Again, I really appreciate how deep you’ve gone into this. I haven’t dealt with these topics for many years and even then, I mostly dealt with the actual physical system of a single cell, not what you can build out of them. However I think that’s were the core of the issue lies anyway.

I recently messed around with a creating a spiking neural net made of “leaky integrate and fire” (LIF) neurons. I had to do the integration numerically which was slow and not precise. However, hardware exists that does run every neuron continuously and in parallel.

So you ran a simulation of those neurons?

LIF neurons can be physically implemented by combining classic MOSFETs with Redox cells. Like: Pt/Ta/TaOx with x<1. Or with Hafnium or Zirconia instead of Tantal.

The oxygen vacancies in the oxide form tiny conductive filaments few atoms think. While the I-V-curve is technically continuous, the number of different currents you can actually measure is limited. Shot noise even plays a significant role, where the discreetness of elections matters.

Under absolutely perfect conditions, you can maybe distinguish 300 states. On a chip at room temperature maybe 20 to 50. If you want to switch fast it’s 5 to 20.

That’s not continuous, it’s only quasi-continuous. It’s still cool, but not outside the mathematical scope of the theorems used in the paper.

And yes, continuity is not everything. You’re right about busy beavers being not computable in principle. But this applies to neuromorphic computing just the same.

Theoretically, if a continuous extension of the busy beaver numbers existed, then it should be possible for a Liquid State Machine Neural Net to approximate that function.

But it doesn’t. No such extension can be meaningfully defined. If it could be calculated, then it could solve the halting problem. That’s impossible for purely logical reasons, independently of what you use for computation (a brain, neuromorphic computing, or anything else). Approximations would be incredibly slow, as the busy beaver function grows faster than any computable function.

Not saying this is necessarily a problem, but the main author of the paper is also an executive manager of the journal that published it. You can find that information by clicking on “editorial board” on the journals webpage. Now, I assume, he was not actually involved in editorial decisions about his own article, because that would be a conflict of interest and they haven’t declared any. It’s not a secret and it’s easy to find on the webpage, but I think they could have made this fact a bit more prominent in the paper itself. Let’s wait how the larger scientific community reacts to this paper.

Therefore, wouldn’t it be strange to rule out something using our current math/physics systems?

I get the thought, but math and physics are not the same. Math includes logic. When the authors of that paper make that argument, they don’t rely on our current understanding of physics. The theorems they use rely only logic. They are true independent of how the physics and the computation works.

Blackholes, neutron stars, quasars and other funny things that can’t be explained exactly DO exist after all

Yes, black holes inspired the paper. They do make the assumption, that a theory of quantum gravity would explain them. That’s what most people want out of such a theory.

I love how in depth you went into this. And I agree with everything, except I’m not sure about neuromorphic computing.

However, I think neuromorphic hardware is able to bypass this limitation. Continuous simultaneous processes interacting with each other are likely non-algorithmic.

I worked in neuromorphic computing for a while as a student. I don’t claim to be an expert though, I was just a tiny screw in a big research machine. But at least our lab never aimed for continuous computation, even if the underlying physics is continuous. Instead, the long-term goal was to have like five distinguishable states (instead of just two binary states). Enough for learning and potentially enough to make AI much faster, but still discrete. That’s my first point, I don’t think any one else is doing something different.

My second point is, no one could be doing something continuous in principle. Our brains don’t even really. Even if changes in a memory cell (or neuron) were induced atom by atom, those would still be discrete steps. Even if truly continuous changes were possible, you still couldn’t read out that information because of thermal noise. The tiny changes in current or whatever your observable is would just drown in noise. Instead you would have to define discrete ranges for read out.

Thirdly, could you explain, what exactly that non-algorithmic component is that would be added and how exactly it would be different from just noise and randomness? Because we work hard to avoid those. If it’s just randomness, our computers have that now. Every once in a while, a bit gets flipped by thermal noise or because it got hit by a cosmic particle. It happens so often, astronomers have to account for it when taking pictures and correct all the bad pixels.

AI is algorithmic and deterministic, because it runs on normal processors. Step by step like any other program. It only seems random, because it’s complex.

How is it in any way narrow? The three theorems they use (Goedel, Tarski, Chaitin) are actually incredibly broad. They absolutely include things we can not even imagine.

Smith goes into great detail in “The wealth of Nations” about how landlords are parasites. He explains why theoretically and empirically and gives specific examples. He lacked an understanding of historical materialism, so he wrongly thought capitalism would naturally get rid of them.

Vienna, Austria is a classic example. Don’t know about the current situation, though.

No, I think that’s just you.

Geese eat mostly grass though. And seeds. Both on land.

That’s ridiculous! Falangists practically invented fascism.

Okay, but how does this relate to the meme about prison population?

Yes, but there are bosses right now. And they would still be very powerful, even if they lost control of the state. They don’t care about what’s best for everyone. They care about what’s best for them. They would still control all those machines, institutions, money, private armies, the media and they would have the total support of all the capitalist militaries of the world, ready to come in and completely crush horizontal power and suppress mutualism. So the class of bosses wouldn’t magically disappear over night.

If people organized (either “horizontally” or otherwise) to form some thing, some kind of organization or institution or loose federation of grassroots cooperatives or whatever you want to call it, that would be able to suppress this boss class and their military and everything. That thing would be what marxist leninists call a state by definition. Because when we talk about a state, we mean nothing more or less than a weapon able to force the will of one class upon another. Even if that will is just:“stop forcing your will on us non-bosses”. How horizontal it is internally dosn’t matter at all for the definition of a state.

Not at all. The Spanish revolutionaries were communists. Some in the communist party, but even the Spanish anarchists called what they fought for “libertarian communism”.

Most time would be spent solving the integrals of the trigonometric functions. Those are the kind, that you either just know, or would typically look up in a table, which is where they were taken from for the meme. Though you could do them by hand using substitution.

It is?

I’m happy for you and your dad but you say

“Sometimes I wish you were still Republican, so I’d have someone to yell at.”

as if there weren’t still plenty of very good reasons to yell at Democrats…

Play Balatro instead. It’s fun without money and has all the poker hands.