the more traditionally applied fields of probability theory, analysis, and linear algebra. These pure fields have grown and developed over the last century to handle high levels of abstraction and complexity, helping mathematicians make discoveries about spaces, algebraic objects, and combinatorial processes that at first glance seem beyond human intuition. These capabilities promise to address many of the biggest challenges in modern deep learning.

In this article we will explore several areas of current research that demonstrate the enduring ability of mathematics to guide the process of discovery and understanding in machine learning.

Figure 1: Mathematics can illuminate the ways that ReLU-based neural networks shatter input space into countless polygonal regions, in each of which the model behaves like a linear map [2, 3, 4]. These decompositions create beautiful patterns. (Figure made with SplineCam [5]).

Describing an Elephant from a Pin Prick

Suppose you are given a 7 billion parameter neural network with 50 layers and are asked to analyze it; how would you begin? The standard procedure would be to calculate relevant performance statistics. For instance, the accuracy on a suite of evaluation benchmarks. In certain situations, this may be sufficient. However, deep learning models are complex and multifaceted. Two computer vision models with the same accuracy may have very different generalization properties to out-of-distribution data, calibration, adversarial robustness, and other “secondary statistics” that are critical in many real-world applications. Beyond this, all evidence suggests that to build a complete scientific understanding of deep learning, we will need to venture beyond evaluation scores. Indeed, just as it is impossible to capture all the dimensions of humanity with a single numerical quantity (e.g., IQ, height), trying to understand a model by one or even several statistics alone is fundamentally limiting.

One difference between understanding a human and understanding a model is that we have easy access to all model parameters and all the individual computations that occur in a model. Indeed, by extracting a model’s hidden activations we can directly trace the process by which a model converts raw input into a prediction. Unfortunately, the world of hidden activations is far less hospitable than that of simple model performance statistics. Like the initial input, hidden activations are usually high dimensional, but unlike input data they are not structured in a form that humans can understand. If we venture into even higher dimensions, we can try to understand a model through its weights directly. Here, in the space of model weights, we have the freedom to move in millions to billions of orthogonal directions from a single starting point. How do we even begin to make sense of these worlds?

There is a well-known fable in which three blind men each feel a different part of an elephant. The description that each gives of the animal is completely different, reflecting only the body part that that man felt. We argue that unlike the blind men who can at least use their hand to feel a substantial part of one of the elephant’s body parts, current methods of analyzing the hidden activations and weights of a model are akin to trying to describe the elephant from the touch of a single pin.

Tools to Characterize What We Cannot Visualize

Despite the popular perception that mathematicians exclusively focus on solving problems, much of research mathematics involves understanding the right questions to ask in the first place. This is natural since many of the objects that mathematicians study are so far removed from everyday experience that we start with very limited intuition for what we can hope to actually understand. Substantial effort is often required to build up tools that will enable us to leverage our existing intuition and achieve tractable results that increase our understanding. The concept of a rotation provides a nice example of this situation since these are very familiar in 2- and 3-dimensions, but become less and less accessible to everyday intuition as their dimension grows larger. In this latter case, the differing perspectives provided by pure mathematics become more and more important to gaining a more holistic perspective on what these actually are.

Those who know a little linear algebra will remember that rotations generalize to higher dimensions and that in $n$-dimensions they can be realized by $n times n$ orthogonal matrices with determinant $1$. The set of these are commonly written as $SO(n)$ and called the special orthogonal group. Suppose we want to understand the set of all $n$-dimensional rotations. There are many complementary approaches to doing this. We can explore the linear algebraic structure of all matrices in $SO(n)$ or study $SO(n)$ based on how each element behaves as an operator acting on $mathbbR^n$.

Alternatively, we can also try to use our innate spatial intuition to understand $SO(n)$. This turns out to be a powerful perspective in math. In any dimension $n$, $SO(n)$ is a geometric object called a manifold. Very roughly, a space that locally looks like Euclidean space, but which may have twists, holes, and other non-Euclidean features when we zoom out. Indeed, whether we make it precise or not, we all have a sense of whether two rotations are “close” to each other. For example, the reader would probably agree that $2$-dimensional rotations of $90^circ$ and $91^circ$ “feel” closer than rotations of $90^circ$ and $180^circ$. When $n=2$, one can show that the set of all rotations is geometrically “equivalent” to a $1$-dimensional circle. So, much of what we know about the circle can be translated to $SO(2)$.

What happens when we want to study the geometry of rotations in $n$-dimensions for $n > 3$? If $n = 512$ (a latent space for instance), this amounts to studying a manifold in $512^2$-dimensional space. Our visual intuition is seemingly useless here since it is not clear how concepts that are familiar in 2- and 3-dimensions can be utilized in $512^2$-dimensions. Mathematicians have been confronting the problem of understanding the un-visualizable for hundreds of years. One strategy is to find generalizations of familiar spatial concepts from $2$ and $3$-dimensions to $n$-dimensions that connect with our intuition.

This approach is already being used to better understand and characterize experimental observations about the space of model weights, hidden activations, and input data of deep learning models. We provide a taste of such tools and applications here:

Intrinsic Dimension: Dimension is a concept that is familiar not only from our experience in the spatial dimensions that we can readily access, 1-, 2-, and 3-dimensions, but also from more informal notions of “degrees of freedom” in everyday systems such as driving a car (forward/back, turning the steering wheel either left or right). The notion of dimension arises naturally in the context of machine learning where we may want to capture the number of independent ways in which a dataset, learned representation, or collection of weight matrices actually vary.

In formal mathematics, the definitions of dimension depend on the kind of space one is studying but they all capture some aspect of this everyday intuition. As a simple example, if I walk along the perimeter of a circle, I am only able to move forward and backward, and thus the dimension of this space is $1$. For spaces like the circle which are manifolds, dimension can be formally defined by the fact that a sufficiently small neighborhood around each point looks like a subset of some Euclidean space $mathbbR^k$. We then say that the manifold is $k$-dimensional. If we zoom in on a small segment of the circle, it almost looks like a segment of $mathbbR = mathbbR^1$, and hence the circle is $1$-dimensional.

The manifold hypothesis posits that many types of data (at least approximately) live on a low-dimensional manifold even though they are embedded in a high-dimensional space. If we assume that this is true, it makes sense that the dimension of this underlying manifold, called the intrinsic dimension of the data, is one way to describe the complexity of the dataset. Researchers have estimated intrinsic dimension for common benchmark datasets, showing that intrinsic dimension appears to be correlated to the ease with which models generalize from training to test sets [6], and can explain differences in model performance and robustness in different domains such as medical images [7]. Intrinsic dimension is also a fundamental ingredient in some proposed explanations of data scaling laws [8, 9], which underlie the race to build ever bigger generative models.

Researchers have also noted that the intrinsic dimension of hidden activations tend to change in a characteristic way as information passes through the model [10, 11] or over the course of the diffusion process [12]. These and other insights have led to the use of intrinsic dimension in detection of adversarial examples [13], AI-generated content [14], layers where hidden activations contain the richest semantic content [11], and hallucinations in generative models [15].

Curvature: While segments of the circle may look “straight” when we zoom up close enough, their curvature means that they will never be exactly linear as a straight line is. The notion of curvature is a familiar one and once formalized, it offers a way of rigorously measuring the extent to which the area around a point deviates from being linear. Care must be taken, however. Much of our everyday intuition about curvature assumes a single dimension. On manifolds with dimension $2$ or greater, there are multiple, linearly independent directions that we can travel away from a point and each of these may have a different curvature (in the $1$-dimensional sense). As a result, there are a range of different generalizations of curvature for higher-dimensional spaces, each with slightly different properties.

The notion of curvature has played a central role in deep learning, especially with respect to the loss landscape where changes in curvature have been used to analyze training trajectories [16]. Curvature is also central to an intriguing phenomenon known as the ‘edge of stability’, wherein the curvature of the loss landscape over the course of training increases as a function of learning rate until it hovers around the point where the training run is close to becoming unstable [17]. In another direction, curvature has been used to calculate the extent that model predictions change as input changes. For instance, [18] provided evidence that higher curvature in decision boundaries correlates with higher vulnerability to adversarial examples and suggested a new regularization term to reduce this. Finally, motivated by work in neuroscience, [19] presented a method that uses curvature to highlight interesting differences in representation between the raw training data and a neural network’s internal representation. A network may stretch and expand parts of the input space, generating regions of high curvature as it magnifies the representation of training examples that have a higher impact on the loss function.

Topology: Both dimension and curvature capture local properties of a space that can be measured by looking at the neighborhood around a single point. On the other hand, the most notable feature of our running example, the circle, is neither its dimension nor its curvature, but rather the fact that it is circular. We can only see this aspect by analyzing the whole space at once. Topology is the field of mathematics that focuses on such “global” properties.

Topological tools such as homology, which counts the number of holes in a space, has been used to illuminate the way that neural networks process data, with [20] showing that deep learning models “untangle” data distributions, reducing their complexity layer by layer. Versions of homology have also been applied to the weights of networks to better understand their structural features, with [21] showing that such topological statistics can reliably predict optimal early-stopping times. Finally, since topology provides frameworks that capture the global aspects of a space, it has proved a rich source of ideas for how to design networks that capture higher order relationships within data, leading to a range of generalizations of graph neural networks built on top of topological constructions [22, 23, 24, 25].

While the examples above have each been useful for gaining insight into phenomena related to deep learning, they were all developed to address challenges in other fields. We believe that a bigger payoff will come when the community uses the geometric paradigm described here to build new tools specifically designed to address the challenges that deep learning poses. Progress in this direction has already begun. Think for instance of linear mode connectivity which has helped us to better understand the loss landscape of neural networks [26] or work around the linear representation hypothesis which has helped to illuminate the way that concepts are encoded in the latent space of large language models [27]. One of the most exciting occurrences in mathematics is when the tools from one domain provide unexpected insight in another. Think of the discovery that Riemannian geometry provides some of the mathematical language needed for general relativity. We hope that a similar story will eventually be told for geometry and topology’s role in deep learning.

Symmetries in data, symmetries in models

Symmetry is a central theme in mathematics, allowing us to break a problem into simpler components that are easier to solve. Symmetry has long played an important role in machine learning, particularly computer vision. In the classic dog vs. cat classification task for instance, an image that contains a dog continues to contain a dog regardless of whether we move the dog from one part of the image to another, whether we rotate the dog, or whether we reflect it. We say that the task is invariant to image translation, rotation, and reflection.

The notion of symmetry is mathematically encoded in the concept of a group, which is a set $G$ equipped with a binary operation $star$ that takes two elements of $G$, $g_1$, $g_2$ as input and produces a third $g_1star g_2$ as output. You can think of the integers $mathbbZ$ with the binary operation of addition ($star = +$) or the non-zero real numbers with the binary operation of multiplication ($star = times$). The set of $n$-dimensional rotations, $SO(n)$, also forms a group. The binary operation takes two rotations and returns a third rotation that is defined by simply applying the first rotation and then applying the second.

Groups satisfy axioms that ensure that they capture familiar properties of symmetries. For example, for any symmetry transformation, there should be an inverse operation that undoes the symmetry. If I rotate a circle by $90^circ$, then I can rotate it back by $-90^circ$ and return to where I started. Notice that not all transformations satisfy this property. For instance, there isn’t a well-defined inverse for downsampling an image. Many different images downsample to the same (smaller) image.

In the previous section we gave two definitions of $SO(n)$: the first was the geometric definition, as rotations of $mathbbR^n$, and the second was as a specific subset of $n times n$ matrices. While the former definition may be convenient for our intuition, the latter has the benefit that linear algebra is something that we understand quite well at a computational level. The realization of an abstract group as a set of matrices is called a linear representation and it has proven to be one of the most fruitful methods of studying symmetry. It is also the way that symmetries are usually leveraged when performing computations (for example, in machine learning).

We saw a few examples of symmetries that can be found in the data of a machine learning task, such as the translation, rotation, and reflection symmetries in computer vision problems. Consider the case of a segmentation model. If one rotates an input image by $45^circ$ and then puts it through the model, we will hope that we get a $45^circ$ rotation of the segmentation prediction for the un-rotated image (this is illustrated in 1). After all, we haven’t changed the content of the image.

Figure 2: The concept of rotation equivariance illustrated for a segmentation model. One gets the same output regardless of whether one rotates first and then applies the network or applies the network and then rotates.

Figure 3: Equivariance holds when taking the top path (applying the network first and then the symmetry action) gives the same result as taking the bottom path (applying the symmetry transformation and then the network).

This property of a function (including neural networks), that applying a symmetry transformation before the function yields the same result as applying the symmetry transformation after the function is called equivariance and can be captured by the diagram in Figure 3. The key point is that we get the same result whether we follow the upper path (applying the network first and then applying the group action) as when we follow the lower path (applying the group first and then applying the network). Conveniently, the concept of invariance, where applying a symmetry operation to input has no effect on the output of the function is a special case of equivariance where the action on the output space is defined to be trivial (applying symmetry actions does nothing).

Invariance and equivariance in deep learning models can be beneficial for a few reasons. Firstly, such a model will yield more predictable and consistent results across symmetry transformations. Secondly, through equivariance we can sometimes simplify the learning process with fewer parameters (compare the number of parameters in a convolutional neural network and an MLP of similar performance) and fewer modes of variation to learn in the data (a rotation invariant image classifier only needs to learn one orientation of each object rather than all possible orientations).

But how do we ensure that our model is equivariant? One way is to build our network with layers that are equivariant by design. By far the most well-known example of this is the convolutional neural network, whose layers are (approximately) equivariant to image translation. This is one reason why using a convolutional neural network for dog vs cat classification doesn’t require learning to recognize a dog at every location in an image as it might with an MLP. With a little thought, one can often come up with layers which are equivariant to a specific group. Unfortunately, being constrained to equivariant layers that we find in an ad-hoc manner often leaves us with a network with built-in equivariance but limited expressivity.

Fortunately, for most symmetry groups arising in machine learning, representation theory offers a comprehensive description of all possible linear equivariant maps. Indeed, it is a beautiful mathematical fact that all such maps are built from atomic building blocks called irreducible representations. Happily, in many cases, the number of these irreducible representations is finite. Understanding the irreducible representations of a group can be quite powerful. Those familiar with the ubiquitous discrete Fourier transform (DFT) of a sequence of length $n$ are already familiar with the irreducible representations of one group, the cyclic group generated by a rotation by $360 ^circ/n$ (though we note that moving between the description we give here and the description of the DFT found in the signal processing literature takes a little thought).

There is now a rich field of research in deep learning that uses group representations to systematically build expressive equivariant architectures. Some examples of symmetries that have been particularly well-studied include: rotation and reflection of images [28, 29, 30, 31], 3-dimensional rotation and translation of molecular structures [32] or point clouds [33], and permutations for learning on sets [34] or nodes of a graph [35]. Encoding equivariance to more exotic symmetries has also proven useful for areas such as theoretical physics [36] and data-driven optimization [37].

Equivariant layers and other architectural approaches to symmetry awareness are a prime example of using mathematics to inject high-level priors into a model. Do these approaches represent the future of learning in the face of data symmetries? Anecdotally, the most common approach to learning on data with symmetries continues to be using enough training data and enough data augmentation for the model to learn to handle the symmetries on its own. Two years ago, the author would have speculated that these latter approaches only work for simple cases, such as symmetries in 2-dimensions, and will be outperformed by models which are equivariant by design when symmetries become more complex. Yet, we continue to be surprised by the power of scale. After all, AlphaFold3 [38] uses a non-equivariant architecture despite learning on data with several basic symmetries. We speculate that there may be a threshold on the ratio of symmetry complexity on the one hand and the amount of training data on the other, that determines whether built-in equivariance will outperform learned equivariance [39, 40].

If this is true, we can expect to see models move away from bespoke equivariant architectures as larger datasets become available for a specific application. At the same time, since compute will always be finite, we predict that there will be some applications with exceptionally complex symmetries that will always require some built-in priors (for example, AI for math or algorithmic problems). Regardless of where we land on this spectrum, mathematicians can look forward to an interesting comparison of the ways humans inject symmetry into models vs the way that models learn symmetries on their own [41, 42].

Figure 4: A cartoon illustrating why adding a permutation and its inverse before and after a pointwise nonlinearity produces an equivalent model (even though the weights will be different). Since permutations can be realized by permutation matrices, the crossed arrows on the right can be merged into the fully-connected layer.

Of course, symmetry is not only present in data but also in the models themselves. For instance, the activations of hidden layers of a network are invariant to permutation. We can permute activations before entering the non-linearity and if we un-permute them afterward, the model (as a function) does not change (Figure 4). This means that we have an easy recipe for generating an exponentially large number of networks that have different weights but behave identically on data.

While simple, this observation produces some unexpected results. There is evidence, for instance, that while the loss landscape of neural networks is highly non-convex, it may be much less non-convex when we consider all networks that can be produced through this permutation operation as equivalent [43, 44]. This means that your network and my network may not be connected by a linear path of low loss, but such a path may exist between your network and a permutation of my network. Other research has looked at whether it may be possible to use symmetries to accelerate optimization by ‘teleporting’ a model to a more favorable location in the loss landscape [45, 46]. Finally, permutation symmetries also provide one type of justification for an empirical phenomenon where individual neurons in a network tend to encode more semantically meaningful information than arbitrary linear combinations of such neurons [47].

Taming Complexity with Abstraction

When discussing symmetry, we used the diagram in Figure 3 to define equivariance. One of the virtues of this approach is that we never had to specify details about the input data or architecture that we used. The spaces could be vector spaces and the maps linear transformations, they could be neural networks of a specific architecture, or they could just be sets and arbitrary functions between them–the definition is valid for each. This diagrammatic point of view, which looks at mathematical constructions in terms of the composition of maps between objects rather than the objects themselves, has been very fruitful in mathematics and is one gateway to the subject known as category theory. Category theory is now the lingua franca in many areas of mathematics since it allows mathematicians to translate definitions and results across a wide range of contexts.

Of course, deep learning is at its core all about function composition, so it is no great leap to try and connect it to the diagrammatic tradition in mathematics. The focus of function composition in the two disciplines is different, however. In deep learning we take simple layers that alone lack expressivity and compose them together to build a model capable of capturing the complexity of real-world data. With this comes the tongue-in-cheek demand to “stack more layers!”. Category theory instead tries to find a universal framework that captures the essence of structures appearing throughout mathematics. This allows mathematicians to uncover connections between things that look very different at first glance. For instance, category theory gives us the language to describe how the topological structure of a manifold can be encoded in groups via homology or homotopy theory.

It can be an interesting exercise to try to find a diagrammatic description of familiar constructions like the product of two sets $X$ and $Y$. Focusing our attention on maps rather than objects we find that what characterizes $X times Y$ is the existence of the two canonical projections $pi_1$ and $pi_2$, the former sending $(x,y) mapsto x$ and $(x,y) mapsto y$ (at least in more familiar settings where $X$ and $Y$ are, for example, sets). Indeed, the product $X times Y$ (regardless of whether $X$ and $Y$ are sets, vectors spaces, etc.) is the unique object such that for any $Z$ with maps $f_1: Z rightarrow X$ and $f_2: Z rightarrow Y$, there is a map $h: Z rightarrow X times Y$ that satisfies the commutative diagram in Figure 5.

While this construction is a little involved for something as familiar as a product it has the remarkable property that it allows us to define a “product” even when there is no underlying set structure (that is, those settings where we cannot resort to defining $X times Y$ as the set of pairs of $(x,y)$ for $x in X$ and $y in Y$).

Figure 5: The commutative diagram that describes a product $X times Y$. For any $Z$ with maps $f_1: Z rightarrow X$ and $f_2: Z rightarrow Y$, there exists a unique map $h: Z rightarrow X times Y$ such that $f_1 = pi_1 circ h$ and $f_2 = pi_2 circ h$ where $pi_1$ and $pi_2$ are the usual projection maps from $X times Y$ to $X$ and $X times Y$ to $Y$ respectively.

One can reasonably argue that diagrammatic descriptions of well-known constructions, like products, are not useful for the machine learning researcher. After all, we already know how to form products in all of the spaces that come up in machine learning. On the other hand, there are more complicated examples where diagrammatics mesh well with the way we build neural network architectures in practice.

Figure 6: Fiber bundles capture the notion that a space might locally look like a product but globally have twists in it.

Fiber bundles are a central construction in geometry and topology that capture the notion that a space may locally look like a product but may have twists that break this product structure globally. Compare the cylinder with the Möbius band. We can build both of these by starting with a circle and taking a product with the line segment $(0,1)$. In the case of the cylinder, this really is just (topologically) the product of the circle and the segment $(0,1)$, but to form the Möbius band we must add an additional twist that breaks the product structure. In these examples, the circle is called the base space and $(0,1)$ is called the fiber. While only the cylinder is a true product, both the cylinder and the Möbius band are fiber bundles. Here is another way of thinking about a fiber bundle. A fiber bundle is a union of many copies of the fiber parametrized by the base space. In the Möbius band/cylinder example, each point on the circle carries its own copy of $(0,1)$.

We drew inspiration from this latter description of fiber bundles when we were considering a conditional generation task in the context of a problem in materials science. Since the materials background is somewhat involved, we’ll illustrate the construction via a more pedestrian, animal-classification analogue. Let $M$ be the manifold of all possible images containing a single animal. We can propose to decompose the variation in elements of $M$ into two parts, the species of animal in the image and everything else, where the latter could mean differences in background, lighting, pose, image quality, etc. One might want to explore the distribution of one of these factors of variation while fixing the other. For instance, we might want to fix the animal species and explore the variation we get in background, pose, etc. For example, comparing the variation in background for two different species of insect may tell the entomologist about the preferred habitat for different types of beetles.

Figure 7: A cartoon visualizing how the set of all animal images could be decomposed into a local product of animal species and other types of variation.

One might hope to solve this problem by learning an encoding of $M$ into a product space $X_1 times X_2$ where $X_1$ is a discrete set of points corresponding to animal species and $X_2$ is a space underlying the distribution of all other possible types of variation for a fixed species of animal. Fixing the species would then amount to choosing a specific element $x_1$ from $X_1$ and sampling from the distribution on $X_2$. The product structure of $X_1 times X_2$ allows us to perform such independent manipulations of $X_1$ and $X_2$. On the other hand, products are rigid structures that impose strong, global topological assumptions on the real data distribution. We found that even on toy problems, it was hard to learn a good map from the raw data distribution to the product-structured latent space defined above. Given that fiber bundles are more flexible and still give us the properties we wanted from our latent space, we designed a neural network architecture to learn a fiber bundle structure on a data distribution [48].

Figure 8: The commutative diagram describing a fiber bundle. The map $pi$ projects from neighborhoods of the total space to the base space, $U$ is a local neighborhood of the base space, and $F$ is the fiber. The diagram says that each point in the base space has a neighborhood $U$ such that when we lift this to the bundle, we get something that is homeomorphic (informally, equivalent) to the product of the neighborhood and the fiber. But this product structure may not hold globally over the whole space.

But how do we go from the abstract definition of a fiber bundle above to a neural network architecture that we can code up on a computer. It turns out there is a succinct diagrammatic definition of a fiber bundle (Figure 8) that can serve as a convenient template to build up an architecture from. We were able to proceed in a relatively naïve fashion, taking each of the maps in the diagram and building a corresponding stack of layers. The diagram itself then told us how to compose each of these components together. The commutativity of the diagram was engineered through a term in the loss function that ensures that $pi = textproj_1 circ varphi$. There were also some conditions on $varphi$ and $pi$ (such as the bijectivity of $phi$) that needed to be engineered. Beyond this, we were surprised at the amount of flexibility we had. This is useful since it means this process is largely agnostic to data modality.

This is an elementary example of how the diagrammatic tradition in mathematics can provide us with a broader perspective on the design of neural networks, allowing us to connect deep structural principles with large-scale network design without having to specify small-scale details that might be problem dependent. Of course, all this fails to draw from anything beyond the surface of what the categorical perspective has to offer. Indeed, category theory holds promise as a unified framework to connect much of what appears and is done in machine learning [49].

Conclusion

In the mid-twentieth century, Eugene Wigner marveled at the “the unreasonable effectiveness of mathematics” as a framework for not only describing existing physics but also anticipating new results in the field [50]. A mantra more applicable to recent progress in machine learning is “the unreasonable effectiveness of data” [51] and compute. This could appear to be a disappointing situation for mathematicians who might have hoped that machine learning would be as closely intertwined to advanced mathematics as physics is. However, as we’ve demonstrated, while mathematics may not maintain the same role in machine learning research that it has held in the past, the success of scale actually opens new paths for mathematics to support progress in machine learning research. These include:

Providing powerful tools for deciphering the inner workings of complex models

Offering a framework for high-level architectural decisions that leave the details to the learning algorithm

Bridging traditionally isolated domains of mathematics like topology, abstract algebra, and geometry with ML and data science applications.

Should the way things have turned out surprise us? Perhaps not, given that machine learning models ultimately reflect the data they are trained on and in most cases this data comes from fields (such as natural language or imagery) which have long resisted parsimonious mathematical models.

Yet, this situation is also an opportunity for mathematics. Performant machine learning models may provide a gateway for mathematical analysis of a range of fields that were previously inaccessible. It’s remarkable for instance that trained word embeddings transform semantic relationships into algebraic operations on vectors in Euclidean space (for instance, ‘Italian’ – ‘Italy’ + ‘France’ = ‘French’). Examples like this hint at the potential for mathematics to gain a foothold in complex, real-world settings by studying the machine learning models that have trained on data from these settings.

As more and more of the data in the world is consumed and mathematicised by machine learning models, it will be an increasingly interesting time to be a mathematician. The challenge now lies in adapting our mathematical toolkit to this new landscape, where empirical breakthroughs often precede theoretical understanding. By embracing this shift, mathematics can continue to play a crucial, albeit evolving, role in shaping the future of machine learning.

The author would like to thank Darryl Hannan for help with figures, Davis Brown, Charles Godfrey, and Scott Mahan for useful feedback on drafts, as well as the staff of the Gradient for useful conversations and help editing this article. For resources and events around the growing community of mathematicians and computer scientists using topology, algebra, and geometry (TAG) to better understand and build more robust machine learning systems, please visit us at https://www.tagds.com.

References

[1] Richard Sutton. “The bitter lesson”. In: Incomplete Ideas (blog) 13.1 (2019), p. 38.

[2] Guido F Montufar et al. “On the number of linear regions of deep neural networks”. In: Advances in Neural Information Processing Systems 27 (2014).

[3] Boris Hanin and David Rolnick. “Complexity of linear regions in deep networks”. In: International Conference on Machine Learning. PMLR. 2019, pp. 2596–2604.

[4] J Elisenda Grigsby and Kathryn Lindsey. “On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networks”. In: SIAM Journal on Applied Algebra and Geometry 6.2 (2022), pp. 216–242.

[5] Ahmed Imtiaz Humayun et al. “Splinecam: Exact visualization and characterization of deep network geometry and decision boundaries”. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023, pp. 3789–3798.

[6] Phillip Pope et al. “The intrinsic dimension of images and its impact on learning”. In: arXiv preprint arXiv:2104.08894 (2021).

[7] Nicholas Konz and Maciej A Mazurowski. “The Effect of Intrinsic Dataset Properties on Generalization: Unraveling Learning Differences Between Natural and Medical Images”. In: arXiv preprint arXiv:2401.08865 (2024).

[8] Yasaman Bahri et al. “Explaining neural scaling laws”. In: arXiv preprint arXiv:2102.06701 (2021).

[9] Utkarsh Sharma and Jared Kaplan. “A neural scaling law from the dimension of the data manifold”. In: arXiv preprint arXiv:2004.10802 (2020).

[10] Alessio Ansuini et al. “Intrinsic dimension of data representations in deep neural networks”. In: Advances in Neural Information Processing Systems 32 (2019).

[11] Lucrezia Valeriani et al. “The geometry of hidden representations of large transformer models”. In: Advances in Neural Information Processing Systems 36 (2024).

[12] Henry Kvinge, Davis Brown, and Charles Godfrey. “Exploring the Representation Manifolds of Stable Diffusion Through the Lens of Intrinsic Dimension”. In: ICLR 2023 Workshop on Mathematical and Empirical Understanding of Foundation Models.

[13] Xingjun Ma et al. “Characterizing adversarial subspaces using local intrinsic dimensionality”. In: arXiv preprint arXiv:1801.02613 (2018).

[14] Peter Lorenz, Ricard L Durall, and Janis Keuper. “Detecting images generated by deep diffusion models using their local intrinsic dimensionality”. In: Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023, pp. 448–459.

[15] Fan Yin, Jayanth Srinivasa, and Kai-Wei Chang. “Characterizing truthfulness in large language model generations with local intrinsic dimension”. In: arXiv preprint arXiv:2402.18048 (2024).

[16] Justin Gilmer et al. “A loss curvature perspective on training instabilities of deep learning models”. In: International Conference on Learning Representations. 2021.

[17] Jeremy Cohen et al. “Gradient descent on neural networks typically occurs at the edge of stability”. In: International Conference on Learning Representations. 2020.

[18] Seyed-Mohsen Moosavi-Dezfooli et al. “Robustness via curvature regularization, and vice versa”. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019, pp. 9078–9086.

[19] Francisco Acosta et al. “Quantifying extrinsic curvature in neural manifolds”. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023, pp. 610–619.

[20] Gregory Naitzat, Andrey Zhitnikov, and Lek-Heng Lim. “Topology of deep neural networks”. In: Journal of Machine Learning Research 21.184 (2020), pp. 1–40.

[21] Bastian Rieck et al. “Neural persistence: A complexity measure for deep neural networks using algebraic topology”. In: arXiv preprint arXiv:1812.09764 (2018).

[22] Mustafa Hajij, Kyle Istvan, and Ghada Zamzmi. “Cell complex neural networks”. In: arXiv preprint arXiv:2010.00743 (2020).

[23] Cristian Bodnar. “Topological deep learning: graphs, complexes, sheaves”. PhD thesis. 2023.

[24] Jakob Hansen and Robert Ghrist. “Toward a spectral theory of cellular sheaves”. In: Journal of Applied and Computational Topology 3.4 (2019), pp. 315–358.

[25] Yifan Feng et al. “Hypergraph neural networks”. In: Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 33. 01. 2019, pp. 3558–3565.

[26] Felix Draxler et al. “Essentially no barriers in neural network energy landscape”. In: International Conference on Machine Learning. PMLR. 2018, pp. 1309–1318.

[27] Kiho Park, Yo Joong Choe, and Victor Veitch. “The linear representation hypothesis and the geometry of large language models”. In: arXiv preprint arXiv:2311.03658 (2023).

[28] Taco Cohen and Max Welling. “Group equivariant convolutional networks”. In: International Conference on Machine Learning. PMLR. 2016, pp. 2990–2999.

[29] Maurice Weiler, Fred A Hamprecht, and Martin Storath. “Learning steerable filters for rotation equivariant cnns”. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2018, pp. 849–858.

[30] Daniel E Worrall et al. “Harmonic networks: Deep translation and rotation equivariance”. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2017, pp. 5028–5037.

[31] Diego Marcos et al. “Rotation equivariant vector field networks”. In: Proceedings of the IEEE International Conference on Computer Vision. 2017, pp. 5048–5057.

[32] Alexandre Duval et al. “A Hitchhiker’s Guide to Geometric GNNs for 3D Atomic Systems”. In: arXiv preprint arXiv:2312.07511 (2023).

[33] Nathaniel Thomas et al. “Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds”. In: arXiv preprint arXiv:1802.08219 (2018).

[34] Manzil Zaheer et al. “Deep sets”. In: Advances in Neural Information Processing Systems 30 (2017).

[35] Vıctor Garcia Satorras, Emiel Hoogeboom, and Max Welling. “E (n) equivariant graph neural networks”. In: International Conference on Machine Learning. PMLR. 2021, pp. 9323–9332.

[36] Denis Boyda et al. “Sampling using SU (N) gauge equivariant flows”. In: Physical Review D 103.7 (2021), p. 074504.

[37] Hannah Lawrence and Mitchell Tong Harris. “Learning Polynomial Problems with SL(2,mathbb R) −Equivariance”. In: The Twelfth International Conference on Learning Representations. 2023.

[38] Josh Abramson et al. “Accurate structure prediction of biomolecular interactions with AlphaFold 3”. In: Nature (2024), pp. 1–3.

[39] Scott Mahan et al. “What Makes a Machine Learning Task a Good Candidate for an Equivariant Network?” In: ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling.

[40] Johann Brehmer et al. “Does equivariance matter at scale?” In: arXiv preprint arXiv:2410.23179 (2024).

[41] Chris Olah et al. “Naturally Occurring Equivariance in Neural Networks”. In: Distill (2020). https://distill.pub/2020/circuits/equivariance. doi: 10.23915/distill.00024.004.

[42] Giovanni Luca Marchetti et al. “Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networks”. In: arXiv preprint arXiv:2312.08550 (2023).

[43] Rahim Entezari et al. “The role of permutation invariance in linear mode connectivity of neural networks”. In: arXiv preprint arXiv:2110.06296 (2021).

[44] Samuel K Ainsworth, Jonathan Hayase, and Siddhartha Srinivasa. “Git re-basin: Merging models modulo permutation symmetries”. In: arXiv preprint arXiv:2209.04836 (2022).

[45] Bo Zhao et al. “Symmetry teleportation for accelerated optimization”. In: Advances in Neural Information Processing Systems 35 (2022), pp. 16679–16690.

[46] Bo Zhao et al. “Improving Convergence and Generalization Using Parameter Symmetries”. In: arXiv preprint arXiv:2305.13404 (2023).

[47] Charles Godfrey et al. “On the symmetries of deep learning models and their internal representations”. In: Advances in Neural Information Processing Systems 35 (2022), pp. 11893–11905.

[48] Nico Courts and Henry Kvinge. “Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps”. In: International Conference on Learning Representations. 2021.

[49] Bruno Gavranović et al. “Position: Categorical Deep Learning is an Algebraic Theory of All Architectures”. In: Forty-first International Conference on Machine Learning.

[50] Eugene P Wigner. “The unreasonable effectiveness of mathematics in the natural sciences”. In: Mathematics and Science. World Scientific, 1990, pp. 291–306.

[51] Alon Halevy, Peter Norvig, and Fernando Pereira. “The unreasonable effectiveness of data”. In: IEEE Intelligent Systems 24.2 (2009), pp. 8–12.

0 notes