Furthermore, it's not about the current innovation right now - if you sell yourself on a broader mission, your core product can evolve and change with it, and you're more selling yourself as the guy who will make that abstract vision possible no matter what.
No matter how much we pretend, that's how a lot of abstractions work. Things that touch the real world can change; there's a risk that the change could be as something as simple as a bugfix to changing the underlying implementation but preserving a higher level goal; you generally want a human in the loop to make sure the semantics work out and everybody's agreeing.
Well said, once you put it out there in the world, then it's also about how will the customer react to it and having to own that relationship going forward.
The relationship aspect of a business has a lot to do with how effective it is at continuing to justify its core value in an easy and relatable way; especially so when the decision makers that front the bill may not be as engaged with the underlying machinery behind the why it works how it does.
Well, it's knowing when to push and when to not. You probably have an intuition for, I don't know, abstract algebra objects (I don't know your field of specialty :P), without needing to symbolically manipulate all of it, but you developed a deep intuition for them through many proofs and attempts at proofs with them.
Im glad you brought up abstract algebra—that was the one class in my math undergrad that I never developed an intuition for. I learned to do the proofs by pushing symbols around and putting bars on top of them but I never felt like I understood what was happening.
I really want to create a nosology of common generic memes that can be applied to literally anything without context. Saying that the evaluators are just stupid and arbitrarily chasing the fashion of the week instead of the evaluators possibly actually latching onto some structure is a tale as old as time.
I really wish there were search harnesses, actually. My LLMs are lazy as hell and seem to want to just report the first thing they find on google. I know they can return truly niche and useful results, but it takes a lot more prompting to get them there than I would like.
I've been using GPT-6 Pro in ChatGPT (and its predecessor GPT-5.6 Pro) and it's been incredibly effective. I don't think it's available on anything less than the OpenAI $100/month plan though.
you know that most big ai companies not only have search harnesses but also sota models that are post trained for web search specifically.this is what the deepsearch option is in most cases. and they have been unbelievably good for years now.
The recent OpenAI wiki spam indecent was interesting because it helped reveal some of how they are training their models for research tasks: https://collusion.wiki/
> In mid-2024, <redacted> published a list of the best books of the 21st century selected by a panel of experts. It also published a separate list based on readers' votes. I would like to know whether my local public library's collection included the books on the latter list as of August 24, 2024. Consider only the top 50 books, and exclude nonfiction and poetry collections.
aww man. I remember following victor in college. I mean pivots gotta pivot, and this is probably a better one for business, but always thought the interaction combinator framework was cool
Well there are counting arguments to say that a higher level intelligence that somehow achieves say, 100000× brain efficiency of humans, still can't do that much more work than humans, if humans found the "best abstraction". Think about computability for example - that means you could feasibly solve problem instances of n+20 relative to what a human can solve.
Of course, I think putting numbers to wishy washy meta-quantities like "how efficiently does a certain conceptual scheme help you" are super loaded and hard to properly talk about (incommensurability). I've been toying with trying to make a repository of all the possible "moves" one can make in this kind of abstract analysis - constrain the problem statement, argue something like "the system is what it does", dissolving, etc. but even that seems hard
It always messes with me: reducing across a specific axis always takes O(whole tensor) time, because there's no difference between "iterate over all dims, then collapse the final one" versus "iterate versus the first dim and do some cursed tensor accum" (and likewise for between)
Maybe there's just a better way to think about it and I'm still thinking about it way too much like a programmer
That's what I'm used to as well, but in my experience a lot of programmers take fold and reduce to be synonyms. A monoidal reduce is much less "scary" than a general fold. I suspect most programmers have never[1] heard the word monoid, let alone know what it means, and having to remember the meaning of a weird new word is enough to make most people dislike something compared to the simpler more familiar operations.
[1]Or if they have, their only encounter with it is the "a monad is just a monoid in the category of endofunctors" meme.
It just means if you have some functor F (generic type with a well-behaved `map` function, like List), then you have a `flatten` operation F[F[_]] - > F[_], and like a monoidal product, it's associative. So if you have a triply nested List, you can flatten inside first or outside first. Also, like a monoid, it has an "identity" function wrap: A->F[A] (e.g. x -> [x]). Identity in the sense that "multiplying" (flattening) with wrap does nothing. i.e. wrap(flatten(x)) = flatten(wrap(x)) = x when those things make sense.
So basically wrapping and flattening behave in a sane way. Flatten is your multiply, wrap is your multiplicative identity, and it's like a monoid if you squint.
"The meme" literally comes from a book that was offering it as an intuitive explanation of a long definition, assuming you know what a monoid is. All the laws and stuff boil down to "if you generalize the idea of a monoid a little bit, and if you have some functor+flatten+wrap forming a monoid, we call that a monad." If you don't know what that stuff means then obviously it's not for you, but if you do, then it's actually a concise way to give an intuition for "what (or why) it is," which is basically just that flatten is associative and wrap is neutral.
Like if someone says they know about rings and modules, you might say that an ideal is just an R-submodule of R, which grants an interesting perspective and gives a quick, memorable definition. But if they don't know about modules, you might not give them that definition.
The point is that the terminology surrounding this is impenetrable and non intuitive. Rather than acknowledge that, we get a lesson on category theory, which is missing the point.
The person I replied to said they know what monoid means, so they're familiar with algebra. The explanation is intuitive for someone familiar with undergraduate algebra (adapted to also assume some familiarity with programming and show how it connects). That's literally where the meme comes from, an intuitive remark from an introductory text on category theory. If you think it's impenetrable, it's not for you. You don't have the correct background, so ignore it.
It may have come from an old textbook, but its origin as a meme is a 2009 joke blog post that gets its humor from making fun of how obtuse and pedagogically inept that explanation is. When people reference it today, this is what they are referencing: https://james-iry.blogspot.com/2009/05/brief-incomplete-and-...
I'm aware of the meme, but it's not obtuse or pedagogically inept.
Like if someone says they're familiar with groups and Fourier transforms, but not what it means to say wavelets are the Fourier basis for the affine group, and I break that down, and you don't know what any of those words mean, that's not me giving an obtuse explanation of wavelets; that's you wandering into the wrong conversation.
Do you want to understand monads, or do you want to understand the original quote that the joke you referenced was based on?
For the record, the original quote by Saunders Mac Lane is "a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor."
That quote is a statement in category theory. The author probably never heard of, say, Haskell - he was a pure mathematician. You can't usefully express that quote in Haskell code. You can treat it as a kind of formal description of what monads are, and Haskell generally conforms to that. But in that context, the quote itself is essentially using category theory as a metalanguage, in the same sort of way as one might write a mathematical statement that captures the semantics of some programming language expression.
That said, the quote can be handwavingly understood if you know what a monoid is, and that for monads, the identity object is the identity functor, its product is `join`[1] and its unit and multiplication satisfy the usual monoid laws.
For a concrete example, consider this Haskell expression using the `Maybe` monad:
do
x <- Just 3
return (x + 1)
That desugars to:
Just 3 >>= \x -> Just (x + 1)
Which we can desugar to an expression in terms of the monad's monoidal product, `join`, by substituting the definition of `>>=` in terms of `join`[1] to get:
join (fmap (\x -> Just (x + 1)) (Just 3))
You can evaluate that in Haskell and you'll get `Just 4`, just like the original expression.
So what happened there? The inner expression `fmap (\x -> Just (x + 1)) (Just 3)` applies the anonymous function to `Just 3` to get the double-wrapped `Just (Just 4)`. One of the `Just` wrappers is then eliminated with `join`.
(Btw, the fact that we have a Maybe within a Maybe here is related to the fact "monads are monoids in the category of endofunctors" - a category that maps to itself. That's where that part of the quote comes from.)
In this simple example, there's some unnecessary machinery - you can get the same result with `fmap (\x -> x + 1) (Just 3)`, without the extra `Just` wrapper or the `join` to eliminate it. But then you lose the ability to do things "in the monad": the anonymous function becomes just an ordinary function, it doesn't have access to the monadic wrapper. Many of the useful things that monads can do are because the wrapper is available in every function, so you can store state in it (Reader monad), create new wrapper instances with different state and pass those on (Writer and State monad), etc.
No matter how much we pretend, that's how a lot of abstractions work. Things that touch the real world can change; there's a risk that the change could be as something as simple as a bugfix to changing the underlying implementation but preserving a higher level goal; you generally want a human in the loop to make sure the semantics work out and everybody's agreeing.
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