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Toby Bartels

@tobybartels.name
1.1K followers 361 following 6.7K posts

Probably the only anglophone Toby Bartels. They/them. Mathematics instructor at a community college in Nebraska. Tolstoyan ex-Catholic. 🏴🚩🏳️‍🌈🏳️‍⚧️ mathstodon.xyz/@TobyBartels

PostsRepliesMedia
Toby Bartels @tobybartels.name · 10h
I'm mad at them for the more important things that they're *not* talking about, but it's hard to be mad at them for what they *are* talking about.
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Toby Bartels @tobybartels.name · 12h
making the ceramic < wrapping the ceramic
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Toby Bartels @tobybartels.name · 14h
Maxima (or Wolfram Alpha for convenience) has been computing derivatives for decades using a proper algorithm, not vibes. In the case of Maxima, you can even inspect the algorithm for yourself.
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Toby Bartels @tobybartels.name · 30/09/2026
I'm so sorry. Also for the patients that he's probably going to abuse.
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Assigned Media @assignedmedia.org · 29/09/2026
Democrats seem headed for big wins, but one avenue for self-sabotage would be adopting R's framing on trans rights. @billiejsweeney.bsky.social spoke with insiders incl Lanae Erikson of Third Way and Rep. Sarah McBride for this substanial piece of new reporting. assignedmedia.org/breaking-new...
assignedmedia.org
Democrats Lose by Punching Down on Trans Issues, Strategists Say - Assigned Media
Insiders, including at centrist think tank Third Way, are cautioning Democratic candidates against echoing Republican talking points on trans rights.
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Prisonculture @prisonculture.bsky.social · 12/09/2026
REBUILD is doing much needed work. I hope that some of you might donate to keep it going: www.mightycause.com/story/Rebuil...
Informational flyer for Darkness RISING REBUILD, detailing therapy services for justice-involved people of color, program benefits, contact info, and impact stats, with green and yellow accents and a woman giving a thumbs up.
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Toby Bartels @tobybartels.name · 29/09/2026
Wow, this is real! My favourite line: The atoms of the constituent were scattered in the grass, in the rivers, in the air, in the ground. A woman gathered the atoms; she drank and ate and inhaled; and the woman assembled the constituent, in her body, which later required a birth certificate.
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Toby Bartels @tobybartels.name · 29/09/2026
When I was an autistic boy, learning about consent in relationships from watching '80s romcoms did not go well.
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Eb @ebthen.bsky.social · 29/09/2026
Explaining to non-Autistic people that actually I'm not being ableist when I suggest that Autistic boys (and kids in general) maybe do need to be explicitly told about how consent works even though apparently all the other boys understand consent without being told.
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Toby Bartels @tobybartels.name · 29/09/2026
You have to be extremely well read and intelligent to understand its deepest levels of obscenity.
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Toby Bartels @tobybartels.name · 29/09/2026
Animals can always tell, I guess. 🤷
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Toby Bartels @tobybartels.name · 29/09/2026
They gave me paroxetine, but it didn't really help. The talk therapy helped though.
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Toby Bartels @tobybartels.name · 28/09/2026
Everyone should have exactly the right amount of tech skills. Which happens to be exactly the tech skills that I have. No more and no less.
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Toby Bartels @tobybartels.name · 28/09/2026
And it's still jamming stupid bullshit down people's throats while simultaneously being genuinely good at some things, sometimes the same things. It's very easy for one half or the other to be invisible to someone.
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Toby Bartels @tobybartels.name · 28/09/2026
To be fair to Green (and, well, for my own interest), I have now read the interview and the five-page preview that comes with it. And it's more clear than ever that Green did not read them. My only hope now is that he is a very dry parodist.
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Toby Bartels @tobybartels.name · 28/09/2026
I obviously haven't read the comic either, and I haven't even read the interview, but I have at least read the excerpts of the interview that Avi Green quoted in his article, and I think that's more than Avi Green ever did. I think he just scanned them for keywords to misinterpret.
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Guardian US @us.theguardian.com · 28/09/2026
Gone are the mass raids and militarized metro operations. Gone are the pomp and pageantry. But ICE arrests have hit record levels. ICE operations are no longer concentrated in large American cities. Immigration enforcement officials are also working in suburban and rural areas, all across the US.
A map of the United States that shows immigration arrests per 100,000 people since ICE's new enforcement strategy began under DHS secretary Markwayne Mullin.
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Trash @trashxdiscourse.bsky.social · 28/09/2026
This blew up, so if you need help relocating from an anti-trans state to the relatively safe Pacific Northwest, Traction's Project Open Arms is a resource, and if you have money, Traction's Project Open Arms could use that money. More resources/donation links coming. tractionpnw.org/open-arms/
tractionpnw.org
Project Open Arms – TRACTION
A community project supporting trans+ red state refugees seeking sanctuary.
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🏴‍☠️ MC Pablo ∴ @p4bl0.net · 26/09/2026
How we learned to stop worrying and love campus surveillance cameras (with AI!). fnl.mit.edu/how-we-learn...
fnl.mit.edu
How We Learned to Stop Worrying and Love Campus Surveillance – MIT Faculty Newsletter
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Toby Bartels @tobybartels.name · 28/09/2026
It hadn't ended yet, but it was already going downhill in his opinion: ‘In recent times - the fourth season - the quality has gone far downhill, alas. The comments below should be taken as referring to the first through third seasons.’ is an editorial remark near that part of the document.
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Toby Bartels @tobybartels.name · 28/09/2026
Bluesky doesn't run ads at all yet.
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Toby Bartels @tobybartels.name · 28/09/2026
The election is over, so the case is moot.
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Toby Bartels @tobybartels.name · 27/09/2026
But was that in the same neighborhood? Maybe she never expected Michael Myers to stab *her* face.
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Toby Bartels @tobybartels.name · 27/09/2026
I like the ‘file cabinet’ marketing suggestion by vlad and JMiao later down. I had to think back to whether I still had a filing cabinet in 2007, and the answer is Yes.
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Toby Bartels @tobybartels.name · 27/09/2026
#2 is correct (as Drew Houston acknowledges in the reply). But did ‘viral’ really mean ‹income-generating› back then? I don't remember that. Offering it for free can only help it go viral, especially if you're still advertising it (as Drew was doing, even if Brandon didn't know why).
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Toby Bartels @tobybartels.name · 27/09/2026
But maybe you should ignore the whole thread of replies above and just look at this one: bsky.app/profile/toby...
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Toby Bartels @tobybartels.name · 27/09/2026
… I also have these other nonstandard things within me that I believe are axioms when obviously (to you) they're nothing of the sort, but that's no great shock; you already know that I believe that ⊥ is a theorem, so I must have nonstandard things within me that I think are proofs.
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Toby Bartels @tobybartels.name · 27/09/2026
Maybe you should ignore the 5-post reply I made a few minutes ago, and I'll just start here. This makes sense, but I don't see how this contradicts (1). For each axiom P that ZF actually has, I (the model) believe P; that's my version of (1). I even believe that P is an axiom. …
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Toby Bartels @tobybartels.name · 27/09/2026
It can be extra difficult because of the distinction in levels between object language and metalanguage. (This sort of thing certainly can come up in other parts of mathematics, but sometimes those other parts of mathematics are secretly logic as well.)
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Toby Bartels @tobybartels.name · 27/09/2026
Oh, and the linked post seems to be saying something yet different from all of these: ∃ P ∈ L, ¬P ∧ M ⊨ (P ∈ Ax(ZFC)), which I *can* make sense of, by instantiating P. But that doesn't contradict (1). (It still doesn't seem right though, since being an axiom is decidable.)
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Toby Bartels @tobybartels.name · 27/09/2026
In M ⊨ (∃ P ∈ Ax(ZFC), ¬P), I can't make sense of ¬P, since P is not a sentence in the language L but rather a variable for a natural number that we think of as encoding a sentence from within M. But natural numbers aren't true or false. I can turn a statement into a number but not the reverse.
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Toby Bartels @tobybartels.name · 27/09/2026
I don't know what M ⊨ ¬P means inside M, because M is an actual model, not a description of something in the language L of ZFC, which is what M has access to. If I could define M within M, then I could make sense of M ⊨ (∃ P ∈ Ax(ZFC), M ⊨ ¬P), but I don't know how to do that.
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Toby Bartels @tobybartels.name · 27/09/2026
Unless I'm *really* confused, if M is a model of ZFC, then it's not possible that ∃ P ∈ Ax(ZFC), M ⊨ ¬P. But I don't think that you're saying that; I think that you're saying M ⊨ (∃ P ∈ Ax(ZFC), M ⊨ ¬P) or simply M ⊨ (∃ P ∈ Ax(ZFC), ¬P). However, I don't know what either of these means!
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Toby Bartels @tobybartels.name · 27/09/2026
Can you explain what it means for the model to *think* that something is *false*? That's what I tried to eliminate from my version of (1). If L is a language, M is a model of L, and P is a statement in L, then I know what it means to say that P is false in M, that is M ⊭ P, or M ⊨ ¬P.
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Toby Bartels @tobybartels.name · 27/09/2026
Correction: more than 2^65535 characters: bsky.app/profile/toby...
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Toby Bartels @tobybartels.name · 27/09/2026
But I guess when elsewhere I was talking about proofs with more than 2^65536 lines, I should have talked about proofs with more than 2^65536 characters. For all I know, there's a 5-line proof of ⊥, but then it necessarily uses an axiom with more than 2^65536 characters, so I'll never see it.
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Toby Bartels @tobybartels.name · 27/09/2026
Right, a nonstandard axiom becomes a nonstandard proof. So nonstandard axioms aren't important; what's important is that there are nonstandard proofs, whether that's because they have nonstandard length, nonstandard axioms, or both.
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Toby Bartels @tobybartels.name · 27/09/2026
(‘I’ here am a model of ZF+¬Con(ZF). This is what that model believes, or ‘thinks’ as you put it elsewhere in the thread. The real Toby is a fictionalist who believes whatever I want to believe for the purpose of the discussion, just as if we were talking about The Lord of the Rings.)
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Toby Bartels @tobybartels.name · 27/09/2026
I guess since ZF has axioms of arbitrary length, a nonstandard model must have nonstandard axioms within it. But we could be having this conversation about NBG, so I think nonstandard axioms are a red herring. The point is that the model has nonstandard proofs of nonstandard theorems (like ⊥).
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Toby Bartels @tobybartels.name · 27/09/2026
Of course, (4′) is an axiom that I accept on faith; I don't have this proof. Indeed, it follows from (1)–(3) that I believe that any such proof has more than 2^65536 lines, so I'll never see it. I believe in it like Kierkegaard believes in God, not because of the evidence but in spite of it.
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Toby Bartels @tobybartels.name · 27/09/2026
So (1) for each axiom of ZF, I believe it; (2) for each entailment in FOL between sentences in the language of ZF, if I believe all the premises, then I believe the conclusion; (3) I don't believe any contradiction in the language of ZF; and (4′) I believe there's a proof of a contradiction in ZF.
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Toby Bartels @tobybartels.name · 27/09/2026
What is truth? I might casually say ‹I believe X to be true›, but it's better to say ‹I believe X› unless I have some definition of truth in mind and want to talk about that instead of X. (I *am* talking about my beliefs though; ‘believe’ is not taboo here.)
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Toby Bartels @tobybartels.name · 27/09/2026
It's too long to worry about. The smallest such proof has more than 2^65536 lines, so none of us will ever produce it.
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Toby Bartels @tobybartels.name · 27/09/2026
It's only grim if you think that mathematics should be about real things.
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Toby Bartels @tobybartels.name · 27/09/2026
There's no danger as long as ZF+Con(ZF) is consistent, which it seems to be, but I don't see how ZF+¬Con(ZF) is incoherent. It's a little weird, but it also seems to be consistent (indeed it's consistent if ZF+Con(ZF) is), so there's no danger.
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Toby Bartels @tobybartels.name · 27/09/2026
You're assuming that if you believe in ZF, you should also believe in the consistency of ZF, even though ZF ⊬ Con(ZF) (or so I believe).
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Mark Jacob @markjacob.bsky.social · 27/09/2026
No more shoulder-shrugging when a machine programmed by a person commits a crime. That means the person, not the machine, has committed a crime.
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Hope For The Planet @h4tp.bsky.social · 24/09/2026
We now have rigorous pooled data showing that even without active restoration efforts, cleared rainforest can rebound to 75% of their former species composition and 90% of species diversity within just thirty years. #goodnews
optimistdaily.com
Rainforest biodiversity rebounds within a single generation | The Optimist Daily
A major Ecuador study finds cleared rainforests can recover 90 percent of their species diversity in just 30 years, as long as humans leave the land alone.
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Toby Bartels @tobybartels.name · 27/09/2026
static.klipy.com
Mad Max: Fury Road - That's Bait
Alt: Mad Max: Fury Road - That's Bait
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McSweeney's @mcsweeneys.net · 27/09/2026
"To stop the WALL OF SHIT LAVA from WRECKING YOUR HOUSE AND BICYCLE, you will actually need to purchase the SHIT DAM, which is SOLD SEPARATELY." buff.ly/giIjvin
buff.ly
We Must Create the Shit Machine
“For as long as humans have created SHIT with our BODIES AND BUTTS, we have been asking this FUNDAMENTAL QUESTION: What if there were a COMPUTER that could A...
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