Brains aren’t impressive because of their compute (which is both immense and absurdly efficient) or their ability to predict the future (technically the main function of evolved minds). They’re impressive because they’re conscious. The fact that organic brains can also engage in hierarchical abstraction, which no digital computer (or Turing machine) can do by definition, is icing on the cake.
(The halting problem and Godel’s incompleteness and Traski’s undefinability theorems all seem to suggest that analog, not digital computation is more likely to be involved in consciousness, if at all.)
You’re going to have to do a lot more to justify the leap from Godel’s Incompleteness and the Halting Problem to “digital is limited, analog is not”, because neither of those things have anything to do with digital processes at all, and in fact both came about before we’d invented digital computers.
To me this comment sounds like when popsci gets ahold of a few sciency words and suddenly decides everything is crystal vibrations universal harmonics string theory quantum tunneling aligning resonance with those around you.
Analog signals are not digitally irreducible without presuming there’s no level of noise floor under which greater detail is irrelevant, Turing’s machines are not digital by their construction and predate the concept by a long time, and the first computers we built were analog and we invented digital computers later because they were cheaper and more efficient and easier and more reliable.
Also the halting problem doesn’t say “there are things which a computer can’t know but a human can”, it says “there are some things that cannot be known”.
Similarly Gödel proved that there will always be true things about a system that cannot be proven from within the system, that is using its axioms. That was a real bummer for folks trying to prove all of math with a small set of axioms. But that does not mean there are things math can’t know that humans magically can, it just means there’s other math, outside the axioms, that are true without following from them, in math. He proved it with math, after all. It doesn’t claim to give any special abilities to human brains.
And also, again, nothing Gödel or Turing ever said has anything to do with the concept of “digital” anything. I think you’re using the term “digital” to mean “rulesy”? Which is not even close to what it means?
Turing’s machines are notdigital by their construction
I won’t argue with you, because some of what you wrote isn’t even wrong.
However, on the off chance that you actually care about what is true, I urge you to take a theoretical computer science course. Lectures from MIT and Carnegie Mellon are available on YouTube.
Stop watching podcasts with pseudo-intellectual media grifters and read the actual research literature by real philosophers and mathematicians on these otherwise arcane topics.
I’m only about 15% sure you yourself aren’t an AI bot making a beautifully ironic and satirical play here. But I think we can agree not to argue any longer 🤝
I don’t see why there would be any fundamental difference between analog and digital computing. Digital computers can emulate analog computing, and I doubt consciousness arises from having theoretically infinite decimal precision, because in practice analog systems cannot use infinite precision either. Analogs (heh!) of the halting problem and the theorems you mention also exist for analog computing.
Quantum effects in the brain are a slightly more plausible explanation for consciousness, but currently they teeter on magical thinking because we don’t really know anything about what they would actually do in the brain. It becomes an “a wizard did it” explanation.
Also, I never said computers can’t be conscious. I said that digital computers (Turing machines) probably can’t. Quantum and analog computers have no such theoretical constraints and they’re far, far more prevalent given that they’re found in every living creature.
Sure, you say you’re conscious. I can get an LLM to say it’s conscious too. This is why we need some method for measuring it. Otherwise how can I tell which of you is telling the truth?
This is called the problem of other minds. Of course I can’t be certain about the consciousness of others. I can only be certain about my own.
We do have a way of measuring the correlates of consciousness. But we have no clue how to detect the presence of subjective experience using quantitative methods.
Philosophy departments (which is where any discovery on this front will originate) are heavily defunded. If you’re waiting for physicists or biologists to figure this out you’ll be waiting even longer.
Exactly, which is why it’s IMO a bit presumptuous to say with confidence that humans are conscious while LLMs are categorically not conscious. We don’t even really know what that means.
I don’t personally think LLMs are conscious, at least not yet or not to the same degree that humans are. But that’s purely based on vibe, it’s not something I can know. We need to figure out what consciousness really is and how to measure it before we can say we know this with any certainty.
It is not presumptuous at all. Inference to the best explanation is how you know (almost) anything.
This table isn’t conscious.
This is my justified belief. No inferential claim is guaranteed and all objective claims are inferential (which is why scientific claims aren’t absolute).
That said, I have strong reasons to think that tables aren’t conscious. They might be, but I’m epistemically compelled to believe otherwise.
ChatGPT isn’t conscious.
Ditto. It would be irrational for me to believe otherwise given the strong evidence.
That you “don’t know for sure” is an implied disclaimer for every scientific claim.
If the evidence is ambiguous, we say so. Regarding ChatGPT, the evidence is unambiguous.
I am conscious.
This is a non-inferential claim that I know through direct contact with reality. It is a priori.
Right, your own thoughts. So I can be sure I’m conscious, but you commenting “I know I’m conscious” on here doesn’t tell me anything about your consciousness. The robot can do that, and does.
(The halting problem and Godel’s incompleteness and Traski’s undefinability theorems all seem to suggest that analog, not digital computing is responsible for consciousness.)
I hear that argument from time to time, and I never found a source for it. I want to understand the original claim. Because it doesn’t make any sense when people bring it up. because both theorems do not have anything to do with the areas it’s applied to. I understand why people think it does, but it just doesn’t
You’re misunderstanding the implications of both the halting problem and Gödel’s first incompleteness theorem.
What Turing and Gödel independently proved is that a human observer can (theoretically) always have insights about mathematics and programming that are incomputable. That is, you cannot program or axiomatize or formalize or digitize everything that a mind can do. Period.
Analog computers are sufficiently different from digital systems to potentially emulate brain activity. But digital (discrete) methods are probably too constrained.
What Turing and Gödel independently proved is that a human observer can (theoretically) always have insights about mathematics and programming that are incomputable. That is, you cannot program or axiomatize or formalize or digitize everything that a mind can do. Period.
that is not what either of them proved. like… at all
You will find what I said in any philosophy of mathematics textbook dealing with the subject. In fact, I am paraphrasing the Oxford logician Joel David Hamkins.
You’re welcome to also read Shapiro’s famous paper for a rephrasing. These results have been well understood for half a century, although because the implications are ultimately metaphysical and not mathematical, we can’t be sure of the wider consequences, if any.
Going through some of the related paper abstracts, including speculative comments by Gödel: this is pure philosophy. Nothing that is set in stone. Which now points me back to my initial statement, where we can discuss all we want, but in the end it’s philosophy. Not “hard” (“provable”) science
There can be no enumerable list of axioms for the true statements of mathematics. No computational procedure could exist to determine whether propositions are valid, provable, or even equivalent. And no matter how you formulate the number-theoretic axioms, a mathematician would always have insights (for instance, about whether a Diophantine equation has a solution) that are both clearly “true” and obviously unprovable. This holds true for all digital systems.
Here is what we don’t know for sure:
The metaphysical implications.
Your distinction between science and philosophy is incorrect. Science is inductive and abductive. It can’t “prove” things. It’s not deductive. Mathematics and philosophy can prove things.
Philosophy also determines the formal systems we use as a basis of reasoning, for instance, in science.
Brains aren’t impressive because of their compute (which is both immense and absurdly efficient) or their ability to predict the future (technically the main function of evolved minds). They’re impressive because they’re conscious. The fact that organic brains can also engage in hierarchical abstraction, which no digital computer (or Turing machine) can do by definition, is icing on the cake.
(The halting problem and Godel’s incompleteness and Traski’s undefinability theorems all seem to suggest that analog, not digital computation is more likely to be involved in consciousness, if at all.)
You’re going to have to do a lot more to justify the leap from Godel’s Incompleteness and the Halting Problem to “digital is limited, analog is not”, because neither of those things have anything to do with digital processes at all, and in fact both came about before we’d invented digital computers.
To me this comment sounds like when popsci gets ahold of a few sciency words and suddenly decides everything is crystal vibrations universal harmonics string theory quantum tunneling aligning resonance with those around you.
The situation is the following.
We’ll probably need analog computation, currently in its infancy, to get artificial (inorganic) consciousness.
I study metaethics and philosophy of mathematics. These problems are real, and I am being honest with you.
That is not the situation. 😛
Analog signals are not digitally irreducible without presuming there’s no level of noise floor under which greater detail is irrelevant, Turing’s machines are not digital by their construction and predate the concept by a long time, and the first computers we built were analog and we invented digital computers later because they were cheaper and more efficient and easier and more reliable.
Also the halting problem doesn’t say “there are things which a computer can’t know but a human can”, it says “there are some things that cannot be known”.
Similarly Gödel proved that there will always be true things about a system that cannot be proven from within the system, that is using its axioms. That was a real bummer for folks trying to prove all of math with a small set of axioms. But that does not mean there are things math can’t know that humans magically can, it just means there’s other math, outside the axioms, that are true without following from them, in math. He proved it with math, after all. It doesn’t claim to give any special abilities to human brains.
And also, again, nothing Gödel or Turing ever said has anything to do with the concept of “digital” anything. I think you’re using the term “digital” to mean “rulesy”? Which is not even close to what it means?
I won’t argue with you, because some of what you wrote isn’t even wrong.
However, on the off chance that you actually care about what is true, I urge you to take a theoretical computer science course. Lectures from MIT and Carnegie Mellon are available on YouTube.
Stop watching podcasts with pseudo-intellectual media grifters and read the actual research literature by real philosophers and mathematicians on these otherwise arcane topics.
I’m only about 15% sure you yourself aren’t an AI bot making a beautifully ironic and satirical play here. But I think we can agree not to argue any longer 🤝
deleted by creator
I don’t see why there would be any fundamental difference between analog and digital computing. Digital computers can emulate analog computing, and I doubt consciousness arises from having theoretically infinite decimal precision, because in practice analog systems cannot use infinite precision either. Analogs (heh!) of the halting problem and the theorems you mention also exist for analog computing.
Quantum effects in the brain are a slightly more plausible explanation for consciousness, but currently they teeter on magical thinking because we don’t really know anything about what they would actually do in the brain. It becomes an “a wizard did it” explanation.
So in the end, we just don’t know.
Then why not take a course on Theoretical Computer Science? Or do you not care about the differences?
I have a master’s degree in computer science.
Obviously I meant “I don’t see why there would be any fundamental difference between analog and digital computing [when it comes to consciousness].”
deleted by creator
deleted by creator
I’m still awaiting a widely accepted method of actually measuring “consciousness.” It’s a conveniently nebulous property.
And simply defining it as something computers can’t do is even more convenient.
That doesn’t change the fact that I am conscious.
Also, I never said computers can’t be conscious. I said that digital computers (Turing machines) probably can’t. Quantum and analog computers have no such theoretical constraints and they’re far, far more prevalent given that they’re found in every living creature.
Sure, you say you’re conscious. I can get an LLM to say it’s conscious too. This is why we need some method for measuring it. Otherwise how can I tell which of you is telling the truth?
This is called the problem of other minds. Of course I can’t be certain about the consciousness of others. I can only be certain about my own.
We do have a way of measuring the correlates of consciousness. But we have no clue how to detect the presence of subjective experience using quantitative methods.
Philosophy departments (which is where any discovery on this front will originate) are heavily defunded. If you’re waiting for physicists or biologists to figure this out you’ll be waiting even longer.
Exactly, which is why it’s IMO a bit presumptuous to say with confidence that humans are conscious while LLMs are categorically not conscious. We don’t even really know what that means.
I don’t personally think LLMs are conscious, at least not yet or not to the same degree that humans are. But that’s purely based on vibe, it’s not something I can know. We need to figure out what consciousness really is and how to measure it before we can say we know this with any certainty.
It is not presumptuous at all. Inference to the best explanation is how you know (almost) anything.
This is my justified belief. No inferential claim is guaranteed and all objective claims are inferential (which is why scientific claims aren’t absolute).
That said, I have strong reasons to think that tables aren’t conscious. They might be, but I’m epistemically compelled to believe otherwise.
Ditto. It would be irrational for me to believe otherwise given the strong evidence.
That you “don’t know for sure” is an implied disclaimer for every scientific claim.
If the evidence is ambiguous, we say so. Regarding ChatGPT, the evidence is unambiguous.
This is a non-inferential claim that I know through direct contact with reality. It is a priori.
This is pretty much what Descartes meant with “cogito ergo sum”. The only thing you can be sure are 100% real, are your thoughts
Right, your own thoughts. So I can be sure I’m conscious, but you commenting “I know I’m conscious” on here doesn’t tell me anything about your consciousness. The robot can do that, and does.
I hear that argument from time to time, and I never found a source for it. I want to understand the original claim. Because it doesn’t make any sense when people bring it up. because both theorems do not have anything to do with the areas it’s applied to. I understand why people think it does, but it just doesn’t
The simplest way to understand this problem is as follows.
Analog computation is not digitally reducible. (Brains are analog computers.)
Turing’s infamous Halting Problem.
I can write more about this and point you to more technical discussions if you want.
I really don’t see what either gödels or turnings theorems have to do with it
All they (basically) tell you is that you can’t tell if a computation will guarantee to halt , and that you can’t proof everything with math
It’s not excluding consciousness on a digital basis. Unless you already prerequisite some special property of consciousness to begin with
You’re misunderstanding the implications of both the halting problem and Gödel’s first incompleteness theorem.
What Turing and Gödel independently proved is that a human observer can (theoretically) always have insights about mathematics and programming that are incomputable. That is, you cannot program or axiomatize or formalize or digitize everything that a mind can do. Period.
Analog computers are sufficiently different from digital systems to potentially emulate brain activity. But digital (discrete) methods are probably too constrained.
that is not what either of them proved. like… at all
You will find what I said in any philosophy of mathematics textbook dealing with the subject. In fact, I am paraphrasing the Oxford logician Joel David Hamkins.
You’re welcome to also read Shapiro’s famous paper for a rephrasing. These results have been well understood for half a century, although because the implications are ultimately metaphysical and not mathematical, we can’t be sure of the wider consequences, if any.
ah, now we’re getting somewhere.
Going through some of the related paper abstracts, including speculative comments by Gödel: this is pure philosophy. Nothing that is set in stone. Which now points me back to my initial statement, where we can discuss all we want, but in the end it’s philosophy. Not “hard” (“provable”) science
Here is what we know for sure:
There can be no enumerable list of axioms for the true statements of mathematics. No computational procedure could exist to determine whether propositions are valid, provable, or even equivalent. And no matter how you formulate the number-theoretic axioms, a mathematician would always have insights (for instance, about whether a Diophantine equation has a solution) that are both clearly “true” and obviously unprovable. This holds true for all digital systems.
Here is what we don’t know for sure:
The metaphysical implications.
Your distinction between science and philosophy is incorrect. Science is inductive and abductive. It can’t “prove” things. It’s not deductive. Mathematics and philosophy can prove things.
Philosophy also determines the formal systems we use as a basis of reasoning, for instance, in science.