hmm, very interesting. I don't think it works like that anymore. The next step has got to be commercial availability. else investors to would loose money or worse, some Chinese company could "steal" the future profits from this valuable novel technology painstakingly developed by the publishing group.
Even if it turns out to be true, this result is still very far from commercial applications. It would be a fantastic thread to continue for academic research groups at universities, but pretty much noone else will care about it.
like how success of a species becomes the failure of the same species. the endless cycles of success and failure.
also in multi-generational wealth: poor and hard working become successful (when society allows it) then the descendants are lazy and loose the wealth, and finally further descendants are poor and may learn to work hard.
that is, until societies re-organize and stop rewarding hard-work with success; what happens next is still happening, it's what we see in our actual political leadership, it's not very effective and is dragging the world into a seemingly unavoidable war. (both china and USA blaming each other for the escalating: "they (the other) should change course cuz we won't"
Yup. But the thing I would like to alert to *GPT startup hopefuls is that first-to-market won't cut it here. Raising will require wow tech that cannot be replicated by the VC's 11-year old kid with an OpenAI API key.
category theory is 'native 2-dimensional' math. i.e. category theory explains everything in terms of graphs, where a graph is made from two different sorts of 'entities', nodes and vertices i.e. categories and morphisms
this being math, I wonder to which extent can category theory be re-expressed in terms of sets.
perhaps a better question is if category theory can be re-expressed (or founded on) functions?
lastly, I wonder if category theory can be expressed in terms of functions (i think maybe it can, without sets?) why shouldn't it be expressible in terms of sets (for some reason I don't think just sets are sufficient, may have to define functions (which possible in terms of sets) before 'expressing' categories starting with set theory)?
Set theory is fine, see the (Stack Project)[https://stacks.math.columbia.edu/browse] which develops a ton of modern Category Theory on ZFC (Zermelo-Fraenkel Set Theory with the Axiom of Choice) alone.
Alternative foundations of mathematics (Set Theory, Category Theory, Type Theory, and all their variations) can all mutually interpret the other by just postulating sufficiently large universes. You don't pick or advocate one based off its ability to encode mathematics, but instead based on its ability to express your intention and ideas.
Really its no different from programming language preference in my book.
In computer science we typically count from zero, not from one. So even though a category has two different sorts of entities: objects and morphisms, since we count from zero, ordinary categories are one-dimensional. Objects are zero dimensional and morphisms are one dimensional.
Since you are concerned with sets and functions, the following analogy is helpful to build your intuition for the subject.
Dimension 0: sets
Dimension 1: functions
Dimension 2: commutative squares
Dimension 3: commutative cubes
The majority of categories, expressed in terms of structured sets and functions, never touch on the second dimension. That is the domain of 2-categories, which although they have three types of elements are nonetheless considered to be two dimensional because we count from zero. That is also where commutative squares come in to play, because as you can imagine squares are quite obviously two dimensional.
Functions are 1-dimensional lines or arrows from one place to another. Sets are more analogous to points then anything else, and so naive set theory is zero dimensional. But I think you have the wrong question. You should ask the opposite question: what if functions can be re-expressed or founded on higher dimensional category theory?
This is routinely dealt with through Grothendieck universes. Those are a fancy name for what is pretty much an inaccessible level of the cumulative hierarchy, indeed ZFC+"every set belongs to a Grothendieck universe" is equiconsistent with ZFC+"there is a proper class of inaccessible cardinals". This is not a strong assumption over pure ZFC compared to those set theorists interested in large cardinals work with
While category of sets technically could not be expressed as a ZFC set, the idea behind the set theory is enough. Also you could add an axiom[0] in ZFC to make category of set a set.
Set theory is going the way of the dodo. There are modified versions of set theory, but afaik a lot of the more exciting work is happening around type theory and proof assistants these days.
Set theory is not going anywhere. It may be pushed to the sidelines by new developments in category theory but that is not the same as going extinct like the dodo.
This also requires universes/inaccessible cardinals to even be stated for categories that are not locally small. But as I mentioned in another comment assuming enough universes exist is not a big deal for set theorists
> The author is proposing a model that [allegedly] does a good job of explaining why we see unexpected behavior
I agree, and go even further:
models that explain behavior are all we have ever had.
it's all only "models that explain this or that" all the way to the 'bottom'. To suppose we can really directly access the "the real objective truth of what's happening" is to ignore the way in which we connect with the "real objective truth"; the same as fish who ignore the ocean.
to argue about what is really happening is to argue about which words to use to describe what is really happening without noticing the nature of languages/words and frameworks or 'systems of thought' which we are using to argue (and indeed, are arguing about)
all this summed up by this quote from about about the pedagogy programing languages: "Sometimes the truest things can only be said in fiction"
sounds to me like a wave with a positive and a negative part.
which IMO is what drives constructive/destructive interference in waves.
my take away is that any LLM that can behave "good" must also be able to behave "badly"; philosophically, because it's not possible to encode "good" without somehow "accidentally" but unavoidably also encoding "bad/evil".
This is well aligned with the rest of my understanding about the nature of reality including it's mathematically determined limitations (diagonals, infinities, paradoxes) and so on.
> my take away is that any LLM that can behave "good" must also be able to behave "badly"; philosophically, because it's not possible to encode "good" without somehow "accidentally" but unavoidably also encoding "bad/evil".
That's a really good non-technical summary of the OP's hypothesis. Thanks!
nonetheless, to witness the entire cognitive process of the author, as misguided as you find their conclusions, is a positive constructive experience isn't it?
IMO, the main point of the article is to assert that in some fields (medicine and science) this "assumption that his ontological conclusions exist as objective reality" is needed, and that to do away with this 'assumption' is 'irrational' and sends one down the path towards authoritarianism.
> this "assumption that his ontological conclusions exist as objective reality" is needed, and that to do away with this 'assumption' is 'irrational' and sends one down the path towards authoritarianism.
When you understand that the author is ok with authoritarianism so long as it validates his symbolic universe because it's draped in the fineries of rationalism, the sooner the piece clicks. The author is fine with authoritarianism so long as its his authoritarianism and he doesn't get to call it authoritarianism, he gets to call it reality. To him it is reality and anyone disagreeing with him is denying reality. When we talk about the most insidious delusions, it's his. It's intellectual narcissism. And that's why it's epistemologically vacuous.
Anyone who's studied epistomology knows he's arguing from within a system instead of outside it and it comes across as naive realism because it is.
on the other hand, this same pattern of "authoritarianism" is what we all learn to have when becoming adult members of our societies/cultures: it's an expression of one persons' individual consciousness with the ability to control their own behavior.
this gets weird when projecting our individual consciousness into the systems we construct to rule over ourselves (governments)... better known as our tendency (and capacity) to anthropomorphize anything.
I think atm the Fed is the main force holing the USA together, considering all the bi-partisan polarization
all ways to divert the "voltage" across elite and commoner classes which are the real source of this tension.
I'm saying that wealth inequality creates something quite comparable to 'voltage', this creates a tension which WILL get released (because physics). But due to active (social-)technological management this tension is getting re-focused into blue Vs red bi-partisan politics, as well as other expressions of winners fighting losers (including gender 'equality' tensions, trans and transphobics, etc..)
I fear the end game of a fully propieatary software world is that the only real way people interact with computers is app stores, programming is not something people can learn online anymore (but it used to). not even command line, just app stores. the new "hello world" in this dystopia is "go to app store, buy hello world the app, done".
hmm, very interesting. I don't think it works like that anymore. The next step has got to be commercial availability. else investors to would loose money or worse, some Chinese company could "steal" the future profits from this valuable novel technology painstakingly developed by the publishing group.