Biological neurons are actually more digital than artificial neural nets are. They fire with equal intensity, or don’t fire (that at least is well understood). Meanwhile, a node in your LLM has an approximately continuous range of activations.
They’re just tracking weighted averages about what word comes next.
That’s leaving out most of the actual complexity. There’s gigabytes or terabytes of mysterious numbers playing off of each other to decide the probabilities of each word in an LLM, and it’s looking at quite a bit of previous context. A human author also has to decide the next word to type repeatedly, so it doesn’t really preclude much.
If you just go word-by-word or few-words-by-few-words straightforwardly, that’s called a Markov chain, and they rarely get basic grammar right.
Like you said, the issue is how to do it consistently and not in an infinite sea of garbage, which is what would happen if you increase stochasticity in service of originality. It’s a design limitation.
Sure, we agree on that. Where we maybe disagree is on whether humans experience the same kind of tradeoff. And then we got a bit into unrelated philosophy of mind.
and you can literally program an LLM inside a fax machine if you wanted to.
Absolutely, although it’d have to be more of an SLM to fit. You don’t think the exact hardware used is important though, do you? Our own brains don’t exactly look like much.
Biological neurons are actually more digital than artificial neural nets are.
There are three types of computers.
Digital
Analog
Quantum
Digital means reducible to a Turing machine. Analog, which includes things like flowers and cats, means irreducible by definition. (Otherwise, they would be digital.)
Brains are analog computers (maybe with some quantum components we don’t understand).
Making a mathematical model of an analog computer is like taking a digital picture of a flower. That picture is not the same as the flower. It won’t work the same way. It will not produce nectar, for instance, or perform photosynthesis.
Everything about how a neuron works is completely undigitizable. There’s integration at the axon hillock; there are gooey vesicles full of neurotransmitters whose expression is chemically mediated, dumped into a synaptic cleft of constantly variegated width and browning motion to activate receptors whose binding affinity isn’t even consistent. The best we can do is build mathematical models that sort of predict what happens next on average.
These crude neural maps are not themselves engaged in brain activity — the map is not the territory.
Idk where you got the idea that neurons can be digitized, but someone lied to you.
It’s not about irreducibility - that’s not a feature any part of physics has. Even quantum states can be fully simulated by a digital computer, just with prohibitive (ie. exponential in qubits) overhead. It’s about continuous vs. discrete, and a very large number of discrete states can become indistinguishable from continuousness. Sometimes provably.
It’s true that the internal functions the determine whether neurons fire are poorly understood. Once we have that data it will absolutely be possible to simulate, though. It’s long been done for individual organoids, and at this point the hardware has scaled enough to look at doing an entire bacterium and it’s nearby environment. If the interactions of a random patch of water molecules can be neglected - and usually biochemists do so - that software could be made much much lighter yet.
I’d like to point out Earth’s weather systems are continuous, bigger and far more chaotic. If biology was irreducible, meteorology would be as well.
I explicitly explained that you can model an analog machine using a digital computer. When you make a topological map of a weather system (or a brain) or take a digital picture of a flower, you are generating a model. This is the subject of the articles you linked me.
No matter how accurate your digital model of a weather system, however, it will never produce rain. The byproduct of Turing machines (digital models) is strictly discrete.
Thoughts are a byproduct of brains, just as rain is a byproduct of weather and torque is a byproduct of internal combustion engines.
You could generate rain, torque (and maybe thoughts) in various contexts, of course. But not with Turing machines, whose only possible outputs are 1s and 0s.
You can model digital computers using analog computers. And the reverse is also possible. But digital systems are substrate-independent, whereas analog systems are substrate-dependent. They’re fundamentally inextricable from the stuff of which they’re made.
On the other hand, digital models aren’t made of stuff. They’re abstract. You can certainly instantiate a digital model within a physical substrate (silicon chips), the way you can print a picture of an engine on a piece of paper, but it won’t produce torque like an actual engine let alone rain like an actual weather system.
On a separate note, you reallllly need to acquaint yourself with Complexity Theory, if you actually believe our models will ever be anything other than decent estimates.
Correct. It’s theoretical computer science. Again, analog systems are irreducible to digital ones by definition. They can only be modeled (functionally and crudely).
If how exactly it’s implemented matters, regardless of similarity in internal dynamics and states, and there’s an imminent tangibility to it like rain or torque, I think you’re actually talking about a soul.
Behaviorally, analog systems are not substrate dependent. The same second-order differential equations describes RLC circuits, audio resonators and a ball on a spring, for example.
Analog AI chips exist, FWIW.
If you’re looking at complexity theory, I’m pretty sure all physics is in EXPTIME. That’s a strong class, which is why we haven’t solved every problem, but it’s still digital and there’s stronger ones that can come up, like with Presburger arithmetic. Weird fundamentally-continuous problems exist, and there was a pretty significant result in theoretical quantum computer science about it this decade, but actual known physics is very “nice” in a lot of ways. And yes, that includes having numerical approximations to an arbitrary degree of precision.
To be clear, there’s still a lot of problems with the technology, even if it can replace a graphics designer. Your screenshot is a great example of hallucination (particularly the bit about practical situations), or just echoing back a sentiment that was given.
Behaviorally, analog systems are not substrate dependent.
This is partly true, as I already explained at length, since the behavior of any system can be crudely modeled. It’s how LLMs work! But it’s also a non-sequitur.
Modeling what a system can do and doing what a system can do are not the same.
Biological neurons are actually more digital than artificial neural nets are. They fire with equal intensity, or don’t fire (that at least is well understood). Meanwhile, a node in your LLM has an approximately continuous range of activations.
That’s leaving out most of the actual complexity. There’s gigabytes or terabytes of mysterious numbers playing off of each other to decide the probabilities of each word in an LLM, and it’s looking at quite a bit of previous context. A human author also has to decide the next word to type repeatedly, so it doesn’t really preclude much.
If you just go word-by-word or few-words-by-few-words straightforwardly, that’s called a Markov chain, and they rarely get basic grammar right.
Sure, we agree on that. Where we maybe disagree is on whether humans experience the same kind of tradeoff. And then we got a bit into unrelated philosophy of mind.
Absolutely, although it’d have to be more of an SLM to fit. You don’t think the exact hardware used is important though, do you? Our own brains don’t exactly look like much.
There are three types of computers.
Digital means reducible to a Turing machine. Analog, which includes things like flowers and cats, means irreducible by definition. (Otherwise, they would be digital.)
Brains are analog computers (maybe with some quantum components we don’t understand).
Making a mathematical model of an analog computer is like taking a digital picture of a flower. That picture is not the same as the flower. It won’t work the same way. It will not produce nectar, for instance, or perform photosynthesis.
Everything about how a neuron works is completely undigitizable. There’s integration at the axon hillock; there are gooey vesicles full of neurotransmitters whose expression is chemically mediated, dumped into a synaptic cleft of constantly variegated width and browning motion to activate receptors whose binding affinity isn’t even consistent. The best we can do is build mathematical models that sort of predict what happens next on average.
These crude neural maps are not themselves engaged in brain activity — the map is not the territory.
Idk where you got the idea that neurons can be digitized, but someone lied to you.
I’m not trying to be cheeky or dismissive, but: https://en.wikipedia.org/wiki/Analog_signal
It’s not about irreducibility - that’s not a feature any part of physics has. Even quantum states can be fully simulated by a digital computer, just with prohibitive (ie. exponential in qubits) overhead. It’s about continuous vs. discrete, and a very large number of discrete states can become indistinguishable from continuousness. Sometimes provably.
It’s true that the internal functions the determine whether neurons fire are poorly understood. Once we have that data it will absolutely be possible to simulate, though. It’s long been done for individual organoids, and at this point the hardware has scaled enough to look at doing an entire bacterium and it’s nearby environment. If the interactions of a random patch of water molecules can be neglected - and usually biochemists do so - that software could be made much much lighter yet.
I’d like to point out Earth’s weather systems are continuous, bigger and far more chaotic. If biology was irreducible, meteorology would be as well.
I explicitly explained that you can model an analog machine using a digital computer. When you make a topological map of a weather system (or a brain) or take a digital picture of a flower, you are generating a model. This is the subject of the articles you linked me.
No matter how accurate your digital model of a weather system, however, it will never produce rain. The byproduct of Turing machines (digital models) is strictly discrete.
You can model digital computers using analog computers. And the reverse is also possible. But digital systems are substrate-independent, whereas analog systems are substrate-dependent. They’re fundamentally inextricable from the stuff of which they’re made.
On the other hand, digital models aren’t made of stuff. They’re abstract. You can certainly instantiate a digital model within a physical substrate (silicon chips), the way you can print a picture of an engine on a piece of paper, but it won’t produce torque like an actual engine let alone rain like an actual weather system.
On a separate note, you reallllly need to acquaint yourself with Complexity Theory, if you actually believe our models will ever be anything other than decent estimates.
To learn more, please take a Theoretical Computer Science course.
Correct. It’s theoretical computer science. Again, analog systems are irreducible to digital ones by definition. They can only be modeled (functionally and crudely).
If how exactly it’s implemented matters, regardless of similarity in internal dynamics and states, and there’s an imminent tangibility to it like rain or torque, I think you’re actually talking about a soul.
Behaviorally, analog systems are not substrate dependent. The same second-order differential equations describes RLC circuits, audio resonators and a ball on a spring, for example.
Analog AI chips exist, FWIW.
If you’re looking at complexity theory, I’m pretty sure all physics is in EXPTIME. That’s a strong class, which is why we haven’t solved every problem, but it’s still digital and there’s stronger ones that can come up, like with Presburger arithmetic. Weird fundamentally-continuous problems exist, and there was a pretty significant result in theoretical quantum computer science about it this decade, but actual known physics is very “nice” in a lot of ways. And yes, that includes having numerical approximations to an arbitrary degree of precision.
To be clear, there’s still a lot of problems with the technology, even if it can replace a graphics designer. Your screenshot is a great example of hallucination (particularly the bit about practical situations), or just echoing back a sentiment that was given.
This is partly true, as I already explained at length, since the behavior of any system can be crudely modeled. It’s how LLMs work! But it’s also a non-sequitur.
Modeling what a system can do and doing what a system can do are not the same.