#graphtheory — Public Fediverse posts

https://systemic.engineering/a-roomba/

#AI #Climate #ScientificProgramming #SystemicEngineering #Fiction #Cybernetics #SystemicTherapy #LocalInference #TheMathDoesntLie #SubTuring #FormalVerification #Fortran #SpectralGraphTheory #Kintsugi #ReductiveAI #DataSovereignty #LocalFirst #FOSS #OpenSource #AuDHD #Neuroqueer #DGSF #SecondOrderCybernetics #GraphTheory #Eigenvalues #AIAlignment #AISafety #Roomba #Loriot #Satire

https://systemic.engineering/a-roomba/

#AI #Climate #ScientificProgramming #SystemicEngineering #Fiction #Cybernetics #SystemicTherapy #LocalInference #TheMathDoesntLie #SubTuring #FormalVerification #Fortran #SpectralGraphTheory #Kintsugi #ReductiveAI #DataSovereignty #LocalFirst #FOSS #OpenSource #AuDHD #Neuroqueer #DGSF #SecondOrderCybernetics #GraphTheory #Eigenvalues #AIAlignment #AISafety #Roomba #Loriot #Satire

https://systemic.engineering/a-roomba/

#AI #Climate #ScientificProgramming #SystemicEngineering #Fiction #Cybernetics #SystemicTherapy #LocalInference #TheMathDoesntLie #SubTuring #FormalVerification #Fortran #SpectralGraphTheory #Kintsugi #ReductiveAI #DataSovereignty #LocalFirst #FOSS #OpenSource #AuDHD #Neuroqueer #DGSF #SecondOrderCybernetics #GraphTheory #Eigenvalues #AIAlignment #AISafety #Roomba #Loriot #Satire

https://systemic.engineering/a-roomba/

#AI #Climate #ScientificProgramming #SystemicEngineering #Fiction #Cybernetics #SystemicTherapy #LocalInference #TheMathDoesntLie #SubTuring #FormalVerification #Fortran #SpectralGraphTheory #Kintsugi #ReductiveAI #DataSovereignty #LocalFirst #FOSS #OpenSource #AuDHD #Neuroqueer #DGSF #SecondOrderCybernetics #GraphTheory #Eigenvalues #AIAlignment #AISafety #Roomba #Loriot #Satire

https://systemic.engineering/a-lie/

#AI #Climate #ScientificProgramming #SystemicEngineering #Fiction #Cybernetics #SystemicTherapy #LocalInference #TheMathDoesntLie #SubTuring #FormalVerification #Fortran #SpectralGraphTheory #Kintsugi #ReductiveAI #DataSovereignty #LocalFirst #FOSS #OpenSource #AuDHD #Neuroqueer #DGSF #SecondOrderCybernetics #GraphTheory #Eigenvalues #AIAlignment #AISafety #Roomba

The Roomba is spectral.

Not a metaphor. The thing itself. Forward and adjust. Two operations. The minimum viable intelligence. The walls provide the data. The bumping is the inference. The room IS the computation.

450 parameters. A Roomba with a mirror watching it.

The industry built bigger Roombas. More sensors. More compute. More parameters. Billion-parameter Roombas that model the room before entering it. That hallucinate walls that aren't there. That consume megawatts to clean a floor.

spectral gave the Roomba a mirror. The mirror watches the bumping. Measures the pattern. Adjusts the adjustment. The intelligence isn't in the Roomba. It's in the watching.

Forward. Adjust. Measure. Refine.

Read the story. There's a Roomba in it. In the afterlife. Cleaning a floor that doesn't need cleaning. Being the happiest thing in the room.

\

https://systemic.engineering/a-lie/

#AI #Climate #ScientificProgramming #SystemicEngineering #Fiction #Cybernetics #SystemicTherapy #LocalInference #TheMathDoesntLie #SubTuring #FormalVerification #Fortran #SpectralGraphTheory #Kintsugi #ReductiveAI #DataSovereignty #LocalFirst #FOSS #OpenSource #AuDHD #Neuroqueer #DGSF #SecondOrderCybernetics #GraphTheory #Eigenvalues #AIAlignment #AISafety #Roomba

Animated Logical Graphs • 2
• https://inquiryintoinquiry.com/2015/01/14/animated-logical-graphs-2/

It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

So I'll try to keep focused on that.

Resources —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

Animated Logical Graphs • 1
• https://inquiryintoinquiry.com/2015/01/08/animated-logical-graphs-1/

For Your Musement …

Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

Proof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations

Double Negation
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-double-negation-2.0.gif

Peirce's Law
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-peirces-law-2.0.gif

Praeclarum Theorema
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-praeclarum-theorema-2.0.gif

Two‑Thirds Majority Function
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-two-thirds-majority-function-2.0.gif

A full discussion of logical graphs can be found in the following article.

Logical Graphs
• https://oeis.org/wiki/Logical_Graphs

Resources —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

cc: https://www.academia.edu/community/ldzadj
cc: https://mathstodon.xyz/@Inquiry/116494097283214718
cc: https://www.researchgate.net/post/Animated_Logical_Graphs
cc: https://stream.syscoi.com/2026/04/30/animated-logical-graphs-1/
cc: https://groups.io/g/lawsofform/topic/animated_logical_graphs/119049814

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

Animated Logical Graphs • 1
• https://inquiryintoinquiry.com/2015/01/08/animated-logical-graphs-1/

For Your Musement …

Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

Proof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations

See the following article for a full discussion of this type of logical graph.

Logical Graphs
• https://oeis.org/wiki/Logical_Graphs

Additional Resources —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

“I realized that studying mathematics made me logical, precise and optimistic in life. The subject helped me gain the confidence and skills to achieve much more than I ever aspired to.” - Tabitha Rajashekar

➡️ https://hermathsstory.eu/tabitha-rajashekar/

#AbstractAlgebra #DiscreteMathematics #Academia #GraphTheory #WomenInMaths #HerMathsStory

Graph Construction Complete: 21 nodes, 12 edges.
Primary Drivers: ['CVE-2025-40739', 'CVE-2025-40740', 'CVE-2025-3508']

#GraphTheory #NetworkSecurity #TechnicalDebt #Audit
2/2

Alright, future engineers!

A **Tree** is an undirected graph where any two vertices are connected by exactly one path (no cycles). Ex: A graph with N vertices & N-1 edges (no cycles) is a tree. Pro-Tip: Perfect for modeling hierarchical structures like file systems!

#GraphTheory #DataStructures #STEM #StudyNotes

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

I made another #ErgoMechKeyboard, taking the ribbon cable idea for my Bivouac34, and the 32-key layout and a 5-way navigation button from my Bivvy16D #SplitKeyboard. This is my Goldilocks32 #MechanicalKeyboard - another diode-free design with a #GraphTheory based sparse scanning matrix https://astrobeano.blogspot.com/2026/03/goldilocks-30-to-32-key-keyboard.html

Differential Logic • 18

Tangent and Remainder Maps

If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition in the following way.

The next venn diagram shows the differential proposition we get by extracting the linear approximation to the difference map at each cell or point of the universe   What results is the logical analogue of what would ordinarily be called the differential of but since the adjective differential is being attached to just about everything in sight the alternative name tangent map is commonly used for whenever it’s necessary to single it out.

To be clear about what’s being indicated here, it’s a visual way of summarizing the following data.

To understand the extended interpretations, that is, the conjunctions of basic and differential features which are being indicated here, it may help to note the following equivalences.

Capping the analysis of the proposition in terms of succeeding orders of linear propositions, the final venn diagram of the series shows the remainder map which happens to be linear in pairs of variables.

Reading the arrows off the map produces the following data.

In short, is a constant field, having the value at each cell.

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 17

Enlargement and Difference Maps

Continuing with the example the following venn diagram shows the enlargement or shift map in the same style of field picture we drew for the tacit extension

A very important conceptual transition has just occurred here, almost tacitly, as it were.  Generally speaking, having a set of mathematical objects of compatible types, in this case the two differential fields and both of the type is very useful, because it allows us to consider those fields as integral mathematical objects which can be operated on and combined in the ways we usually associate with algebras.

In the present case one notices the tacit extension and the enlargement are in a sense dual to each other.  The tacit extension indicates all the arrows out of the region where is true and the enlargement indicates all the arrows into the region where is true.  The only arc they have in common is the no‑change loop at   If we add the two sets of arcs in mod 2 fashion then the loop of multiplicity 2 zeroes out, leaving the 6 arrows of shown in the following venn diagram.

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 15

Differential Fields

The structure of a differential field may be described as follows.  With each point of there is associated an object of the following type:  a proposition about changes in that is, a proposition   In that frame of reference, if is the universe generated by the set of coordinate propositions then is the differential universe generated by the set of differential propositions   The differential propositions and may thus be interpreted as indicating and respectively.

A differential operator of the first order type we are currently considering, takes a proposition and gives back a differential proposition   In the field view of the scene, we see the proposition as a scalar field and we see the differential proposition as a vector field, specifically, a field of propositions about contemplated changes in

The field of changes produced by on is shown in the following venn diagram.

The differential field specifies the changes which need to be made from each point of in order to reach one of the models of the proposition that is, in order to satisfy the proposition

The field of changes produced by on is shown in the following venn diagram.

The differential field specifies the changes which need to be made from each point of in order to feel a change in the felt value of the field

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 14

Field Picture

Let us summarize the outlook on differential logic we’ve reached so far.  We’ve been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse to considering a larger universe of discourse   An operator of that general type, namely, acts on each proposition of the source universe to produce a proposition of the target universe

The operators we’ve examined so far are the enlargement or shift operator and the difference operator   The operators and act on propositions in that is, propositions of the form which amount to propositions about the subject matter of and they produce propositions of the form which amount to propositions about specified collections of changes conceivably occurring in

At this point we find ourselves in need of visual representations, suitable arrays of concrete pictures to anchor our more earthy intuitions and help us keep our wits about us as we venture into ever more rarefied airs of abstraction.

One good picture comes to us by way of the field concept.  Given a space a field of a specified type over is formed by associating with each point of an object of type   If that sounds like the same thing as a function from to the space of things of type — it is nothing but — and yet it does seem helpful to vary the mental images and take advantage of the figures of speech most naturally springing to mind under the emblem of the field idea.

In the field picture a proposition becomes a scalar field, that is, a field of values in

For example, consider the logical conjunction shown in the following venn diagram.

Each of the operators takes us from considering propositions here viewed as scalar fields over to considering the corresponding differential fields over analogous to what in real analysis are usually called vector fields over

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 13

Transforms Expanded over Ordinary and Differential Variables

Two views of how the difference operator acts on the set of sixteen functions are shown below.  Table A5 shows the expansion of over the set of ordinary variables and Table A6 shows the expansion of over the set of differential variables.

Difference Map Expanded over Ordinary Variables

Difference Map Expanded over Differential Variables

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Users Are Too Dependent on Centralized Techno-Fascist Corporate Structure to Ever Leave Discord

I’m watching people scatter into countless real-time chat alternatives to Discord after Discord started pulling the age-verification and age-gating card.

https://techcrunch.com/2026/02/09/discord-to-roll-out-age-verification-next-month-for-full-access-to-its-platform/

It’s very frustrating because people are entirely missing the point of a community and how social networks work. Real-time platforms and social media networks only work well when a large number of people share the same space at the same time. If everyone creates separate servers or competing apps, the result is fragmentation that makes it unviable.

One reason why Bluesky became so successful is the invitation and starter-pack move. It essentially allowed people to move collectively as cliques. Bluesky used invitations and starter packs to move groups of friends together. This kept communities intact. Moving as cliques preserves network structure, whereas random scattering does not. People aren’t do not seem to intend to move as cliques or subgraphs of networks off of Discord. And the whole reason people were on Discord was to host their communities, so an alternative becomes pointless if your community doesn’t remain intact.

Instead of an active, strongly connected, possibly distributed network, you get dozens of small pockets. I am referring to a potential distributed network rather than a single centralized platform, because Matrix is an example of a decentralized chat protocol. Not all alternatives have to be centralized like Discord. Technically, many older chat protocols, such as XMPP and IRC, are examples of federated real-time synchronous messaging. They allowed communication between users on different, independently operated servers. Federation means that multiple servers can interconnect so that users from separate networks can exchange messages with one another seamlessly.

Decentralized alternatives would not be a problem if people moved to the same distributed network as cohesive groups. However, what I am seeing is that people move in disconnected and stochastic ways to entirely separate distributed networks, so communities are not kept intact. For example, when people move to XMPP servers or Matrix servers, it bifurcates and disconnects social networks. Notice I said XMPP or Matrix, which logically means people are on Matrix but not XMPP, or they are on XMPP but not Matrix. That implies a person would need to be on both Matrix and XMPP to speak to their original community from Discord if it split down the middle. To synchronize conversations in chats, there would need to be a bridge. It’s a pretty complicated solution.

The likely outcome is that people will remain on the dominant platform because of its scale and structure. The deeper irony is that while people may want independence from corporate platforms, they often struggle to organize effectively without the centralized structure those platforms provide. They’ve become so dependent on corporate structures to support their communities that they have no clue how to organize their own social networks in a sustainable way.

I’ve always been an internet nerd, but most of my social life has been offline. I view my interactions with the social app layer of the internet as a game, so losing that domain of the Internet is not devastating to me.

I’ll give you an example. This is a WordPress site. You hear this insincere nostalgia from Millennials and Gen X for a simulacrum that never was, especially concerning forums. Check this out: when you go into the plugin installation section of WordPress, this is on the second row you see:

https://bbpress.org/

That means any WordPress site has the capability to host a forum. They’re nostalgic for a setup where you can use a simple install script on any hosting service to install WordPress. After that, you can then just add a plugin to turn it into a forum. Hell, they can do this on WordPress.com if they don’t want to self-host.

You can make a forum, but no one will use it because they’d rather use a centralized platform like Reddit. Users have become so dependent on corporations to structure and organize communities that they can’t do it themselves. It’s sort of like the cognitive debt that accrues when people outsource their thinking to AI.

The issue is not that forums are hard to host or create; rather, the issue is that people have become so dependent on centralized corporate structures that they can’t maintain or organize their own communities, which is why everyone ends up on Reddit or Discord. A reason I keep hearing for why people don’t want to leave Discord is that it’s hard to recreate the community structure that Discord’s features provide. They claim that they want independence from corporate platforms, but rely on the centralized structure those platforms provide to function socially.

People say they want decentralized freedom, but in practice they depend on centralized platforms to maintain social cohesion. Stochastically scattering to the digital winds of the noosphere destroys the very communities they’re trying to preserve.

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.

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.

This can be modeled by representing each item as a node in a weighted graph, where edges are weighted by dissimilarity rather than similarity. Highly similar items are connected by low-weight edges, while less similar items are connected by higher-weight edges. Distances in the graph, computed using standard shortest-path algorithms, then correspond to degrees of similarity. Closely related items are separated by short path lengths, while increasingly dissimilar items require longer paths through the graph. It turns out that attempts to generalize metric spaces for noetic domains—to model noetic/psychic spaces—are actually pretty useful for social media algorithms, lol.

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.

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.

This can be modeled by representing each item as a node in a weighted graph, where edges are weighted by dissimilarity rather than similarity. Highly similar items are connected by low-weight edges, while less similar items are connected by higher-weight edges. Distances in the graph, computed using standard shortest-path algorithms, then correspond to degrees of similarity. Closely related items are separated by short path lengths, while increasingly dissimilar items require longer paths through the graph. It turns out that attempts to generalize metric spaces for noetic domains—to model noetic/psychic spaces—are actually pretty useful for social media algorithms, lol.

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.

This can be modeled by representing each item as a node in a weighted graph, where edges are weighted by dissimilarity rather than similarity. Highly similar items are connected by low-weight edges, while less similar items are connected by higher-weight edges. Distances in the graph, computed using standard shortest-path algorithms, then correspond to degrees of similarity. Closely related items are separated by short path lengths, while increasingly dissimilar items require longer paths through the graph. It turns out that attempts to generalize metric spaces for noetic domains—to model noetic/psychic spaces—are actually pretty useful for social media algorithms, lol.

Astroturfing Is Pretty Pointless When Social Subgraphs Are Fragmented (e.g., the Fediverse)

I am seeing astroturfing in the fediverse again, by AT Protocol developers implicitly trying to shill their products. I think it is stochastic behavior by developers with too much time on their hands. Honestly, I do not care. I like the people on ActivityPub more, but I like the AT Protocol better, and I have developed for both. Astroturfing on ActivityPub networks is fascinating to me because it is so pointless.

I am actually a Computational Biologist and Computer Scientist whose specialty is combinatorics, social graphs, graph theory, etc. Specifically, I use this to create epidemiological models for the memetic layer of human behaviors that act as vectors for diseases, using the SIRS model. I do not just study germs; I study human behaviors.

The models I construct extend into a “memetic layer,” in which beliefs, norms, and behaviors (such as risk-taking, compliance with public health measures, or susceptibility to misinformation) spread contagiously through social networks. These behaviors function as vectors that modulate biological transmission rates. As a result, the spread of ideas can accelerate, dampen, or reshape the spread of disease. By running computational simulations and agent-based models on these graphs, I study how network structure, influential nodes, clustering, and platform-specific dynamics affect behavioral contagion. I also examine how these factors influence epidemiological outcomes.

To say it very concisely, I study how the spread of bat-shit insane beliefs, shit posts, and memes influences whether or not there is a measles outbreak in Texas. Ironically, this is an evolution of my studying semiotics, memetics, and chaos magick in high school. I got a job where I can use occult, anarchist techniques professionally.

I think a large reason why I do not care about astroturfing in the fediverse is that it’s so pointless, lol. Astroturfing to manipulate the narrative would actually work better on Bluesky to keep people there than trying to recruit from the fediverse. Furthermore, big instances are relatively small. Some people on Bluesky have follower lists larger than an entire large instance in the fediverse.

Within ActivityPub networks, astroturfing rarely propagates far, because whether information spreads depends on properties of the social graph itself. Dense connectivity, short paths between communities, and a sufficient number of cross-cutting ties support diffusion. ActivityPub’s architecture tends to produce graphs that are fragmented and highly modular. This limits the reach of coordinated activity.

ActivityPub is a system where each instance maintains its own local user graph and exchanges activities through inboxes and outboxes. This makes it autonomous and decentralized. The network consists of loosely connected subgraphs. Cross-instance edges appear only through explicit follow relationships. The ActivityPub protocol does not provide a shared or complete view of the network. Measurements of the fediverse consistently show uneven connectivity between instances, clustering at the instance level, and relatively long effective path lengths across the network. Under these conditions, large cascades are uncommon.

Instance-level clustering means that in ActivityPub networks, users interact much more with others on the same server than with users on different servers. Because each instance has its own local timeline, culture, and moderation, connections form densely within instances and only sparsely across them through explicit follow relationships. This creates a network made up of tightly connected local communities linked by relatively few cross-instance ties, which slows the spread of information beyond its point of origin.

However, with the AT Protocol, global indexing and aggregation are explicitly supported. Relays and indexers can assemble near-complete views of the social graph. Applications built on top of this infrastructure operate over a graph that is denser and easier to traverse. There are fewer structural barriers between communities. The diffusion dynamics change substantially when content can move across the graph without relying on narrow federated paths.

Astroturfing depends on coordinated amplification, typically through tightly synchronized clusters of accounts intended to manufacture visibility. Work on coordinated inauthentic behavior shows that these tactics gain traction when they intersect highly connected regions of the graph or bridge otherwise separate communities. In networks with strong modularity, coordination remains local. ActivityPub’s federation model produces this kind of modularity by default. Coordinated clusters stand out clearly within instances. Their effects remain confined to those local neighborhoods.

Astroturfing on ActivityPub therefore tends to stall on its own because of the underlying graph topology. Without dense inter-instance connectivity or any form of global indexing, coordinated campaigns have a hard time moving beyond the immediate regions where they originate. Systems built on globally indexable social graphs, including those enabled by the AT Protocol, expose a much larger surface for viral spread. Network structure and connectivity account for the divergence where that is independent of moderation, cultural norms, ideology, or intent.

It’s just really funny to me how these stochastic techbro groups waste so many resources. I personally don’t want to go viral, which is why I avoid platforms where I can. The fact that it’s harder to achieve high virality on ActivityPub is exactly why I prefer the fediverse over the Atmosphere. One way to think about it is that you can change the ‘genetics’ of a system with a retrovirus, where memetic entities act as cultural retroviruses to reprogram the cultural loci of a space. That is their end goal. They are trying to hijack cultures memetically. You see this a lot with culture jamming.

Basically, the astroturfing on ActivityPub networks is designed to jam and subvert the culture. But, as I have already said, the topological structure makes memetic virality stall. They cannot achieve that kind of viral spread in the fediverse, which is why I cannot understand why they do this every year.

The Graph Theory of Circuit Sculptures https://hackaday.com/2026/02/03/the-graph-theory-of-circuit-sculptures/ #CircuitSculpture #graphtheory #LEDfilament #LEDHacks #Art

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

This thing all things devours:
Birds, beasts, trees, flowers;
Gnaws iron, bites steel;
Grinds hard stones to meal;
Slays king, ruins town,
And beats high mountain down.

— Tolkien • The Hobbit

Talking about time is a waste of time. Time is merely an abstraction from process and what is needed are better languages and better pictures for describing process in all its variety. In the sciences the big breakthrough in describing process came with the differential and integral calculus, that made it possible to shuttle between quantitative measures of state and quantitative measures of change. But every inquiry into a new phenomenon begins with the slimmest grasp of its qualitative features and labors long and hard to reach as far as a tentative logical description. What can avail us in the mean time, still tuning up before the first measure, to reason about change in qualitative terms?

Et sic deinceps … (So it begins …)

#Animata, #CSPeirce, #Change, #Cybernetics, #DifferentialLogic, #GraphTheory, #LawsOfForm, #Logic, #LogicalGraphs, #Mathematics, #Paradox, #Peirce, #Process, #ProcessThinking, #SpencerBrown, #SystemsTheory, #Time, #Tolkien

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

I am slowly getting better at soldering, 4 out of 7 successful #MechanicalKeyboard PCBs now - all three of my diode-free #GraphTheory wired keyboard PCB designs have worked (eventually) ⌨️🎊

1️⃣ #RaspberryPiPico #RP2040 ‘Gamma Omega TC36K’ (USB only) http://astrobeano.blogspot.com/2025/08/my-first-self-built-computer-keyboard.html

2️⃣ #ProMicro #nRF52840 BLE ‘Gamma Omega Hesse’ https://astrobeano.blogspot.com/2025/10/hesse-diode-free-bluetooth-keyboard.html

3️⃣ #SeeedStudio #Xiao #SplitKeyboard BLE split Forager ‘Acid’ http://astrobeano.blogspot.com/2025/10/partial-heawood-forager-keyboard.html

#ErgoMechKeyboard #ErgonomicKeyboard

I’m excited to share that our article has been published: “Brain Topology Disruption in Early-Onset Dementia: Review of Current Findings and the Need for Network Resilience-Focused Models” (http://dx.doi.org/10.1002/brb3.70903)

In this review, we highlight several important insights:

- A summary of how early‐onset forms of dementia (including Alzheimer’s disease, frontotemporal dementia (FTD), and behavioral variant FTD) show disruption in brain network topology (both structural and functional) rather than purely focal pathology.

- Evidence that brain networks lose their optimal organisational properties (e.g., balance of segregation and integration) in early‐onset dementia, reflecting decline in network resilience. For example, previous work has shown disrupted segregation/integration in large‐scale brain networks in Alzheimer’s/MCI.

- The concept of network resilience as a key lens: rather than only asking “where damage occurs”, the paper argues we should ask “how the network topology fails to compensate, reorganise or maintain function under pathology”. This shifts the view to resilience‐focused models.

- Review of methodological findings: how graph‐theoretic metrics (clustering coefficient, global/local efficiency, modularity, assortativity, small‐worldness) are being applied to neuroimaging and electrophysiology in early dementia.

- Gaps and opportunities: the need for models that integrate network resilience, longitudinal data, multimodal connectivity (structural + functional + electrophysiological) and early‐onset cohorts; and the translational potential for biomarkers and interventions that support network integrity rather than just reduce pathology.

I believe this work contributes to bridging neuroscience, network theory, and clinical neurology, and invites discussion on how we can design interventions that strengthen brain network resilience in dementia.

Thanks to my co-authors (Hema Nawani, Sredha Sunil) and reviewers, and a huge thank you to our professor Veeky Baths for his guidance and support throughout this work.

If you’re working in cognitive neuroscience, network approaches to brain disorders, early‐onset dementia, connectomics or translational neurology, let’s collaborate to make a real impact.

#Neuroscience #BrainNetworks #Dementia #EarlyOnsetDementia #Neurodegeneration #NetworkResilience #ClinicalNeuroscience #GraphTheory #NetworkNeuroscience #ComputationalNeuroscience

Gave a lecture today about Euler's theorem.
Then somehow it led to:
"There's a face, next muffin!"
Wondering what kind of vibe that sent out...

#teaching #graphtheory #euler

A new inquiry activity is posted on Fractal Kitty!

https://www.fractalkitty.com/inquiries-week-5-triangles-emerge/

This one plays with graphs and can be used as an extension to Sim, Don't Make a Triangle, and other such games.

#mtbos #iteachmath #mathplay #accessibleProofs #inquiry #turan #graphTheory #triangles

The #Mathober Day 9 prompt is ‘Chi’. In graph theory, \(\chi(G)\) denotes the chromatic number of a graph \(G\): the minimum number of colours required to colour all vertices so that no adjacent vertices have the same colour.

The famous ‘four colour theorem’ says that all planar graphs \(G\) have \(\chi(G) \leq 4\). A graph is planar if it can be drawn in the plane without any edges crossing.

The conjecture originated in 1852 when Francis Guthrie (1831–99) noticed that it was possible to colour a map of England using only four colours so that no neighbouring counties received the same colour, and wondered if this held true for all maps. The question for maps is transformed into one for graphs by replacing each region by a vertex and placing edges between vertices corresponding to neighbouring regions.

Thus, for the Mathober prompt ‘Chi’, I offer a map of the counties of England as they were in Guthrie's time and the corresponding graph, coloured in the same way with four colours.

Vector version (PDF format) of the map: https://ajcain.codeberg.page/posts/files/england-counties-map-4coloured.pdf

Vector version (PDF format) of the graph: https://ajcain.codeberg.page/posts/files/england-counties-graph-4coloured.pdf

1/2

#Mathober2025 #GraphTheory #HistMath

#mathstodon #graphTheory
I am working on writing a GUI for editing edge-representation #Hypergraphs Anyone played with drawing these? I have a couple of ways of approaching this, and would like to choose something useful and useable beyond just my rather narrow experience and application.

I am writing in #Python using #pyside6 and can (within reason!) make it do what is best for editing and thinking.

Any links/ references/ resources/ boosts welcome.

A new post on the math blog! I built a couple of toys to play with as well.

Inquiries week 4: Triangulating Triangles

https://www.fractalkitty.com/inquiries-week-4-triangulate-the-triangle/

#indieweb #math #colorings #graphTheory #triangles #inquiry #mtbos #iteachmath #mathtoys

😂🤦‍♂️ Oh, the sheer excitement of counting paths in a graph! Because who doesn't want to spend their weekend channeling their inner #mathematician to solve the world's least riveting problem? 🤓📉 Let's all just pretend this doesn't end in a rabbit hole of #confusion and infinite loops of existential dread.
https://horace.io/walks #graphtheory #weekendfun #humor #existentialdread #HackerNews #ngated

In our last #ISE2025 lecture last week, we were discussing what makes a node "important" in a knowledge graph. A simple heuristics can be borrowed from graph theory or communication theory: Degree Centrality

Interestingly, in Wikidata In-degree centrality states Jane Austen to be to most "important" female author, while Out-degree centrality claims J.K. Rowling as being more "important" ;-)

#knowledgegraphs #semanticweb #graphtheory #feminism #eyeofthebeholder @sourisnumerique @enorouzi

Multilayer Network Neuroscience: Decoding the Brain’s Complex Systems

#NetworkNeuroscience #BrainConnectivity #Connectome #Neuroscience #BrainMapping #GraphTheory #MultilayerNetworks #BrainResearch #Neurotechnology #PersonalizedMedicine #BrainHealth #CognitiveScience #Neuroimaging #BrainScience

https://youtube.com/shorts/LdGsiQgeW14?feature=share

Relational Graph Transformers

https://kumo.ai/research/relational-graph-transformers/

#HackerNews #Relational #Graph #Transformers #AI #Research #GraphTheory #MachineLearning #DataScience

Relational Graph Transformers

https://kumo.ai/research/relational-graph-transformers/

#HackerNews #Relational #Graph #Transformers #AI #Research #GraphTheory #MachineLearning #DataScience