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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 brownian 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.
What's the difference?
A map isn't a territory, but there's no such a thing as a tangible mind you can hold (or there is, and we're arguing about mysticism, which isn't really a good use of my time). As far as I can see, it's all maps.