#topology — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #topology, aggregated by home.social.
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Although those interested in measure theory here are a set of measure zero, I have nonetheless written an article on the subject. Along with a bit of inappropriate humor, I have careened off of continuity, equivalence classes, orderings, lattices and semilattices, order topologies, and metrics. Oh, and the subject is change of variable.
https://www.skewray.com/articles/continuity-induced-metrics-on-measures
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I'm Anthony, a #math phd candidate at George Mason University! I like to think about stochastic #topology, #probability, random #algorithms, and quantitative justice. let me know if you're going to the AMS Eastern Sectional at GWU in October, I'd love to say hi :)
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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.
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:
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.
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Hypersphere slow motion explanation
#silent #digital #animation of a #hypersphere. 2.5-min.❛❛ In #math, a hypersphere or 3-sphere is a 4-dimensional #analogue of a #sphere, and is the 3-dimensional n-sphere. In 4-dimensional #Euclidean #space, it is the set of #points equidistant from a fixed central #point. ❜❜
🔗 https://www.youtube.com/watch?v=XFW769hqa1U 2012 Jul 04
🔗 https://Wikipedia.org/wiki/N-sphere … #nSphere
🔗 https://Wikipedia.org/wiki/3-sphere … #3Sphere#Community #TimeTravel #Research #Topology #Geometry #Kronodon
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Differential Propositional Calculus • 10
Special Classes of Propositions (cont.)
Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general. We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions. The case for 3 variables is exemplary enough for a start.
Linear Propositions
The linear propositions, may be written as sums:
One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that
In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.
At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.
Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.
Next are the three linear propositions of rank 1, which are none other than the three basic propositions,
At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple
Resources
cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization
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History of GIS - Video – CGIS, The First Operational GIS, Canada [1967]
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https://youtu.be/3VLGvWEuZxI?si=dp64Np3FhyMSTirt <-- shared video
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https://en.wikipedia.org/wiki/Canada_Geographic_Information_System <-- Canada GIS wiki page
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“Early [1967] video description of the first operational GIS, the Canada GIS. The "father of GIS," Roger Tomlinson is highlighted. It is also an excellent description of how GIS operates today although the technology is considerably more advanced than when CGIS was first developed…”
#GIS #spatial #mapping #topology #cartography #spatialanalysis #gischat #appliedscience #solutions #history #canada #RogerTomlinson #CGIS #CanadaGeographicInformationSystem #CanadaLandInventory #canadaday -
Christian Pfleiderer, Professor of #Topology of Correlated Systems, is the new Scientific Director of Research Neutron Source Heinz Maier-Leibnitz (FRM II) from January 1, 2024. 👏 He aims to make the research accessible to the entire #scientificcommunity: http://go.tum.de/509989
📷A.Eckert
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Exploring the #topology of a fused #latentspace , made of two fine-tuned #stablediffusion models – my #solarpunk model, and my 'gold' #portrait model.
Working in this way means letting go, prompting at a higher-level of abstraction, and discovering the characters who inhabit this mysterious #manifold
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