#combinatorics — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #combinatorics, aggregated by home.social.
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Registration is open for the 2026 colloquia in #combinatorics on 13+14 of May, 2026, in London.
#scientificConference #mathematics
https://2dcic.github.io/ -
Registration is open for the 2026 colloquia in #combinatorics on 13+14 of May, 2026, in London.
#scientificConference #mathematics
https://2dcic.github.io/ -
Registration is open for the 2026 colloquia in #combinatorics on 13+14 of May, 2026, in London.
#scientificConference #mathematics
https://2dcic.github.io/ -
Registration is open for the 2026 colloquia in #combinatorics on 13+14 of May, 2026, in London.
#scientificConference #mathematics
https://2dcic.github.io/ -
Registration is open for the 2026 colloquia in #combinatorics on 13+14 of May, 2026, in London.
#scientificConference #mathematics
https://2dcic.github.io/ -
Alright, future engineers!
**Combinations:** Ways to *choose* items from a set where the order *doesn't* matter.
Ex: Picking 3 teammates from 5 friends: `C(5,3) = 10` ways.
Pro-Tip: If swapping items doesn't create a new outcome, it's a combination!
#DiscreteMath #Combinatorics #STEM #StudyNotes -
Alright, future engineers!
**Combinations:** Ways to *choose* items from a set where the order *doesn't* matter.
Ex: Picking 3 teammates from 5 friends: `C(5,3) = 10` ways.
Pro-Tip: If swapping items doesn't create a new outcome, it's a combination!
#DiscreteMath #Combinatorics #STEM #StudyNotes -
Alright, future engineers!
**Combinations**: ways to choose items where order *doesn't* matter.
Ex: Choose 2 teammates from 5 friends: `C(5,2) = 5!/(2!3!) = 10` ways.
Pro-Tip: Think 'choosing a committee' – the group is what matters, not selection order!
#Probability #Combinatorics #STEM #StudyNotes -
Alright, future engineers!
**Combinations**: ways to choose items where order *doesn't* matter.
Ex: Picking 3 committee members from 5 people: C(5,3) = 10 ways.
Pro-Tip: Think 'selecting ingredients for a soup' – the order you add them doesn't change the final soup! -
Alright, future engineers!
**Combinations**: ways to choose items where order *doesn't* matter.
Ex: Picking 3 committee members from 5 people: C(5,3) = 10 ways.
Pro-Tip: Think 'selecting ingredients for a soup' – the order you add them doesn't change the final soup! -
Alright, future engineers!
**Permutations**: ways to arrange items where order matters.
Ex: Arranging 3 books (A,B,C) is 3! = 6 ways.
Pro-Tip: Think 'President, VP, Secretary' - roles are distinct! -
Alright, future engineers!
**Combinations** count selections where order *doesn't* matter. Ex: Picking 3 teammates from 10. Formula: C(n,r) = n! / (r!(n-r)!). Pro-Tip: If reordering items yields the *same* group, it's a combination!
#Probability #Combinatorics #STEM #StudyNotes -
Alright, future engineers!
A **Combination** is a selection of items where order *doesn't* matter. Ex: Choosing 3 people for a committee from 10. `C(N,K) = N!/(K!(N-K)!)`. Pro-Tip: Use for groups, not sequences!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
A **Combination** is a selection of items where order *doesn't* matter. Ex: Choosing 3 people for a committee from 10. `C(N,K) = N!/(K!(N-K)!)`. Pro-Tip: Use for groups, not sequences!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
A **Combination** is a selection of items where order *doesn't* matter. Ex: Choosing 3 people for a committee from 10. `C(N,K) = N!/(K!(N-K)!)`. Pro-Tip: Use for groups, not sequences!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
A **Combination** is a selection of items where order *doesn't* matter. Ex: Choosing 3 people for a committee from 10. `C(N,K) = N!/(K!(N-K)!)`. Pro-Tip: Use for groups, not sequences!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
A **Combination** is a selection of items where order *doesn't* matter. Ex: Choosing 3 people for a committee from 10. `C(N,K) = N!/(K!(N-K)!)`. Pro-Tip: Use for groups, not sequences!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
Registration is open for the 31st British Combinatorial Conference in Cardiff in Early July. Besides the plenary talks, there are minisymposia on various topics of #combinatorics and related areas of #mathematics , participants can submit abstracts for 20-min contributed talks.
Registration is cheaper before 17 May.
https://sites.google.com/view/bcc2026/home -
Visualizing the shifting proof of the Sauer-Shelah lemma: https://www.cs.columbia.edu/~djhsu/sauer_shift.html #sauershelah #combinatorics #shifting
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Visualizing the shifting proof of the Sauer-Shelah lemma: https://www.cs.columbia.edu/~djhsu/sauer_shift.html #sauershelah #combinatorics #shifting
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Visualizing the shifting proof of the Sauer-Shelah lemma: https://www.cs.columbia.edu/~djhsu/sauer_shift.html #sauershelah #combinatorics #shifting
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Visualizing the shifting proof of the Sauer-Shelah lemma: https://www.cs.columbia.edu/~djhsu/sauer_shift.html #sauershelah #combinatorics #shifting
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Visualizing the shifting proof of the Sauer-Shelah lemma: https://www.cs.columbia.edu/~djhsu/sauer_shift.html #sauershelah #combinatorics #shifting
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An email landed in my inbox about some local mathematical news. It somehow prompted me to look up where a paper of one of my former PhD students ended up. This was actually one of his thesis chapters:
https://doi.org/10.1090/jams/1069
Congrats Eoin!
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Alright, future engineers!
**Permutations:** Arrangements where order *does* matter.
Ex: Arranging 3 people for 3 specific roles (Pres, VP, Sec) from 5 options. P(5,3) = 5!/(5-3)! = 60.
Pro-Tip: Think 'ranking' or 'sequence' – position is crucial! -
Alright, future engineers!
**Combinations:** Choosing items from a set where order *doesn't* matter.
Ex: Picking 3 teammates from 10. Formula: C(n,k) = n!/(k!(n-k)!).
Pro-Tip: Think 'committee' selection—roles are identical, order is irrelevant! -
RE: https://mathstodon.xyz/@kangmeister/116136852073418222
It was almost exactly two years ago in Lunteren after a pitch by Ton de Kok (director of CWI at the time) that the idea for this popped into mind. And now (after a lot of hard work!) it is in full swing. An exciting mix of people at the confluence of combinatorics, algorithms, probability, brought together in Amsterdam over the next couple of months!
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A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.
However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/
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A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.
However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/
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A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.
However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/
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A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.
However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/
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A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.
However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/
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Permutations count arrangements where order matters. Ex: How many ways to arrange 3 books? 3! = 6 ways. Pro-Tip: 'Order matters' is your key phrase. If reordering creates a *new* valid outcome, it's a permutation!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
https://arxiv.org/abs/2603.12358
Here is the *third* manuscript coming out of the "Topics in Ramsey theory" online-only problem-solving session (https://sparse-graphs.mimuw.edu.pl/doku.php?id=sessions:2025sessions:2025session1) of the Sparse (Graphs) Coalition, which took place less than a year ago.
It is still surprising to realise what one can make of such events, if they are set up well.
#combinatorics #remoteconferences #graphtheory #extremalcombinatorics #openscience
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#paperOfTheDay for Friday was "Tree hook length formulae, Feynman rules and B-series" from 2014. This is a #mathematics paper, more specifically #combinatorics . It deals with rooted trees, that is, connected graphs without cycles and with one distinguished vertex. For a given vertex, the subtree is the unique tree that is obtained by taking the vertex as a root, and discarding everything that was above the new root in the original tree. One then defines a "hook length formula" to be a mapping from rooted trees to some ring, which is given by evaluating some function on each subtree and multiplying the result. The classical example is the "tree factorial", where the function on the subtree is the number of vertices, so that the entire tree evaluates to the product of the number of vertices of all subtrees (which equals the ordinary factorial if the tree is a path). This construction might seem obscure, but it is widely used, and the present paper makes an effort to unify these results. For example, Runge-Kutta schemes for numerical integration of differential equations have an algebraic form called B-series, which essentially is a hook length formula. Also, renormalization of divergent subdiagrams in #quantumFieldTheory has this structure. The present paper discovers various new closed-form expressions for hook length formulae. From the perspective of QFT, what they do is invent new toy model Feynman rules that give rise to nice closed-form Green functions. I find this quite useful for a systematic qualitative understanding of QFT, even if these particular Feynman rules don't have an immediate physical interpretation. https://arxiv.org/abs/1412.6053
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"""
the ! at the end is because the addresses are happy to participate
"""
--- me, explaining to my cat squeaks why the formula <addresses>! explains why the rate of expansion in the universe is slightly accelerating===
"""
your math only works when the number of addresses are small, by the time you account for routing and network effects that cause many of those writes to land back on existing addresses, the rate of expansion is more likely to fall on a curve plotted by n(n-1)/2
"""
--- squeaks, writely skeptical===
"""
your homonym puns are week and i really wanted to make a factorial joke this once!
"""
--- me, explaining to my cat squeaks why homonym puns don't work when you're having a vocal debate===
"""
i could have arranged for a better pun
"""
--- squeaks, getting too tired to finish the joke properly===
"""
and my jokes all landed where they were supposed to... nowhere
"""
--- me, finally understanding why derangement notation uses factorials -
As part of the CWI thematic research semester programme Phase Transitions in Combinatorics, Algorithms and Probability (PhaseCAP), we organise a series of three colloquia in Amsterdam. Please register via the links below if you want to attend. Registration closes a week before the meeting or when capacity is reached.
Thursday, 2 April — PhaseP colloquium
13:30–14:00 Coffee reception
14:00–15:00 Christina Goldschmidt (Oxford): Stable trees
15:00–16:00 Tom Bohman (Carnegie Mellon): Notes on two-point concentration in random graphs
16:00–17:30 Drinks receptionFriday, 17 April — PhaseC colloquium
13:30–14:00 Coffee reception
14:00–15:00 Penny Haxell (Waterloo): Algorithms for Independent Transversals and Reconfiguration
15:00–16:00 Rob Morris (IMPA): Recent results in Ramsey theory
16:00–17:30 Drinks receptionFriday, 29 May — PhaseA colloquium
14:00–15:00 Leslie Goldberg (Oxford): Fundamental Instability of Backoff Protocols
15:00–16:00 Amin Coja-Oghlan (Dortmund): The cavity method
16:00–17:30 Drinks receptionPlease feel free to share this announcement with colleagues who may be interested.
#combinatorics #probability #algorithms #amsterdam #phasetransitions #CWI
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In May, there will be a Colloquium on #combinatorics in London! #mathematics https://2dcic.github.io/speakers.html
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That was fun! Here's hoping that it won't be another 17 years before the next time I am at the Combinatorial Theory Seminar here...
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📑 A new paper by CPC-CG members introduces the first method that can predict how many relatives of any kind a person is likely to have at different points in their life, and how likely each outcome is:
https://www.demographic-research.org/articles/volume/54/9#demography #kinship #mathematicaldemography #populationstudies #lifeCourse #mortality #fertility #probability #matrixalgebra #combinatorics #convolution #kin #familyStructure #analyticModel #populationResearch #population #family #familystructures #demographicforecasting
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📑 A new paper by CPC-CG members introduces the first method that can predict how many relatives of any kind a person is likely to have at different points in their life, and how likely each outcome is:
https://www.demographic-research.org/articles/volume/54/9#demography #kinship #mathematicaldemography #populationstudies #lifeCourse #mortality #fertility #probability #matrixalgebra #combinatorics #convolution #kin #familyStructure #analyticModel #populationResearch #population #family #familystructures #demographicforecasting
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📑 A new paper by CPC-CG members introduces the first method that can predict how many relatives of any kind a person is likely to have at different points in their life, and how likely each outcome is:
https://www.demographic-research.org/articles/volume/54/9#demography #kinship #mathematicaldemography #populationstudies #lifeCourse #mortality #fertility #probability #matrixalgebra #combinatorics #convolution #kin #familyStructure #analyticModel #populationResearch #population #family #familystructures #demographicforecasting
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📑 A new paper by CPC-CG members introduces the first method that can predict how many relatives of any kind a person is likely to have at different points in their life, and how likely each outcome is:
https://www.demographic-research.org/articles/volume/54/9#demography #kinship #mathematicaldemography #populationstudies #lifeCourse #mortality #fertility #probability #matrixalgebra #combinatorics #convolution #kin #familyStructure #analyticModel #populationResearch #population #family #familystructures #demographicforecasting
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📑 A new paper by CPC-CG members introduces the first method that can predict how many relatives of any kind a person is likely to have at different points in their life, and how likely each outcome is:
https://www.demographic-research.org/articles/volume/54/9#demography #kinship #mathematicaldemography #populationstudies #lifeCourse #mortality #fertility #probability #matrixalgebra #combinatorics #convolution #kin #familyStructure #analyticModel #populationResearch #population #family #familystructures #demographicforecasting
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This 2-min piece was composed on a musical dodecahedron at dodecahedron.newritual.com — 12 faces, 12 pitch classes, 7 modes. Each face holds a unique key. How many possible dodecahedra are there? Burnside's lemma meets music theory: ~110 quadrillion distinct configurations, after accounting for rotational symmetry. This is just one. #musictheory #dodecahedron #combinatorics #math #generativemusic #composition
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This 2-min piece was composed on a musical dodecahedron at dodecahedron.newritual.com — 12 faces, 12 pitch classes, 7 modes. Each face holds a unique key. How many possible dodecahedra are there? Burnside's lemma meets music theory: ~110 quadrillion distinct configurations, after accounting for rotational symmetry. This is just one. #musictheory #dodecahedron #combinatorics #math #generativemusic #composition
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This 2-min piece was composed on a musical dodecahedron at dodecahedron.newritual.com — 12 faces, 12 pitch classes, 7 modes. Each face holds a unique key. How many possible dodecahedra are there? Burnside's lemma meets music theory: ~110 quadrillion distinct configurations, after accounting for rotational symmetry. This is just one. #musictheory #dodecahedron #combinatorics #math #generativemusic #composition
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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.
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.
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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.
