@thinkingheights

A neuro-convergent person.

Joined January 2026
  • Tweets5.5K
  • Following1K
  • Followers630
516Media
I should've added that in the internal logic / type theory of any topos FunExt always holds. So, my thread below in fact proves that the following categories are not topoi: - Poly(C), for any category C with pullbacks - Game Categories - The syntactic category of TTs
Immemorial@thinkingheightsOct 20
naively, functional extensionality (funext) says if two functions take equal values, then they are equal. Two observations about funext: 1. If you're new to type theory, it's instructive to think about why funext fails in the initial/syntactic model – don't cheat with ai!
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call them the biased and unbiased, similar to the def of tensor product in the monoidal categories. interestingly in Rngs, your condition (2) can't be expressed, so there's no good unifying definition. but, one should work *constructively* with prime filters anyway:
Ben Spitz (63/100 improv meals)@DiracDeltaFunk1h
You know how "prime ideal" is annoyingly a conjunction of two conditions? (1) ab ∈ P ⇒ a ∈ P or b ∈ P (2) 1 ∉ P These can be combined!
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∏∅∈F forces the filter F to contain the top multiplicative element, so must be non-empty.
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Does Microsoft pay for this?
Microsoft News and Stories
@MSFTnews23h
Volkswagen Group has brought Microsoft Copilot to more than 330,000 employees, embedding secure AI-powered assistance across its business and enabling teams to focus on higher-value tasks. Learn more: msft.it/6013aazVf

Microsoft empowers more than 330,000 Volkswagen Group employees with Copilot - Source

news.microsoft.com
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Immemorial retweeted
Vali Nasr
@vali_nasr15h
All indications are that U.S. is heading back to war. The next round could be larger and more devastating for Iran but also for the Middle East. It may not be the end of the conflict but the start of a broader unraveling for the region with lasting consequences for the global economy as well. Washington and Israel want to knock out Iran with bigger blows but likelihood of that is low. There will be a lot of devastation before there is an end in sight
Al Jazeera English
@AJEnglish20h
Iran says it is preparing to unveil a weapon called the “father of all bombs”, amid reports Trump has ordered plans for strikes on Iran’s energy infrastructure using the “mother of all bombs”, the largest non-nuclear bomb in the US arsenal. LIVE updates: aje.news/r3rtel
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Iranians increasingly are aware of Israeli intel (Aman) using info-ops, media propaganda, and violent proxies to foment hate and division in Iran. With Iranian nationalism rising, what is Israel’s longterm plan? A war of attrition will result in Israel's destruction as a state.
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how long can you bank on the daddy US to come to your aid every 6 months? how sustainable is this?
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Iran getting nukes is the best for both, and the peace, imo.
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‼️ BREAKING: The EU opened a formal investigation into Booking com over fake listings and phishing scams. Scammers list homes they don't own or hijack host accounts to ask guests for more money. An EU official called what Booking has done "absolutely substandard".
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Lol.
𝓠𝓪𝓼𝓲 🇬🇷@qasirejaaaaOct 21
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Immemorial retweeted
Seth Harp@sethharpesq14h
I already reported in my book (see chapter 10, especially page 134) that the Pentagon sends active-duty US Army soldiers to spy on China under deep cover, specifically pretending to be American businessmen, but I'm glad to see other reporters furthering this important story.
The Washington Post
@washingtonpost17h
Exclusive: The Pentagon is looking to build a more robust deep-cover spying program to conduct economic warfare against China and other U.S. competitors, according to people familiar with the initiative. wapo.st/4dSEqt5

Pentagon looks to build a deep-cover spy program to confront China

Economic espionage is a new priority at the Defense Department. But the Pentagon doesn’t have a great track record with human spying.

washingtonpost.com
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The ENTIRE U.S. Iran War strategy: Civilian suffering. That is all.
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اجمل مشهد لليوم
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The end of the bone-saw dictator MBS is near إِنْ شَاءَ ٱللَّٰهُ. God speed.
ابراهيم ناجي Ibrahim Naji
@Ibrahim___Yemen16h
Saudi Arabia is currently experiencing its worst days since its founding, and the Saudi regime is on the verge of collapse. All this, and we are still only at the beginning. Alhamdulillah
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lol
Bruno Maçães
@MacaesBrunoOct 21
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Immemorial retweeted
Carl Bildt
@carlbildt18h
War is about to start up again. The 🇺🇸 would not do this move if they were not planning to restart military operations.
Al Jazeera English
@AJEnglish19h
The US State Department is preparing to order the departure of embassy staff and their families from across the Gulf amid fears of renewed regional hostilities, Reuters reports, citing unnamed US officials. 🔴 LIVE updates: aje.news/r3rtel
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The new set of targets after Nov. 3: undersea internet cables, AI data centers and energy infrastructure across the Persian Gulf. We're staring into an abyss.
Vonbury Research
@VonburyResearchOct 20
🇮🇷 After Nov. 3, all bets are off. Look at what Iran is doing: - Iran is preparing for renewed US and Israeli attacks - Iran is more vocal about threatening undersea internet cables, AI data centers and energy infras across the Gulf - Iran is expanding its attacks on commercial shipping - Iran is pushing to accelerate cooperation with Russia recently with Lavrov visiting Tehran on Oct 19 - Iran's Defense Ministry saying military cooperation with Russia and China remains active, with some consultations intensifying - Iran is rebuilding its missile capabilities, including work on underground facilities - Iran is fortifying its nuclear facilities
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xitter.cf/MerruX/status/21130117…
Ali
@MerruX17h
NBC now reporting US Troop are leaving bases and diplomats are evacuating across the middle east !! Clearly the state dept is lying. Trump moving forward with iran
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you can just do things, you can just destroy the surveillance state like that.
Mario Nawfal
@MarioNawfalOct 21
🇦🇱 WAIT, WHAT?! A student in Tirana, Albania, CLIMBED a really high lamppost to take down police cameras 😳 Most people would never even think about going that high just to mess with a camera, but there they are. Writer: Lucas
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WTF, Greek Police randomly throwing FLASHBANG GRENADE!
Anonymous TV 🇺🇦
@YourAnonTVOct 21
🚨🇬🇷 BREAKING: GREEK RIOT POLICE THROW A FLASHBANG GRENADE INSIDE AN ATHENS METRO STATION! ⚡️ Disturbing footage from Omonia, Athens, shows a riot police officer throwing a flashbang grenade into the metro station after a massive student protest was held today. #Greece #StudentProtests
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republicans cannot tactically hide their desire for enabling child sexual abuse because it’s the central pillar of their party
FactPost
@factpostnews21h
Vance defends Vivek Ramaswamy's ad featuring Amy Acton's estranged mother: "The media and Democrats are obsessed because Vivek Ramaswamy had the audacity to run a TV commercial that calls it like it is"
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It's absurd that the Trump administration responded to the Iranian proposal to reopen the Strait of Hormuz by demanding that Iran ship out its stockpile of enriched uranium. The MOU, which Trump himself signed, specified that the HEU would be eliminated by "downblending on site under the supervision of the IAEA." So not only did the administration introduce an extraneous demand, they insisted on something that violated the agreement they signed in the summer. Moves like this are some of the many, many reasons that trust is at rock bottom.
محسن رضایی@ir_rezaeeOct 20
Not a single gram of enriched uranium will be removed from Iran. There will be no negotiations until the United States takes steps to build trust. That process must begin with the full fulfillment of all Iran’s conditions.
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