jacksnipe

Measuring value that way is precisely what “from a business perspective” means. Things can also be judged on artistic or technical merits, among many other perspectives.

There are downsides, it’s just that it’s the best move from a business perspective. That doesn’t make it the best move from any other angle.

Futures contracts were a mistake, god damn

Up until very recently I would have said definitely not, but we're talking about LLM scrapers, who knows how much they've got crammed into their context windows.

It’s not great, but you could add it to the body of a 429 response.

You mean plagiarized it?

Is this not belligerently ignoring the fact that this work is already done imperfectly? I can’t tell you how many serious errors I’ve caught in just a short time of automating the generation of complex spreadsheets from financial data. All of them had already been checked by multiple analysts, and all of them contained serious errors (in different places!)

She’s not doing either. In that same conversation, she goes on to talk about how we don’t live in that world and can’t return there, and what the implications should be for policy.

If I’m not mistaken, she goes on to say “but we don’t live in that world, and so we must…” and goes on to argue for policy that doesn’t neglect the poorest and least fortunate members of society.

The author has previously published an article with a detailed analysis of the math of GU, and why it doesn't work: https://files.timothynguyen.org/geometric_unity.pdf

The reception of that article by the group in question, and their refusal to engage on the math side of it, is what led to him writing this blog post in the first place.

I wonder if bundling it with ai is to deal with that pesky internal issue where engineers are always trying to turn off ads for their yt accounts

Sorry, but citation needed. Means testing might seem “obvious” from first principles, but from a policy point of view, it makes little to no sense.

The macroeconomic effects of welfare programs create a society that is better for everyone to live in. Reducing the issue to a matter of personal responsibility is a reframing that allows you to completely lose sight of the big picture, and create programs that are destined to fail by not reaching many of the people they need to.

I mean, that's a very corporate accounting way of looking at it. But countries are not corporations, or even banks, and the abstraction is so leaky it's pretty much never worth using.

Llama was kind of a forced hand though. Yknow, when the model was leaked?

Wordcels discover category theory lol

There are plenty of places where consumption taxes DON’T have a strong effect, like vice taxes on tobacco and alcohol. It’s absolutely worth actually testing it.

I have interrogated it in those cases. I was not misunderstanding.

We’re was autocorrected from where

In my own experience, the vast majority of people using this phrase ARE using it as a source of authority. People will ask me about things I am an actual expert in, and then when they don’t like my response, hit me with the ol’ “well, I asked chatGPT and it said…”

I do not need people to lead on that. That’s precisely why leading on “I asked ChatGPT and it said…” makes me trust something less — the speaker is actively assigning responsibility for what’s to come to some other agent, because for one reason or another, they won’t take it on themselves.

That’s exactly how I feel

I see nobody here blaming tools and not people!

Something that really frustrates me about interacting with (some) people who use AI a lot is that they will often tell me things that start “I asked ChatGPT and it said…” stop it!!! If the chatbot taught you something and you understood it, explain it to me. If you didn’t understand or didn’t trust it, then keep it to yourself!

Sure, but how would they go about capturing that money?

Gene drives scare me. Being able to forcibly propagate a gene through a population seems like a strong candidate for causing an ecological disaster.

Second addendum, chapter 4 is about second order logic and apparently I just forgot that exercise 1 is simply showing that you get all of the structure built up in Chapter 3 with Peano's original formulation in second-order logic. Seems that here I'm the one suffering from a lack of historical context!

I think from a logic standpoint this also makes sense -- getting to undecidability quickly makes taking the direct route through first-order logic more appealing.

If I'm being honest, I now do feel a little bit deprived, I probably would have enjoyed the categorical view when I was learning this too.

Oh, then yeah, I totally agree. In general I think it's a shame that so little emphasis is placed on the history of mathematics, though at the same time I appreciate that most of my peers just didn't care :(

It’s not really considered throwing away Peano’s work. Peano was working in the very infancy of logical formalism.

As it turns out, further work developing on his discovered that using a recursively enumerable schema for induction rather than a second-order induction axiom gives rise to a simpler abstraction that still has all the properties that Peano actually desired, and which makes further developments in the space much easier.

Continuing to call it Peano Arithmetic is respect for the fact that the guy got it mostly right, and it took the mathematics community many more years to refine the ideas to their current point.

Is it a shame that Galois theory isn’t presented as a historical fossil and frozen to its state of development in Galois’s lifetime? I may be making a rather big assumption, but I like to think he would be proud, and so would Peano.

No, they are axioms. Peano arithmetic itself is a first-order theory, and a theory is just a recursively enumerable set of axioms.

Enderton, “A Mathematical Introduction to Logic, 2nd Ed.”, p,203,269-270

Kleene, “Mathematical Logic”, p.206

EDIT: It seems like you're talking about Peano's original historical formulation of arithmetic? That's all well and good but it is categorically not what is meant by "Peano Arithmetic" in any modern context. I've provided two citations from pretty far apart in time editions of common logic texts (well, "Mathematical Logic" is a bit of a weird book, but Kleene is certainly an authority) and I hope that demonstrates this.

There's a lot of reasons that the theory is pretty much always discussed as a first-order theory. The biggest, of course, is that when taken as a first-order theory it fits neatly into the proof and statement of Godel's Incompleteness Theorems, but iiuc it's just generally much less useful in a model theoretic context to take it as a second order theory (to the point where I only ever saw this discussed as a historical note, not as a mathematical one).

EDIT 2: This is all a digression anyway. Both first- and second-order PA label the start of the Z-chain as 0; so any model of PA contains 0 when interpreted as a model of PA.

Sorry, but that’s incorrect. Multiplication is defined in the Peano axioms, in terms of S(x).

2 of the axioms are:

1. For all x, x*0 = 0

2. For all x, y: x*S(y) = x*y + y