Henry Towsner
@substitutedepsilon.bsky.social
Associate professor of mathematics at UPenn. Logic and related topics. Sometimes distracted by RPGs and Judaism. He/him/his.
I seem to recall something about a freeze except for critical positions, and hearing about how departments were going without administrative support because they weren't allowed to replace retiring staff.
October 22, 2025 at 3:05 PM
I seem to recall something about a freeze except for critical positions, and hearing about how departments were going without administrative support because they weren't allowed to replace retiring staff.
To be fair, our HR platform was already plenty shitty before it got LLM-ified.
October 3, 2025 at 2:19 PM
To be fair, our HR platform was already plenty shitty before it got LLM-ified.
Oh, that indeed looks like it works.
October 1, 2025 at 4:53 PM
Oh, that indeed looks like it works.
It's not obvious to me that there's an immediate answer from the syntactic form of the statement. I *suspect* the answer is no, because the values of the unique solution are close enough to definable using an integral which can be expressed in a first-order way, but it requires at least some work.
September 25, 2025 at 4:26 PM
It's not obvious to me that there's an immediate answer from the syntactic form of the statement. I *suspect* the answer is no, because the values of the unique solution are close enough to definable using an integral which can be expressed in a first-order way, but it requires at least some work.
This is going to depend a bit on what you mean. For *any* theorem about the reals, sufficiently robust non-standard extensions will satisfy the analogous theorem (in this case, every *internal* f with suitable other properties gives an ODE with a unique *internal* solution).
September 25, 2025 at 1:02 PM
This is going to depend a bit on what you mean. For *any* theorem about the reals, sufficiently robust non-standard extensions will satisfy the analogous theorem (in this case, every *internal* f with suitable other properties gives an ODE with a unique *internal* solution).
Definitely.
September 21, 2025 at 10:33 PM
Definitely.
But the g you’ve defined isn’t *f, so there’s no reason to think the derivative it gives you is the derivative of f.
*f isn’t uniquely determined, but it is pretty constrained. In particular, being differentiable is basically equivalent to saying that the derivative is determined.
*f isn’t uniquely determined, but it is pretty constrained. In particular, being differentiable is basically equivalent to saying that the derivative is determined.
September 20, 2025 at 10:52 PM
But the g you’ve defined isn’t *f, so there’s no reason to think the derivative it gives you is the derivative of f.
*f isn’t uniquely determined, but it is pretty constrained. In particular, being differentiable is basically equivalent to saying that the derivative is determined.
*f isn’t uniquely determined, but it is pretty constrained. In particular, being differentiable is basically equivalent to saying that the derivative is determined.
There’s not a unique way to extend to *R. (Indeed, the statement doesn’t really make sense, because *R doesn’t describe a unique object.)
But you don’t need that, because the facts you care about *are* determined. (Ultraproducts don’t change this, because they’re also not unique.)
But you don’t need that, because the facts you care about *are* determined. (Ultraproducts don’t change this, because they’re also not unique.)
September 20, 2025 at 10:41 PM
There’s not a unique way to extend to *R. (Indeed, the statement doesn’t really make sense, because *R doesn’t describe a unique object.)
But you don’t need that, because the facts you care about *are* determined. (Ultraproducts don’t change this, because they’re also not unique.)
But you don’t need that, because the facts you care about *are* determined. (Ultraproducts don’t change this, because they’re also not unique.)
It’s not a restriction at all, because you can always expand your language to include whatever function you want. All of calculus survives.
September 20, 2025 at 10:10 PM
It’s not a restriction at all, because you can always expand your language to include whatever function you want. All of calculus survives.
I’m reasonably sure a lot of students were using it during our last day of class no stakes final exam review game last semester.
August 21, 2025 at 2:47 PM
I’m reasonably sure a lot of students were using it during our last day of class no stakes final exam review game last semester.
Is was told they named it Workday because that’s how long it takes to do anything in it.
August 12, 2025 at 12:49 PM
Is was told they named it Workday because that’s how long it takes to do anything in it.
Also lots of random interruptions to monologue about their character's backstory.
June 12, 2025 at 2:23 PM
Also lots of random interruptions to monologue about their character's backstory.
You can sort of see how he might have mangled the studies that are out there into this - Pew says the median number of close friends is between 3 and 4 (www.google.com/url?sa=t&sou...) though other studies (journals.plos.org/plosone/arti...) report higher numbers.
www.google.com
May 2, 2025 at 2:11 PM
You can sort of see how he might have mangled the studies that are out there into this - Pew says the median number of close friends is between 3 and 4 (www.google.com/url?sa=t&sou...) though other studies (journals.plos.org/plosone/arti...) report higher numbers.
As someone who’s definitely used that example, I’m curious why. (Especially why one would prefer forcing CH when that’s not needed to establish the consistency of CH, and historically not how it was first established.)
April 29, 2025 at 9:15 PM
As someone who’s definitely used that example, I’m curious why. (Especially why one would prefer forcing CH when that’s not needed to establish the consistency of CH, and historically not how it was first established.)
It’s only on the faculty listserv if it’s actually on the listserv. This is just sparkling reply all rants.
March 23, 2025 at 9:36 PM
It’s only on the faculty listserv if it’s actually on the listserv. This is just sparkling reply all rants.
There are lots of models of V=L; CH is true in all of them. If you’re sitting in some fixed universe of ZFC, there’s a single L which is the unique constructible inner model of this model. But there are other models of ZFC, and they have their own versions of L. (All satisfying CH.)
March 19, 2025 at 9:12 PM
There are lots of models of V=L; CH is true in all of them. If you’re sitting in some fixed universe of ZFC, there’s a single L which is the unique constructible inner model of this model. But there are other models of ZFC, and they have their own versions of L. (All satisfying CH.)
I think the uniqueness you’re thinking of says that *given a particular model V of ZFC* there’s a unique inner model of V=L. But there are many different models of ZFC which give rise to different versions of L.
March 19, 2025 at 9:04 PM
I think the uniqueness you’re thinking of says that *given a particular model V of ZFC* there’s a unique inner model of V=L. But there are many different models of ZFC which give rise to different versions of L.
It definitely doesn’t have only one model. For instance, it has nonstandard models which contain ill-founded sets (which the model doesn’t know are ill-founded); in some cases, those ill-founded sets appear in the model to be nonstandard proofs of the sentence you asked about.
March 19, 2025 at 9:02 PM
It definitely doesn’t have only one model. For instance, it has nonstandard models which contain ill-founded sets (which the model doesn’t know are ill-founded); in some cases, those ill-founded sets appear in the model to be nonstandard proofs of the sentence you asked about.
Relatedly, being in the model L isn’t really significant here; arithmetic facts like probability are absolute between inner models - whatever your model of V, the corresponding of model of L will agree about which things are provable.
March 19, 2025 at 9:00 PM
Relatedly, being in the model L isn’t really significant here; arithmetic facts like probability are absolute between inner models - whatever your model of V, the corresponding of model of L will agree about which things are provable.
True, because it’s indeed not provably. (And, relatedly, not provably so from ZFC+V=L.)
March 19, 2025 at 8:57 PM
True, because it’s indeed not provably. (And, relatedly, not provably so from ZFC+V=L.)
Canvas has a systematic hostility to labeling things accurately that seems too consistent to be an accident.
February 6, 2025 at 2:04 PM
Canvas has a systematic hostility to labeling things accurately that seems too consistent to be an accident.