A chicken & egg paradox in the claim that the Human Mind predates the Big Bang

[barakman]

Your claim:

The "intelligent impulses" or even "human mind" itself (because a musician can understand these impulses) had existed long before the "Big Bang" happened.

The problem here, is that you are relying on your own "human mind" in order to determine that these pulses are "intelligent".

In other words, based on the fact that your human mind has interpreted these pulses as intelligent, you have concluded that the human mind must be as old as the data with which you have generated them.

So you've essentially used your own claim in order to prove it.

To put this in more precise (and perhaps tedious) details:

• Let M denote the human mind
• Let f(x) denote whether or not x predates the Big Bang
• Let g(x, y) denote whether or not x interprets y as intelligent pulses
• Let h(x) be your hash function

Your claim can subsequently be formulated as:

Which obviously depicts incorrect logical inference.

---

Note that the above (along with your initial claim) doesn't even take into account the fact that there are many human minds - one per person, some would say (although I guess it depends on your personality as well as your local environment).

If we were to rephrase your claim based on the more generalized assumption that different humans have different minds:

Then it wouldn't even adhere to the most basic logical inference.

At best, you could use it in order to claim that some human minds (yours included) have existed before the Big Bang, and of course - that wouldn't actually resolve the logical error; it would only "decay" into the less obvious error described above.

[avaneev]

Oh, so much work on your side, thanks. Please remove "denote whether or not x predates the Big Bang", because initial state of Big Bang is probably formulated with math which means math existed the moment Big Bang happened otherwise one can't use mathematical equations and make a progression. It's a very simple logic yet you added it as a question.

SETI also searches for intelligent life in some way. What blocks your understanding is "evolutionary theory" which is incorrect in my opinion - I'm also a developer of a very powerful evolutionary optimization algorithm BiteOpt. There can be no evolution without specific goal. If specific goal is just to survive, there would be no life beyond amoebas. As simple as that.

[avaneev]

I mean, if you use equations to model "first nanoseconds" of Big Bang, then you are relying on math that exists that moment. If math didn't exist then scientists cannot use math to model Big Bang and a lot of things turn into wordy philosophy.

[avaneev]

So, your equation will transform into analysis of information "generated" by prvhash-1 for intelligence. That's what SETI does as well, it's not pseudo-science. I do not know which criteria SETI uses, I'm not their scientist, so if you are actually curious, ask SETI for hypothesis checks. I assume generated imagery is also an information under question.

[kravening]

I mean, if you use equations to model "first nanoseconds" of Big Bang, then you are relying on math that exists that moment. If math didn't exist then scientists cannot use math to model Big Bang and a lot of things turn into wordy philosophy.

but the model exists 'now' not back then. just because we're able to adjust parameters now, and 'transport' a formula to the past doesn't mean it started existing back then.

[kravening]

So, your equation will transform into analysis of information "generated" by prvhash-1 for intelligence. That's what SETI does as well, it's not pseudo-science. I do not know which criteria SETI uses, I'm not their scientist, so if you are actually curious, ask SETI for hypothesis checks. I assume generated imagery is also an information under question.

this reads as a "appeal to authority" logical fallacy to me.

[avaneev]

this reads as a "appeal to authority" logical fallacy to me.

No, it's "appeal to science of what intelligence is", if you have no idea what intelligence is.

[avaneev]

but the model exists 'now' not back then. just because we're able to adjust parameters now, and 'transport' a formula to the past doesn't mean it started existing back then.

By applying a "model" you implicitly assume that your model corresponds to math rules and physics laws at that time.

[dfischer]

If specific goal is just to survive, there would be no life beyond amoebas. As simple as that.

I've thought about the universe as an algorithim for life. In my really early days of broken philosophizing I wrote it all down in a "stream of consciousness" here -> https://dfischer.keybase.pub/journal/metaphysicsmetamind.txt

In reduced terms, given that you had created a universe 'in a box' that doesn't allow your manifestation of being to enter it, how might you come to know about it? It's laws? It's total space of possibility? We may run into this issue as humans in various scenarios but we can suspend that for the thought experient and just focus on a being that made a box they can't enter, how would you probe it?

It seems 'life' is the perfect algorithim that selects for pathfinding the total coordinate space of all possible paths within a 'universe' as it optimizes for survival which maps a coordinate space over paths that lead to more possibilities potentially exhausting the total space. The core 'parameter' driving the survival trait is a 'hunger/eating trait' which offers both survivability (and path expansion) as well as novelty (more path expansion). So it creates this positive feedback loop. Pacman + Kirby basically.

I was trying to identify a Why and How in this line of thinking. I was motivated by trying to identify an 'irreducible size' to what the algorithim of 'life' would be to fulfill such a pathfinding scenario. It made sense to me at a high level anyway.

Anyway just riffing off of it, not critiquing anything said here. This will probably just end up in the void. Appreciate your work(s) @avaneev - you are a gem.

[dfischer]

I mean, if you use equations to model "first nanoseconds" of Big Bang, then you are relying on math that exists that moment. If math didn't exist then scientists cannot use math to model Big Bang and a lot of things turn into wordy philosophy.

Reminds me of

In the beginning was the Word, and the Word was with God, and the Word was God.

Just makes you go hmm.

It's funny though, proof is a hopeless pursuit, because all axioms are created by will of consensus of minds. We literally assign truth to things and whether or not it is valid based on our own rules of complete imagination.

I guess this is why many people have 'epiphanies' and 'cathartic moments of understanding' and many people just can't relate, and maybe some do to some level, like a dream or such.

[avaneev]

It's funny though, proof is a hopeless pursuit, because all axioms are created by will of consensus of minds.

Well, the better the proof the wider the consensus. For example, take those extracted "christmas trees" from prvhash1. By common mathematical understanding they can only be constructed iteratively, as a fractal geometry (Sierpinski triangle). So, what prvhash1 does is literally impossible to do computationally. Until someone proves it is possible to do on a computer without faking it with external memory storage. It's mind-blowing if someone does not get it. Thanks God I was insane enough to accept that without questions.

[avaneev]

I have not revealed the method yet, but prvhash1 can take "function argument" in a specific form, so one can construct a coloured image:

[avaneev]

In reduced terms, given that you had created a universe 'in a box' that doesn't allow your manifestation of being to enter > it, how might you come to know about it? It's laws?

I've thrown away most theoresizing about "how and why" of Universe and God. Mathematics is a good example a model can have any number of dimensions, progressions, and logic. prvhash1 goes deeper - it kind of proves there are higher things exist even relative to mathematics. I would just live a life no questions asked, it's infinitely better than nothing at all. Ruining it with AI and automation is basically killing the life and Nature since it all will degenerate to 1 human operator operating all other humans, a self-made "godlike".

(sorry, @dfischer I've by accident edited your reply, didn't know GitHub allows to edit replies of other participants)

[kravening]

but the model exists 'now' not back then. just because we're able to adjust parameters now, and 'transport' a formula to the past doesn't mean it started existing back then.

By applying a "model" you implicitly assume that your model corresponds to math rules and physics laws at that time.

yes, assume, exactly. that's what a model is, an assumption, description, but not itself truth.

[kravening]

this reads as a "appeal to authority" logical fallacy to me.

No, it's "appeal to science of what intelligence is", if you have no idea what intelligence is.

same thing, logical fallacy either way. it doesn't hold up.

[avaneev]

No, it's "appeal to science of what intelligence is", if you have no idea what intelligence is.

same thing, logical fallacy either way. it doesn't hold up.

Why it's a fallacy? I'm making an offer to use a scientific method. Or do you mean science is an "authority" that turns into "appeal to authority" in any uncertain situation? I do not know what to reply to you. Okay, let it be logical fallacy in your opinion.

[avaneev]

By applying a "model" you implicitly assume that your model corresponds to math rules and physics laws at that time.

yes, assume, exactly. that's what a model is, an assumption, description, but not itself truth.

It's a very strong assumption that scientists are making. Without that assumption Big Bang and other cosmological views are storytales. Because if physical laws were different 13.8 billion years ago, it's seriously uncertain what they are trying to model. A progression of cosmic photos and radio waves, or the real thing? Note that I'm not debating Big Bang, I'm debating your logic.

[avaneev]

@kravening You also have an option to argumentize the shown graphs are "non-intelligent". I'm actually very interested in your argumentation. I'm open to any such arguments. I will edit the page if a reasonable argument is given. Anyway, not a single word in "proof math is engineered" forces my argumentation on anyone (it consists of observations, "if's" and "probably's"). I've only mentioned that to me personally an "intelligence" of the signals was proven. I'm myself a DSP engineer with close to 20 years of experience, I worked with a lot of intelligent signals produced in the music industry. Then I have no idea how to construct Sierpinski triangle of any size scanline-by-scanline without using any pre-computation, that's also an important argument that the "intelligent design" is behind what prvhash1 produces.

[dfischer]

It's funny though, proof is a hopeless pursuit, because all axioms are created by will of consensus of minds.

Well, the better the proof the wider the consensus. For example, take those extracted "christmas trees" from prvhash1. By common mathematical understanding they can only be constructed iteratively, as a fractal geometry (Sierpinski triangle). So, what prvhash1 does is literally impossible to do computationally. Until someone proves it is possible to do on a computer without faking it with external memory storage. It's mind-blowing if someone does not get it. Thanks God I was insane enough to accept that without questions.

Totally agree. Essentially based on ability to have a shared predictable outcome; which doesn't guarantee one experiences the same reality but can at least converge on the same destination in terms of a coordinate space.

Have you seen:

1. https://github.com/advancedresearch/path_semantics
2. https://www.wolframphysics.org/bulletins/2020/06/exploring-rulial-space-the-case-of-turing-machines/

I think you'd find some interesting things with Sven at AdvancedResearch and the various things he's working on. Path Semantics and the various other projects / papers being discussed there.

So, what prvhash1 does is literally impossible to do computationally.

So there is a school of thought that the human mind and consciousness isn't doing "binary/computation" and to reach what the mind does it is somewhere in the realm of "analog computation" - I've contemplated it deeply and it feels exactly related to frequency, harmonics, standing waves, etc. Cymatics is an area of research that needs a lot more attention.

Essentially there's what feels like another paradigm still waiting to be uncovered around frequency, vibration, shapes - and because there is a consistent geometry within those certain frequency spectrums you get a compositional geometry that already has "built-in" logic because it can only fit together in certain ways like Lego's. So "Universal Abyss of Goo" composed of 'cymatic imprints' generating 'the illusion we experience' is how I've been thinking about it.

So obviously we'd converge here since you've been studying and implementing 'frequency and harmonics' in the consideration of musical applications but it obviously implies a greater order which I think you hit and are reasoning about now.

Anyway, a lot of people get shame for exploring such fringe ideas and topics. Fuck the haters.

Praise those who dare to explore and have the foolishness to escape the grip of dogma within the zeitgeist.

Love what you're thinking about!

Related links:

Jenny made use of crystal oscillators and his so-called tonoscope to set plates and membranes vibrating. He spread quartz sand onto a black drum membrane 60 cm in diameter. The membrane was caused to vibrate by singing loudly through a cardboard pipe, and the sand produced symmetrical Chladni patterns, named after Ernst Chladni, who had discovered this phenomenon in 1787. Low tones resulted in rather simple and clear pictures, while higher tones formed more complex structures.[2]

In 1989, an experimental advance was introduced which produced stable single-bubble sonoluminescence (SBSL).[citation needed] In single-bubble sonoluminescence, a single bubble trapped in an acoustic standing wave emits a pulse of light with each compression of the bubble within the standing wave. This technique allowed a more systematic study of the phenomenon, because it isolated the complex effects into one stable, predictable bubble. It was realized that the temperature inside the bubble was hot enough to melt steel, as seen in an experiment done in 2012; the temperature inside the bubble as it collapsed reached about 12,000 kelvins.[4] Interest in sonoluminescence was renewed when an inner temperature of such a bubble well above one million kelvins was postulated.[5] This temperature is thus far not conclusively proven; rather, recent experiments indicate temperatures around 20,000 K (19,700 °C; 35,500 °F).[6]

1. https://en.wikipedia.org/wiki/Ernst_Chladni (Chladni patterns / figures)
2. https://en.wikipedia.org/wiki/Sonoluminescence
3. https://en.wikipedia.org/wiki/Lissajous_curve (Research into Lissajous curve being a fundamental unit of building a new language / alphabet that uses 3d space as a substrate and not just 2d surfaces which are limited to reading/writing)

[dfischer]

I've thrown away most theoresizing about "how and why" of Universe and God. Mathematics is a good example a model can have any number of dimensions, progressions, and logic. prvhash1 goes deeper - it kind of proves there are higher things exist even relative to mathematics. I would just live a life no questions asked, it's infinitely better than nothing at all. Ruining it with AI and automation is basically killing the life and Nature since it all will degenerate to 1 human operator operating all other humans, a self-made "godlike".

Isn't it all natural and emergent regardless? It's the human "bias" that thinks "AI" is unnatural. Might it hint at a universal intelligence? Who's to say we aren't AI? It's just a biased identity term imo. I'm of course leaning into the thought experiment side of things more than considering it as belief to be exactly true, but I don't find it valuable to believe things, rather that I find it valuable to see that things are the same regardless of what you call it.

degenerate to 1 human operator operating all other humans, a self-made "godlike".

That's pretty much the most ancient universal mythology across the globe spanning cultures that allegedly never even communicated with one another. One of the oldest written accounts describing such a thing is the Vedas and Brahman: https://en.wikipedia.org/wiki/Brahman

Just a little funny how well these things map to the same ideas. Universe / Simulation / Illusion / Frequency / Networks / Instances / Firewall / Path-finding / Coordination

[dfischer]

I have not revealed the method yet, but prvhash1 can take "function argument" in a specific form, so one can construct a coloured image:

This is fascinating in regard to compositional pieces of code that resemble a geometry. I was researching this heavily for a while. It's very interesting because it has profound implications on computation and storage/space beside other things. Very interested!

Are you familiar with https://esolangs.org/wiki/Piet - similar ideas in that space but there's a lot more to expand on.

[dfischer]

By applying a "model" you implicitly assume that your model corresponds to math rules and physics laws at that time.

This is one of the more distrubing dogmas of our time because what we're seeing is effectively a matrix being built around 'models' that are dogmatically true and like a self-fulfilling prophecy a vaneer of reality gets erected around those rules when reinforced by technology implementing those rules as objectively true; and when those technologies redefine what reality is and how it is literally rendered as we integrate more and more of it... then we effectively live in a simulacrum which sadly prevents further probing into actual reality because the inertia and confidence surrounding such models become co-dependent with the frame of reference for reality. End result is that one doesn't even see that they are blind.

Perhaps we'll be able to make balance with the dogma. It got pretty bad as of a year ago but there is a slight shift in the tide towards awareness over models/statistics dictating reality.

[bvssvni]

Sven here. You might find this paper interesting Consciousness in Wolfram Models. For the reading sequence, click here.

Basically, when the hypergraph rewriting happens, the awareness or mind generated experience is like a "button push" on the nodes that get matched against the rule. Each node is only "pushed" once, so when a rule matches different nodes, it generates more consciousness on average than when matching the same node multiple times.

[avaneev]

Sorry, I'm not much keen discussing philosophies. This topic is about proving/disproving "intelligence" behind prvhash1. For example, I'll be much interested to hear arguments about constructing Sierpinski triangle. There's more to it: during output of proof_christmas_tree one can notice that further levels become bit-shifted to the right. They create a seamsless larger image (as shown) if sub-images are attached to each other from the right side right, and in two rows. For a programmer, it's just an essence of intelligent design. Literally, sub-image A contains elements of sub-image B. It's exactly as written - "reading" information from "some source". Please do not downplay these observations with philosophy talks. My work is not about philosophy.

[dfischer]

Sorry, I'm not much keen discussing philosophies. This topic is about proving/disproving "intelligence" behind prvhash1. For example, I'll be much interested to hear arguments about constructing Sierpinski triangle. There's more to it: during output of proof_christmas_tree one can notice that further levels become bit-shifted to the right. They create a seamsless larger image (as shown) if sub-images are attached to each other from the right side right, and in two rows. For a programmer, it's just an essence of intelligent design. Literally, sub-image A contains elements of sub-image B. It's exactly as written - "reading" information from "some source". Please do not downplay these observations with philosophy talks. My work is not about philosophy.

Philosophy is the beginning of a logical discussion. Alas, you too, are dismissive. Oh well. Good luck!

"Downplay with philosophy talks" - don't forget about the forest as you pass by a tree.

@bvssvni shared https://github.com/advancedresearch/path_semantics/blob/master/sequences.md#consciousness-in-wolfram-models which is related to your discussion and insights and you didn't do as much as anything else as be dismissive when others are engaging at communicating towards finding a common ground. The common ground here is literally everything so, forgive me for attempting to share some philosophy as an attempt to align the fuckin' universe as an ontology to make sense of.

Why even try?

[avaneev]

You won't align anything until you can show a computer program that generates Serpinski triangle the same way prvhash1 produces. There's just no connection between two realities, nothing to discuss.

[bvssvni]

Not sure if this is relevant, but I have a working space-time solver for Rule 110 (which is proven to be Turing complete): https://github.com/advancedresearch/quickbacktrack/blob/master/examples/rule_110.rs

E.g. if one has some knowledge about the output (across any moment in space-time), then the solver can produce some initial conditions (if possible) that generates that space-time.

Wolfram also experimented with generating Sierpinski triangles in his early research on cellular automata. The model for fundamental physics is hypergraph rewriting. I participated in the Wolfram Winter School a few years back.

Wolfram hypothesized that there are rules that are very simple yet Turing complete. This was later proven mathematically. Other rules can generate periodic patterns such the Sierpinski triangle. However, it does not prove that the universe had a creator or intelligent mind behind it. On the contrary, it makes it more likely that the early universe might be thought of some unintelligent process. The rest is observer selection effects, which in an eternally inflating space-time (from inflationary cosmology) can be extreme. The problem is to explain how the universe can be this normal when we expect a-priori to be "freak observers".

I am focusing on extending logic with a "qubit" operator ~ that has congruence up to tautological identity only, which in the classical implementation uses randomness. See Pocket-Prover. Based on this research and other topics, I am hypothesizing that consciousness can be simplified in physics by making various assumptions that fit general hypergraph rewriting. I suggest that there is a very simple way of extending the semantics of hypergraph rewriting that aligns with the intuition of how consciousness works.

The actual precise model of consciousness is likely to be much more complex and hidden, due to extreme observer selection effects across Everett branches in the multiverse. On top of that, we have cultural biases that sets arbitrary boundaries for consciousness, which obscures the problem.

I have no intention to discuss philosophy here. If you read the paper, you'll see it is about a making various assumptions and whether they are reasonable. Ofc my research is backed by serious philosophy (I've studied ideas of Hegel, Heidegger, Zizek among the modern philosophers in philosophy reading groups), but my point is since @dfischer thought that there was some relevance between my work and yours, it would be worth checking it up.

[avaneev]

Please, no philosophy here, you are just ruining the topic obviously. If you can create Sierpinski fractal like prvhash1 does - show me, do not hypothesize that "simple algorithms can create some visual forms", that's true, but irrelevant. It is known how to create Sierpinski fractal in human programming/mathematical terms. Show me an easier way to create it, like somebody is holding an algorithm complexity competition.

[bvssvni]

Rule 60, 90 and 102 produces the Sierpinski triangle according to https://mathworld.wolfram.com/SierpinskiSieve.html

I think it is very hard to beat this in an algorithm complexity competition.

Notice that Rule 110 is more interesting, as it is Turing complete.

Also, you made a small error as I never hypothesized "simple algorithms can create some visual forms". I hypothesize that a simple extension of the semantics of general hypergraph rewriting aligns with the intuition of how consciousness works in fundamental physics under reasonable assumptions which might be yield very accurate predictions assuming the correct Wolfram model is known for our universe (computationally).

[avaneev]

"Consciousness" is a philosophical category, I have no information it was physically measured and mathematically quantified.

About those "rules". They are logical. prvhash1 is completely linear. I hope you understand this important distinction. What prvhash1 does is simply not possible in our reality. And I would like to hear your arguments against.

[bvssvni]

By linear, do you mean that there is no CPU branching? Pocket-Prover does classical propositional calculus using 64 bit patterns (to exploit 64bit CPUs speedup) and hence there is no branching in classical theorems. I'll take a closer look at your code.

(btw, we have some data about consciousness even it's vague which corresponds to "consciousness is centered somewhere inside the skull". Some theories, like IITC, try to describe a scalar field measuring its density. I am trying to make progress toward making this more precise in fundamental physics)

[avaneev]

By linear, do you mean that there is no CPU branching? Pocket-Prover does classical propositional calculus using 64 bit patterns (to exploit 64bit CPUs speedup) and hence there is no branching in classical theorems. I'll take a closer look at your code. I do not mean branching, I literally mean LTI system - note that it is better analyzed in DSP terms. If some code you are referring contains e.g. AND logical operation, it's not linear. XOR is linear.

[barakman]

By linear, do you mean that there is no CPU branching? Pocket-Prover does classical propositional calculus using 64 bit patterns (to exploit 64bit CPUs speedup) and hence there is no branching in classical theorems. I'll take a closer look at your code. I do not mean branching, I literally mean LTI system - note that it is better analyzed in DSP terms. If some code you are referring contains e.g. AND logical operation, it's not linear. XOR is linear.

Logical AND ==> Branching.

[bvssvni]

I was able to translate "proof_christmas_tree.c" to Rust:

const PH_HASH_COUNT: usize = 200;
const READ_MODE: u8 = 1; // 0 or 1
const READ_WIDTH: usize = PH_HASH_COUNT + 1;
const READ_HEIGHT: usize = READ_WIDTH * 32;

pub fn prvhash_core1(
    seed: &mut u8,
    lcg: &mut u8,
    hash: &mut u8,
) -> bool {
    *hash ^= *seed ^ 0x1;
    *lcg ^= *seed ^ READ_MODE;
    let out: u8 = *lcg ^ *seed;
    *seed ^= *hash;
    (out & 1) == 1
}

fn main() {
    let mut seed: u8 = 0;
    let mut lcg: u8 = 0;
    let mut hash = [0; PH_HASH_COUNT];
    let mut hash_pos: usize = 0;

    let mut i = 0;
    // Remove pixel offset
    loop {
        if i < PH_HASH_COUNT + 2 {break}

        prvhash_core1(&mut seed, &mut lcg, &mut hash[hash_pos]);
        hash_pos += 1;
        if hash_pos == PH_HASH_COUNT {hash_pos = 0};

        i += 1;
    }

    for _ in 0..READ_HEIGHT {
        for _ in 0..READ_WIDTH {
            if prvhash_core1(&mut seed, &mut lcg, &mut hash[hash_pos]) {
                print!("0");
            } else {
                print!(" ");
            }
            hash_pos += 1;
            if hash_pos == PH_HASH_COUNT {hash_pos = 0};
        }
        print!("\n");
    }
}

[bvssvni]

I've extracted a truth table for the read and mutated seed, lcg value:

seed  lcg  hash  out   !lcg   seed'  !hash  lcg' (seed==lcg)
0     0    0     1     1      1      1      1    1
0     0    1     1     1      0      0      1    1
0     1    0     0     0      1      1      0    0
0     1    1     0     0      0      0      0    0
1     0    0     1     1      1      1      0    0
1     0    1     1     1      0      0      0    0
1     1    0     0     0      1      1      1    1
1     1    1     0     0      0      0      1    1

[bvssvni]

Based on the truth table, I can simplify prvhash_core1:

pub fn prvhash_core1(
    seed: bool,
    lcg: bool,
    hash: bool,
) -> (bool, bool, bool) {
    (
        !hash,
        seed == lcg,
        seed == hash
    )
}

I can see form the code that prvhash_core1 would be symmetric (had it not mutated arguments) in the two last arguments:

prvhash_core1(x, a, b) == prvhash_core1(x, b, a)

[bvssvni]

The way READ_WIDTH increases PH_HASH_COUNT with 1 makes the hash vector rotate. You are transferring the context using this rotation. What you get is the analogy of cellular automata where the state, instead of being encoded directly in previous row, is indirectly encoded in the neighboring cells, which in turn depends on the previous row.

I am not certain about what you mean this is not possible in our reality. The prvhash_core1 is 100% logical.

I believe you can substitute with a cellular automata of some Rule X in Wolfram code, perhaps with the added constraint that some initial neighbor cell must start with some fixed configuration. So far, it seems to me the reason you are thinking along these directions are of the same motivation that Wolfram had in early research on cellular automata.

[bvssvni]

Here is the inverse:

pub fn prvhash_core1_inv(
    seed: bool,
    lcg: bool,
    hash: bool,
) -> (bool, bool, bool) {
    (
        seed != hash,
        (seed != hash) == lcg,
        !seed,
    )
}

[avaneev]

@bvssvni I do not understand what you are trying to do. do your transformations produce the same "christmas trees"? prvhash1 uses "feedback delay line" known in DSP, but in binary form. If you do not know DSP, you'll not quite understand it. While it may seem "non-linear", it's really is a linear operation. It's how artificial reverberators work.

[bvssvni]

Yes, I get the same "christmas tree". I am currently trying to find the equivalent Rule X in Wolfram code.

[bvssvni]

It's Rule 217.

[avaneev]

Not even close, visually. If you mean this: http://atlas.wolfram.com/01/01/217/

[bvssvni]

/// ```text
/// 111 110 101 100 011 010 001 000
///  1   1   0   1   1   0   0   1
/// ```
pub fn rule(a: bool, b: bool, c: bool) -> bool {
    match (a, b, c) {
        (false, false, false) => true,
        (false, false, true) => false,
        (false, true, false) => false,
        (false, true, true) => true,
        (true, false, false) => true,
        (true, false, true) => false,
        (true, true, false) => false,
        (true, true, true) => true,
    }
}

[bvssvni]

It could be Rule 38 if the boundary conditions and colors are reversed: http://atlas.wolfram.com/01/01/38/

[bvssvni]

pub fn sierpinski() {
    const n: usize = READ_WIDTH;
    let mut old_state = [false; n];
    let mut state = [false; n];
    old_state[0] = true;
    for k in 0..n {
        print!("{}", if old_state[k] {"o"} else {"-"});
    }
    println!("");
    for i in 0..READ_HEIGHT {
        for k in 0..n {
            state[k] = rule(
                if k == 0 {false} else {old_state[(k + n - 1) % n]},
                old_state[k],
                if k + 1 == n {false} else {old_state[(k + 1) % n]},
            );
            print!("{}", if state[k] {"o"} else {"-"});
        }
        old_state = state.clone();
        println!("");
    }
}

[bvssvni]

Output:

o----------------------------------------
-oooooooooooooooooooooooooooooooooooooooo
-ooooooooooooooooooooooooooooooooooooooo-
-oooooooooooooooooooooooooooooooooooooo-o
-ooooooooooooooooooooooooooooooooooooo---
-oooooooooooooooooooooooooooooooooooo-ooo
-ooooooooooooooooooooooooooooooooooo--oo-
-oooooooooooooooooooooooooooooooooo-o-o-o
-ooooooooooooooooooooooooooooooooo-------
-oooooooooooooooooooooooooooooooo-ooooooo
-ooooooooooooooooooooooooooooooo--oooooo-
-oooooooooooooooooooooooooooooo-o-ooooo-o
-ooooooooooooooooooooooooooooo----oooo---
-oooooooooooooooooooooooooooo-ooo-ooo-ooo
-ooooooooooooooooooooooooooo--oo--oo--oo-
-oooooooooooooooooooooooooo-o-o-o-o-o-o-o
-ooooooooooooooooooooooooo---------------
-oooooooooooooooooooooooo-ooooooooooooooo
-ooooooooooooooooooooooo--oooooooooooooo-
-oooooooooooooooooooooo-o-ooooooooooooo-o
-ooooooooooooooooooooo----oooooooooooo---
-oooooooooooooooooooo-ooo-ooooooooooo-ooo
-ooooooooooooooooooo--oo--oooooooooo--oo-
-oooooooooooooooooo-o-o-o-ooooooooo-o-o-o
-ooooooooooooooooo--------oooooooo-------
-oooooooooooooooo-ooooooo-ooooooo-ooooooo
-ooooooooooooooo--oooooo--oooooo--oooooo-
-oooooooooooooo-o-ooooo-o-ooooo-o-ooooo-o
-ooooooooooooo----oooo----oooo----oooo---
-oooooooooooo-ooo-ooo-ooo-ooo-ooo-ooo-ooo
-ooooooooooo--oo--oo--oo--oo--oo--oo--oo-
-oooooooooo-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o
-ooooooooo-------------------------------
-oooooooo-ooooooooooooooooooooooooooooooo
-ooooooo--oooooooooooooooooooooooooooooo-
-oooooo-o-ooooooooooooooooooooooooooooo-o
-ooooo----oooooooooooooooooooooooooooo---
-oooo-ooo-ooooooooooooooooooooooooooo-ooo
-ooo--oo--oooooooooooooooooooooooooo--oo-
-oo-o-o-o-ooooooooooooooooooooooooo-o-o-o
-o--------oooooooooooooooooooooooo-------
--ooooooo-ooooooooooooooooooooooo-ooooooo

prvhash_core1:

o----------------------------------------
-oooooooooooooooooooooooooooooooooooooooo
-ooooooooooooooooooooooooooooooooooooooo-
-oooooooooooooooooooooooooooooooooooooo-o
-ooooooooooooooooooooooooooooooooooooo---
-oooooooooooooooooooooooooooooooooooo-ooo
-ooooooooooooooooooooooooooooooooooo--oo-
-oooooooooooooooooooooooooooooooooo-o-o-o
-ooooooooooooooooooooooooooooooooo-------
-oooooooooooooooooooooooooooooooo-ooooooo
-ooooooooooooooooooooooooooooooo--oooooo-
-oooooooooooooooooooooooooooooo-o-ooooo-o
-ooooooooooooooooooooooooooooo----oooo---
-oooooooooooooooooooooooooooo-ooo-ooo-ooo
-ooooooooooooooooooooooooooo--oo--oo--oo-
-oooooooooooooooooooooooooo-o-o-o-o-o-o-o
-ooooooooooooooooooooooooo---------------
-oooooooooooooooooooooooo-ooooooooooooooo
-ooooooooooooooooooooooo--oooooooooooooo-
-oooooooooooooooooooooo-o-ooooooooooooo-o
-ooooooooooooooooooooo----oooooooooooo---
-oooooooooooooooooooo-ooo-ooooooooooo-ooo
-ooooooooooooooooooo--oo--oooooooooo--oo-
-oooooooooooooooooo-o-o-o-ooooooooo-o-o-o
-ooooooooooooooooo--------oooooooo-------
-oooooooooooooooo-ooooooo-ooooooo-ooooooo
-ooooooooooooooo--oooooo--oooooo--oooooo-
-oooooooooooooo-o-ooooo-o-ooooo-o-ooooo-o
-ooooooooooooo----oooo----oooo----oooo---
-oooooooooooo-ooo-ooo-ooo-ooo-ooo-ooo-ooo
-ooooooooooo--oo--oo--oo--oo--oo--oo--oo-
-oooooooooo-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o
-ooooooooo-------------------------------
-oooooooo-ooooooooooooooooooooooooooooooo
-ooooooo--oooooooooooooooooooooooooooooo-
-oooooo-o-ooooooooooooooooooooooooooooo-o
-ooooo----oooooooooooooooooooooooooooo---
-oooo-ooo-ooooooooooooooooooooooooooo-ooo
-ooo--oo--oooooooooooooooooooooooooo--oo-
-oo-o-o-o-ooooooooooooooooooooooooo-o-o-o
-o--------oooooooooooooooooooooooo-------

sierpinski prints an extra line.

[bvssvni]

The reason you don't get the same visual is because the Wolfram code is usually evaluated with circle topology, while in your case you have a boundary condition.

[avaneev]

Well, you just made everyone's life harder, because you proved this construct is both linear and non-linear. Think further, it's entertaining.

[bvssvni]

@avaneev Why are you so negative? That's just being emotionally abusive.

I have proved that I can reproduce the output using a Wolfram code with a boundary condition. Further work is to establish whether there exists a circle topology with that boundary for some finite range of output.

[avaneev]

I'm just projecting my negativity I've received from a lot of people so far. I do not really care what anyone finds from now on, I won't change my project page as asked by many insisting I'm "insane".

[bvssvni]

@avaneev I think you owe me an apology.

Don't take it hard. Everyone who learns that what they once thought was correct, actually was wrong, think they've found God until they really start to understand what is going on. It's a long journey, my friend.

If there does not exist a circle topology with this boundary condition, then it could be the reason why you get a Sierpinski triangle with a linear DSP operator. It might seem surprising, but from the perspective of this linear operator the empty surrounding space is some kind of "existential paradox" that leaks in through the future space-time cone. This could be the reason that you thought that this was impossible in reality.