The real fascinating thing is that Impossible Colors exist, which means it’s kind of impossible to actually represent all colors or impossible to precisely represent them.

Imo it seems colors are relative to how our brain and eyes are adapting to their current field of view, meaning the color you experience is not fully dependent on the light an object actually reflects nor the activation of your rods and cones but is dependent on the way your brain processes those signals with each other. Ergo, you can’t actually represent all colors precisely unless you can control every environmental variable like the color of every object in someone’s field of view and where someone’s eyes have been looking previously etc.

I’m not sure I understand what you’re trying to explain with states. Do you mean measured externally? Or does part of the system discretize the signals? Or are you saying that while the driving fields may be continuous the molecular structure enforces some sort of granularity to the signals?

You seem to know much more than me on the hardware side.

The last time I looked at hardware I came across “ferroelectric synapses” which do the STDP learning. I think it had something to do with the way magnetic dipoles align when current is applied. I don’t think it requires measurement at any step and is continuous whether we have good enough hardware to measure those changes or not.

So you ran a simulation of those neurons?

Yes. A very slow and very inaccurate one. I had to approximate the parallelization by setting a time step and then numerically compute the potentials of every neuron and synapse before moving on to the next time step and repeating.

I should state more clearly that I think it’s the temporal aspects of continuity that lead to undecidable behavior rather than just the number of states a neuron has.

Because each neuron in a neuromorphic net is running in parallel with all others, the signals produced by that neuron will not necessarily be in sync with the signals of any other neuron. As in, theoretically no two neurons are really ever firing at the exact same time.

As I previously stated, since timing is everything for STDP the time difference could be very significant when a neuron recieves multiple inputs in a short time window and fires.

An additional thing to note is that in more advanced models of neurons like the Hodgkin Huxley model, one can account for multiple synapses along the same dendritic tree which absolutely makes timing matter more since input to a synapse near the soma causes a localized change in ions that would stop the propagation of signals from the farther reaches of the dendrite. And if a far signal were to propagate to that synapse just prior to a an input signal, that signal might not be strong enough to get through.

Depending on how the hardware is build I’d imagine you could get similar effects from the nearness of electrical signals in a neurochip, where the local signaling causes non-trivial effects to the system.

Anyway, I’ve realized that I likely don’t know enough to say with real certainty whether spiking neural nets are incomputable or not. This is the most rigorous explanation of my thoughts I can write right now:

• If the true state of each neuron (and synapse) is continuous then there are uncountably infinite states to any net built with them.
• If these nets are comprised of densely connected layers with any recursion then the state of the system (assuming LIF neurons) could be represented as a large set of dependent non-linear differential equations.
• Systems of ODEs with more than three variables can give rise to chaotic behavior such that the tiniest changes in input can produce vastly different outputs (the Three Body Problem or the double pendulum are common examples of this) (this also means most likely there would be no “closed form” solution to these systems of differential equations which I don’t think necessarily means uncomputability but it would be a pain to solve one of these numerically and I don’t think runge-kutta would be accurate at all)
• it should then be possible (if not probable) that a spiking neural net gives rise to chaotic behavior
• Since we’ve assumed the voltage and current are continuous, they are real numbers that cannot be known with absolute certainty
• This means that even if you were to build an algorithm for determining the future state of the machine from its present state, you would not be able to know the true state well enough to know for certain you are not in a chaotic area for which your error of measurement does not eventually give rise to behavior significantly different than your algorithm predicted.
• Ergo, the neural net could be—at least with our flaws in measurement—uncomputable.

I think the problem is still uncomputable even with fully precise measurements simply due to the continuity and timing I mentioned before, but I guess I don’t have enough knowledge on the topic to prove it so perhaps I’m wrong.

I think someone else in this comment section mentioned analog-computing (which I thought included neuromorphic hardware) being capable of non-algorithmic computing so they might have more answers than me on the topic of what non-algorithmic means.

If it could be calculated it could solve the halting problem.

…would it? I don’t think you can derive a solution to the hard halting problem from knowing the longest finite runtime of a set of machines with n-states.

A function for the busy beaver numbers would only tell you that there exists some machine with n states that halts after a certain number of steps. It cannot be used to determine if any specific machine of that size halts or not, just that at least one does and it takes x number of steps.

Hell, it doesn’t even tell you what input would make a machine halt at that many steps only that there is at least one input for which you get that output.

So I think that means—if by some miracle you were able to construct an oracle for the busy beaver numbers—you wouldn’t really solve the halting problem yes? (Again wayy outside my expertise but still fascinating)

I’m definitely not an expert on the topic, but 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.

LIF neurons don’t technically have a finite number of states because their voltage potential is continuous. Similarly, despite the fact they either fire or don’t fire, the synapses between the neurons also work with integration and a decay constant and hence are continuous.

This continuity means that neurons don’t fire at discreet time intervals and—coupled with the fact inputs are typically coded into spike chains with randomness—you get different behavior basically every time you turn the network on.

The curious part is that it can reliably categorize inputs and the fact that inputs are given some amount of noise leads to robust functionality. A paper I read was using a small, 2 layer net to recognize MNIST numbers and were able to remove 50% of their neurons after training and still have a 60% success rate on identifying the numbers.

Anyway, as for your second question, analog computing, including neuromorphic hardware, is continuous since electric current is necessarily continuous (electricity is a wave unfortunately). You are right that other things will add noise to this network, but changes in electric conductivity from heat and/or voltage fluctuations from electromagnetic interference are also both continuous.

Most importantly is that these networks—when not hardcoded—are constantly adapting their weights.

Spike Timing Dependent Plasticity (STDP) is, as it sounds, dependent on spike timing. The weights of synapses are incredibly sensitive to timing so if you have enough noise that a neuron fires before another, even by a very tiny amount, that change in timing changes which neuron is strengthened most. Those tiny changes will add up as the signals propagate through the net. Even for a small network, a amount of noise is likely to change its behavior significantly over enough time. And if you have any recurrence in the net, those tiny fluctuations might continually compound forever.

That is also the best answer I have for your third question. The non-algorithmic part is due to the fact no state of the machine can really be used to predict a future state of the machine because it is continuous and its behavior is heavily dependent on external inherent noise. Both the noise and the tiniest of changes from the continuity can create novel chaotic behavior.

You are right in saying that we can minimize the effects of noise; people have used SNNs to accurately mimic ANNs on neuromorphic hardware for faster compute times, but those networks do not have volatile weights and are built to not be chaotic. If they were non-algorithmic you wouldn’t be able to do gradient descent. The only way to train a truly non-algorithmic net would be to run it.

Anyway the main point of “non-algorithmic” is that you can’t compute it in discrete steps. You couldn’t build a typical computer that can fully simulate the behavior of the system because you’ll lose information if you try to encode a continuous signal discretely. Though I should note, continuity isn’t the only thing that makes something non computable since the busy beaver numbers are incomputable but still entirely discrete and very simple machines.

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. Meaning we could technically build an analog-computer capable of computing an uncomputable/undecidable problem.

This isn’t about simulating atom by atom. It is just saying that there exist pieces of the universe that can’t be simulated.

If we find undecidable aspects of physics (like we have) then they must be part of this simulation. But it’s not possible to simulate those by any step by step program. Ergo, the universe cannot be a simulation.

The use of render optimization tricks has no effect on this.

You can’t even patch it like you said with wiping minds because it would require you to do the undecidable work which can’t be done by any algorithm.

Bro our hyperfixations are slightly aligned, I was thrown into this rabbit hole because I was once again trying to build a formal symbolic language to describe conscious experience using qualia as the atomic formulae for the system. It’s also been giving me lots of fascinating insight and questions about the nature of thought and experience and philosophy in general.

Anyway to answer your question: yes and no.

If you require that the AGI be built using current architecture that is algorithmic then yes, I think the implication holds.

However, I think neuromorphic hardware is able to bypass this limitation. Continuous simultaneous processes interacting with each other are likely non-algorithmic. This is how our brains work. You can get some pretty discrete waves of thoughts through spiking neurons but the complexity arising from recurrence and the lack of discrete time steps makes me think systems built on complex neuromorphic hardware would not be algorithmic and therefore could also achieve AGI.

Good news: spiking neural nets are a bitch to prototype and we can’t train them fast like we can with ANNs so most “AI” is built on ANNs since we can easily do matrix math.

Tbf, I personally don’t think consciousness is necessarily non-algorithmic but that’s a different debate.

Edit: Oh wait, that means the research only proves that you just can’t simulate the universe on a Turing-machine-esque computer yeah?

As long as there are non-algorithmic parts to it, I think a system of some kind could still be producing our universe. I suppose this does mean that you probably can’t intentionally plan or predict the exact course of the “program” so it’s not really a “simulation” but still that does make me feel slightly disappointed in this research.

Meant to reply to you but ended up replying to the main post. I’m only an amateur mathematician but maybe you’ll find my take useful

Disclaimer: an engineering student not a logician. However, one of my recent hyper fixations lead me down the rabbit hole of mathematics specifically to formal logic systems and the languages and semantics of them. So here’s my understanding of the concepts.

TLDR: Undecidable things in physics aren’t capable of being computed by a system based on finite rules and step-by-step processes. This means no algorithm/simulation could be designed to actually run the universe.

A language is comprised of the symbols used in a formal system. A system’s syntax is basically the rules by which you can combine those symbols into valid formulas. While a system’s semantics are what determines the meaning behind those formulas. Axioms are formulas that are “universally valid” meaning they hold true in the system regardless of of the values used within them (think of things the definitions of logical operators like AND and NOT etc)

Gödel’s incompleteness theorems say that any system which is powerful enough to define multiplication is incomplete. This means that you could write a syntactically valid statement which cannot be proven from the axioms of that system even if you were to add more axioms.

Tarski’s undefinability theorem shows that not only can you write statements which cannot be proven true or false, you cannot actually describe the system using itself. Meaning you can’t really define truth unless you do it from outside the formal language you’re using. (I’m still a little fuzzy on this one)

Information-theoretic incompleteness is new to me, but seems to be similar to Gödel’s theorem but with a focus on computation saying that if you have a complex enough system there are functions that won’t be recursively definable. As in you can’t just break it down into smaller parts that can be computed and work upwards to it.

The paper starts by assuming there is a computational formal system which could describe quantum gravity. For this to be the case, the system

• must have a finite set of axioms and rules
• be able to describe arithmetic
• be able to describe all physical phenomena and “resolve all singularities)

Because the language of this system can define arithmetic, Gödel’s theorems apply. This leads to the fact that this system, if it existed, can’t prove that it itself is sound.

I don’t know what it means for the “truth-predicate” of the system to not be defined, but it apparently ties into Chaitan’s work and means that there must exist statements which are undecideable.

Undecidable problems can’t be solved recursively by breaking them into smaller steps first. In other words you can’t build an algorithm that will definitely lead to a yes/no or true/false answer.

All in all this means that no algorithmic theory could actually describe everything. This means you cannot break all of physics down into a finite set of rules that can be used to compute reality. Ergo, we can’t be in a simulation because there are physical phenomena that exist which are impossible to compute.

Thanks, it wasn’t too bad. Like I felt like I generally knew what the questions were asking for, but I didn’t really have time to scan for mistakes so who knows how well I actually did. I hate timed exams.

I wasn’t able to get a refill for last week. This sucked because I had an exam and two major projects to work on. My mother however seemed very happy to learn I wouldn’t be taking meds.

They’re good memes, keep up the good work!

I heard that it might be that they want the traction, like something they can dig their claws into while they convulse

Well that makes non-binary people either Iron-Copper (fitting but lame) or Mercury (less commonly used symbol for non-binary/genderfluid but a pure element)

And it’s powered by love! …also you have to wind it.

Funnily enough the alchemical symbol for Iron is ♂, the symbol for the male gender lol

I think the point is that the emotions of the family trauma are more focused on.

• Snow White in the movie seems like just this kid who this lady really wants to murder. You don’t really see much indicating that she’s been through a rough childhood till that point.
• Cinderella does go deeper into more prolonged torture, but it doesn’t feel like they are family at all. She’s not being gaslit by family members she wants to trust, she’s literally just a slave to these assholes who stole her house.
• Sleeping beauty is more about forbidden love than generational trauma. Both of the dads seem pretty alright if a bit short tempered lol (I need to watch the movie again just for that fight)

This is in contrast to

• Brave focuses on the misunderstanding and miscommunication between parents and children where both can cause each other significant pain/stress without noticing and then those emotions can lead to rash actions damaging relationships
• Moana is similar to brave but also with more added stress of trying to discover who you are when you’ve been repressing that part of yourself due to family pressure
• Frozen is much more focused on that latter emotion but also shows miscommunication between loved ones leading to significant problems neither wanted to cause

Point is there’s a difference between saying something traumatizing happened and focusing on the effects of that traumatic experience. I mean look, half the Disney characters have dead parents so there’s trauma there but that’s not the same as making that trauma a main focus of the story.

Aladdin and Jasmine have dead parents but the film focuses on their desires for “freedom”. Whereas, in Treasure Planet, it shows Jim growing up with an absent father and how that has affected both him and his mother. It also shows him growing fond of a surrogate father figure which becomes a source of internal conflict because that surrogate father figure has significant flaws. The former movie has family trauma; the latter is about family trauma.

Fry: Amy, you know how at first you like chocolate but then you get tired of it because it always wants to hang out with you?

Amy: Huh? You don’t like chocolate?

Fry: Could chocolate just let me finish?

Wait didn’t Reddit have its own .onion domain? I suppose I shouldn’t be surprised by the hypocrisy at this point lol

I had the same thought and I was like damn this person is going to lose those fingers

I know :( the issue is I’m in ME and school is fucking expensive. Oh and I am working in a research lab getting paid for my work, not much though.

I would love nothing more than to stay in school and get like 82 different degrees in various topics. I would love to do a PhD in math, and one in physics, and one in cs, and linguistics, and psychology…

But the world forces me to specialize if I want to have enough money to live well. I chose ME because I knew it had a lot of overlap with a bunch of different fields. And yeah I’m taking grad level math and cs courses, but like you said, lots of the stuff I’m interested in is PhD level stuff.

Also Idk if you’re in America, but the money for research here is getting scarcer every day. It could likely be more effective for me to sell my soul to a defense company and then build my own personal lab with that blood money to do research I want to do than it would be to get a PhD and be a professor and simply hope the projects I want to work on will get funding.

Of course that’s assuming the country doesn’t fully collapse (or kill me) before I enter the job force. And assuming I could work for a defense company without deciding to kill myself out of guilt of building civilian killing murder machines.

Anyway, point is that you are right but I lack the financial security to justify trying to get a PhD in math right now.

Trying to resize encrypted partitions, sweating bullets because I feel like I’ll fuckup and lose everything.

(Yes I am aware I should backup my data I’m simply a poor idiot lol)