I Watched Roger Penrose Descibe the Incomputability of Consciousness So You Don't Have To!

Roger Penrose is not a public speaker. He has a brilliant mind, and like so many extraordinarily clever people, his ability to explain it to less clever people, like you and me, lacks a commonality with how we see the world and how he sees it. I've watched a couple of his explanations using Gödel's Theorems of incomputability and, because of its inherent complexity, it's soemthing he can only explain to the initiated, to minds like his. So, I sought the explanations posited by those who can actually understand him, and I think I begin to understand why consciousness cannot be simulated on any computational machine we can build right now.

So, here's my crack at explaining it in lay terms.

1. Quantum Superposition

In Schrodinger's analogy of the cat in a box, he leads us to understand that, if we know the cat is alive, we no longer have a superposition that is incomputable, there is now only the state we observed, because the indeterminacy of the superposition has collapsed to the state we observed. Before we observed the state, we could not predict it, it was a "crap shoot." A roll of the die. And that collapse is, from a purely thought experiment POV is now irreversable. We close the box, wait a random amount of time, is the cat alive or dead? We can't compute it again, until we open the box, and the quantum field state collapses. What is your cat? Alive or dead? Until I see my cat, I cannot predict it's state, and on seeing the cat, that is not a prediction, it is an observation.

A prediction is not computable. You can guess, your guess may turn out to be correct, but you cannot know until you observe, and neither a guess nor an observation is a calculation, because a calculation accurately predicts, to within a measurable tolerance, the state of a matter or an energy. For example, Ohm's law accurately predicts, to an acceptable precision, what electrical current is flowing through a load when we know the voltage applied and the impedance of the load. Equally we can transpose the formula to calculate the unknown from the two know factors. Computers do thises kinds of calculations billions of times per second to simulate worlds, and we can know the outcomes with great accuracy. Computers cannot predict "if the cat lives" without observing "the cat being alive." It is incomputable with any current computational technology.

2. Neuronal Microtubules

Penrose posits that the microtubal organs(?)/components(?) of the neurons in brains present a cat-in-a-box scenario as living creatures think. When a neuron is triggered by the firing of sense or neuron before it, we cannot predict before or during the firing, which way a microtubal will "switch" the signal. We can only measure the state after a neuron has fired. Neuronal operation has an incomputability about it. The microtubal's state is incalculable before a neuron is triggered and is only observable in its actual state after triggering. There is no formula for which way this will go, we can only wait until the field equation collapses and see what happened.

Penrose posits that this is what is behind consciousness, and why a computational machine cannot develop consciousness. Einstein struggled to understand the uncertainty of electron spin - "God does not play dice!" He was the last classicist, the one smart and bold enough to usher in the quantum age, it took others, standing on his giant shoulders, to understand the uncertainty inherent in a quantum state - the literal incomputability-before-the-fact. The cat in the box. The electron's spin. A decision made by a single neuron. There is no calculable prediction that can be made before the fact! Only observations afterwards, and this is why Von Neumann machines cannot develop sentience!

And, it would be wrong to think that, say, the microtubals could be simulated by a random number generator. Random numbers in computers are only pseudo-random. Randomness, true randomness is also incalculable. There is an inherent calculation in a random number generator that returns false to Gödel's Theorem of Calculability and, if the theorm returns a false it's calculable, while a true, is incalculable. The wave collapse formula passes Gödel's test, Von Neuman machines don't. Microtubal states in neurons pass Gödel's test, logic gates do not.

3. Boolean Logic

Modern computers are built from logic gates. The simplest to understand is the OR gate, if one input OR the other (or both are) is high, the output will be high. You can predict with 100% accuracy the output state of the gate by measuring its input states. The AND gate is equally as predictable, the output will ONLY lightup if both inputs are lit up. These devices prove they are calculable billions of times over every nanosecond, on every computer, in every corner of the world. These machines can allow us to visualise data in ways that help us see patterns, even in the readings from partical accelerators measuring quantum uncertainty outcomes, but they cannot predict these patterns without pre-existing data. They cannot predict if the cat is alive or dead, they can only observe it with us. Humans can imagine because our neurons have "quantum" states that incalculably change, with no predictable indicator before the fact.

Conclusion

And that is why AI is not actually intelligent. It's a pattern recognition trick, applied to pre-existing data. It is not sentient, it is not intelligent, it isn't even truly predictive. It can fold proteins because these are calculable. It cannot invent, because it doesn't have that quantum uncertainty and we can't give it that quantum uncertainty, because we can't describe pre-existing data in ways which are incalculable... because the data is already calculated and pre-existing, nothing new can come from it, only patterns which are already there.. Seriously, if you're invested in AI, pull your money out of it. Sooner or later, somebody's AI will prove that no AI works as AI. And then the market wil crash like a 747 with empty feul tanks.