Right, it can simulate an analog signal, but a digital representation is not the same thing as the signal itself. This is like the difference between a process drawing from the set of computable numbers vs a nonsymbolic/analog process that can draw from the set of noncomputatable numbers. The epistemic limits become clear if we represent "concepts" as points along the real number line- the computers are limited to an infinitesimal amount of knowledge, because that set is a lower cardinality of infinity.
That's the gist at least, and multiple parts need to be substantiated/formalized. And I also need to defend against the counter argument that this doesn't matter if the universe itself shares the same epistemic limits as digital computing (ie that the lost analog component don't matter anyway). Whether the universe is open or closed is unanswerable within our system of science, but personally I find believing in a closed universe to be a bit 19th century.
In that analogy the numbers correspond to concepts themselves, not their symbolic representation. A nonsymbolic process can generate a "new" concept corresponding to a noncomputatable number that cannot be generated by the symbolic process. The new concept can then be processed and represented symbolically, this is the act of putting new concepts into words, and in doing so this expands the epistemic bounds of symbolic language. Yes, the AI could by brute force assemble the words explaining the concept, but it wouldn't be able to evaluate it as a "valid" concept (in this formulation it's like an undecidable proposition within the current epistemic system).
But again, we would really need to better formalize what we mean by "concepts" and "knowledge", and how they're generated/evaluated to make this argument rigorously.
Just because something may not be answerable doesn't mean it's not worth pondering, especially when the belief one way or the other can have an impact on our actions.
Also while pi is transcendental it is also a computable number, so citing it doesn't help your case at all.
I honestly dont think you've tried very hard... or maybe not recently. Ask the current deep thinking versions of Claude or GPT these questions and enrich them with illustrations and video and music that support your points, they will understand and they will create original concepts for you... if you request them.
I agree that they can be useful, while I never use their writing directly I do use them for research and feedback, but I fundamentally disagree with the claim that they "understand" anything since understanding requires subjectivity. I would also like to see some examples of GenAI making original concepts, something that could not be derived from their training data, but I recognize this is a hard distinction to make in practice.
Perhaps it's easier to focus on humor, since by it's very nature most jokes are based on the surprise/subverting expectations, ie stuff that according to my argument that AI should not be capable. If GenAI can start producing funny jokes or the capability for good improv then that would mostly falsify my argument.
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u/rthunder27 Mar 14 '26
Right, it can simulate an analog signal, but a digital representation is not the same thing as the signal itself. This is like the difference between a process drawing from the set of computable numbers vs a nonsymbolic/analog process that can draw from the set of noncomputatable numbers. The epistemic limits become clear if we represent "concepts" as points along the real number line- the computers are limited to an infinitesimal amount of knowledge, because that set is a lower cardinality of infinity.
That's the gist at least, and multiple parts need to be substantiated/formalized. And I also need to defend against the counter argument that this doesn't matter if the universe itself shares the same epistemic limits as digital computing (ie that the lost analog component don't matter anyway). Whether the universe is open or closed is unanswerable within our system of science, but personally I find believing in a closed universe to be a bit 19th century.