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> When implementing an algorithm as a computer program by means of some kind of formal language (including those based on recursive functional programming parad

by elil17 4y ago

> When implementing an algorithm as a computer program by means of some kind of formal language (including those based on recursive functional programming paradigms), we must introduce specific data and code structures, their properties and interactions, as well as the set of operations we are allowed to perform on them, in order to represent the objects and relations that are relevant for our computation. In other words, we must provide a precisely defined ontology on which the program can operate deductively, e. g., by drawing inferences or by ordering tasks for solving a given problem. In an algorithmic framework, novelty can only be represented combinatorially: it manifests as new combinations, mergers, and relations between objects in a (potentially vast, but predefined) space of possibilities. This means that an algorithm cannot discover or generate truly novel properties or relations that were not (at least implicitly) considered in its original ontology. Therefore, an algorithm operating in a deductive manner cannot jury-rig, since it cannot find new causal properties of an object that were not already inherent in its logical premises. This argument is not convincing to me. In fact, there seem to be real world counterexamples to their argument. If the AI agent is operating, on say, text, why is that space “potentially vast, but predefined”? A text stream of arbitrary length is arbitrarily vast. An AI agent could, conceivably, define new ontologies textually. As an example, this person used ChatGPT to invent a new language: https://maximumeffort.substack.com/p/i-taught-chatgpt-to-invent-a-language https://maximumeffort.substack.com/p/i-taught-chatgpt-to-inv... That strikes me as an example of generating “truly novel properties or relations that were not (at least implicitly) considered in its original ontology,” albeit in a rudimentary way.

dr_dshiv 4y ago
Gorp!
Garlef 4y ago
>> This means that an algorithm cannot discover or generate truly novel properties or relations that were not (at least implicitly) considered in its original ontology. > A text stream of arbitrary length... Maybe you could state this in some form of "turing completeness": As soon as a program has [vast enough output space] and allows for [enough recursive recombinations] then it can produce [everything]. In the wording of the article: If everything is implicitly considered, then there's nothing that can not be produced.
naasking 4y ago
> This argument is not convincing to me. It shouldn't be because it's trivially false: create a Turing machine that enumerates all other Turing machines. All computable ontologies are so discoverable, no matter how seemingly "novel".
- mjburgess 4y ago
  If it's first step was to enumerate the machine which computed Pi, then this enumerating machine would never take a second step. Geometry isnt computable, and all physical ontology is geometric.
  - tsimionescu 4y ago
    Pi is very much computable, and I don't know what aspect of geometry you think is not computable.
  - elil17 4y ago
    Is it true to say that geometry isn’t computable? You can symbolically compute geometry. You wouldn’t be able to compute the decimal circumference of a circle, for example, but you can represent it as 2pir in a symbolic system. You can then use that to do things like symbolically derive other geometric properties (e.g. surface area of a sphere). It’s not clear that the universe “computes” the circumference of a circle to infinite precision. The best candidate I can think of would be the event horizon of a black hole, which is not composed of particles as I understand it, but I believe the jury is still out on whether the Plank length means that the shape of such a thing is still quantized at some level. Plus, humans can’t compute pi either. We can conceive of it, though, and I don’t see an argument for why an AI agent can’t conceive of it too (or at least behave like it conceived of it).
  - naasking 4y ago
    First, all of physics is computable to arbitrary precision. Continuous quantities in physics are being systematically removed because they almost inevitably introduce absurdities [1]. Measures lose all meaning below Planck length anyway. Second, the point of enumerating all Turing machines is not to run them to completion, it's simply to create them, so your objection is inapplicable. The Turing machine itself defines an ontology. The claim was that algorithms do not have access to novel ontologies, which conflicts with the basic construction of recursively enumerable functions that defines computation. Third, even if it were true that geometry is not computable, don't mistake the formalism we currently use as somehow necessary. Geometry is powerful enough to model physics, but it could also be too powerful, ie. there could be some formalism less powerful than geometry that would also suffice for physics. For instance, we use real numbers in physics for convenience, but real numbers almost certainly don't really exist as we define them. [1] Baez's, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
nairboon 4y ago
From the excerpt it looks like they want to make the classic "computers-can't be creative" argument (although I haven't read the article). There, one school makes the argument that only humans can make truly creative discoveries, like Einstein. But without even discussing the merits of this argument, that distinction is really not yet important. Presently, most of the people interested in AGI, are concerned with building the general intelligence in the first place. The kind of intelligence present in the average human and not the one from Einstein. Very few people are trying to tackle the artificial-Einstein problem before the AGI one.

by elil17 4y ago

dr_dshiv 4y ago

Gorp!

Garlef 4y ago

>> This means that an algorithm cannot discover or generate truly novel properties or relations that were not (at least implicitly) considered in its original ontology. > A text stream of arbitrary length... Maybe you could state this in some form of "turing completeness": As soon as a program has [vast enough output space] and allows for [enough recursive recombinations] then it can produce [everything]. In the wording of the article: If everything is implicitly considered, then there's nothing that can not be produced.

naasking 4y ago

> This argument is not convincing to me. It shouldn't be because it's trivially false: create a Turing machine that enumerates all other Turing machines. All computable ontologies are so discoverable, no matter how seemingly "novel".

mjburgess 4y ago
If it's first step was to enumerate the machine which computed Pi, then this enumerating machine would never take a second step. Geometry isnt computable, and all physical ontology is geometric.
- tsimionescu 4y ago
  Pi is very much computable, and I don't know what aspect of geometry you think is not computable.
- elil17 4y ago
  Is it true to say that geometry isn’t computable? You can symbolically compute geometry. You wouldn’t be able to compute the decimal circumference of a circle, for example, but you can represent it as 2pir in a symbolic system. You can then use that to do things like symbolically derive other geometric properties (e.g. surface area of a sphere). It’s not clear that the universe “computes” the circumference of a circle to infinite precision. The best candidate I can think of would be the event horizon of a black hole, which is not composed of particles as I understand it, but I believe the jury is still out on whether the Plank length means that the shape of such a thing is still quantized at some level. Plus, humans can’t compute pi either. We can conceive of it, though, and I don’t see an argument for why an AI agent can’t conceive of it too (or at least behave like it conceived of it).
- naasking 4y ago
  First, all of physics is computable to arbitrary precision. Continuous quantities in physics are being systematically removed because they almost inevitably introduce absurdities [1]. Measures lose all meaning below Planck length anyway. Second, the point of enumerating all Turing machines is not to run them to completion, it's simply to create them, so your objection is inapplicable. The Turing machine itself defines an ontology. The claim was that algorithms do not have access to novel ontologies, which conflicts with the basic construction of recursively enumerable functions that defines computation. Third, even if it were true that geometry is not computable, don't mistake the formalism we currently use as somehow necessary. Geometry is powerful enough to model physics, but it could also be too powerful, ie. there could be some formalism less powerful than geometry that would also suffice for physics. For instance, we use real numbers in physics for convenience, but real numbers almost certainly don't really exist as we define them. [1] Baez's, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421

nairboon 4y ago

From the excerpt it looks like they want to make the classic "computers-can't be creative" argument (although I haven't read the article). There, one school makes the argument that only humans can make truly creative discoveries, like Einstein. But without even discussing the merits of this argument, that distinction is really not yet important. Presently, most of the people interested in AGI, are concerned with building the general intelligence in the first place. The kind of intelligence present in the average human and not the one from Einstein. Very few people are trying to tackle the artificial-Einstein problem before the AGI one.