#topology — Public Fediverse posts

💁🏻‍♀️ TIL: 🧵🌐 The hairy ball #theorem says you can’t comb a #sphere smooth without a cowlick somewhere.

The same rule explains why #Earth always has a #cyclone spinning, why #fusion reactors use #doughnut shapes, and why omnidirectional antennas can’t exist. #Wind patterns over the #Arctic and #Antarctic circles illustrate the proof.

👉 https://www.scientificamerican.com/article/how-maths-hairy-ball-theorem-could-explain-bad-hair-days/

#topology #math #weather #hurricane #nuclearfusion #tokamak #plasma #science #hair

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.

Почему структура Ur, Uz не случайна даже при случайном k в ECDSA: математика за топологией цифровых подписей

В данной работе мы доказали, что структура параметров в ECDSA является строго детерминированной и не зависит от случайности . Это свойство вытекает из линейного соотношения , которое формирует регулярную сетку параллельных линий на торе. Мы применили методы топологического анализа данных (Mapper, персистентная гомология) для визуализации этой структуры и показали её криптографические последствия.

https://habr.com/ru/articles/954536/

#ecdsa #cryptography #bitcoin #signature #algorithm #topology

Топологический аудит ECDSA: Практическая реализация с минимальными входными данными

Топологический аудит ECDSA: как найти уязвимости с одной подписью Традиционный анализ безопасности ECDSA требует сотен подписей для выявления уязвимостей. Но что делать, когда у вас есть только одна подпись из блокчейна? Мы разработали AuditCore — систему топологического аудита, которая анализирует безопасность ECDSA, используя лишь публичный ключ и одну реальную подпись. Система автоматически генерирует необходимое количество валидных подписей и проводит глубокий анализ пространства (u_r, u_z) как топологического тора. Ключевые возможности: Определение уязвимостей по топологическим инвариантам (числам Бетти) Расчет TVI Score — количественной метрики уязвимости Автоматическое обнаружение паттернов: фиксированный k, линейные зависимости, кластеры Генерация необходимого количества данных для статистически значимого анализа Система состоит из нескольких специализированных модулей: TopologicalAnalyzer для вычисления персистентных гомологий BettiAnalyzer для интерпретации топологических показателей CollisionEngine для поиска коллизий SignatureGenerator для создания валидных подписей TCON для оценки соответствия топологии тора AuditCore позволяет обнаруживать уязвимости, которые традиционные методы пропускают, включая слабые места в генераторах случайных чисел и системах, подобные той, что привела к компрометации ключей Sony PS3. Полная реализация доступна на GitHub: https://github.com/miroaleksej/AuditCore/tree/main/Scripts

https://habr.com/ru/articles/942190/

#криптография #cryptography #cryptoauditor #cryptoanalysis #topology #tor #криптоанализ #Криптоаудит #топологический_аудит #ecdsa

Топологический анализ безопасности ECDSA

Новый подход к анализу безопасности алгоритма цифровой подписи на эллиптических кривых (ECDSA) через призму алгебраической топологии.

https://habr.com/ru/articles/939560/

#ecdsa #topology #cryptography #audit #cryptoauditor #bitcoin

The following list identifies the longest escarpments on the planet. Escarpments are defined as follows:

Escarpment: “A steep slope or long cliff that results from erosion or faulting and separates two relatively level areas of differing elevations.”

Source: The American Heritage® Dictionary of the English Language, 5th Edition

If you have ever driven along the Ohio Turnpike near Cleveland, you have gone up/down the Portage Escarpment. Similarly, between Toronto and London Ontario, one would have to cross the Niagara Escarpment. In fact, Niagara Falls, on the New York/Ontario border, are literally a part of the Niagara Escarpment. The falls are where the elevation drops dramatically between Lake Erie (571 feet above sea level) on the upper side and Lake Ontario (243 feet above sea level) on the lower side of the escarpment. The Welland Canal was specifically built to bypass the falls and cross the escarpment.

Similar examples of lengthy escarpments can be found worldwide on every continent including Antarctica. And the steepness/sheerness of them can vary too, as the Cody Scarp in northern Florida is comparatively quite mild. However, most escarpments are quite bold, rapidly rising to elevations well above the surrounding terrain. The sharp change can often be measured in hundreds or thousands of feet.

In several cases, hiking trails or scenic byways have been developed along or near the rim of these magnificent natural features, providing amazing visiting fr those trekking them. Blue Ridge Parkway, Mogollon Rim Road and Skyline Drive are examples of scenic byways while the Knobstone Trail in Indiana and the developing Mogollon Rim Trail in Arizona are hiking routes.

For proposes of this post a minimum length of 10 miles was required and escarpments which are primarily situated underwater (ocean/sea/lake, etc.) are not included. Those shown in italics the author has seen or traveled across. Peace!

1. Great Escarpment of Southern Africa = 3,107 miles/5,000 km

2. Great Escarpment (Oceania) = 2,200 miles/3,600 km

3. Grande Escarpa do Brasil (South America) = 1,600 miles/2,600 km

4. Niagara Escarpment (North America) = 1,000 miles/1609 km

5. Atlantic Seaboard Fall Line (North America) = 900 miles/1,400 km

6. Portage Escarpment (North America) ~ 653 miles/1051 km

7-8. Darling Scarp (Oceania) and Madagascar East Coast Escarpment (Africa) = 620 miles/1,000 km

9. Blue Ridge Escarpment (North America) = 550 miles/885 km

10. Tuwaiq Escarpment (Asia) = 500 miles/800 km

11. Zambezi Escarpment (Africa) = 497 miles/800 km

12. Manitoba/Pembina Escarpment (North America) = 419 miles/675 km

13-14. Sierra Escarpment (North America) = 400 miles/644 km Balcones Escarpment (North America) ~ 400 miles/644 km

15. Book Cliffs Escarpment (North America) = 250 miles/402 km *longest continuous escarpment in the world

16-17. Caprock Escarpment (North America) and Mogollon Rim (North America) = 200 miles/320 km

18. Usas Escarpment (Antarctica) = 199 miles/320 km

19. Roan Cliffs Escarpment (North America) = 190 miles/306 km – separate escarpment atop the Book Cliffs Escarpment

20. Allegheny Front (North America) = 180 miles/290 km

21. Western Andean Escarpment (South America) = 155 miles/250 km

22. North Downs Chalk Escarpment = 153 miles/246 km

23. Knobstone Escarpment (North America) = 150 miles/241 km

24. Nullarbor Scarp (Oceania) = 130 miles/210 km

25. Missouri Escarpment (North America) = 100 miles/161 km

26-27. Bandiagara Escarpment (Africa) and Vermillion-Echo Cliffs Escarpment (North America) = 90 miles/160 km

28. South Downs Chalk Escarpment (Europe) = 68 miles/110 km

29. Onondaga Escarpment (North America) = 62 miles/100km

30. Illawarra Escarpment (Oceania) = 57 miles/92 km

31-32. Lincoln/Trent Cliff (Europe) and Mescalero Ridge (North America) = 50 miles/80 km

33. Chiltern Escarpment (Europe) = 45 miles/72 km

34. Côte d’Or (Europe) = 30 miles/48 km

35. Catskills Escarpment (North America) = 24 miles/38 km

36. Palisades Escarpment (North America) = 20 miles/34 km

37. Wenlock Edge (Europe) = 19 miles/31 km

38. Chinese Wall Escarpment (North America) = 12 miles/19 km

39-40. Duluth Escarpment (North America) and Black Mountain Escarpment (Europe) = 11 miles/18 km

Other Escarpments – More Information Needed

• Cody Scarp (North America)
• Elgeyo Escarpement (Africa)
• Eardley Escarpment (North America) = 40+ km
• Kaimai Escarpment (Oceania)
• Muldraugh Hill Escarpment (North America)
• Pottsville/Cumberland Escarpment (North America)
• Sharon Escarpment (Asia)
• Gotland–Saaremaa Klint (Europe) = 180+ km
• Wulian Feng (Asia)

SOURCES:

• https://en.wikipedia.org/wiki/Escarpment
• https://www.britannica.com/place/Niagara-Escarpment
• https://www.britannica.com/place/Serra-do-Mar
• https://www.dmr.nd.gov/ndgs/ndnotes/pembina/Pembina.htm
• personal knowledge
• https://www.manitoba.ca/iem/geo/mgstracker/images/region6/2010_fieldtrip.pdf
• https://www.greatnortherncatskills.com/how-thru-hike-escarpment-trail
• https://en-academic.com/dic.nsf/enwiki/4787527
• https://falzguy.com/escarp-niag-onon.html#:~:text=The%20Onondaga%20Escarpment%20begins%20at,600%20feet%20above%20sea%20level.
• https://www.geneseo.edu/sites/default/files/2023-08/Brett%20and%20Brett%20SDS%202023%20Part%201%20-%20Niagara%20Frontier.pdf
• https://oldleacounty.com/2021/07/13/mescalero-ridge/
• https://www.sciencedirect.com/science/article/pii/S0040195101002128
• https://en.wikipedia.org/wiki/Tuwaiq
• https://www.researchgate.net/profile/Nigel-Barker-2/publication/234834352_The_Great_Escarpment_of_Southern_Africa_A_New_Frontier_for_Biodiversity_Exploration/links/0fcfd510128f337795000000/The-Great-Escarpment-of-Southern-Africa-A-New-Frontier-for-Biodiversity-Exploration.pdf
• https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022JF007001#:~:text=Eastern%20Madagascar%20is%20characterized%20by,et%20al.%2C%202021).
• https://en.wikipedia.org/wiki/Bunda_Cliffs
• https://kentdowns.org.uk/north-downs-way/#:~:text=Passing%20through%20153%20miles%20of,life%2Dchanging%20long%20distance%20walk.
• https://www.blackmountainswalking.co.uk/the-black-mountains-magic
• https://thevinofiles.typepad.com/the_vino_files/2008/09/burgundy-2.html#:~:text=For%20all%20its%20notoriety%2C%20the,past%20Santenay%20in%20the%20south.
• https://www.looduskalender.ee/klint/eng/5.html
• https://www.neilyworld.com/neilyworld/eegpnw.htm
• https://www.swimdrinkfish.ca/lake-ontario-waterkeeper/blog/19870
• https://en.wikipedia.org/wiki/The_Palisades_(Hudson_River)
• https://suwa.org/multimedia/map/book-cliffsdesolation-canyon-region/#:~:text=Winding%20for%20250%20miles%20across,continuous%20escarpment%20in%20the%20world.
• https://en.wikipedia.org/wiki/Roan_Cliffs#:~:text=Stretching%20nearly%20190%20miles%20(310,the%20Carbon%E2%80%91Duchesne%20county%20line.
• https://duluthmn.gov/media/7719/skyline_map.pdf
• https://www.lakesuperiorstreams.org/understanding/geology.html
• https://falzguy.com/escarp-niag-onon.html
• https://howardfalls.org/2023/08/24/the-portage-escarpment/
• https://janelcurry.com/blog1/understanding-western-new-york
• https://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=3134&context=geosci_geo_peteng_facwork

https://panethos.wordpress.com/2024/01/11/natures-sheer-cliffs-the-worlds-longest-escarpments/

#bluffs #cliffs #ecology #ecosystems #environment #escarpments #geology #hiking #history #landUse #mountains #planning #rims #topology #travel

#introduction

Part of the Migration. Moved from @[email protected]

Interested in #topology (for fun and #TDA )
#GraphicalLinearAlgebra and similar notations like string diagrams and #ExistentialGraphs
#CurryHowardIsomorphism
#Semantics for humans and computers
#topoi
#CategoryTheory
#WordEmbeddings (in #NLP )
#language
#logic
#SFF
#History of science, math, societies
etc.

Trans rights are human rights; blm; workers solidarity; native rights; and all the various other ways of not being vile to people

“It might help to think of the universe as a rubber sheet, or perhaps not”*…

You have most likely encountered one-sided objects hundreds of times in your daily life – like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles.

This mathematical object is called a Mobius strip. It has fascinated environmentalists, artists, engineers, mathematicians and many others ever since its discovery in 1858 by August Möbius, a German mathematician who died 150 years ago, on Sept. 26, 1868.

Möbius discovered the one-sided strip in 1858 while serving as the chair of astronomy and higher mechanics at the University of Leipzig. (Another mathematician named Listing actually described it a few months earlier, but did not publish his work until 1861.  Indeed, it had already appeared in Roman mosaics from the third century CE.)…

The discovery of the Möbius strip in the mid-19th century launched a brand new field of mathematics: topology: “The Mathematical Madness of Möbius Strips and Other One-Sided Objects.”

* Terry Pratchett, Hogfather

###

As we return from whence we came, we might wish a Joyeux Anniversaire to Denis Diderot, contributor to and the chief editor of the Encyclopédie (“All things must be examined, debated, investigated without exception and without regard for anyone’s feelings.”)– and thus towering figure in the Enlightenment; he was born on this date in 1713.  Diderot was also a novelist (e.g., Jacques le fataliste et son maître [Jacques the Fatalist and his Master])…  and no mean epigramist:

From fanaticism to barbarism is only one step.

We swallow greedily any lie that flatters us, but we sip only little by little at a truth we find bitter.

Man will never be free until the last king is strangled with the entrails of the last priest.

A thing is not proved just because no one has ever questioned it.

 source

#diderot #encyclopedie #encyclopedia #history #literature #mathematics #mobiusStrip #mobius #topology