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- เผยแพร่เมื่อ 22 มิ.ย. 2024
- If you are completely new to programming, you may face issues while trying to recreate the results in the video. In that case, copy & paste the code from this repo:
github.com/hunar4321/mandelbrot
If you still have problems, then this universe is set up against you becoming a programmer. Congratulations! It is your lucky universe and you are going to live a life free from bugs ;)
Note: The canonical way to code Mandelbrot is to use complex numbers which results in a more elegant equation, however, this will require using an external library and also introduction to complex numbers which overall makes the video longer and harder to follow.
Other related videos:
Artificial Life Simulation: • Create Artificial Life...
Local & Global Maxima: • Who Wins in a Simulati...
Watch the entire Mandelbrot zoom from Math Town Channel: • Eye of the World - Man...
Music used in this video:
Ivan Torrent - Afterlife (feat. Celica Soldream): • Ivan Torrent - Afterli...
Death Note - Low of Solipsism
Nico Staf - Fast and Run
Godmode - To Pass Time
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Topics:
00:00 Wolfram Physics Project
01:50 Mandelbrot Code Walk-through
06:00 The Mandelbrot Universe
09:25 A Simulated Reality
#simulation #Mandelbrot #wolfram #programming
fractals, Mandelbrot, cellular automata, particle life, game of life, simulation hypothesis, big bang,
quantum mechanics, entanglement, bell's theorem, determinism, theory of everything, free will, the matrix, existential crisis
Wolfram Physics Project
Programming, JavaScript
Bell's Theorem, Determinism, Causality, Non-Locality, Realism - วิทยาศาสตร์และเทคโนโลยี
Hey. So I spent a lot of time studying the Wolfram Model and prior to that, Complexity Theory. Politely saying this: There *are* some analogies that are wrong here...or rather outdated in relation to the Wolfram Model, which I can clear up.
The Wolfram model as it was presented in 2020, has since been revised. It's no longer about "the one rule" that governs the universe. The reason for this, has to deal with how this mechanism works, and it follows the below line of reasoning :
A Turing machine, is a machine that will compute all computable functions at infinite time, on an infinite tape. One of the things Wolfram showed, is that very simple rules can create Turing Universal behavior. Therefor if one were to run a Turing universal rule like 110, then rule 110 given enough time on an infinite tape, will compute all computable functions, including the other elementary cellular automata (rules 0-255)... and of course the entire universe.
Consider the following question, that if you did have one rule running at the lowest level of the universe, would it matter what rule you actually picked if all rules are computationally equivalent to one another? If almost all rules are capable of being Turing machines, with the ability to run all possible rules, then it doesn't matter what rule is actually at the bottom.
Wolfram realized this some time in 2021, and placed more focus on the notion that what's important is the Ruliad, rather than "the one rule" because in actuality, the universe isn't just one rule, it *is* running all possible rules... The Ruliad being the abstraction of a Turing machines rule-space.
Stated more precisely : *If the one rule at the bottom is Turing universal, then the universe is running all possible rules...if almost all rules are computationally equivalent, then all rules are universal and capable of creating a universe of all possible rules.*
The above statement is actually the elegant beauty of the model...The Ruliad is a self-referential object...capable of creating everything, with basically everything. It sounds whimsical with it's name, but it's just the object with which one permutes the statespace/rulespace of a finite turing machine. Like the 100x100 grid, you can just permute it and every configuration of the grid is obviously isomorphic to every other state of the grid. So a 100x100 image of the Mandelbrot set, is equivalent to a 100x100 image of Mario from Mario Party and equivalent to a homogenous grid of white squares...all that's needed to go between the three is a mapping of the three states, and thus there is a function (a rule) that can take you from one configuration to the other, and these rules share in this isomorphism of the state-space.
One more thing to mention. Notice how I said "all rules" rather than "most rules." Wolfram's Principle of Computational Equivalence clearly state that rules that "aren't obviously simple" will be computationally universal. The reason for this language in that principle, is that it is working within the confines of what current proofs of universality are...but there is strong reason to believe that the way we define the proof for Turing Completeness is not a good enough definition for universality.
Currently how mainstream physics define Turing completeness is that a system has to emulate another Turing universal system. Mainstream physics has limitations on this proof because all systems given infinite time or with an arbitrarily complex initial condition will be Turing Complete, and simulate some other system. So mainstream physics omits infinite time or an infinitely complex initial condition as a proof of completeness since all rules would be complete like this. Rule 0 for example generates only white squares. But given a specific initial condition, Rule 0 can calculate all computable functions in the first time step, prior to collapsing to all white in the next step if that initial condition was of course, the configuration of all possible computed functions. There is a paper by Jurgen Riedel called "Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Universality" which states this problem, and that the way one should see universality, is of course on a spectrum, like the problem alludes to as being a solution that satisfies the Principle Computational Equivalence as an absolute.
Thanks for your comment. I agree, some examples are outdated in relation to Wolfram's newer model. My aim here was to generate interest and showcase creating complex structures from simple rules in a fun and accessible way.
Wolfram's newer models are better expressed using hyper-graphs instead of Mandelbrot or simple cellular automata.
The concept of infinity is a tricky concept. A universe of all possible rules will imply that eventually everyone is right including all religions! It may also clear up the determinism vs non-determinism argument. But "Infinite possibilities" is a non-falsifiable non-testable concept.
I would love to hear your take about Local Realism & Local Hidden Variables as you know the recent Nobel prize was about Bell's theorem which points to violation of Local Realism.
@@brainxyz Hey, thanks for the reply. I’m really glad your shining some attention on the subject actually! I just wanted to clear up things because the wolfram physics project is still a work in progress by Wolfram and his collaborators, and the subject matter can be confusing cause it involves science most people aren’t fully aware of (complex systems for example)
I wanted to say a couple things; the first thing is that I think the way you illustrate the Wolfram Model is perfectly okay. The 2d cellular automata is a great way and probably the most intuitive way to show how it works. The Hypergraphs used in the model are constructs from complex systems and network theory, but more importantly the Wolfram Model is fundamentally a description of metamathematics…meaning you can construct the wolfram model with any kind of computational system where mathematics and the hypergraphs is one such form of many forms of computation. Wolfram has very long videos and papers on the Metamathematics part of his model, and it’s worth looking into that too because it’s very interesting.
2nd thing I wanted to mention is that you are absolutely on point with the religion think. This is exactly the implication of the model…that because of how this mechanism works, all religion and all physics are realized (and this is not so surprising given that the multi-verse in other TOE's imply the same thing). How that happens in the model is actually really cool, but it can be a bit hard to see why without a background in Complex Systems and Computational Complexity. But essentially it boils down to the same explanation as the initial comment, which is that the state-space of the universe is essentially just being permuted (given that the universe has a finite number of elements, will reoccur). And the Ruliad functions as the permutation group of its rule space. It’s inferred that all possible physics in this model is realized via a selection process (consistent with evolution), where at the bottom all physics is being “constructed” but because most rules collapse to a statistical equilibrium state, what we see as visible physics are the structures that persist from the previous levels below it.
There is a very cool experiment you can do to show this in action and it would be really cool if you did it to show others because it’s truly mind blowing: take a random initial configuration of game of life. The game of life will almost instantly collapse to a statistically neutral state…some cells are alive and others are dead and automatons move around consuming the dead cells. But then go and do a coarse graining of this state of the game of life, by blurring it by about a factor of 5x-10x. What you will see is that the state of this game turns into something complete foreign to the rules below it…in fact it looks like a quantum mechanical soup, where little blobs teleport around and do things that look nothing like the rules below it. This is the Wolfram Models principles in action, showing how the rules “above” in this coarse graining is following some new set of rules then the rules below…and that what constitutes this new behavior is the statistical average behavior of those rules at the bottom. This behavior goes up and up so if you were to coarse grain, the coarse graining (100x blurring) you’d see NEW behavior on top of that coarse grained layer of the initial game. I actually made a video of this myself i just never exported it out...i might just email it to you, but i would definetly encourage trying it out yourself, my computer ain’t strong enough to create a large enough initial condition to coarse grain higher than 10x unfortunate but you might have better luck as a programmer.
Final thing: the bell inequality thing, the Wolfram model doesn’t conflict with this discovery, rather the Wolfram Model requires entanglement to be real in that model. This is way to deep to explain in a short comment, but in short there’s no conflict there, and it’s actually a good thing that objective realism doesn’t exist. In the Wolfram Model, objective properties are created by subjective relationships between things…like the game of life example above.
sorry for the sloppy comment and late reply here I’m just on a phone. It’s been a busy week for me
Cheers,
@@NightmareCourtPictures Thanks for the thoughtful comment. I always like your analogies and the way you are explaining it. The coarse gaining experiment in game of life by blurring the lower levels is very interesting. I made some experiments with Artificial Particle Life which is somewhat similar to game of life but it uses attraction & repulsion rules and looks further than just the neighboring cells. The emerging patterns are really interesting. When particles aggregate to form a stable shape, the entire stable shape now acts like a bigger more complex particle that attracts or repels other bigger shapes according to new emerging attraction & repulsion rules.
@@NightmareCourtPictures
Hey man, I enjoyed reading your comment. Here are just some shower thoughts:
"this new behavior is the statistical average behavior of those rules at the bottom" I believe this principle can be applied to gravity since our current "rules" (relativity in this case) fall apart at quantum scales (the rules below) and at galactic scales (the rules above). The latter is currently explained by dark matter, however no proof has been found for it's existence despite extensive research and in my opinion it's kind of the "easy" answer to a hard problem. A similar phenomena can be observed in thermodynamics where the average kinetic energy of a system defines it's temperature .
While temperature can be described by rules itself, these rules emerged from the individual rules particles obey. Quantum Field Theory does the same thing describing the rules that space time emerged from (excluding gravity).
Entropic Gravity is something worth locking into more closely in my opinion.
However here is the real question to ask: is there a rule that describes how rules evolve, so that if you know one rule you could know every other rule, above or below, that is a consequence of the given rule?
Am I crazy to assume that this somewhat touches the P-NP Problem?
Ever since I heard about Wolframs physics project at Lex Friedman's podcast, I am convinced that if there is a way to answer such fundamental questions, the direction Wolfram is taking is the right one.
Thoughts?
@@NightmareCourtPictures great thread guys, many new things for me. I love it! One little thing regarding the last paragraph. I cannot imagine how you discuss about objective reality and ontology in general, as those things have relation with consciousness right? I mean objective reality means to consider that something exists independently regardless of any subjective perception. I understand the relations part etc but not the things that require subjects. Can you please explain ?
What an incredible mixture of programming, CS, math, cosmology, physics, philosophy and humor.. masterpiece!
... and BS. You forgot to mention a thick layer of complete BS on top of all that.
Btw, math is pretty simple. It's hust that we aren't used to see complex structures out of simple math.
@@DimaZheludko ummmmm jealouuuss
His accent gives a really good charm on his humor
@@scrung A simple mandelbrot introduction + pre-rendered mandelbrot + some simplistic pseudo-philosophical gibberish. The philosophical part contains both true banalities as well as unfounded assumptions stated as true.
Production is ok, I guess. Time spent to produce this is significant.
Do you really thing there is something to be jealous of? What exactly?
@@DimaZheludko cope jealous
To add more colour, try replacing the if(H)... line with:
red = (Math.sin((t-85)/20)+1)/2
green = (Math.sin((t-170)/20)+1)/2
blue = (Math.sin((t-255)/20)+1)/2
if(H){atom(x,y,"rgb(" + t*red + "," + t*green + "," + t*blue + ")"); break}
It takes longer to load the images, but the higher-scale ones look amazing!
Is everyone sure he’s got the exact code down there? I copied it line for line exactly, and it is going through up to a point (the pill shape), then after that it’s not working. I tried the exact same thing, all I get is a black screen. :/
I tried both his version and yours…
@@greatsol2444 Did you make sure that the code now ends with THREE closing curly braces (}}})? It gets changed from two to three at this point in the video.
Thanks for the nice addition.
I also want to add that to zoom very far, one must increase the number of the time steps from 200 to 2000 to get sharper images (the more, the better but that'll increase the time to render dramatically).
For those who are following the code but stuck with problems, you can check your code with the one provided in the description section.
Best Regards
@@gary.h.turner BRILLIANT. Thanks guys, but I got it! Haha, I recommend noobs don’t do this whilst half asleep at 3am… I had put H = d200. Astounding- that these mathematical phrases make these creations! Beautiful.
Move the color calculation into the if(H) statement, since it's only executed once as the loop breaks afterwards. This makes it perform as fast as in the video (you are currently calculating the values n times, but only need them once and disregard the other n - 1 calculations immediately), i.e.,
for (let y = 1; y < 1000; y++) {
for (let x = 1; x < 1000; x++) {
const dx = (x - 500) / 2000 - 0.12;
const dy = (y - 500) / 2000 - 0.82;
let a = dx;
let b = dy;
for (let t = 1; t < 200; t++) {
const d = (a * a) - (b * b) + dx;
b = 2 * (a * b) + dy;
a = d;
if (d > 200) {
const red = (Math.sin((t - 85) / 20) + 1) / 2;
const green = (Math.sin((t - 170) / 20) + 1) / 2;
const blue = (Math.sin((t - 255) / 20) + 1) / 2;
atom(x, y, `rgb(${t * red}, ${t * green}, ${t * blue})`);
break;
}
}
}
}
this is simply incredible, creating such things with tiny amounts of code like that is actually insane
Yes and no - it is elegant and short (I wanted to add nice but the formatting is terrible :D). But that's what software developers (should) do daily. I mean those who are not paid by number of lines. Great video!
It is also 2 dimensional, limited, and an illusion. It's pretty. But it's not serving anything. It only proves a greater intelligence - Jesus Christ. Look up super string holographic theory and then read the first part of the Bible where it says the Word is God (Jesus) and that He spoke things into existence.
Words = vibration.
He is real.
I made it to about 2min and had to rage-quit. There's too many false dichotomies. Math is created to explain reality. Computers operate entirely on math. It's just one after another after another, I assume this continues throughout the whole video.
Creating Some-Thing from No-Thing is even more incredible, yet here *We Are*
Much Ado About No-Thing indeed.
@@jacknov5525 Those who pay depending on the number of lines probably end up with something like Yander Simulator kind of code
You absolutely need to do something with the Feigenbaum constant / logistic map next, your format is AMAZING for truly conveying the beauty of math. Your videos always leave me awestruck.
I almost never post comments but now i just have to say that this video is amazing, even this headphone microphone adds to the climate. It feels like the best school presentation ever. Can’t wait to see more of your content.
The death note music in the background 😂
man, idk but you just hit a sweet spot with the pace, your humor, the music, i don’t even know but I LOVE the flow, the whole thing just clicks, keep on making videos!!
It looks that everyone who watched the video up to the 1:40 mark chose the blue pill despite my warning! (I know this from TH-cam analytics).
Now let’s talk about free will. If you can’t resist your curiosity, how can you resist all the other pressing life issues?
There are two aspects of free will:
1) subjective free will and 2) objective free will.
As a Neuroscientist, I can grant that you have subjective free will.
The big question is whether there is objective free will or not. If there is a model that can predict our future actions with a perfect score, then we live in a deterministic world and hardly have objective free will.
Some studies showcased the ability to predict human behavior from brain signals even before a person has a conscious feeling about their decision, but these results are highly interpretable.
A non-deterministic world doesn’t grant you objective free will by default, but if there is true underlying randomness, things can get a bit more interesting and mystical. In such a world, our conscious interference might contribute to shaping the future of our world.
The non-deterministic world is championed by Quantum Mechanics which describes atomic behaviors in terms of probabilities & wave functions. However, some physicists, including Einstein, believed there are more fundamental deterministic underlying rules that govern the non-deterministic Quantum behaviors. For example, think about an Alien race visiting earth. Their analyst expects the height of the first human they encounter to be 170(+-30)cm (or a normal distribution centered around 170cm with a variance of 30). With their current model, the Aliens can’t predict the exact height of their first human encounter until they meet one. So their best estimates are probabilities, but we know they can't predict the exact height of their first encounter because of the lack of formation not because humans don't have definite heights.
The argument can go the other way too. A deterministic world can emerge from random distributions under certain rules and conditions. Think about a fair six-faced dice. The probability of any number is 1/6. However, if two dice are tossed and you were asked to predict the sum of the two, the probability of 7, the median number, is higher than any other combinations. Likewise, if you toss 1 million dice, then it’ll be very unwise to predict the sum to be around 1 million or 6 million because that will require most dice to lie on the same face. In other terms, the probability distribution will become sharper and more deterministic as the outcomes of more tossed dice are summed together.
There is still an ongoing debate among physicists on whether we live in a deterministic world or a non-deterministic one. To my knowledge, the non-deterministic team currently has the upper hand mainly because QM is still the gold standard in terms of prediction power in the atomic world. More importantly, Bell’s inequality test, an interesting experiment (The 2022 physics nobel prize was awarded on this topic), supports a reality that is in line with QM but the deterministic camp thinks there are loopholes in Bell’s experiment.
Some argue that free will is compatible with a deterministic world because we can never simulate our reality faster than itself (due to the computational irreducibility, any simulated world will lag behind the original one). Hence, our conscious awareness of our predictions for various future outcomes is like an exercise of our free will.
Going back to our starting point, Even-though it looks like everyone (predictably) took the blue pill at the 1:40 mark but there is a visible drop in the viewership earlier at the beginning of the video when I mention the word "existential crises". That means you unpredictably (to me) made your free-willed choice to take the blue pill early at the beginning. So even if your behavior is predictable in the short term, it is very hard to predict your behavior over longer periods. Our conscious mind, scientific method, and A.I. are all attempts in the direction of making our predictions more accurate over the longer term.
There is still much more to say but I’ll leave it here. If you liked this video, you might like our other videos on Artificial Life and Local Maxima as they touch on similar topics.
I'm not reading that essay
@@savageraccoon787 i did, it's interesting
Its all about genetics. How people treat you etc
AI generated.
Free will in non subjective sense is a square circle. True random cannot connect to a will. If random made your choice, why call it your decision in the first place?
Ngl, I kinda skipped ahead pretty much immediately until you started typing the code, and then after seeing the video within, I was hooked until the end and then went back to watch the beginning and now I just want more about this. Just wow! A deep dive into this would be phenomenal!
I'm about to start a PhD in computational cosmology, the idea of a universe "increasing its resolution", which gives it the illusion that it is expanding, is actually really interesting. It would imply that space is quantized (the pixels) and at each time iteration the amount of pixels/quanta of space increases exponentially, which is exactly what we see now. Of course according to the standard model of cosmology, space didn't expand at the same rate always. To explain some features in the cosmic microwave background we need to posit that a phase of extremely accelerated expansion called inflation happened right after the big bang, and then the expansion of space slowed down. So this idea of increased resolution over time is a bit too simplistic, but interesting nonetheless.
When I'll understand more the current state of the art in cosmology, I'll try to see if can formalize the idea into some kind of mathematical theory
Well, I always thought when physicists talk about an expanding space they also implicitly imply that the resolution of the space is increasing too (because they do note the non-homogeneity in the expansion of its constituents) but I'm not sure why they don't explicitly talk in terms of resolution. One of the reasons is because I think the mainstream physics community are overly against space discretization and the Simulation Hypothesis (Maybe rightfully). But there are some respectable physicists like Gerard 't Hooft (Nobel laureate) and Wolfram both are quite keen on using cellular automata as modeling basis.
I should also stress that Simulation Hypothesis means different things for different people. For most people it's something like the Matrix movie or what Nick Bostrom have proposed as an argument for Simulation. In this type of simulation, one should think of the simulator as a highly complex conscious designer. But the other type of Simulation proposal which is championed by Wolfram and discussed in this video is very much in-line with all systems that evolve from simple structures to complex structures and this type of Simulation doesn't need an external conscious designer as a starter.
@@brainxyz yay I'm 2nd
As the space is expanding it's the universe resolution that is increasing, not the space per cubic meter.
Btw it doesn't change the fact that I love your videos but you are wrong about one thing. You can't repeat the same OUR universe if the amount of simulations you run isn't infinite. Our universe is undefined, meaning we cannot predict future precisely even if we had all the numbers and rules that we need. It's been proven it's truly random on fundamental level.
the beauty of the mandlebrot set lies in the fact that you can explore it forever and never see all of it.
in this realm even parallel lines diverge
Hey! In case anyone needs a little help, In order to lower the brightness of the simulation, divide the t variable in the RGB function by a number instead of multiplying. This will help increase the contrast if you are zooming in really far.
What value should I change tho help me win the lottery?
@@wiredvibe1678 sample size! Buy an ass load of lottery tickets and it increases your chance of winning!
@@jameslogantinker6567 Possible lottery numbers are finite. Just do it the pokemon way and you should win.
@@Sym0S This guy just solved lottery
@@waltercapa5265 in the Lotto game there are 8,145,060 possible combinations of numbers that players can choose.
I’m not smart enough to understand this. But the editing, music, and voice had me mesmerized. I truly enjoyed this so much
You don't need to be extraordinarily smart to understand the concepts. It's like a joke, you either have the information to "get it" or you don't. I'll try to summarize it.
The Universe is governed by so-called laws. Gravity, the speed of light, the elements, etc. all work the same way no matter where in the Universe you are.
Science has been figuring out the laws that govern reality. Think of it like we're pulling a really long pearl necklace from a hole, and each pearl is one new formula. Once we have in our hands the whole necklace we'll be able to (in theory) calculate anything, from the shape of the Universe to whether a coin will fall on its heads or tails side. This is called the Theory of Everything. If we ever discover it we could simulate it in a computer, make a mini Universe and could even prove if free will exists or if everything is predetermined.
The bit about programming is just to illustrate how simple rules can result in complex, infinite patterns.
💀
Some things are harder to understand. Not understanding at first sight doesn't mean you're not smart enough
Well done. You inflicted a existential crisis upon me. Subscribed.
I didn't learn how to render the mandelbrot set in html and js in any programming class I took, but somehow, this random youtube video recommended by the mysterious youtube algorithm did.
nothing mysterious about that, it's just recommending your type of videos while being clickable, that's all
one of the best videos of all time. great job. compartmentalized wolfram's ideas into visuals & overall something pretty easy to understand
With the game of life, I guess these are the tiniest and most impressive pieces of code to share with non-IT friends ... and to meditate on. Thank you Maestro for sharing !
Love it. The reveal of the code is awesome. Nice balance of deep dive and clear messaging. 💯
I love how you call the mandel brot equasion a magic spell. I love it.
Man that was an incredible video, despite the doom and gloom, it was also oddly inspirational. Thank you for conveying the complicated information in a quick and digestible manner. Well done!
Well, this is about as refreshing as it gets.
MORE OF THIS, PLEASE!
Thank you.
I saw the thumbnail. I'm a programmer. I'm familiar with the Mandelbrot set and other fractals and have even implemented visualizations of them myself. Yet for some reason I was still shocked when you changed a plus sign to a minus sign and the rhombus turned into that familiar, beautiful shape that has fascinated me for years. Fantastic video.
yep
The sudden change at 5:22 just kills me, woah
Amazing video by the way... love your humor and gentle way of talking. You get us straight to the point while not being overly loud!!
Sweet! Nice continuation of the last video!
Love the Mandelbrot, and your video is great. Hope you still get your million dollars on whatever setting. SUBBED.
such a good video man
i laughed out loud multiple times, i love your attitude and pace
hopefully we break out of the simulation soon.
This video is a gift. I've been making similar-ish screens like this in Perchance, a simplified javascript system, and this has pushed me to learning it in javascript!
Fantastic video. Love the added humor and sarcasm!
Brilliant work and loved your message at the end. Big fan of your work
I absolutely don't understand why you have not more subscribers. Your content is genius. Thank you!
That soundtrack is perfect for the fractal zooming! It's meditative!
very nice man!!!! Congratulations!
never seen a more beautiful code made in javascript im my life👏🏻👏🏻
Dude, I got backed into the Mandelbrot set and I liked it.
Mind blowing video! Can't wait for more
This channel is going to blow up
it's been 2 years I'm brainstorming on this existential crisis !!! This video is exactly what I feel every single day ! thank you so much that was super
I pause video sometimes so you could take a breath bro
i only believe in notepad supermacy now
Very interesting your little thought experiment about someone simulating our universe and creating an infinite loop. I would argue that you should not be scared of this as you would not be reliving your life infinitely, not any more than if the universe was simulated only once. Assuming the simulated universe is indistinguishable from the one you are in, why do you consider them as two separate entities? Also, consider that by your own reasoning, time in any simulation is an illusion. As an element of this simulation, at any moment you are thinking that you are in the present moment and that time is moving forward, but the simulation might as well be a static 4D image, with time as one of the dimensions (don't take my words literally as time is waaay more complicated than that, this is purely for illustration purposes). This idea that you would be living your life linearly then living it again in all the nested simulations is the same kind of illusion. Even in a single simulation, you are living your life eternally because past, present and future all exist.
That is true, the problem is if someone is not happy with his life in this universe, it means he is going to re-live it again many times (hypothetically). It is true that he will not remember his/previous experiences but my current realization of that possibility is a bit disturbing. Stephen Wolfram has some really interesting ideas about multi-realities, one of them is that all rules in the Ruliad will merge again at some point in future. I don't know what is the right interpretation for that but one could say there is ultimate justice if we re-live through all the possibilities
@@brainxyz Is it really possible to stare straight into the abyss and get stuck infinitely? I love playing with mise-en-abyme (with mirrors, cameras and screencasting), but at some point I get bored and move on to something else. Why would it be any different when simulating one's own universe? Likely we want to play around with slight variations of the viewing angle to see alternative timelines.
I love that you made those pics of the old guys at the end with dalle thats dope
mind blown crazy video never seen a video like this so cool keep up the good work
first time watching your videos, dude this is so good, please never stop
Great video. Keep up the good work!
I love your videos! Especially your narration. Keep it up :)
Iwant to add that there's no need for e to go to the circus. I live in it.
This is one of the greatest YT videos on this platform. Thanks:)
Very nice video dude! Also love your dry humor sprinkled in. Have you read Permutation City by Greg Egan? I found a lot of the ideas you mentioned (especially about what it's like to live in a simulation) in that book, it's maybe my favorite book of all.
My favorite part of Permutation City is the idea that, in a perfectly computed universe, you can run time not only at different speeds but also backwards or randomly jumping to different moments, in the same way that you can zoom in and out of a fractal or change what part you are viewing entirely, but the fractal as a whole is unchanged.
We need more of this man
You got me at your final message. Thanks for the video!
I'm impressed by your work !
Brilliant, just brilliant. This needs to go viral
This is so well put together absolutely brilliant. Thankyou
As a lover of highly theoretical things, math, and especially programming, Man this is so foking beautiful. I have so much thoughts in my mind that I cannot express it here wow.
Best video I have seen this years, thanks pal.
Very well done, definitely earned my sub and like. Thank you!
What's wrong with a deterministic universe? There are only 2 possible options for the reasoning of each decision you make:
1. It's determined by the past + the present
2. It's random
There's no option 3 where suddenly there's some other factor that's somehow independent of everything else. It's just logically impossible.
At least in a deterministic universe, my past and present shape my decisions. In a random universe, I basically have no control and will just make random decisions over and over again.
a bit black and white. what about a mixture eg. one moment determined the next random, such that exists a veritable infinity of mixed up evolving determined and random potentialities? Your determined seems to unreasonably imply that things can only be 100% determined moment to moment, which seems a completely bogus presumption...
@@blengi well sure, you can combine option 1 and 2 (though I personally only think purely option 1 is the most likely one). My gripe was more about the video insinuating there's a "better" option 3 which grants some kind of control to some other decision making mechanism (i.e. the so-called "freewill").
@@iruns1246 Hi and thanks for reply. Doesn't uncertainty principle basically empirically undermine 1 though, or are you of the view that random quantum transitions are not truly random and are in fact the product of hidden variables?
@@blengi hey, don't mention it 🙂. Yeah, I think uncertainty principle is just about our limited capability to know something in such a small scale, not about the fundamental nature of the physics itself.
That was a really great video, I truly enjoyed it . .love fractals . . .Liked and subscribed.
If we can simulate the universe faster than itself, it would lead to some interesting paradoxes. Even if this is done through a trick, like using a fast square root, you can essentially play games with information... Perhaps consciousness is like a jpeg version of the universe, in that it captures a low quality version of the original image.
If I was an animal trying to survive, being able to "out-think" my environment would be very useful. It's essentially the same thing as running a simulation of reality faster than reality. It doesn't need to be a perfect image, it just needs to be good enough to make useful predictions.
Yes, that is why Brain and Scientific method are useful tools in our world. Most of the models that we use to successfully predict experiments are "Coarse-grained" approximations (Look for Coarse-grained modeling on Wikipedia).
If someone has an aggressive cancer, doctors can predict with a good level of accuracy the outcome. Likewise, if you throw a ball to the sky, we can predict its fall. In both cases, we don't need to simulate all atomic constituents in the universe to make a fairly good prediction.
If the universe is predictable, we should be able to simulate it. With this simulation, we can fast-forward to where we are simulating it, then see the future, and do something different from what it says. This means that the prediction was wrong, and so it isn't predictable. Thoughts?
@@garklein8089 If a storm is forming in the Atlantic, we would draw up multiple paths for its travel. If our predictions suggested that certain regions should evacuate, then our prediction leads to an "alternate reality" or set of events. If we evacuated everyone out of a region using the information from our prediction, their movement could alter the course of the storm into another region.
An imperfect simulation or algorithm cannot account for all variables, and therefore would always have a chance of being wrong.
If we used a perfect simulation of reality, and we were able to fast forward it to our current position in time in order to see current/ future events, I imagine that we would end up with some weird butterfly effect type emergent effects, sort of like generating a Mandelbrot set using an analog computer. Either that or instant cassettes from Spaceballs... lol
Great job visualizing this idea! I had similar thoughts when I saw the mandelbrot set for the first time but I don't think it would devalue our universe, if anything it completely discards the idea of value. It shows us that we can create value out of nothing! Having realized this kind of even makes you free in a sense. So what its all predetermined? We live in a hologram, nothing matters come have a beer.
Brilliant video, you earned a subscriber!
Thanks for the simple code, gonna enjoy cycling values here
These videos are incredible keep it up!
My god, I didn't realize how easy it could be to do graphics in javascript until this video. Thank you so much, this is crazy
bro this was insane🔥🔥🔥
you just gained a sub
This video has inspired me enormously ❤️
This video is incredible keep making videos like this. Thank you for this
Where has this channel been all my life?
I've been playing with fractal gens for a about 25 year or more, now I'm playing with the maths.. thanks for an amazing video.
Ok we already have Navier Stokes equations and chemistry - good luck simulating earth with those.
Equations alone aren’t near enough
Subbed coz of this amazing video, keep doing it
Brilliantly entertaining! 👏
I can't wait for consciousness video
nice move in the
right direction
keep going!
that was crazyyyyy and super motivational for some big reconsiderations
The framerate thing you mentioned @14:05 was scary. You gave me an anxiety attack lol.
great video, a perfect mix
This is crazy, I understand almost nothing, but yet I still do. I believe we can influence our universe with just our conciousness
almost nothing, same here
Wow... Great and motivational video!
FANTASTIC!! Had major personal breakthrough understanding of entanglement thank you for the video 🙏
Awesome video. The DeathNote background soundtrack was also amazing
a peculiar thing to note, if the universe is fractal like, any small part of it can let you know about the whole.
Amazing! Beautiful! Thanks!🥰👋
I'm super annoyed/jealous because I really tried hard to make a program in BASIC to make the Mandelbrot set appear (in any recognizable way) on my TI-83 calculator in middle school back ~20 years ago. I couldn't do it but I KNEW it was possible with so few lines of code!
So of course I had to follow the tutorial, and have finally fulfilled that dream (albeit in JavaScript and on a computer lol). Thank you!
I'm going to try to "boil down" the equation now to something that's not spread over so many lines of code.
genuinely amazing
The problem with simulating our universe is that to do so in real time in an IDEAL computer would take at minimum exactly as much energy and matter as exists in the universe.
👍incredible , keep going👍
Of course the performance of the universe you create matters.
What's the maximum age of the machine? Even with a Dyson sphere-powered super-hyper-mega-ultra computer that can run your universe at the speed of 1 second per day (which would be INSANELY fast), that computer will have to survive trillions of our years before it starts simulating human beings.
Which would mean it will need to move to a different star every time the one powering it dies. Millions of times.
If somehow it manages to survive that long, then in order to get the simulated universe inside that simulated universe to also start simulating human beings, that computer will practically have to survive the heat death of the universe.
TLDR: just because you can simulate a universe, doesn't mean you've created an infinite recursion of universes.
Not to mention that to simulate the whole universe as we know it, you still have to use some kind of RAM to run it, and since it would need to have all the positions of all the elementary particles and the values of their properties stored in it, the RAM itself would need to be the size of the universe we want to simulate, using some elementary particle properties as bits. That alone makes it impossible to do the whole "Okay I simulate our universe in a computer and they simulate the universe in their computer and so on" because that would require all matter in the universe AND more to be used as some kind of memory. We would always be creating rip off universes that don't come even close to the complex nature of ours.
Thanks so much for introducing me to the music of Ivan Torrent!!! Great video too. Definitely earned my subscription
What worries me is a hierarchical set of simulations where encoded are laws that mean finding a theory of everything is a hard impossibility, which is entirely possible: to have a giant wall where we cannot know past. Not necessarily by design but by feature, error or chance of a particular permutation of the equation (similar to measurement problem/uncertainty principle ir the unfalsifiable nature of the theories discussed here)
Quantum mechanics is the definition of making impossible calculations, possible.
This is fucking wild, a wild theory but fun to think about no less, what a trip this video was. Mr Discover The Universe Equation Guy.... please change the settings.
fun fact, each branch on the mandelbulb plays out a certain musical frequency sounds much like our 7-tone equal western music theory. weird
Dude you are a freaking genius how do you come up with these video ideas and how do you edit them so perfectly?!
Very interesting glad I found out your channel
Will is so free that we can't stop it from reminding us about embarrassing things we did in the past, thanks free will.
Proud of you doctor gyan, it was incredible.
Super cool!
Loved the video man beautiful, powerful and funny! Got yourself a new subscriber that will share the word of the Python Universe using Ruliad modules, running in a pregnancy test in our campus in Brazil!
Also, a question! Let's assume we find the rule for our universe and can predict the next calculus test with our abacuses, may we also be able to run another simulation like, Ricky from Earth 43b too? Will they all be, then, connected somehow?
Big love from astrophysics undergrad course in Brazil!
I don't think that our universe is a fractal (where fractal universe is a universe, in which any state F could be described as F(x,y,z,t), where x,y,z is a space coordinates and t is a time coordinate), because
1. Fractals are infinitely small. There's no smallest things that could exist. Our universe, however, has a clear limit to how small (constant elementary particle size, plank length, heisenberg's uncertainty) and how big (speed of light paired with an expansion of universe) things can be.
2. Fractal universe wouldn't have a causality. You could render any part of a fractal without rendering anything else, or, in the language of universe, predict any event in the stated space-time coordinates without knowing what happened before in that space - something you clearly can't do in our universe. In fact, there wouldn't be any difference between time and space, while in our universe there is (even in Special Relativety Theory they counted differently).
3. Our universe doesn't even seem to have an universal coordinate greed, with even simultaniety being relative.
So... Yeah, fractal universe is unlikely.
Your point 2 is wrong! This note is made by some other comments too but I'll stress again that this is wrong. Just look at the code again and tell me how can you predict what happens after the 200 time steps without calculating all the previous time steps too in the inner loop? The answer: You cannot. This is called computational irreducibility (coined by Wolfram). This is a disturbing limitation for science!
Just like the absolute maximum speed limit of light is a disturbing limitation for our traveling ability,
Computational irreducibility is a disturbing limitation of our ability to predict the very distant future accurately (without simulating the previous steps), this is true for Mandelbrot, Rule 30 cellular automata, game of life, and other chaotic deterministic iterative functions.
Human brain is able to generalize from the past events and make some approximate predictions of the future (but 100% is not achievable even if the grand rule was deterministic)
@@brainxyz oh, yeah, didn't understand the function for time at first.
I'm should correct my argument a little bit. You can't solve the fractal (at least the Mandelbrot fractal) without knowing what was in the past (I.e. without calculating previous time steps, as you said), but you can solve any part of it without knowing what is in other parts (I.e. to know only what happens in a square from (450,450) to (550,550) with coordinates like in your code, for example). This clearly couldn't be done in our universe.
Tbh, my arguments is not really against the determinism. It's more against the thesis, that our universe could be simulated by a simple computer in our universe. You can make the function, that would check other space coordinates (like Conway's game of life you mentioned), but then you'll have to store information about these space coordinates. If we assume that the smallest possible space step is 10^-35 (Plank length is about 1,6*10^35), to simulate even one square meter you'll need to store information about 10^105 cells - which couldn't be achieved even if you'll turn whole Earth in one big HDD.
And determinism... Meh. I wouldn't want to be non-determenistic creature. That would've mean that any decision is made not by me, but by some universal RNG. Imagine if you'll need need to toss a coin whenever you need to decide "Do I go to my college/work or lie on my bed whole day", or "Do i propose to the woman i like or repulse her and live all my life in solitude"? People say that determinism undermine freedom of will, but is it really a freedom if you forced to do random shit that you by definition cannot control and that could potentially ruin your life?
thank you so much...didn't know by now, that math can be so beautiful...
I've always watched fractal videos and been very very interested in them for many years, but theres never been a clear explanation and demonstration of what they actually represent and how to create them. Thank you for this video. I do have a question, is there a way to slightly alter your equations to change the shape of your universe? Or would the resulting fractal end at some point (and not be a fractal)
Thank You this helped a lot on a project I'm working on 😃