I think everyone should avoid talking about consciousness unless someone in the conversation provides a clear definition of it. If no one provides a definition, we can replace the word “consciousness” with the word “spirit”, and basically nothing about the conversation would change. Without a definition, every conversation about AI consciousness devolves into one camp saying that humans are special and consciousness is unique to them, and another camp that waves their hands about consciousness “duck typing”.
For example, we could define consciousness as the ability to communicate claimed internal states. Perhaps there could be a complexity metric that gives us a metric of consciousness.
We could define consciousness as the ability to respond to stimuli in complex ways. This would make a supermarket’s automatic doors slightly conscious.
Personally, I don’t really care how it is defined in any particular conversation, so long as it is defined. Otherwise we’re just flailing at each other in the dark.
Consciousness is not definable because we don't know enough about it. That doesn't mean it can't be discussed; we didn't have a good definition of "number" until the 1800s. That didn't make arithmetic meaningless because people had an understanding of the concept. The lack of formal definition pointed to a gap in logic that took thousands of years to be filled. Likewise there is a gap in experimental neuroscience that will take many decades to be filled.
FWIW as someone in the "first camp" my real claim is that many animals are meaningfully conscious, including all birds and mammals, and no claims of LLM consciousness are even bothering to reconcile with this. It is extremely frustrating that there are essentially two ideas of consciousness floating around:
- the scientifically interesting one: a vague collection of cognitive abilities and behaviors found in all vertebrates, especially refined in birds and mammals
- the sociologically interesting one: saying "cogito ergo sum" in a self-important tone
Claude has the second type in spades, no doubt. The first is totally absent. And I have a good dismissal of the second type of consciousness: it appears to be totally absent in all conscious animals except humans. So it is irrational and unscientific to take this behavior as a sign of consciousness in Claude, when Claude is missing all the other signs of consciousness that humans actually do have in common with other animals.
Sometimes I seriously wonder if people at Anthropic consider dogs to be conscious. Or even Neanderthals.
We cannot. And our definitions mean nothing to reality. We can all define something as something else, means nothing to how it behaves.
But ultimately, as I said in a previous comment, we have no choice but to agree or not. It cannot be tested, in any way, that makes it absolutely certain, because it's a logical issue. We cannot even have certainty anyone else but ourselves even is conscious. We all sort of agree everyone else must be.
The issue with defining it is someone could potentially find a way to make a machine that mimics it but works nothing like a consciousness generating brain does. So, if it meets our definition criteria, is that conscious? Where's the certainty? How do we prove it is?
Anything we could ever dare call conscious must work exactly like a human brain does. Any deviation from that loses certainty on it having consciousness or not.
And let's not ignore the huge incentive corporations would have in meeting your definition with something that has nothing to do with consciousness, just so they can profit off it.
>The issue with defining it is someone could potentially find a way to make a machine that mimics it but works nothing like a consciousness generating brain does. So, if it meets our definition criteria, is that conscious? Where's the certainty? How do we prove it is?
This sentence of yours makes me think you've missed the point of the post you're replying to.
Unless you're actually agreeing with them, but I can't tell.
If you're willing to reduce metaphysical questions to definitions (which I'm basically on board with), then the stakes aren't that high in the first place, so we should carry on using "consciousness" in its everyday sense because there's no precious reason to avoid it.
> No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations.
I was taught that these were all hypergeometric functions. What distinction is being drawn here?
Hypergeometric functions are functions with 4 parameters.
When you have a function with many parameters it becomes rather trivial to express simpler functions with it.
You could find a lot of functions with 4 parameters that can express all elementary functions.
Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before.
A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed.
> Hypergeometric functions are functions with 4 parameters.
Granted, but the claim in the abstract says:
>> computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations
And I don't see how this is true as to hypergeometric functions in a way that isn't shared by the approach in the paper.
> Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before.
> A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed.
These statements seem to be in direct conflict with each other; you can use the second parameter of a binary function to identify a unary function just as you can use the fourth parameter of a quaternary function to identify a trinary one.
There is an essential difference between binary functions and unary functions.
With binary functions you can compose them using a very complex composition graph.
With unary functions you can compose them only linearly, so in general it is impossible to make a binary function with unary functions.
You can make binary functions from unary functions only by using at least one other binary function. For instance, you can make multiplication from squaring, but only with the help of binary addition/subtraction.
So the one function that can be used to generate the others by composition must be at least binary, in order to be able to generate functions with an arbitrary number of parameters.
This is why in mathematics there are many domains where the only required primitives are a small number of binary functions, but there is none where strictly unary functions are sufficient. (However, it may be possible to restrict the binary functions to very simple functions, e.g. making a tuple from components, for instance the CONS function of LISP I.)
I think that you may have replied before I saved my entire response, so I am not sure how much of it you had read before replying yourself.
I have replied to your last statement:
> "you can use the second parameter of a binary function to identify a unary function just as you can use the fourth parameter of a quaternary function to identify a trinary one."
As I have explained above, what you propose does not work. It works in functions with 3 or more parameters, but it does not work in binary functions, because you cannot make binary functions from unary functions (without using some auxiliary binary functions).
> As I have explained above, what you propose does not work. It works in functions with 3 or more parameters, but it does not work in binary functions, because you cannot make binary functions from unary functions (without using some auxiliary binary functions).
I have no idea what you're trying to say. If you can use one parameter to identify a desired function, then obviously you can use a function of arity n+1 to define as many functions of arity n as you want, and it doesn't matter what the value of n is.
For example:
selector(3, "sin") = sin 3
selector(3, "log2") = log₂ 3
This works going from arity 4 to arity 3, and it also works going from arity 2 to arity 1. Your "response" talks about going from arity 1 to arity 2, a non sequitur.
he is saying that if you reserve the second argument of a binary operator as a "function selection indicator", that you have restricted yourself to an alphabet of unary functions. This means that you could at most effectively model some unary functions, but not arbitrary expression involving +,x,-,/, ^, etc.
Unless you had hit upon a very magical binary function where certain special values of the second parameter happens to coincide with useful unary functions, without those values trampling on a useful binary mode or region of your binary function, but the search space for such a special binary function is so large that you shouldn't demand us to disprove the existence, but rather employ your non-surprisal at the EML result and challenge you to present such a binary function, so we can challenge you to demonstrate how it captures binary functions like addition,products, exponentiation with arbitrary base etc.
So, can we see your construction, or if you refuse to present one, we may conclude you have implicitly reconsidered your position and understand the theoretical elegance this EML (and presumably many other) basis brings?
The subject of the parent article is expressing all the "elementary functions".
This requires expressing binary functions, like addition and multiplication.
You cannot do this by using only the set of unary functions, which can indeed be generated by a function with 2 parameters, one of which selects an unary function.
If you've never worked through a derivation/explanation of the Y combinator, definitely find one (there are many across the internet) and work through it until the light bulb goes off. It's pretty incredible, it almost seems like "matter ex nihilo" which shouldn't work, and yet does.
It's one of those facts that tends to blow minds when it's first encountered, I can see why one would name a company after it.
It’s because they’re playing with monopoly money. If you leverage all the money on itself repeatedly, you can make the numbers look insane. Then, you hand pieces of the leveraged money (stock options) to a bunch of executives who will be watched very closely. You don’t sell stock that’s going to go up in value, so they have to be very careful about when and how much they sell. If they sell too much, then the facade can break, and the leverage evaporates.
To be clear, there is real, underlying value & revenue. But there’s a lot of froth right now
Modern AI is a miracle. The math that makes it work is beautiful and really impressive. For example, if you wanted to map all knowledge on earth, how would you do it? AI answers that question by building a high dimensional vector space of embeddings, and traversing that space moves you through a topology of basically every concept that humans have.
Or another thought; why is it that a stochastic parrot can solve logic puzzles consistently and accurately? It might not be 100%, but it’s still much better than what you might expect from a markov model of ngrams.
Openclaw is only sort of interesting. How to vibe code your first product is uninteresting. Claims about productivity increase from model usage are speculative and uninteresting. Endless think pieces on the effects of AI slop are uninteresting. There’s a lot of hype and grift and bullshit that is downstream of this very interesting technology, and basically none of that is interesting. The cool parts are when you actually open the models up and try to figure out what’s going on.
So no, I’m not bored of talking about AI. I’m not sure I ever will be. My suspicion is that those who are bored of it aren’t digging deep enough. With that said, that will likely only be interesting to people who think math is fun and cool. On the whole, AI is unlikely to affect our lives in proportion to the ink spilled by influencers.
This is a really intersting take, and maybe shows that I haven't been thorough enough with my reading. My guess is that the deep technical articles are few and far between and the higher level 'hot takes' are what fills the room. Do you have any recommendations for interesting places to start?
> Or another thought; why is it that a stochastic parrot can solve logic puzzles consistently and accurately? It might not be 100%...
It can't. As you say in the very next sentence. If it isn't solving any given puzzle with a 100% success rate, but randomly failing, then it isn't consistent.
The short answer, as far as I’m aware, is that no one really knows. The longer answer is that we have a lot of partial answers that, in my mind, basically boil down to: model architectures draw a walk through the high dimensional vector space of concepts, and we’ve tuned them to land on the right answer. The fact that they do so consistently says something about how we encode logic in language and the effectiveness of these embedding/latent spaces.
I don’t think this problem is that hard to solve, it just requires political will that doesn’t exist. The solution is to make it the platform’s problem. If the platform doesn’t want to deal with fraud, they don’t get to operate in that jurisdiction. Sue them into submission. If they don’t care about that geography, then there is now a gap in the market for a more local business to fill.
> I don’t think this problem is that hard to solve, it just requires political will that doesn’t exist
This is equivalent to saying "I don't think the problem is hard, it just requires an a simple solution that doesn't exist". Problems are hard problems specifically because simple easy solutions for them don't exist.
You have to read it all the way through. It’s a pretty hefty investment, but the series is truly a masterpiece. I had to read the whole series twice to feel like I was actually starting to understand some of the symbolism. I don’t blame people for not being able to get into it; it’s dense. But it’s so epic and there is so much symbolism and philosophy packed in.
I have quite a bit of family in Germany, and have had several friends move from the US to Europe. Europe absolutely knows that they have an opportunity to capture a ton of talent right now. If you have skills that are in demand, basically any country in the Schengen zone will find a way to get you a visa. For example, if you’re a trans researcher, you will find open arms at academic institutions in Europe.
You could also lie and claim your address as a US address, and then just live in another country. This is obviously illegal, but I’ve met a few people who made it work for a while. But I’m also speaking abstractly on the internet, so maybe I’m just making all this up.
For example, we could define consciousness as the ability to communicate claimed internal states. Perhaps there could be a complexity metric that gives us a metric of consciousness.
We could define consciousness as the ability to respond to stimuli in complex ways. This would make a supermarket’s automatic doors slightly conscious.
Personally, I don’t really care how it is defined in any particular conversation, so long as it is defined. Otherwise we’re just flailing at each other in the dark.
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