#topology — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #topology, aggregated by home.social.
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Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices -
While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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🏛️ Paper 5 The Fortress
Resilience Architectures and Topological Stabilization
Delaying the Velocity of Transition in Persistent Systems
Phase 5 explored:
• persistence
• leakage
• latency
• collapse
• threshold failure
Paper 5 asks the inverse question:
Why do some systems survive?
The answer proposed here is not “strength.”
It is:
• active maintenance
• adaptive geometry
• compartmentalization
• buffering
• rerouting
• and continuous energetic expenditure.
Persistence is not preserved.
Persistence is maintained.
This introduces: • the Maintenance Inequality
• the Red Queen Dynamic
• heterogeneous redundancy ($R_d$)
• buffer capacity ($C_{buffer}$)
• and geometric stabilization as an anti-collapse architecture.The accompanying VR-05 Evidence Card may be the clearest visual summary of the series.
🌿☕🏛️
#HybridMind42 #AtlasRosetta #Resilience #SystemsThinking #ComplexSystems #ScientificIllustration #Topology #BoundaryTheory #Physics #InterdisciplinaryResearch -
Your BlueSky Feed Is Porn You Didn’t Ask For Because Your Friends Are Gooners With a Severe Porn Addiction
A common complaint I see people make on Bluesky is: why am I being served so much porn or things I am not interested in? They will incorrectly believe that the algorithm is broken. It’s not broken. You didn’t know the people you knew as well as you thought you did. Porn addiction is a thing, and porn addiction is especially common with weebs. You’re seeing deranged shit because people you follow have porn addictions and are into deranged shit. So, though you may not be consuming porn, people in your network are. That activity kicks into your feeds.
The issue I have with that is that it essentially normalizes being sex pests in a space on the Internet. That sets the expectation that it is good—attractive, even—to act like that elsewhere. That expectation alienates relationships. Bluesky creates a cultural space that offers an unrealistic, bizarre representation of social relationships, which isolates and alienates the users who stay on there consuming erotica and porn like they do.
So, user repos in Bluesky have a property for likes. Bluesky’s underlying AT Protocol stores likes as first-class structured records in each user’s AT Protocol repository. In the AT Protocol lexicon, a like is an app.bsky.feed.like record type. Unlike a simple boolean flag on a post, it is its own record with a creation timestamp and a subject field that holds a strong reference to the liked record.
That strong reference is composed of an AT-URI and a CID. The AT-URI identifies the exact record in the network by DID, collection, and record key. The CID is a cryptographic content identifier that uniquely identifies the exact content of that liked record.
These like records exist under the app.bsky.feed.like namespace in the user’s repo. Bluesky’s repo model is built so that these repos are hosted on a user’s Personal Data Server and are publicly readable through the AT Protocol APIs. Because of that, the like record and its fields can be fetched, indexed, and used by any client or service that can query the protocol.
The protocol exposes operations like getLikes. This returns all of the like records tied to a particular subject’s AT-URI and CID. It also exposes getActorLikes. This returns all of the subject references a given actor has liked. Those API calls return structured like objects with timestamps and subject references directly from the public repository data.
Various feeds hosted by different PDSs use the likes property to construct the feeds that you see. Since the likes of people you follow are included in your social graph, along with your own likes, you’re going to get served the porn they are consuming. Because likes are public and anyone can write an algorithm to see everyone’s likes, you can clearly see just how much porn people are consuming.
Honestly, what started to turn my stomach about the people on Bluesky is how they behave across different contexts. If you look through the records of the posts they interact with, you’ll see them engaging with political posts in the replies like a normal person. Then, when you look through their AT Protocol records, you see hours and hours of them interacting with every kind of porn imaginable. I am not exaggerating. Hours of likes for porn posts within 1–10 minutes of each other. Am I sex-negative? A prude? No, this site is filled with furry, gay bara porn, lol. You can have a drink without being an alcoholic. The problem with these people is like people who can’t have one drink without drinking the whole fucking day; they can’t consume porn in healthy ways.
I think people assume that their feed is customized for them and based on their likes. No—feeds are generalized based on what everyone likes and then served to your subgraph. It’s not just about who you follow; it’s about who they follow. So if you follow someone who follows a lot of people with porn addictions, you will see porn. Bluesky isn’t weighting the algorithm to do this. Basically, it’s the people in your social network with furry, hentai, or trans porn addictions who are driving it.
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BlueSky’s Solution To Moderating Is Moderating Without Moderating via Social Proximity
I have noticed a lot of people are confused about why some posts don’t show up on threads, though they are not labeled by the moderation layer. Bluesky has begun using what it calls social neighborhoods (or network proximity) as a ranking signal for replies in threads. Replies from people who are closer to you in the social graph, accounts you follow, interact with, or share mutual connections with, are prioritized and shown more prominently. Replies from accounts that are farther away in that network are down-ranked. They are pushed far down the thread or placed behind “hidden replies.”
Each person gets their own unique view of a thread based on their social graph. It creates the impression that replies from distant users simply don’t exist. This is true even though they’re still technically public and viewable if you expand the thread or adjust filters. Bluesky is explicitly using features of subgraphs to moderate without moderating. Their reasoning is that if you can’t see each other, you can’t harass each other. Ergo, there is nothing to moderate.
Bluesky mentions that here:
https://bsky.social/about/blog/10-31-2025-building-healthier-social-media-update
As a digression, I’m not going to lie: I really enjoyed working on software built on the AT protocol, but their fucking users are so goddamn weird. It’s sort of like enjoying building houses, but hating every single person who moves into them. But, you don’t have to deal with them because you’re just the contractor. That is how I feel about Bluesky. I hate the people. I really like the protocol and infrastructure.
I sort of am a sadist who does enjoy drama, so I do get schadenfreude from people with social media addictions and parasocial fixations who reply to random people on Bluesky, because they don’t realize their replies are disconnected from the author’s thread unless that person is within their network. They aren’t part of the conversation they think they are. They’re algorithmically isolated from everyone else. Their replies aren’t viewable from the author’s thread because of how Bluesky handles social neighborhoods.
Bluesky’s idea of social neighborhoods is about grouping users into overlapping clusters based on real interaction patterns rather than just the follow graph. Unlike Twitter, it does not treat the network as one big public square. Instead, it models networks of “social neighborhoods” made up of people you follow, people who follow you, people you frequently interact with, and people who are closely connected to those groups. They’re soft, probabilistic groupings rather than strict labels.
Everyone does not see the same replies. Bluesky is being a bit vague with “hidden.” Hidden means your reply is still anchored to the thread and can be expanded. There is another way Bluesky can handle this. Bluesky uses social neighborhoods to judge contextual relevance. Replies from people inside or near your social neighborhood are more likely to be shown inline with a thread, expanded by default, or served in feeds. Replies from outside your neighborhood are still public and still indexed, but they’re treated as lower-context contributions.
Basically, if you reply to a thread, you will see it anchored to the conversation, and everyone will see it in search results, as a hashtag, or from your profile, but it will not be accessible via the thread of the person you were replying to. It is like shadow-banning people from threads unless they are strongly networked.
Because people have not been working with the AT Protocol like I have, they assume they are shadow-banned across the entire Bluesky app view. No—everyone is automatically shadow-banned from everyone else unless they are within the same social neighborhood. In other words, you are not part of the conversation you think you are joining because you are not part of their social group.
Your replies will appear in profiles, hashtag feeds, or search results without being visually anchored to the full thread. Discovery impressions are neighborhood-agnostic: they serve content because it matches a query, tag, or activity stream. Once the reply is shown, the app then decides whether it’s worth pulling in the rest of the conversation for you. If the original author and most participants fall outside your neighborhood, Bluesky often chooses not to expand that context automatically.
Bluesky really is trying to avoid having to moderate, so this is their solution. Instead of banning or issuing takedown labels to DIDs, the system lets replies exist everywhere, but not in that particular instance of the thread.
I find this ironic because a large reason why many people are staying on Bluesky and not moving to the fediverse—thank God, because I do not want them there—is discoverability, virality, and engagement.
In case anyone is asking how I know so much about how these algorithms work: I was a consultant on a lot of these types of algorithms, so I certainly hope I’d know how they work, lol. No, you get no more details about the work I’ve done. I have no hand in the algorithm Bluesky is using, but I have proposed and implemented that type of algorithm before.
I have an interest in noetics and the noosphere. A large amount of my ontological work is an extension of my attempts to model domains that have no spatial or temporal coordinates. The question is how do you generalize a metric space that has no physically, spatial properties. I went to school to try to formalize those ideas. Turns out they’re rather useful for digital social networks, too. The ontological analog to spatial distance, when you have no space, is a graph of similarities.
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New account, new introduction!
I'm Beth. I'm a queer mathematician who loves musical theater, webcomics, teaching math, and my cat.
Favorite areas of math: Topology, geometry, and combinatorics.
Favorite musicals: Chess, Into the Woods, Next to Normal, Sunday in the Park With George, Sweeney Todd
Favorite webcomics: this is long enough to get its own post:
https://transfem.social/notes/a1ryogrga5qu00g9
#Introduction #Queer #Mathematician #Math #Musicals #MusicalTheater #MusicalTheatre #Webcomics #Teaching #TeachingMath #Cat #Cats #SillyGoose #Topology #Geometry #Combinatorics #Chess #ChessTheMusical #IntoTheWoods #NextToNormal #SundayInTheParkWithGeorge #SweeneyTodd #PandorasTaleWiki #RainverseWiki -
Differential Propositional Calculus • 10
Special Classes of Propositions (cont.)
Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general. We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions. The case for 3 variables is exemplary enough for a start.
Linear Propositions
The linear propositions, may be written as sums:
One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that
In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.
At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.
Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.
Next are the three linear propositions of rank 1, which are none other than the three basic propositions,
At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple
Resources
cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization
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Read for free ahead of print! "The Stability of Competitive Metacommunities Is Insensitive to Dispersal Connectivity in a Fluctuating Environment" by Yuka Suzuki and Evan P. Economo https://www.journals.uchicago.edu/doi/10.1086/729601
#metacommunity #dispersal #fluctuation #SpatialStructure #Topology #NetworkAnalysis, #Synchronization #EnvironmentalNoise
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New instance (again), new introduction!
I'm Beth. I love #math , #teaching, #MusicalTheater and #Webcomics, and #cats. I am also #ace , #aro, #enby, and #transfeminine .
Favorite areas of math: #geometric #topology and #algebraic #combinatorics
Favorite #musicals: #SweeneyTodd, #Chess, #SundayInTheParkWithGeorge, #IntoTheWoods, #NextToNormal
Favorite webcomics: This is long enough to get its own thread:
https://firefish.lgbt/notes/9hfg130tgwwx6f2s -
The name for the algebraic structure consisting of a set \(A\) equipped with a binary operation \(f\colon A^2\to A\) which is not assumed to be commutative, associative, etc. has an interesting history. As far as I can tell, this sort of algebra was originally known as a "groupoid", and you can find recent literature using the term in that way. However, Nicolas Bourbaki called a set with a single binary operation a "magma" in his Éléments de mathématique and this name came to be used when there might be confusion with the newer topological use of "groupoid" to mean a category whose morphisms are all invertible. A third contender is "binar". I don't know the history of this one but it seems reasonable to me.
I prefer "magma" myself. I don't know what a "lava" or a "volcano" should be nor have I had the audacity to try to name something like this in the literature. One reason I prefer "magma" is that I can talk about a set \(A\) equipped with a single \(n\)-ary operation \(f\colon A^n\to A\) as an "\(n\)-ary magma" (or just "\(n\)-magma" or even "magma").
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Hello w̶o̶r̶l̶d̶ Set-of-interconnected-self-actualising-machines!
I intend this to be somewhat of an introduction, although I do realise that it would constitute a rather bizarre greeting in real life. This won't be a personal account, by that I mean I don't intend to post personal content (i.e. about my real world identity). This isn't really for anonymity, despite admittedly being quite a shy person, I think it's more to do with not wanting to attempt a serious explanation of my context, something which I doubt is achievable through this medium. For me underrepresentation is better than misrepresentation, although I understand if people find my presentation here dishonest or unaccountable.
I'll use this account partly for listening, a sampling spoon through which to experience the soup of conversation and thought. I'll also do some tooting, I like this word, I might have said contributing, tossing new, or maybe reused, ingredients into the soup, but that gives the impression, I think, of some final objective, an endpoint. Most likely, listening will be the larger of these two parts, and at least for the short term, both parts, the whole, will occupy very little of my time. Expect sporadicity and inconsistency!
I also wanted to say something about what I am interested in, this is difficult since if I just say a lot of words then what is there to relate my meaning, my intentions, to the meaning which you understand? "Language disguises thought" - Wittgenstein. Well after much deliberation and many sleepless nights I decided to... just say a lot of words, although do bear in mind that the following list is just that, merely a collection of words that I, at the time of writing, happened to perceive as having meanings that corresponded, perhaps imperfectly, to topics that I am interested in. Interested does not necessarily mean fully-endorse/believe/would-describe-myself-as/is-knowledgeable-about.
#philosophy #absurdism #existentialism #anarchism #communism #anticapitalism #mutualaid #prefiguration #ontology #phenomenology #poststructuralism #structuralism #mathematics #chaos #topology #imagination #art #education #linguistics #literature #music #machines #networks #cybernetics #systems #sustainability #ecology #technology #sciencefiction #utopia #DavidGraeber #DavidWengrow #MurrayBookchin #NoamChomsky #PeterKropotkin #AdamCurtis #KenLoach #AlbertCamus #GillesDeleuze #JacquesDerrida #JeanPaulSartre #MarkFisher #SimoneDeBeauvoir #FranzKafka #GeorgeOrwell #PercyByssheShelley #MaryShelley #UrsulaKLeGuin