jonmsterling

jonmsterling, 1 day ago to random

Ult: all that each of these “results” comparing artificial intelligences to human minds can reveal is the limitations of the underlying theoretical framework of the “experiment” (which is often in complete ignorance of the field of cognitive science, and rife with unjustified assumptions)...

One thing I have found that AI people seem not to understand is that theories exist only in relation to some prior idea of the thing they are meant to model. So taking a model of human cognition and applying it to an autocompleter yields no insight at all absent some theoretical explanation or hypothesis that human cognition and autocompletion should be so closely related that they can be studied using the same tools.

For example, human medicines are often tested on mice. This testing is only meaningful by virtue of our prior knowledge that mice share many physiological qualities with humans; and we do not do mouse tests when we think that the pertinent aspect of mouse physiology is too different from human physiology to yield a useful result.

mevenlennonbertrand, 2 days ago to random

I just realised that inductively defining an indexed inductive family T : B -> Type and then quotienting each T x by a family of relations R : Π x : B, T x -> T x -> Type is not the same as the corresponding quotient inductive type: if R is not a congruence, then the quotient-after-the-fact is not right, because it does not know that you also want to quotient the other fibers by their relation.

Is this the whole point of QITs that had completely gone over my head until now?

jonmsterling, 5 days ago to random

I think the reason so many "personal knowledge management" products are starting to integrate LLMs might be that many people who “use” these things (or try to be influencers in this area) really have filled them with the kind of content that could be generated by LLMs. And it seems plausible to me that a chat session with one of those LLMs might be kind of similar to a chat session with a happy user of such tools — utterly devoid of intellectual content and just saturated with vapidity.

If you look in these people's knowledge bases, it's all meta-crap about success and business and knowledge or something, without any actual area of practice. In the end, people get sold on a hopeless get smart quick scheme.

jonmsterling, 7 days ago to random

I'm working on figuring out how to explain the practice of mathematics to students who've never done it before...

There are too many things that we leave unsaid, and then use crudely to separate those who already know from those we won't bother to teach...

jonmsterling, 9 days ago to random

I have a lot of professional experience teaching people how to program — usually in a pairing environment. One thing I noticed almost universally is that people start off wanting to 'forward chain' all their code, meaning, they try to predict the leaves of the code and then build them up. The other thing they do is they leave their code in an inoperable (even non-parsing) state until the very last minute where it is completely done — and then are completely flummoxed when it doesn't work.

The problem with the first practice is that it is entirely hopeless, in most cases, to predict the smallest finishing touches of code that accomplishes some goal or purpose — because, naturally, ideas and rational thinking about the purpose of some code gives rise to decompositions of the problem at hand, whereas just thinking about all the things you have on hand gives rise to no useful decomposition whatsoever.

It is a real struggle to get people to (1) think from the root to the leaves, and (2) write their code in small steps after which it is always possible to take stock and see if you understand what you have written.

I learned to write code this way by being a Haskell and Agda programmer — I was lucky enough to be professionally writing Haskell around the time they introduced typed holes, which made this methodology much more systematic and applicable than it had been before.

jonmsterling, 12 days ago to random

Thinking about how to teach students about isomorphisms (between sets).

It is easy to teach them about bijection (injective + surjective): you can give an example about checking that two piles are equinumerous, and walk through how you want to match each widget from one pile with one from the other without leaving any left over.

But isomorphism (in the sense of left and right inverse) is somehow much more abstract and hard to think about for someone who doesn't already get it.

Have any of you got a successful way to teach this concept without first introducing bijection?

jonmsterling, 21 days ago to random

Ultimately we have to ask ourselves if it was overall a good thing that computer science as a discipline ceased to be part of mathematics — rather than broadening the horizons of mathematics and bridging the gap between mathematics and social science. I am not speaking purely rhetorically, as there are legitimate arguments to be made on both sides.

jonmsterling, 28 days ago to random

At some point, at the risk of becoming a personal knowledge management cult leader, I really need to explain how I use my forest 🌳 to manage my life… It is a life saver.

jonmsterling, 1 month ago to random

I see so many people treating AI tools as “intelligence as a service” and “literacy as a service”... I really mean this — people who acknowledge that they aren’t that smart (or at least self-identify this way), who then think that they can use AI to get enough of an edge to meet “smarter” people as equals in the marketplace. And, naturally, I see so many grifters trying to build products that are marketed to this demographic.

Putting aside the obvious problems with this point of view (including the meaningless of “intelligence” as usually quantified), ultimately the tragedy here is (1) extremely poor quality of public education, which has reached the point of mass illiteracy and semi-literacy of people who have in fact made it through secondary school, and (2) the way that people are pitted against each other as free agents in the marketplace without any regard to the relationship between needs and abilities... It is not in the least bit surprising that we see the growth of this "industry" in light of those two factors.

jonmsterling, 1 month ago to random

As a “democratic” society, we have to ask — what exact kind of “democracy” is it when a small number of people can decide to drop $100M training a “next-word predictor”, when we have millions of people living in environments that are literally poisoning them?

What exact kind of “democracy” are we doing, when meaningful popular reforms are structurally impossible to achieve through “democratic” channels?

It can be hard to understand what people mean when they go on about how democracy has a class character — that is, when they say that there is no such thing as democracy per se, but there is rather democracy qualified by a class: e.g., bourgeois democracy and proletarian democracy. But examples like this bring into the sharpest relief how democracy for the bourgeoisie (== the bourgeoisie being allowed to decide amongst themselves the direction of the society) is invariably a dictatorship over the proletariat, who would (if it were at liberty) legislate appropriate solutions to the great social problems of the day.

boarders, 1 month ago to random

Topos theory confusion: If I consider the topos Set/ℕ then this has a global element n : ℕ (generic natural number), and I think you shouldn't be able to prove: n = 0 ∨ n ≠ 0 since this number is 'generic'

On the other hand, this topos is classical as it is isomorphic to Set^|ℕ| - so the law of excluded middle should hold. how do I resolve these two things? Is it something to do with internal vs external interpretations of a logical statement?

highergeometer, 1 month ago to random

Here's how Bourbaki rigorously define a "canonical map":

"The definitions given above show that an intrinsic term for (s_0) is none other than a term (V) which contains no letters other than the constants of (\mathcal{T}_\Sigma), and which is transportable relative to (\Sigma), for the typification (T_0)."

"When a term (V), intrinsic for (s_0), is such that the relation "(V) is an mapping from (X) to (Y)" is a theorem of (\mathcal{T}_\Sigma) ((X) and (Y) being two intrinsic terms for (s_0)), we say that (V) is a canonical mapping for (s_0)."

This is from §4 of the Appendix to the standalone, first release of Chapitre IV of Théorie des Ensembles. This Appendix was removed for the second edition of this chapter, and never reinstated in the completed Théorie des Ensembles.

The arithmetic geometer Bill Messing has mentioned this "suppressed" definition a few times (on the fom and categories mailing lists) in the past decade and a half.

I want to understand it!

jonmsterling, 1 month ago to random

How true this is, and the inelegant phrasing does not make it less true! We are guilty as charged... https://borretti.me/article/type-inference-was-a-mistake

jonmsterling, 1 month ago to random

I'm very sad to hear that my colleague Ross Anderson has passed away this week. I did not know him well, but what stood out from my few interactions with him was his passion for justice at every level. Ross did not let an opportunity go by to expose an ongoing and taken-for-granted narrative as just that, and re-ground discussions in reality.

It is clear that Ross will be missed. I'm sad I did not get a chance to know him better and learn first-hand why he has sparked such strongly positive feelings in those whose paths crossed his.

danielgratzer, 1 month ago to random

It has proven shockingly hard, but I feel as though I'm converging on a motivation for univalence for these lecture notes which motivates how it improves the behavior of universes without delving into descent, object classifiers, or the other mathematics that underlays the explanation...

Notably, I didn't want to simply say that "SIP and the consequences of univalence are cool, so ...". SIP and the consequences of univalence are indeed cool, but I think motivating things purely in this manner makes univalence appear completely miraculous and inscrutable instead of something which evolves inevitably from taking universal properties seriously.

collin, 2 months ago to random

When Europeans say Americans don't know geography, do they just mean we don't know European geography as well as they do? Like, would they do any better placing US states or countries in South America, Asia, or Africa than us? I feel like we tend to know the things that are relevant to our lives.

jonmsterling, 2 months ago to random

I've been enjoying using SourceHut as my code forge, but I am surely not the only one who is struggling with managing communities based on plain text email — I like it, but it is very much against the grain for the software that most people find easy to run today.

There are some good tips on https://useplaintext.email, but to supplement this,
I have written up a few tips for users of macOS to set up the MailMate client to send correctly formatted plain text email: http://www.jonmsterling.com/jms-00QB.xml

jonmsterling, 2 months ago to random

I am really not looking forward to the advent of quote posts on mastodon... I agree they are useful, but there is so much bad behavior and piling on that we have avoided here. i've seen some pile-ons of course, but nothing compared to what will come next.