#topos theory

[pv1isalsoimportant]

(Semi-regularly updated) list of resources for (not only) young mathematicians interested in logic and all things related:

Igor Oliveira's survey article on the main results from complexity theory and bounded arithmetic is a good starting point if you're interested in these topics.

The Complexity Zoo for information on complexity classes.

The Proof Complexity Zoo for information on proof systems and relationships between them.

Computational Complexity blog for opinions and interesting blog posts about computational complexity and bunch of other stuff.

Student logic seminar's home page for worksheets on proof complexity, bounded arithmetic and forcing with random variables (great introduction for beginners).

Eitetsu Ken's list for resources on proof complexity, computational complexity, logic, graph theory, finite model theory, combinatorial game theory and type theory.

Jan Krajíček's page is full of old teaching materials and resources for students (click past teaching) concernig logic, model theory and bounded arithmetic. I also recommend checking out his books. They are basically the equivalent of a bible for this stuff, although they are a bit difficult to read.

I also recommend the page of Sam Buss, there are downloadable versions of most of his articles and books and archive of old courses including resources on logic, set theory and some misc computer science. I especially recommend his chapters in Hnadbook of Proof Theory.

Amir Akbar Tabatabai's page for materials on topos theory and categories including lecture notes and recordings of lectures.

Andrej Bauer's article "Five stages of accepting constructive mathematics" for a funny and well-written introduction into constructive mathematics.

Lean Game Server for learning the proof assistant Lean by playing fun games.

[m---a---x]

Welcome to the premier of One-Picture-Proof!

This is either going to be the first installment of a long running series or something I will never do again. (We'll see, don't know yet.)

Like the name suggests each iteration will showcase a theorem with its proof, all in one picture. I will provide preliminaries and definitions, as well as some execises so you can test your understanding. (Answers will be provided below the break.)

The goal is to ease people with some basic knowledge in mathematics into set theory, and its categorical approach specifically. While many of the theorems in this series will apply to topos theory in general, our main interest will be the topos Set. I will assume you are aware of the notations of commutative diagrams and some terminology. You will find each post to be very information dense, don't feel discouraged if you need some time on each diagram. When you have internalized everything mentioned in this post you have completed weeks worth of study from a variety of undergrad and grad courses. Try to work through the proof arrow by arrow, try out specific examples and it will become clear in retrospect.

Please feel free to submit your solutions and ask questions, I will try to clear up missunderstandings and it will help me designing further illustrations. (Of course you can just cheat, but where's the fun in that. Noone's here to judge you!)

Preliminaries and Definitions:

B^A is the exponential object, which contains all morphisms A→B. I comes equipped with the morphism eval. : A×(B^A)→B which can be thought of as evaluating an input-morphism pair (a,f)↦f(a).

The natural isomorphism curry sends a morphism X×A→B to the morphism X→B^A that partially evaluates it. (1×A≃A)

φ is just some morphism A→B^A.

Δ is the diagonal, which maps a↦(a,a).

1 is the terminal object, you can think of it as a single-point set.

We will start out with some introductory theorem, which many of you may already be familiar with. Here it is again, so you don't have to scroll all the way up:

Exercises:

What is the statement of the theorem?

Work through the proof, follow the arrows in the diagram, understand how it is composed.

What is the more popular name for this technique?

What are some applications of it? Work through those corollaries in the diagram.

Can the theorem be modified for epimorphisms? Why or why not?

For the advanced: What is the precise requirement on the category, such that we can perform this proof?

For the advanced: Can you alter the proof to lessen this requirement?

Bonus question: Can you see the Sicko face? Can you unsee it now?

Expand to see the solutions:

Solutions:

This is Lawvere's Fixed-Point Theorem. It states that, if there is a point-surjective morphism φ:A→B^A, then every endomorphism on B has a fixed point.

Good job! Nothing else to say here.

This is most commonly known as diagonalization, though many corollaries carry their own name. Usually it is stated in its contraposition: Given a fixed-point-less endomorphism on B there is no surjective morphism A→B^A.

Most famous is certainly Cantor's Diagonalization, which introduced the technique and founded the field of set theory. For this we work in the category of sets where morphisms are functions. Let A=ℕ and B=2={0,1}. Now the function 2→2, 0↦1, 1↦0 witnesses that there can not be a surjection ℕ→2^ℕ, and thus there is more than one infinite cardinal. Similarly it is also the prototypiacal proof of incompletness arguments, such as Gödels Incompleteness Theorem when applied to a Gödel-numbering, the Halting Problem when we enumerate all programs (more generally Rice's Theorem), Russells Paradox, the Liar Paradox and Tarski's Non-Defineability of Truth when we enumerate definable formulas or Curry's Paradox which shows lambda calculus is incompatible with the implication symbol (minimal logic) as well as many many more. As in the proof for Curry's Paradox it can be used to construct a fixed-point combinator. It also is the basis for forcing but this will be discussed in detail at a later date.

If we were to replace point-surjective with epimorphism the theorem would no longer hold for general categories. (Of course in Set the epimorphisms are exactly the surjective functions.) The standard counterexample is somewhat technical and uses an epimorphism ℕ→S^ℕ in the category of compactly generated Hausdorff spaces. This either made it very obvious to you or not at all. Either way, don't linger on this for too long. (Maybe in future installments we will talk about Polish spaces, then you may want to look at this again.) If you really want to you can read more in the nLab page mentioned below.

This proof requires our category to be cartesian closed. This means that it has all finite products and gives us some "meta knowledge", called closed monoidal structure, to work with exponentials.

Yanofsky's theorem is a slight generalization. It combines our proof steps where we use the closed monoidal structure such that we only use finite products by pre-evaluating everything. But this in turn requires us to introduce a corresponding technicallity to the statement of the theorem which makes working with it much more cumbersome. So it is worth keeping in the back of your mind that it exists, but usually you want to be working with Lawvere's version.

Yes you can. No, you will never be able to look at this diagram the same way again.

We see that Lawvere's Theorem forms the foundation of foundational mathematics and logic, appears everywhere and is (imo) its most important theorem. Hence why I thought it a good pick to kick of this series.

If you want to read more, the nLab page expands on some of the only tangentially mentioned topics, but in my opinion this suprisingly beginner friendly paper by Yanofsky is the best way to read about the topic.

[ms-foobles]

IF 𝒞 IS A TOPOS THEN 𝒞↓I IS ALSO A TOPOS FOR ALL OBJECTS I??????!!?!!!!!

[max1461]

california bans riemannian geometry because it is kinda white supremacist to put a metric on a manifold. florida bans topos theory becuase grothendieck was Woke

[twocubes]

Hey I asked you this a while a while ago on anon but hey we're mutuals I can ask you on non anon I think. So uh. So I've been working on this longterm-ish project of, uh, trying to understand what mathematical induction Really Is. And in the course of this I've started reading about the theory of sketches, because I think I need sketches to answer this question. And you know about sketches I think, I think you've used sketches for your project...

What is your project again?

But anyway, so. I'm on hiatus from my project cause I got brain damage. Uh.

Oh right the other thing that seems important for my deal is institutions, have you heard of institutional model theory?

So I guess my question is:

what is your project again? with topos theory(?)?

did you use sketches?

did you use any institutional model theory?

Uh. Well. Tha'ts my questions sorry this ask is disjointed as fuck.

sorry, i kept going to answer this ask and then getting distracted with like, looking into various math things i like (currently: codensity monads, synthetic differential geometry (well i was trying to read about C^∞ algebras), and how-do-you-define-(lax/pseudo)-transfors-between-weak-n-categories-anyways)

so, i haven't worked on my project in a while because ive been just having life problems full time instead. but i'm doing a little better now, so i've been doing math again, so i might get back on it.

my project is: i want to generalize the notion of topos so you can write classifying "toposes" for theories written in more general types of logics. stuff like linear logic or maybe stuff with like richer 2-structure. idk. there's a theorem in the depths of the Elephant (the big book on topos theory) that i thought might lead the way, but in order to do that i have to read and understand a majority of that book. this is kind of a way to force myself to like. Learn A Big Important Thing Fully. because of course this idea might just not work out. its research.

I ran into sketches when i was teaching myself category theory out of the Handbook of Categorical Algebra; they're presented there as like, a broad approach to model theory from a categorial perspective? You learn about them in the context of the equivalence between categories of models of sketches and accessible categories. Sketches are sort of tangential to topos-algebra stuff, although i think they're like. So, given a fairly general type of algebraic theory, there is a classifying topos for that theory; conversely every grothendieck topos is a classifying topos for some theory. probably a sketch is a good way to express that. idk it's in volume D of the elephant and i was going through it sequentially.

ive never heard of institutional model theory at all?

[proof-by-intimidation]

alright, Lurie's higher topos theory hits so hard. Can't wait to get into it seriously

[vladdocs]

Greetings!

Time has come for me to also ask you a question :D. I would like to know more about the claim that Vlad III had beggars and homeless people burned alive. I've read that he might've stopped the spreading of the plague to Wallachia, and that he himself said about those people that he ended their suffering for better afterlife. Did he really burn them ALIVE though? That seems unnecessarily cruel. Before he made the impression on me of being tough but just, however not sadistic. Of course we probably can't be sure, as we never can when it comes to history, but what is your theory? (I haven't got the time to translate CD yet, apologies). Thank you for your kind reply! May God rejoice over you.

Don't worry about translating CD, It has plenty of info but nothing on that subject, The propaganda texts will be in vol 2 that will come out next year. That story is part of the German propaganda, and it's a topos. That means you will find the same story in other's people cases Other stories that are topos are Vlad killing the lazy wife of a man with ripped shirt or Vlad nailing the turbans of the ottomans messengers, this one with massagers it even funnier because it had the habit to change the messengers and the hats instead of the evil characters so in some countries we have the diabolical tyrant Trakale punishing the Italian messengers by nailing their berets to their head. That story is a lot more popular because it was used by communists to show how cruel the monarchy was. So all the cruel story you hear about Vlad were already existing before him but with other characters, so it is after Vlad with someone else. You most likely wonder where do they originate in the first place, Dr. Albert Weber researched this and found out that almost all the stories about Vlad can be tracked down to... this might come as a surprise to some but for most as an "Of course him"... The emperor Nero

In CD vol 2 we gonna learn everything about those stories, their source and follow-ups until then here are some CD videos on this subject:

[geronimosothercadilac]

Art Theory - The reason why people think Geronimo Stilton is not male.

First look how masculine Geronimo Stilton is in earlier illustrations like this one below.

Think again:-

He looks noticeably slimmer and more like a fox/jackal. Notice how feminine he looks in this remake of this one above.

The Theory - Possible attempt to make character appeal to female audiences. Another thing is that he is based on a combination of famous literary personalities like most detectives (Sherlock Holmes, Hercule Poirot and more), other rats (like those of Beatrix Potter or Anthony Browne), and Lewis Carroll's Alice! His features (physical and mental) might be taken from those characters. Interestingly enough, those are all British works I mentioned, however he may also be influenced by Topo Gigio (Italian cartoon series).

[ishtaraletheia]

Course notes for Axiomatic Set Theory by Tom Leinster at the University of Edinburgh

I ran into these notes on accident, and they answered a question that had lurked in the back of my mind for ages, namely, what properties uniquely characterize the category of sets as a category? The answer is the ten axioms of (a variant of) Lawvere's Elementary Theory of the Category of Sets. Turns out, the properties end up being pretty nice!

Insights include:

Elements can be, and perhaps should be, thought of as the function from the one-element set "pointing" to said element. Function application is a special case of composition. I knew this already but reading this really hammered it home.

Ordinary mathematical practice is (mostly) strongly typed, while ZFC is not.

Sets are given meaning through functions. {1, 2} and {3, 4} are isomorphic, just different labellings of the two-element set, but you can distinguish them by considering the inclusion functions into ℕ implied by said labellings.

Sets and subsets are different; elements of sets and elements of subsets are different. Subsets of sets and subsets of subsets are different. Sets are "types", subsets are collections of elements of a given "type".

The Axiom of Choice is, in some sense, obvious. The product of sets that each have an element has an element, namely the "tuple" of said elements. It would certainly be something if the product was empty!

There has to be a nicer way to prove that integer operations inherit the properties of natural number operations and so on, without all that boilerplate! Presumably you'd need more machinery to the point there wouldn't be any net gain, but still it's annoying.

I should maybe read up on topos theory?

Big recommendation! Especially if you have any experience with university-level pure mathematics.

[the-girl-who-didnt-smile]

THE ESU-ELEGBARA COLLECTIVE

How Èṣù-Ẹlẹ́gbára pertains to “The Spirit at the Crossroads”, and possibly Hoodoo Saint Peter

THE “ESU-ELEGBARA COLLECTIVE”

Across the African diaspora, there exists a collection of “trickster” deities, including Esu, Legba, Elegua, and their many derivatives. While these deities are different from each other, they can be grouped together because of their common origin in Èṣù-Ẹlẹ́gbára.

Just as the Romans borrowed from the Greek pantheon, the kingdom of Dahomey borrowed from the Yoruba pantheon. The orisa and vodún were transmitted to the New World via the transatlantic slave trade, where they continued to undergo transformations. 

When the Yoruba orisa Esu (Èṣù-Ẹlẹ́gbára) was transmitted to the kingdom of Dahomey, he became the vodún Legba. When the vodún Legba was transmitted to Haiti, he refracted into the lwa Papa Legba and Mèt Kafou. When he was transmitted to Cuba, he became Elegua and Lucero Mundo. 

Henry Louis Gates Jr. proposed the concept of an “Èṣù-Ẹlẹ́gbára collective” in The Signifying Monkey (1988): 

"Of the music, myths, and forms of performance that the African brought to the Western Hemisphere, I wish to discuss one specific trickster figure that recurs with startling frequency in black mythology in Africa, the Caribbean, and South America... This topos that recurs throughout black oral narrative traditions and contains a primal scene of instruction for the act of interpretation is that of the divine trickster figure of Yoruba mythology, Esu-Elegbara. This curious figure is called Esu-Elegbara in Nigeria and Legba among the Fon in Benin. His New World figurations include Exú in Brazil, Echu-Elegua in Cuba, Papa Legba…in the pantheon of the loa of Vaudou of Haiti, and Papa La Bas in the loa of Hoodoo in the United States. Because I see these individual tricksters as related parts of a larger, unified figure, I shall refer to them collectively as Esu, or as Esu-Elegbara. These variations on Esu-Elegbara speak eloquently of an unbroken arc of metaphysical presupposition and a pattern of figuration shared through time and space among certain black cultures in West Africa, South America, the Caribbean, and the United States. These trickster figures, all aspects or topoi of Esu, are fundamental, divine terms of mediation: as tricksters they are mediators, and their mediations are tricks. If the Dixie Pike leads straight to Guinea, then Esu-Elegbara presides over its liminal crossroads, a sensory threshold barely perceptible without access to the vernacular, a word taken from the Latin vernaculus ("native"), taken in turn from verna ("slave born in his master's house").” 

SOURCE: Gates, Henry Louis. The Signifying Monkey: A Theory of African-American Literary Criticism. United States, Oxford University Press, USA, 1988. p. 5  https://archive.org/details/signifyingmonkey0000gate/page/5/mode/2up 

Several other deities can considered “parts” of the Èṣù-Ẹlẹ́gbára collective, including Lucero Mundo and Mèt Kafou (Maitre Carrefour).

While they may differ in appearance, mythology, and worship, the “parts” of the Èṣù-Ẹlẹ́gbára collective have several things in common, including: 

They are divine “tricksters”.

They are associated with a person’s fortune / fate. 

They are associated with liminality and intermediary spaces (e.g., doors, gates, entrances, roads, intersections, crossroads…)

They are associated with an African understanding of the cross. 

They feature prominently in their respective pantheons.

Above all, they share a common origin in Èṣù-Ẹlẹ́gbára.

For a lengthier discussion of this concept, see: Cosentino, Donald. “Who Is That Fellow in the Many-Colored Cap? Transformations of Eshu in Old and New World Mythologies.” The Journal of American Folklore, vol. 100, no. 397, 1987, pp. 261–75. JSTOR, https://doi.org/10.2307/540323. Accessed 10 Sept. 2024.

2. THERE IS MORE THAN ONE HOODOO “SPIRIT AT THE CROSSROADS” 

In Hoodoo, there is an unnamed “Spirit at the Crossroads” who might be connected to the Èṣù-Ẹlẹ́gbára collective. This spirit appears in Volumes 1 and 5 of Harry Middleton Hyatt’s Hoodoo, Conjuration, Witchcraft & Rootwork, where is called “the Devil”:

Hyatt, Hyatt, Harry Middleton. Hoodoo - Conjuration - Witchcraft - Rootwork, Vol. 1. United States, Western Publishing Company, 1970, pp. 97-111. https://archive.org/details/harry-middleton-hyatt-hoodoo-conjuration-witchcraft-rootwork-vols-1-5/HARRY%20MIDDLETON%20HYATT%20-%20Hoodoo%2C%20Conjuration%2C%20Witchcraft%20%26%20Rootwork%20Vo%201/page/97/mode/2up? 

Hyatt, Hyatt, Harry Middleton. Hoodoo - Conjuration - Witchcraft - Rootwork, Vol. 5. United States, Western Publishing Company, 1978, pp. 4003-4013. https://archive.org/details/harry-middleton-hyatt-hoodoo-conjuration-witchcraft-rootwork-vols-1-5/HARRY%20MIDDLETON%20HYATT%20-%20Hoodoo%2C%20Conjuration%2C%20Witchcraft%20%26%20Rootwork%20Vo%205/page/4002/mode/2up? 

An insightful video was posted on Youtube last year, titled “The Man of The Crossroads ( An Intellectual Debate) (Hoodoo)”. In this video, PapaSeer and Chan “The Musical Mystic” debate the identity of “Man at the Crossroads”.

The entire video is worth watching, and several interesting things come out of it. 

At 5:17, Chan describes the crossroads spirit as “an intermediary spirit that governs the portals between the physical and spiritual”. He is associated with “keys” “windows” “doors” and “intersections”. Chan also notes that many spirits of the crossroads are considered “tricksters” , where lengthier discussions of trickster spirits take place at 36:45 and 51:28. 

At 26:13, PapaSeer provides a detailed description of the “Man at the Crossroads”, who is figured as a “Dealmaker”:

“The man at the Crossroads, when he materializes, is typically – from what I’ve always seen – it’s always been in the form of some type of beggar. And it’s not always a Black person… It’s always some type of beggar… somebody that needs something. The man at the Crossroads tends to favor people who are downtrodden, who are in a very bad situation, when your luck is not lucky, when you are just at your wits end, this is when he tends to show some favor to people. Now, outside of that, he want what he wants to give you something back. And I haven’t seen anything outside of that. So when people talk about he’s a spirit of protection, and this, and that, I’m just like ‘No, he’s simple! He want something to give you back something!’ And you have to make some type of pact. You have to form some type of deal for this relationship to flourish. You can’t even just come to him just one time. It’s a succession of times that you have to petition him for it to be effective. This has been my personal experience.”

At 46:01 and 48:46, PapaSeer and Chan both describe the physical appearance of the Spirit at the Crossroads. He is described as a humble, old beggar, who wears tattered clothes and has no interest in material things. 

Importantly, PapaSeer and Chan agree that the Spirit at the Crossroads is more than one thing. They assert that he can manifest as several different deities, including Jesus (Yeshua) and the Christian Devil. 

Notably, both debaters of the Abrahamic Hoodoo tradition. PapaSeer is from Virginia, while Chan is from South Carolina – closer, in proximity, to New Orleans. Folklore involving the Spirit at the Crossroads is described as being “very prevalent” in the Deep South. It is not PapaSeer, but Chan who identifies the Crossroads Spirit with certain African-derived deities - namely, Esu, Elegua, and Legba.

If this Spirit at the Crossroads is a part of the Èṣù-Ẹlẹ́gbára collective, which one(s) could he be?

3. SIMILARITIES WITH ESU

What is arguably the single most fascinating trickster god from any world religion, Esu (Èṣù-Ẹlẹ́gbára) is a deity whose complexity is often compressed and mischaracterized. 

A being with many different names and forms, Ayodele Ogundipẹ describes Esu like so: 

“Èṣù…is the messenger of the gods, the mediator between God and humans between order and chaos, sin and punishment, life and death, fate and accident, certainty and uncertainty. It is no wonder then, that Èṣù in myth knows no master, that he is male and female, that he is tall and short, kind and cruel, an elderly deity of youth who lives at the crossroads.”

SOURCE: Ogundipe, Ayodele. Esu Elegbara: chance, uncertainty in Yorùbá mythology. Kwara State University Press, 2018. p. 130

Funso Aiyejina describes Esu as “the deity of choice and free will”. His behavior reflects the nature of fate itself - unpredictable. His tricks and mischief often serve the purpose of teaching lessons; especially, that one requires complete information and consciousness before exercising judgment. 

SEE: Oyèláràn, Ọlásopé O. "Èṣù and ethics in the Yorùbá world view." Africa 90.2 (2020): 377-407.

Esu is also called onile orita or “the one who lives at the crossroads”, for that is where he dwells. While it is often translated as “crossroads”, the word orita refers to several different types of intermediary spaces, including front yards and gateways. For this reason, Esu is described as both “gatekeeper” and “lord of crossroads”, where the orita symbolizes the intersection of physical and metaphysical realms in Yoruba philosophy.

SEE: Aiyejina, Funso. "Esu Elegbara: A Source of an Alter/Native Theory of African Literature and Criticism." text of a lecture from his work in progress on ‘Decolonising Myth: From Esu to Bachaanal Aesthetics (2010). https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=25a632183b18b3d34abea946fb0fab4e0f6a864f 

While he is often figured as being small and dark-skinned, Esu is a shape-shifter who can assume hundreds of different forms. One of the forms Esu assumes is that of an “old man at the crossroads”. In this form, he smokes a pipe: 

“My informants told me that Èṣù’s pipe accouterments are for his depiction as an old man or an elder, for the elderly in Yoruba society like to relax with a pipe. My informants also told me that since Èṣù lives at the crossroads and in open places, one way people know he is there, especially after dark, is by smoke puffs from his pipe. Seeing the glow from the pipe, passersby would salute him, ‘Epa Èṣù!’”

SOURCE: Ogundipe, Ayodele. Esu Elegbara: chance, uncertainty in Yorùbá mythology. Kwara State University Press, 2018. p. 98

This is similar to how Hyatt’s “Devil at the Crossroads” manifests in different forms, ranging from a “great big black man” to a "a lil' ole funny boy” 

Ogundipe describes Esu as energetic and loving to dance (p. 64), while Gates describes him as limping (p. 6):

"In Yoruba mythology, Esu is said to limp as he walks precisely because of his mediating function: his legs are of different lengths because he keeps one anchored in the realm of the gods while the other rests in this, our human world."

SOURCE: Gates, Henry Louis. The Signifying Monkey: A Theory of African-American Literary Criticism. United States, Oxford University Press, USA, 1988. p. 6 https://archive.org/details/signifyingmonkey0000gate/page/6/mode/2up? 

4. SIMILARITIES WITH PAPA LEBAT (NEW ORLEANS VOODOO)

It is important to note that there are three different deities named Legba: 

Legba of West African Vodún

Papa Legba of Haitian Vodou

Papa Lébat (“Papa La Bas”) of New Orleans Voodoo (Louisiana Voudou)

The most popular name for Papa Lébat was probably “Papa La Bas” or “La Bas” (“Laba”). However, I avoid calling him this, as it is a reference to “Satan”. He was called other names, like "Papa Limba". In the present day, neither “Papa Lébat” nor "Papa La Bas" is commonly used; he is usually just called "Papa Legba", which is actually the accurate pronunciation. So not to confuse him with the West African vodún or the Haitian lwa, I will refer to the spirit of New Orleans Voodoo as “Papa Lébat”. 

Much like the different parts of the Èṣù-Ẹlẹ́gbára collective, these should be considered different deities who are worshiped in different ways.  

As the Romans borrowed Hermes from the Greeks, the Fon borrowed Esu from the Yoruba. In the kingdom of Dahomey, Esu became Legba. 

There are many similarities between Esu and Legba, as described by Steven M. Friedson:

“A divine trickster, Legba, as with that other phallic god Hermes, is also the divine messenger, the linguist (tsiami) who speaks the language of the sky. Because he patrols the borders and protects the threshold, all sacrifice, all libation, ultimately all meaning goes and comes through him, hence his infinite possibilities, his refusal to be pinned down. Translator, trickster, protector, linguist–all this and more comes under the sign of the crossroads where Legba rules, where there are always-already multiple paths, multiple meanings. And lest we think we have finally pinned Legba down as the phallic god par excellence, pregnant with meaning, it is helpful to remember that sometimes, though it is fairly rare, Legba manifests himself in female form complete with clay breasts. Nothing is quite what it seems.”

SEE:  Friedson, Steven M. Remains of ritual: Northern gods in a southern land. University of Chicago Press, 2019. https://staff.washington.edu/ellingsn/Friedson-Remains-Ritual_00_Title-Intro.pdf 

AND: Ogundipe, Ayodele. Esu Elegbara: chance, uncertainty in Yorùbá mythology. Kwara State University Press, 2018. pp. 120-123

Like Esu, Legba presides over crossroads and gates: 

“The assistants knelt in front of a large white basin around which a circle of chalk was inscribed in the sand for Legba, Yewevodu god of crossroads, keeper of gates, and guardian of ritual knowledge.”

SOURCE: Montgomery, Eric, and Vannier, Christian. An Ethnography of a Vodu Shrine in Southern Togo: Of Spirit, Slave and Sea. Netherlands, Brill, 2017. p. 197

Unlike Esu, the vodún Legba is associated with the dog - “the animal is sacred to him”. He also has a different origin myth from Esu, where he was made chief of the gods for his mastery over musical instruments. For this reason, he is associated with music and dancing.

SOURCE: Herskovits, Melville Jean, and Frances Shapiro Herskovits. Dahomean narrative: a cross-cultural analysis. Northwestern University Press, 1958. https://archive.org/details/dahomeannarrativ0000hers/page/138/mode/2up? 

Notably, “The Devil at the Crossroads” is also associated with music, where a section of Hoodoo - Conjuration - Witchcraft - Rootwork, Vol. 1 is titled “Diabolic Music”. For a lengthier discussion about this shared connection, see: Marvin, Thomas F. “Children of Legba: Musicians at the Crossroads in Ralph Ellison’s Invisible Man.” American Literature, vol. 68, no. 3, 1996, pp. 587–608. JSTOR, https://doi.org/10.2307/2928245. Accessed 11 Sept. 2024.

“The Spirit at the Crossroads” might also have an association with dogs. Dogs also appear a few times under Hyatt’s “Sell Self to the Devil”, with one of the most memorable accounts involving "a lil' ole funny boy” – described as a strange dog/human hybrid. In another case, a man goes to the crossroads to acquire musical talent, but is scared off by a big black dog. Because he is associated with other animals, it is unclear whether the Crossroads Spirit has a fondness for dogs, or if it is a mere coincidence.

In Haiti, Legba underwent a dramatic transformation. Where the Dahomean Legba appeared as a hypersexual young man, the Haitian Papa Legba appears as a weary, old man. 

Milo Marcelin described Papa Legba him like so: 

“On se le représente sous les traits d'un vieillard, cassé par l'âge, à demi paralysé, qui s'avance péniblement avec l'aide d'une canne ou d'une béquille. Le nom de Legba-pied-cassé, qui lui est parfois donné, traduit bien l'aspect pitoyable sous lequel on se l'imagine. Legba est coiffé d'un chapeau de paille à large bord, il porte une macoutte (sacoche en feuilles de latanier) et i fume sans arrêt une longue pipe en terre cuite. Son grand chapeau lui permet de protéger les loa de Guinée (d'Afrique) contre les ardeurs du soleil…”

TRANSLATION:

“He is represented as an old man, broken by age, half-paralyzed, who hobbles with the aid of a cane or crutch. The name Legba-pied-cassé, which is sometimes given to him, translates well the pitiful appearance in which he is imagined. Legba dons a large-brimmed straw hat, he carries a macoutte (palm leaf sack) and he endlessly smokes a long, terracotta pipe. His large hat lets him protect the loa from Guinea (Africa) from the heat of the sun…”

SOURCE: MARCELIN, Émile, and A. Métraux. “LES GRANDS DIEUX DU VODOU HAIÏTIEN.” Journal de La Société Des Américanistes, vol. 36, 1947, pp. 51–135. JSTOR, http://www.jstor.org/stable/24601899. Accessed 18 Sept. 2024.

Interestingly, Papa Legba appears similar to the form Esu assumes when disguising himself as an old man, where both smoke a pipe. Like his Fon counterpart, Papa Legba is associated with dogs and described as a “trickster”.

In the present day, Papa Legba is often associated with gates and doors, while the Petwo lwa Mèt Kafou (Maitre Carrefour) is associated with crossroads. However, this distinction does not seem to have always been the case. 

Marcelin described Papa Legba as a lwa with many names and functions, where he is both doorkeeper and “master of crossroads”: 

“Papa Legba ou Atibon-Legba est le dieu des portes, le maître des carrefours et des croisées de chemins et le protecteur des maisons. En vertu de ces différentes fonctions, il est invoqué sous les noms de « Legba-nan- bayè » (Legba des barrières), de « Legba-calfou » (Legba des carrefours) ou « Grand chemin », de « Legba Mait' bitation » ou « Legba Maiť habitation ». En tant que dieu qui sait toutes choses, il porte l'épithète d'Avadra...”

“...Pour invoquer Legba, l'officiant se sert d'une pierre qu'il place sur l'autel. Ensuite il trace un dessin symbolique (vèvè) sur le sol et récite la prière suivante :

Par pouvoir saint Antoine, au nom de M. Avadra Boroy, de Legba-Atibon, le maître des carrefours et des grands chemins, de Legba-Kataroulo, de vaillant Legba, de Legba-Sé, de Alegba-Si, de Legba-Bois, de Legba-Zinchent, de Legba- Caye, de Legba-Misé-ba, de Legba-Clairondé, de Legba-Signangnon, des sept Legba-Kataroulo, vieux, vieux, vieux Legba. Ago, Agoé, Angola.”

TRANSLATION

“Papa Legba or Atibon-Legba is the god of doors, the master of crossroads and the protector of houses. By virtue of these different functions, he is invoke under the names of “Legba-nan- bayè” (Legba of the Barriers), “Legba-calfou” (Legba of the Crossroads) or “Grand chemin”, “Legba Mait’ bitation” or “Legba Mait’ habitation”. As the god who knows all things, he bears the epithet of “Avadra”...”

“...To invoke Legba, the officiant uses a stone that he places on the altar. Then he traces a symbolic drawing (vèvè) on the ground and recites the following prayer: 

By the power of Saint Anthony, in the name of Mr. Avadra Boroy, of Legba-Atibon, the master of the crossroads and great paths, of Legba-Kataroulo, of valiant Legba, of Legba-Sé, of Alegba-Si, of Legba-Bois, of Legba-Zinchent, of Legba-Caye, of Legba-Misé-ba, of Legba-Clairondé, of Legba-Signangnon, of the seven Legba-Kataroulo, old, old, old Legba. Ago, Agoé, Angola.”

SOURCE: MARCELIN, Émile, and A. Métraux. “LES GRANDS DIEUX DU VODOU HAIÏTIEN.” Journal de La Société Des Américanistes, vol. 36, 1947, pp. 51–135. JSTOR, http://www.jstor.org/stable/24601899. Accessed 18 Sept. 2024.

This might explain why New Orleanians - such as Ava Kay Jones and Denise Alvarado - have described Papa Lébat (“Papa La Bas”) as both gatekeeper and guardian of the crossroads. Although I have been referring to it as “New Orleans Voodoo”, this is a misnomer, as the religion was practiced across the Mississippi River Valley of America. New Orleans Voodoo is not Americanized Haitian Vodou, but has a rich history that predates the Haitian migration wave. That being said, several Haitian elements can be identified.

Following the Haitian Revolution, a large number of Haitians fled to the city of New Orleans. With them, they brought their religious practices, which were incorporated into the Voodoo (Voudou) that was already present in America. As there is continuity between Fon Legba and Haitian Papa Legba, there is also continuity between the Haitian Papa Legba and the American Papa Lébat. 

Much like his Haitian counterpart, Papa Lébat was identified with St. Peter, and a similar song was sung asking him to “open the door” (“ouvre baye”):

“Marie Laveau…even taught her a Voodoo song. It went like this:

St. Peter, St. Peter, open the door,

I’m callin’ you, come to me!

St. Peter, St. Peter, open the door …

“That’s all I can remember. Marie Laveau used to call St. Peter somethin’ like ‘Laba.’ She called St. Michael ‘Daniel Blanc,’ and St. Anthony ‘Yon Sue.’”

SOURCE: Source: Tallant, Robert. Voodoo in New Orleans. 1946. Reprint, Gretna, La.: United Kingdom, Pelican Publishing Company, 1983.

The historical record of Papa Lébat is sparse, but it is likely that there were differences between him and Papa Legba. For one, there were already people of Fon/Ewe descent in America, who may have been worshiping the vodún Legba prior to the Haitian migration wave. For two, there is no record of an American version of Maitre Carrefour. In the historical record, it is not Maitre Carrefour, but “Papa La Bas” who is identified with “The Devil”. 

For these reasons, it is not the Haitian lwa, but the American Papa Lébat who might be identified with “The Devil at the Crossroads”. 

5. SIMILARITIES WITH MAITRE CARREFOUR 

It is presently unknown whether Maitre Carrefour was worshiped in New Orleans, or if the division between Papa Legba and Maitre Carrefour existed there. Since he is one of the Petwo lwa, it is possible that he was worshiped in secret. If so, he would have been brought to New Orleans by followers of the Don Pedro sect - the colonial precursor to the Petwo rite.

Similar to Esu and Legba, Maitre Carrefour is sometimes erroneously described as “evil” or a “demon”. 

In Vol. 1 of Hyatt’s Hoodoo Conjuration Witchcraft & Rootwork (5 vol.s), there is a subsection of “SELL SELF TO THE DEVIL”, titled “BIG BLACK MAN”. In one of these interviews, “The Devil” is described as “a great big black man”. In another, he is described as “a big black man” who gives you “the power to accomplish what you want to do.”

Source: “BIG BLACK MAN” under “SELL SELF TO THE DEVIL”, in Hyatt, Harry M. "Hoodoo; Conjuration; Witchcraft; Rootwork (5 Volumes)." Hannibal, MO: Western Publishing Company (Vol. 1) (1970). pp. 103-104: https://archive.org/details/HoodooConjurationWItchcraftRootwork/Hoodoo%20Conjuration%20WItchcraft%20%26%20Rootwork%20Vol%201/page/n167/mode/2up 

Tommy Johnson (unrelated to Robert Johnson) made a similar comment, as quoted by his brother Rev. LeDell Johnson: 

“Take your guitar and you go down to where a road crosses that way, where a crossroad is. Get there, be sure to get there just a little ‘fore twelve o’clock that night so you know you’ll be there. You have your guitar and be playing a piece sitting there by yourself. You have to go by yourself and be sitting there playing a piece. A big black man will walk up there and take your guitar, and he’ll tune it. And he’ll play a piece and hand it back to you. That’s the way I learned how to play anything I want.” Source: Evans, David (1971 ). Tommy Johnson. Studio Vista, London p. 22-23. ISBN978-0289701515.

This is similar to Maya Deren’s description of Maitre Carrefour: 

“This is no ancient, feeble man; Carrefour is huge and straight and vigorous, a man in the prime of his life. His arms are raised strongly in the configuration of a cross. Every muscle of the shoulders and back bulges with strength. No one whispers or smiles in his presence.”

Source: Deren, Maya. Divine Horsemen : The Living Gods of Haiti. New Paltz, NY: McPherson, 1983 (originally published in 1953), p. 101: https://archive.org/details/divinehorsemenli00dere/page/100/mode/2up 

Maitre Carrefour’s colors are red and black, which might be relevant if “The Spirit at the Crossroads” also wears these colors.

In part, the Petwo rite has been misrepresented as “evil” because of the threat it posed to the institution of slavery, with its founder Don Pedro (Jean Petro) being a maroon leader. Lwa within the Petwo rite can grant someone immediate access to power without regard for systems of morality. Naturally, such immediate access to power would be dangerous and easily abused, but it can also be used for just causes, such as the liberation of slaves.

From Maya Deren: 

"If the Rada loa represent the protective, guardian powers, the Petro loa are the patrons of aggressive action….For example, whereas Erzulie, the Rada Goddess of Love, who is the epitome of the feminine principle, is concerned with love, beauty, flowers, jewelry, femininities and coquetries, liking to dance and to be dressed in fine clothes, weeping in a most feminine fashion for not being loved enough, the figure of Erzulie Ge/Rouge, on the Petro side, is awesome in her poignancy. When she possesses a person, her entire body contracts into the terrible paralysis of frustration; every muscle is tense, the knees are drawn up, the fists are clenched so tightly that the fingernails draw blood from the palms. The neck is rigid and the tears stream from the tightly shut eyes, while through the locked jaw and the grinding teeth there issues a sound that is half groan, half scream, the inarticulate song of in/turned cosmic rage.Petro was born out of this rage. It is not evil; it is the rage against the evil fate which the African suffered, the brutality of his displacement and his enslavement. It is the violence that rose out of that rage, to protest against it. It is the crack of the slave/whip sounding constantly, a never-to-be-forgotten ghost, in the Petro rites. It is the raging revolt of the slaves against the Napoleonic forces. And it is the delirium of their triumph. For it was the Petro cult, born in the hills, nurtured in secret, which gave both the moral force and the actual organization to the escaped slaves who plotted and trained, swooped down upon the plantations and led the rest of the slaves in the revolt that, by 1804, had made of Haiti the second free colony in the western hemisphere, following the United States. Even today the songs of revolt, of "Vive la liberte", occur in Petro ritual as a dominant theme.” 

Deren, Maya. Divine Horsemen: The Living Gods of Haiti. United States, McPherson, 1983. pp. 61-62 https://archive.org/details/divinehorsemenli00dere/page/60/mode/2up? 

For this reason, Hoodoo has been likened to the Petwo rite - not the Rada rite - of Haitian Vodou:

“The Petwo side of Vodou is one largely of action; it can be said that it is the Petwo incarnation of Vodou that is recognizable in American Hoodoo Conjure.”

Lane, Megan. Hoodoo heritage: A brief history of american folk religion. Diss. University of Georgia, 2008.  https://getd.libs.uga.edu/pdfs/lane_megan_e_200805_ma.pdf 

If Maitre Carrefour had already split off from Papa Legba, maybe he was incorporated into the Hoodoo community, where he was identified with “The Devil at the Crossroads”. 

6. THE CROSSROADS SPIRIT - A NOVEL ASPECT OF ESU-ELEGBARA?

Rather than being Esu, Papa Lébat, or Maitre Carrefour, “The Spirit at the Crossroads” might be a novel aspect of the Èṣù-Ẹlẹ́gbára collective. 

Every time Èṣù-Ẹlẹ́gbára is transmitted to a new culture, he undergoes transformations. Furthermore, African Americans of the South are ethnically heterogeneous, where some descend from the Yoruba, the Fon, the Ewe, and so on. Historically, Esu and Papa Lébat were both identified with Satan. Over time, African Americans forgot the names Esu and Lébat. He was simply called “the Devil”; later, “The Spirit at the Crossroads”. 

Because they were both identified with “The Devil” and “crossroads”, it is plausible that Esu and Papa Lébat recombined with each other, forming a new part of the Èṣù-Ẹlẹ́gbára collective. This could explain why “The Spirit at the Crossroads” shares traits with Esu and Papa Lébat.

7. ESU-ELEGBARA, THE DEVIL, & JESUS CHRIST

It may be worth noting that parts of the Èṣù-Ẹlẹ́gbára collective are paradoxically associated with both the Devil and Jesus Christ. 

Historically, he was not called “Spirit” but “The Devil at the Crossroads” (see: Harry Middleton Hyatt’s Hoodoo, Conjuration, Witchcraft & Rootwork, Vol. 1 & Vol. 5)

Esu was associated with the Devil, to the extent that the word “Devil” was translated as “Esu” in the Yoruba language. See: Kanu, Ikechukwu Anthony. "The hellenization of African traditional deities: The case of Ekwensu and Esu." AQUINO| Journal of Philosophy 1.3 (2021). https://acjol.org/index.php/aquino/article/download/1830/1808 

In Dahomean Narrative (1958), Herskovits describes how the vodún Legba was identified with the Devil: "It has been conjectured that the Christian missions, by identifying Legba with the Devil, have helped to make him an especially popular figure in Dahomean lore." p. 36

In America, Papa Lébat (“Papa La Bas”, “Papa Limba”) was identified with the Devil by interviewees of the Federal Writer’s Project, which can be found in Robert Tallant’s (1984) Voodoo in New Orleans.

One of these interviews involves Alexander Augustin, described by Noël Mellick Voltz as a “former free person of color”, “an old mulatto”, and a “spiritualist”:

“Alexander Augustin remembered some of the tales of old people which dated to the era of the Widow Paris.

They would thank St. John for not meddlin’ wit’ the powers the devil gave ’em,” he said. “They had one funny way of doin’ this when they all stood up to their knees in the water and threw food in the middle of ’em. You see, they always stood in a big circle. Then they would hold hands and sing. The food was for Papa La Bas, who was the devil. Oldtime Voodoos always talked about Papa La Bas. I heard lots about the Maison Blanche. It was painted white and was built right near the water wit’ bushes all around it so nobody couldn’t see it from the road. It was a kind of hoodoo headquarters.”

SOURCE: Source: Tallant, Robert. Voodoo in New Orleans. 1946. Reprint, Gretna, La.: United Kingdom, Pelican Publishing Company, 1983. pp. 65-66

A second interview involves Josephine McDuffy (“Josephine Green”), described by Jeffrey E. Anderson as a “former slave”: 

Josephine Green, an octogenarian, recalled her mother’s stories about Marie Laveau.

“My ma seen her,” Josephine boasted. “It was back before the war what they had here wit’ the Northerners. My ma heard a noise on Frenchman Street where she lived at and she start to go outside. Her pa say, ‘Where you goin’? Stay in the house!’ She say, ‘Marie Laveau is comin’ and I gotta see her.’ She went outside and here come Marie Laveau wit’ a big crowd of people followin’ her. My ma say that woman used to strut like she owned the city, and she was tall and good-lookin’ and wore her hair hangin’ down her back. She looked just like a Indian or one of them gypsy ladies. She wore big full skirts and lots of jewelry hangin’ all over her. All the people wit’ her was hollerin’ and screamin’, ‘We is goin’ to see Papa Limba! We is goin’ to see Papa Limba!’ My grandpa go runnin’ after my ma then, yellin’ at her, ‘You come on in here, Eunice! Don’t you know Papa Limba is the devil?’ But after that my ma find out Papa Limba meant St. Peter, and her pa was jest foolin’ her.”

SOURCE: Source: Tallant, Robert. Voodoo in New Orleans. 1946. Reprint, Gretna, La.: United Kingdom, Pelican Publishing Company, 1983. Pp. 57-58

This is probably why the most popular name for Papa Lébat is “Papa La Bas”, “La Bas”, or “Laba”. “La Bas” used to mean “Down There”, and was associated with Satanism, while “Laba” is the Creole form of “La Bas”. 

Ironically, the Èṣù-Ẹlẹ́gbára collective is also associated with Jesus Christ, for two reasons:

Both are both figured as connection points between humanity and the divine.

They have a common association with the cross symbol.

In African religious systems, the cross is a cosmographic symbol. It represents the intersection of the spiritual and mortal realms, which are figured as two perpendicular planes. 

A complete discussion of this concept can be found here:

Desmangles, Leslie Gerald. “African Interpretations of the Christian Cross in Vodun.�� Sociological Analysis, vol. 38, no. 1, 1977, pp. 13–24. JSTOR, https://doi.org/10.2307/3709833. Accessed 10 Sept. 2024.

Pictured: Papa Legba’s vèvè

This explains why Papa Legba’s vèvè features a prominent 4-point cross, and why parts of the Èṣù-Ẹlẹ́gbára collective are associated with Jesus. For example, the Haitian author Milo Rigaud identified Legba as “the Voodoo Jesus”, while Eleguá is syncretized with the Child Jesus of Atocha.

It might also relate to why Chan, who is from deeper South, differentiates forks in the road from crossroads. Here, he stresses the importance of the crossroads as a “cross”. The crossroads are figured as having “four specific points”, while forks do not. PapaSeer, who is from further north, disputes the importance of the “four specific points”. He argues that forks and crossroads are the same, in that they are both points of intersection between the spiritual and physical realms.

The parts of the Èṣù-Ẹlẹ́gbára collective are characterized by their extreme unpredictability, where they are capable of Christ-like benevolence and devilish malevolence. This reflects the unpredictable nature of a person’s fate, and the liminal space between ‘good’ and ‘evil’. For this reason, it is possible that different aspects of the Èṣù-Ẹlẹ́gbára collective can manifest as “The Spirit at the Crossroads”. 

On the off chance that someone from the Abrahamic Hoodoo tradition is reading this, I do not mean that Jesus does not appear at the Crossroads, or that Jesus and Èṣù-Ẹlẹ́gbára are the same thing. That would be equally erroneous as equating Èṣù-Ẹlẹ́gbára with the Devil. Rather, I mean that these benevolent and malevolent aspects of Èṣù-Ẹlẹ́gbára might also be able to manifest, alongside Jesus and the Devil. At that, it would be crucial to analyze if and how the Crossroads Spirit(s) is benevolent and/or malevolent.

8. HOODOO SAINT PETER

Hoodoo Saint Peter might also be a part of the Èṣù-Ẹlẹ́gbára collective.

In Hoodoo, Saint Peter is figured differently from European traditions. He is associated with a person’s fate, where he is petitioned to “open” or “close” the doors to opportunities. This is a feature he shares with the Èṣù-Ẹlẹ́gbára collective, which is tied to a person’s fortune / fate, and associated with “doors” “keys” and “entrances”. 

Here is how Legba is described in Dahomean Narrative:

“Myth (hwenoho). The long stories about Legba are particularly useful for a closer analysis of narrative. But before we turn to the stories, we must give attention to the role Legba plays in Dahomean life. As had been shown, he is a figure of the greatest importance both in the generalized form in which he participates in the worship of the vodun pantheons, and more particularly a guardian of entrances to villages, to markets, to shrines, compounds, and houses, until he is brought into the closest association of all—with a man’s personal destiny (his Fa).”

Source: Herskovits, Melville Jean, and Frances Shapiro Herskovits. Dahomean narrative: a cross-cultural analysis. Northwestern University Press, 1958. p. 36 https://archive.org/details/hersokovits-dahomean/page/35/mode/2up 

In Haitian Vodou, Papa Legba was identified with Saint Anthony, but also Saint Peter: 

“Legba est identifié à saint Antoine l'ermite et à saint Antoine de Padoue…Mais Legba est aussi saint Pierre qui, tout comme lui, est un portier divin.”

TRANSLATION:

"Legba is identified with Saint Anthony the Hermit and with Saint Anthony of Padua...But Legba is also Saint Peter who, just like him, is a divine doorkeeper."

SOURCE: MARCELIN, Émile, and A. Métraux. “LES GRANDS DIEUX DU VODOU HAIÏTIEN.” Journal de La Société Des Américanistes, vol. 36, 1947, pp. 51–135. JSTOR, http://www.jstor.org/stable/24601899. Accessed 18 Sept. 2024.

In New Orleans Voodoo, Papa Lébat was associated with Saint Peter. 

From the interview with Josephine McDuffy (“Josephine Green”):

Josephine Green, an octogenarian, recalled her mother’s stories about Marie Laveau.

“My ma seen her,” Josephine boasted. “It was back before the war what they had here wit’ the Northerners. My ma heard a noise on Frenchman Street where she lived at and she start to go outside. Her pa say, ‘Where you goin’? Stay in the house!’ She say, ‘Marie Laveau is comin’ and I gotta see her.’ She went outside and here come Marie Laveau wit’ a big crowd of people followin’ her. My ma say that woman used to strut like she owned the city, and she was tall and good-lookin’ and wore her hair hangin’ down her back. She looked just like a Indian or one of them gypsy ladies. She wore big full skirts and lots of jewelry hangin’ all over her. All the people wit’ her was hollerin’ and screamin’, ‘We is goin’ to see Papa Limba! We is goin’ to see Papa Limba!’ My grandpa go runnin’ after my ma then, yellin’ at her, ‘You come on in here, Eunice! Don’t you know Papa Limba is the devil?’ But after that my ma find out Papa Limba meant St. Peter, and her pa was jest foolin’ her.”

SOURCE: Source: Tallant, Robert. Voodoo in New Orleans. 1946. Reprint, Gretna, La.: United Kingdom, Pelican Publishing Company, 1983. Pp. 57-58

From an interview with a woman named Mary Washington (“Mary Ellis”): 

Mary said that most of the things she knew about Marte Laveau had been told her by an aunt who had been a Voodoo.

“My aunt told me one time she had trouble wit’ her landlord. He told her to git out of her house or he’d have her put in jail,” Mary said. “He even sent a policeman after her. The next day she went to Marie Laveau and she told my aunt to burn twelve blue candles in a barrel half full of sand. She done that and my aunt never did have to move and she never went to jail in her whole life. Marie Laveau used to tell people not to burn candles in church ’cause that gived their luck to somebody else, so they burned ’em in her house instead. She’d tell my aunt, ‘If you gonna fool ’em, fool ’em good, Alice.’ She was real good to my aunt. She even taught her a Voodoo song. It went like this:

St. Peter, St. Peter, open the door,

I’m callin’ you, come to me!

St. Peter, St. Peter, open the door …

“That’s all I can remember. Marie Laveau used to call St. Peter somethin’ like ‘Laba.’ She called St. Michael ‘Daniel Blanc,’ and St. Anthony ‘Yon Sue.’ There was another one she called ‘On Za Tier’; I think that was St. Paul. I never did know where them names come from. They sounded Chinee to me. You know the Chinee emperor sent her a shawl? She wore it all the time, my aunt told me.”

SOURCE: Source: Tallant, Robert. Voodoo in New Orleans. 1946. Reprint, Gretna, La.: United Kingdom, Pelican Publishing Company, 1983.

New Orleans Voodooists hid African-derived spirits like Papa Lébat and Daniel Blanc under the names of Catholic Saints, who were petitioned for the following reasons:

These merchants also sell pictures of saints. To certain Roman Catholic saints particular Voodoo power has been attributed: St. Michael is thought best able to aid in conquering enemies; St. Anthony de Padua is invoked for “luck”; St. Mary Magdalene is popular with women who are in love; St. Joseph (holding the Infant Jesus) is used to get a job. Many Voodoos believe a picture of the Virgin Mary in their homes will prevent illness, and that one of St. Peter (with the Key to Heaven) will bring great and speedy success in financial matters (without the Key to Heaven, St. Peter is still reliable in helping in the achievement of minor successes; the power of the picture is less, however). Pictures of the Sacred Heart of Jesus are believed to have the ability to cure organic diseases.

SOURCE: Source: Tallant, Robert. Voodoo in New Orleans. 1946. Reprint, Gretna, La.: United Kingdom, Pelican Publishing Company, 1983.

In Hoodoo, the real identity of the being petitioned as “Saint Peter” might not be Peter the Apostle, but Papa Lébat, whose name was forgotten over time.

If this is true, it seems that Papa Lébat refracted into two different entities: Hoodoo Saint Peter, and the Hoodoo Spirit at the Crossroads. This is similar to how the vodún Legba refracted into Papa Legba and Mèt Kafou when he was transmitted to Haiti. It is unclear whether these two refractions correspond with each other, or if Hoodoo Saint Peter and The Spirit at the Crossroads should be considered novel aspects of the Èṣù-Ẹlẹ́gbára collective.

9. CONCLUSIONS

The above are merely personal hypotheses of mine, which can readily be verified or debunked by members of the Hoodoo and Voodoo communities. I belong to neither, nor do I have any Black African heritage. It would be these two groups who contain the most accurate information about the Spirit at the Crossroads, Hoodoo Saint Peter, and Papa Lébat.

In other words, they can tell you if this is bullshit or not.

For example, they can tell you if there’s any association between the Spirit at the Crossroads and dogs, if he smokes a pipe, if he wears a hat, if so what kind, if he limps, what his colors are, etc…

Here’s another opinion no one asked for!

Americans have attempted to reconstruct Voodoo by drawing from Haitian Vodou and West African Vodun.  While it is prudent to connect with Haitians and West Africans, American Voodooists should prioritize communication with members of the Hoodoo community. There are many African Americans who descend from the Haitian slaves that arrived in New Orleans following the Haitian Revolution. While there exists an ancestral tie, there is also a large, 200-year discontinuity between this migration wave and the present day. Vodou – of the Mississippi River Valley, and of Haiti – is an ancestral tradition.  The one who has maintained an unbroken ancestral chain is not the Haitian lwa Papa Legba, but the Hoodoo Spirit at the Crossroads. 

In the words of Albert J. Raboteau, “In the United States the gods of Africa died” ...except one! Arguably, the most important one, who “holds the keys” to the other gods…!

AND PEOPLE JUST LEAVE THEIR TRASH IN THE PLACE WHERE HE DWELLS!!!!!

HE DOESN”T EVEN HAVE A NAME!!!!!!!!

…Sorry. I’m a very sensitive person, so this upsets me.

But isn’t that interesting?

In the entire Yoruba pantheon, Èṣù-Ẹlẹ́gbára might be the single most persistent deity!

* * *

Revisiting the origins of Kafou

Up until this point, I have been describing Kafou as a Petro-ified counterpart to Legba, categorizing him as part of Henry Louis Gates Jr.’s Esu-Elegbara collective. However, such description surely understates Kafou’s Central African origins.

The Gatekeeper/Crossroads Spirits Legba and Esu are prominent features of West African religions; however, the 4-point Crossroads were also important to the Central Africans. 

Pictured: Kafou’s veve

Many different veves incorporate Central African symbology into their designs. In particular, the veve of Kafou closely resembles symbols from the Congo, the most famous being the Bakongo Cosmogram. 

Pictured: Bakongo Cosmogram

Rigaud also described Kafou Louvem'bha, surely derived from the word Luvemba. 

SEE:  Rigaud, Milo. La tradition voudoo et le voudoo haïtien: son temple, ses mystères, sa magie. FeniXX, 1953. p. 174. Retrieved from: https://original-ufdc.uflib.ufl.edu/AA00002240/00001/183j 

There are other ethnic groups from the Congo who also worshiped the crossroads, as the 4-point Cross(roads) is an ancient symbol that has variants in many different African cultures. Without attributing it to any particular ethnic group, the Central African influence is undeniable.  

With this in mind, one of two things could be true: 

Kafou is truly Creole in origin; he merges the Crossroads Symbol of Central Africa with the Gatekeeper/Crossroads Spirit of West Africa.

Kafou is simply the embodiment of the Crossroads Symbol of Central Africa; his similarity to Legba and Esu is merely superficial.

If the second is true, it would be incorrect to identify him with the Esu-Elegbara collective, and would explain why Kafou is categorized as a different famille from Legba. 

While Milo Rigaud and Milo Marcelin identified Kafou with Legba, others deny this association, citing a Central African origin instead. 

It was negligent of me not to have mentioned this earlier.

* * *

Revisiting this topic, I think I can debunk myself a bit.

After researching this a bit further,  Hoodoo Saint Peter seems to just be Saint Peter; no connection to the West African Legba.

On the other hand, the origin of the Spirit at the Crossroads was described as “controversial”. Basically, some think a connection to Esu or Legba is possible; others deny this connection.

[pv1isalsoimportant]

"Quantifiers are adjunctions" wasn't on my 2024 math list.

[m---a---x]

Call me the initial object of Cupids topos the way i love noone else

[fundgruber]

Dietmar Dath - Neptunation.

Die Oktopoden werden uns verbinden, wenn wir es nach oben schaffen

Die Mission ist die Verbindung

Connection, Funktoren zwischen Kategorien von Kategorien, zwischen höheren Topoi

Bei Dietmar Dath ist Mathematik zur sozialen Bewegung, zum Implex geworden, eine Diktatur der Programmierer*innen und der Wissenschaft, in der Topos-Coding der Skill ist mit dem Aufhebung funktioniert, mit dem der Formwechsel der Materie gesteuert wird und die gesellschaftliche Reproduktion. In der Gegenwart codiert er selber seine Science Fiction so, mit dem Aufhebungsfunktor. Da wird dann ein Weltraumsozialismus mit transhumanistischem Gesicht (Neukörper) entworfen, in dem eine neue Politik entsteht, neue Kriege, teilweise als Wiederholungen historischer Tragödien. Die Programmierer*innen und die Wissenschaftler*innen spielen darin so eine große Rolle, weil sie im direkten Kontakt sind mit dem Management und der Spekulation. Sie haben Zugriff auf hochwertige Produktionsmittel und Gelder. Und dann im passenden Moment weichen sie ab aus den Kreisläufen des Kapitals, wie in "Menschen wie Gras", wenn die Gentechnik verfrüht freigelassen wird. Daths Faszination für China würde demnach auch nicht bedeuten das was dort passiert zu idealisieren, sondern es ist einfach ein Staat in dem diese Entwicklungen ein Stück brisanter ablaufen, wo eine KP versucht das Ganze zu steuern.

Die Grundlagen für die Freiheit zum Implex hatte eine Partei im Untergrund gelegt, sie hießen die "Gruppe Pfadintegral" (Gippies), dann die "Internationale" (eigentlich die 'Partei', aber er entschied sich dann doch für die Internationale), in unserer Welt sind das Grillabende von Wissenschaftler*innen und Radikalen, wie Barbara Kirchner irgendwo sagt, oder auch Dath immer wieder anklingen lässt. Dath ist das Aushängeschild dieser imaginären Partei (manchmal sieht man sein Formel-Tattoo auf dem Unterarm) im Hier und Jetzt, in den Büchern ist es Cordula Späth oder andere Heldinnen aus Wissenschaft und Musik. Durch seine Doppelrolle beliebter Feuilletonist bei der FAZ und Genosse der DKP zu sein streut er seinen High-Tech Marxismus in beiden Bereichen, und in Zeitschriften wie der Konkret (gerade zum Beispiel ein Text über eine Museumsausstellung über den Faschismus des 21. Jahrhunderts, genannt der "Wechselbalg", in einer zukünftigen Gesellschaft) oder bei Linken.

Die Topos-Codierung kommt auch aus der Musik, kommt auch aus der bildenden Kunst, nur haben die Gesellschaften, die Dath beschreibt das in ihre Raumgestaltung, ihre Körpergestaltung, die Gestaltung ihrer Beziehungen gelegt. Genauso wie das Gärtnern (in den Rechnergärten) oder das Kochen (deswegen auch die Bedeutung der von Dath beworbenen Bücher der Mathematikerin und Musikerin Eugenia Cheng "How to Bake Pi", und "x + y. A Mathematician’s Manifesto for Rethinking Gender", die in diesem Sinne so viel mehr sind als Einführungen). Darin liegt die verführerische Methodik der Kategorientheorie und der Topologie, Erkenntnis und Transformation auf unterschiedlichen Ebenen durchführen zu können. Und das dann wiederum mit Aufhebung zu verkabeln, mit den Klassikern:

"In early 1985, while I was studying the foundations of homotopy theory, it occurred to me that the explicit use of a certain simple categorical structure might serve as a link between mathematics and philosophy. The dialectical philosophy, developed 150 years ago by Hegel, Schleiermacher, Grassmann, Marx, and others, may provide significant insights to guide the learning and development of mathematics, while categorical precision may dispel some of the mystery in that philosophy." F. William Lawvere, Unity and Identity of Opposites in Calculus and Physics. Applied Categorical Structures 4: 167-174, 1996

Hegelianisch-Marxistische abstrakte Algebra befindet sich dann mutmaßlich im Wettstreit mit anderen diagrammatischen Methoden, wie der Lattice Theorie (vgl. Rudolf Wille, “Restructuring lattice theory: An approach based on hierarchies of concepts” 1982). Wenn seit Emmy Noether die Kartierungen Teil der mathematischen Forschung sind (vgl. Lee, C. (2013) Emmy Noether, Maria Goeppert Mayer, and their Cyborgian Counter-parts: Triangulating Mathematical-Theoretical Physics, Feminist Science Studies, and Feminist Science Fiction), bis hin zu Maryam Mirzakhani (in der Nachruferzählung und in der Raumerzählung "Du bist mir gleich" wird das was diese Mathematik mit dem Denken macht in seiner Tragik und transformativen Kraft spürbar), dann ist das was die Netzwerk-Coder (z.B. Fan/Gao/Luo (2007) "Hierarchical classication for automatic image annotation", Eler/Nakazaki/Paulovich/Santos/Andery/Oliveira/Neto/Minghim (2009) "Visual analysis of image collections") und Google Arts & Culture in die digitale Kunstwissenschaft eingeführt haben, man kann es nicht anders sagen, das Gegenteil von all dem. Unhinterfragte Kategorien und unhinterfragte konzeptuelle Graphen (also sowohl Lattice Theorie, als auch Topologie ignorierend), werden ohne Binaritäten oder Äquivalente einfach als gerichtete Graphen, entweder strukturiert von den alten Ordnungen, oder, das soll dann das neue sein, als Mapping von visueller Ähnlichkeit gezeigt (vgl. die Umap Projekte von Google oder das was die Staatlichen Museen als Visualisierungs-Baustein in der neuen Version ihrer online Sammlung veröffentlicht haben). Wenn dann das Met Museum mit Microsoft und Wikimedia kooperiert, um die Kontexte durch ein Bündnis von menschlicher und künstlicher Intelligenz zu erweitern - nämlich Crowdsourcing im Tagging, und algorithmisches Automatisieren der Anwendung der Tags, dann fehlen einfach die radikalen Mathematiker*innen, die diese Technologien mit dem Implex der Museumskritik verbinden können, um ein Topos-Coding durchzuführen, das die Kraft hätte den Raum des Sammelns zu transformieren, so das nichts mehr das Gleiche bliebe. Während die heutigen Code-Künstler*innen großteils im Rausch der KI-Industrie baden, bleiben es einzelne, wie Nora Al-Badri ("any form of (techno)heritage is (data) fiction"), die zum Beispiel in Allianz mit einer marxistischen Kunsthistorikerin die Lektüre des Latent Space gegen das Sammeln wenden (Nora Al-Badri, Wendy M. K. Shaw: Babylonian Vision), und so Institutional Critique digitalisieren.

"Was Künstlerinnen und Künstler seit Erfindung der »Institutional ­Critique«, deren früher erster Blüte auch einige der besten Arbeiten von ­Broodthaers angehörten, an Interventionen in die besagten Räume getragen und dort gezündet haben, von neomarxistischer, feministischer, postkolonialer, medienkritischer, ­queerer Seite und aus unzähligen anderen Affekten und Gedanken, die sich eben nicht allesamt auf eine Adorno’sche »Allergie« wider das Gegebene reduzieren lassen, sondern oft auch aus einer ­Faszination durch dieses, einer Verstrickung in sein Wesen und Wirken geprägt war, liegt in Archiven bereit, die ausgedehnter und zugänglicher sind als je zuvor in der Bildgeschichte. Den Tauschwert dieser Spuren bestimmen allerorten die Lichtmächte. Ihr Gebrauchswert ist weithin unbestimmt. Man sollte anfangen, das zu ändern." Dietmar Dath Sturz durch das Prisma. In: Lichtmächte. Kino – Museum – Galerie – Öffentlichkeit, 2013. S. 45 – 70

[lara635kookie]

Ship Analysis pt.6:

Red Crackle, Carmivy and Carulia.

And about Carmen being mind-wiped he didn't allow to do that. He doesn't have that power. There was nothing he could do to stop Carmen to be brainwashed. We saw how fast V.I.L.E. did it so no one would be able to stop it. Considering the way V.I.L.E. did it, probably everyone that isn't Maelstrom and Doctor Bellum found out that Carmen was evil only after it was already done. And we see is a powerful mind control because Gray heard Doctor Bellum's voice and was exposed to his old V.I.L.E. best friend and didn't remember a thing without the A.C.M.E. machine. So he couldn't just tell evil Carmen about it without V.I.L.E. knowing. And he didn't know how to contact team red so A.C.M.E. really was his only choice.

Another topic is that the only people we see evil Carmen almost killing is Tigress, Zack and Shadowsan. In that order. And Gray clearly wasn't okay with any of these. In the one with Tigress, Gray asks evil Carmen to stop and she stops, simple as that. Look at this, man:

You can't tell me this woman doesn't have a soft spot for Gray. Even in friendship terms, which seems unlikely to me because I have two younger siblings and I don't look to my sister and brother like that. Anyway, the second one is Zack in the ferris wheel. Carmen just warns Gray to stay prepared and act at her signal, but she doesn't explain why and he clearly looks surprised because he didn't know what she was going to do until she does it(that's something that happens a lot with evil Carmen). And the third one is Shadowsan which he could do nothing about because well...He was "dead" on the ground. Coming back to the first one with Tigress, we saw how quickly Carmen listened when Gray told her to stop. Seriously, can you picture dark Carmen listening this fast if it was El Topo, Le Chevre or any other agent? We see Carmen and Crackle were assigned to missions alone, without the rest of their classes. You cannot convince me Crackle was the only one that could calm dark Carmen down. If it wasn't for him, evil Carmen would have killed someone, which doesn't seem to be the case. You cannot tell me V.I.L.E. didn't put them to be assigned partners that always do almost every mission together like El Topo and Le Chevre. Both Carmen and Gray were praised for being one of the best thieves V.I.L.E. ever had. They would only need to kill if they were seen/caught. And together, they wouldn't commit such mistakes. He did say "it was fun while it lasted" but it's another ambiguous, room for multiple interpretations phrases by Gray. I think he meant that having Carmen and his old class with him again, because of the considerations I made of V.I.L.E. before. Honestly, we'll never know for sure what made Gray suddenly decide to help Carmen. Of course he mentions Shadowsan but Gray didn't even care about Shadowsan that much. But he knew Carmen did. And the fact that he decides to help A.C.M.E. because he wants Carmen to be in control of her own path and free his best friend, even willing to go to jail for it, already means he's not truly evil. Yes it took long, but better late than never. Besides, I have a theory that, since Carmen and Gray were assigned partners in crime, and both were the best dynamic power couple duo, V.I.L.E. assigned them to every single possible mission because they knew they wouldn't fail. So my take is that he didn't have the time to act on evil Carmen with Carmen being with him all the time, that's why he does it immediately after Carmen becomes a member of the faculty. Speaking of which, both Carmen and Gray were just back at V.I.L.E. so the faculty had to keep an eye on them. Six months sounds like a fair amount of time to be considered reliable again so after Gray had less faculty eyes on him, he went to A.C.M.E. I feel like, if it wasn't for this factors, he would have done it way before. He was actually smart. It was a clever plan:Waiting for the time to contact A.C.M.E. in the easiest, safest and less likely to go wrong way. So for me it was plenty enough to redeem him. That's what I think.

[yamayuandadu]

It's probably too late for that, but could you do a breakdown of Utu/Shamash?

Not quite sure what do you mean by this, but I can do a quick rundown based on what I wrote on wikipedia long ago if that's what you want. 1. The merge between Utu/Shamash is pretty old, so old that I do not think there's a way to delineate between them. There's a theory that actually the original solar deity of early Akkadian speakers was female, like Shapash in Ugarit or the nameless solar deity in Ebla (the latter is a complex case, I will post about it... eventually) but it's not universally accepted. 2. In addition to the basic solar role, U/Sh. was also responsible for justice and divination. Presumably because going through the sky every day meant he sees everything. His enormous saw attribute might be related to this too, since in both Sumerian and Akkadian, verdicts in legal cases were, to translate the verb literally, "cut". 3. The two primary cult centers of U/Sh. were Sippar and Larsa. Sippar was actually considered older and more venerable, but Larsa had more direct political clout. 4. U/Sh.'s genealogy is virtually invariable, ie. Nanna+Ningal as parents, Inanna as sister (sometimes with bonus siblings like Manzat in Maqlu). His wife is generally consistently the same goddess too, ie. Aya, literally "dawn". Note that Aya's supposed Sumerian name, Sherida, is a possible Akkadian loanword too, from a term referring to red sky in the morning. Their children include figures such as Mamu ("dream", implicitly a meaningful/prophetic one), Kittum ("truth") and so on. Aya has no genealogy and when her relation to any senior deity is ever clarified, it's via her link to her husband, ie. she's only addressed as "daughter in law" (kallatum, literally "bride"). 5. As a Sumerogram, UTU is attested as the writing of virtually every single solar deity from Hattusa to Susa. The Hurrian sun god, Shimige, was pretty closely associated with him in particular, but note the logographic writing did the trick for female solar deities too, like Ugaritic Shapash or Hittite solar goddesses. 6. There are very few, if any, myths focused on U./Sh., but it's effectively a topos that other deities ask him for help: Dumuzi while fleeing the galla, Ninsun in SB Gilgamesh (via Aya), Ninmada in that grain origin myth, etc. Sources are inconsistent about what he was believed to do in the night, and we cannot really neatly chronologically or linguistically delineate whether he was believed to rest or travel through the underworld.

[ouroborussy]

This may not be an incredibly original thought but I think ZFC is summarised kinda succinctly as the "self justifying closure" of it's "toposic" fragment. So we've known for a while that the right interpretation of FO in a (1-)topos reproduces BZC, i.e. ZFC without replacement and with bounded comprehension. This theory (if I'm right) is able to define what a rank *is* but not that every ordinal has an associated rank. Now suppose we recursively add to this axiom system in the following way:

T -> T + there are unboundedly many ranks which are models of T

which is a little stronger than saying "T + (T is consistent)".

I believe at each stage we get another level of replacement, until we have full replacement? Is this true? If so the closure under this operation gives back exactly ZFC. Maybe we need to start with bounded comprehension and bounded replacement but this seems very plausible.