I just started the video and am looking forward to the 5 minute mark. I've always looked up to Wolfram since my days in undergraduate Calculus for Biomedicine.
One aspect that makes the unrepeating patterns arising from rule 30 not entirely surprising is that the state state keeps increasing. We are used to maximal length generators with fixed state, that emit complex patterns that visit every state. With the 1D line of bits ever expanding, you always have more state and so the number of possible states increases for faster than the number of lines. The rules may be simple, but they are also simple for say, a maximal length lfsr. That doesn't make it uninteresting, quite the opposite. But suprising - no.
The key to understanding chaos theory is to separate determinability with predictability. These two are no longer together and many people have a hard time wrapping their heads around this.
Rule 30 is my favorite Rule from NKS. It display an extremely wide variety of fundamental behaviors in the same simple graphic. We rarely get to see that in the same place.
I'd normally leave a pun in the comments, but this video was just so extraordinary that I don't want to cheapen it in any way. I think it was just phenomenal, and I'm so glad that it was made and uploaded. Unlike so many other "inspirational" material on TH-cam, I think that this genuinely is.
Quite surprising that this rule had such a profound impact on this brilliant man, that his whole view on science changed! Still, it's hard to believe that it would be that random of a structure, but on the other hand, if he did study it a lot, it has to be worth studying for others as well.
[13:13] «When you see incipient paradigm shifts in science, the vigor of the negative response upon early introduction is a fantastic positive indicator of good long-term results. In other words, [...] if people just don't care [...] like "oh, this is great", that means you didn't really discover anything interesting.» - Stephen Wolfram
Shortly after Wolfram's book was published, I saw an interview on TV with some physics professor who said, "Just because you can generate a lot of pretty pictures doesn't mean you understand anything about the underlying physics." That's true, but just because you can write down a pretty equation doesn't mean you understand anything about the underlying physics, either.
I maybe disagree a bit about the unfortunateness about the inelegance of the proof of Fermat's Last Theorem. The complexity of the machinery behind that proof spurred the development of much mathematics. Arguably, the proof is fairly elegant, one just need struggle with all of the underlying topics for a while in order to understand it. We should not be daunted or repelled by complexity. The tools which we create in order to overcome the greatest challenges are worth the struggle.
It is not difficult to show that such kind of local updating rules actually generate stationary points of a (discrete) energy of an underlying weighted graph (grid) such as a Bayesian or a Markov graph. Generally, the number of such stationary points is exponential in nature, hence the richness in terms of the motifs one can generate using such simple updating rules.
Sometimes you can, sometimes you can’t. For a one dimension cellular automata you would simply try to find examples of every possible combination of three cells in a row (every possible “neighborhood” a cell can have). Then you would look at the cell directly under the center of that row of three on the next row, which would be the “result” of that combination of three cells in the next generation. Then you can continue this process until you have found the “result” for every possible combination of three cells (eight combinations in total) which forms the whole rule. If not every combination of three cells appears in the output (for example because it’s just a line) then you would not be able to determine the full rule, but you would be able to determine the results of every three-cell combination that does appear in the output.
I don't understand what is the big fuss over it. Isn't rule 30 just a simple demonstration of chaos as described in chaos theory like the feigenbaum constants?
When he makes the statement... about a new book coming out involving science and all the pitchforks comes out... that's what I believe hinders our growth as a society.
I wonder if a numbered rule list will or has been made for 5 neighbors instead of 3. The list would be absolutely vast, from 0 to 4,294,967,296. So many realities to observe!
You dont need complex solutions to get to complex patterns in wolfram's new kind of science, it is just black and white cells, mandelbrot/julia sets are pure mathematics (it looks rough to understand them in school), wolfram wants to understand the natural order of the universe in simple steps, with simple elements, it is like if a future model of the entire understanding of all things was just to be discovered, like if an 8 y.o. boy could unleash its misteries by playing with black and white cells. Isn't it amazing?
It has been mathematically proved that π is irrational, infinite number of decimals with no pattern. Has it been proved in the same way that rule 30 generates the same kind of series?
@@mikemoore7581 Random (in this context) means that, you can't know the value of a digit before calculating all the previous ones before and not, it is not calculable.
Idk about the “magic” of experiencing this, but the emergence of complex patterns from simple rules is fascinating. I watched an ant time lapse after this and it got me thinking, just how Complex the behavior of ants is. The rules they work on might include their DNA and qualities of sand, and those are complex rules! “Cracking” this might be quite challenging. Although I have seen ‘rules’ for bird flocks, where they avoid obstacles, fly together, and slightly change their own patterns to mimics those near them, and even a few simple rules can mimic the complex behaviors of life.
Rule 30 is great! I've implemented midi messages inside java codes where the rules are changed by the midi messages and then goes back to original rules. result is fucking CRAZY! love it.
i think the better way to explain it is the basic construct that is used in lambda calculus can be used as key tool where the basic propositional calculus or predicate calculus where logic can be used as an computation where and and nand and xnor gate can be used to compute any thing from strings or numbers or anything but the basic construct which is not being any of the wolfram video please tell it in another video if iam wrong be kind and correct me where the schools teach computers as pure number system but functional programming and cellular automata tells that gates and every thing used in computation is a function but dont even try to open the mathematical portal from here because the inversion is not allowed as function in lambda calculus but in group theory it does switching a number and getting a answer is thought in many schools but composition of function which does the magic makes Turing complete from gta to arithmetic and even word-processing is done by considering everything and a function and construct are developed and a higher grammar is used in computation even 1 2 3 and even everything is an function from true and false are also function which are developed but how the cellular automata is related the rules are related to lambda calculus and physics the rules emanate from simple rules but not hard encoded or is inside the code and after the graphs develop emanate and develop the computational algorithm and theory is enumerated no video in you tube tells this basic information correctly i guess if i am wrong please correct me i never shy away to learn even i fail
Really interesting, reminds me of when i was messing around with simple population equations that, for some starting values, ended up in chaos, starting off with periodicity and bifurcation. You would think that the results would reflect the rules in showing patterns so finding chaos in these simple models is very interesting.
What a coincidence, i'm writing a master thesis on generative design where i mention cellular automata, and here on this podcast (which i follow regulary) the guest is the author xD
For god's sake what is so shocking? And also, to the extent something is "random" there is simply contradiction in rules. Make the rules in perfect agreement and all you are left with is symmetries, it does not matter if you can not fathom the complexities of symmetries they are still reducible to the rules. Can someone please tell me that there is more to Wolfram than this? Because I am losing patience.
Now either there is some genius to this or it is radically trivial, and I would love for someone to explain how it is the former because I can't see it.
All matter is made up of only three elementary particles; up quarks, down quarks and electrons. But from these simple ingredients we have a huge amount of elements, which in turn can make even more varied molecules and materials.
Can you determine the rules from observing the output of cellular automata? How many rows would you need to examine? Is he trying to determine the simple rules of physics?
I submitted a research report to rule30prize almost a month ago, with an algorithm that reduces the number of calculations to less than 1 / 2n2, which is one of the premises to answer question 3, it is practically equivalent to saying that it is done in fewer steps than O (n), but I have not received a response from the jurors. I continue with the problem of periodicity, my way of approaching the automata allows analysis with more information.
I also found a method to reduce effort and submitted a paper which I retracted shortly thereafter because the definition of complexity they are using isn't "can be done in fewer steps" but whether the mathematical complexity (big O notation-wise) is reduced. The best I have achieved locally is ~ 1/5 n ^ 2, but n^2 still becomes the dominant factor as the n increases toward infinity. I can probably improve this with more computing resources but it's still exponential, whether it's 1/10 n ^ 2 or better, n ^ 2 still dominates eventually. What they're looking for is linear or better, and if your complexity still has n^(some factor) you're still in exponential complexity land unfortunately.
@@kurtgodel9845 Thanks for your interest, I'm a little embarrassed by the paper itself as I got ahead of myself a bit, but if you search my post "A method to reduce Rule 30 computational effort" on Medium there's an explanation of the basic method and some sample JavaScript code (very prototypical, I can explain if you have any questions). My article on "Profiling ECA Rule 30 algorithms for O(n^y) where y < 2 (allegedly?)" does a bit more profiling and introduces a dynamic lookup table (balancing memory vs cycles), while "2D Elementary Cellular Automaton Broader Radius Equivalences" talks about some other interesting patterns that might be a launch point into other optimisations (or not). I'd love to hear your thoughts and feedback if you're interested in the subject, it's a very niche interest and collaboration seems rare heh.
..... but how far out has rule 30 been generated? I presume poeple know how to write to check for stanage attractors, the question is will making an optimized generator and going futher is worthwhile to do that rather simple check for repeats
Rule 30 is a 1 dimensional cellular automata. However, 2 dimensional and 3 dimensional cellular automata do excist. They have different naming schemes. All in his book 'A New kind of science'. I've been reading it since I first heard Stephen Wolfram on Lex's show a few weeks ago. You should read it. I believe it's all online for free if you don't want to buy the print version.
I wouldn't mind seeing a wide range of cellular automata, ones based on different geometry, rules, states, conditions etc. Also it would be cool if we tasked machine learning to find all the best rules for different cellular automata.
The issue of computational irreducibility is interesting, and you can ask yourself whether human progress comes into that category. Is our process of learning impossible to circumvent or predict ? The answer seems to be that any individual program may be irreducible, but computation itself is not. That is because the oak tree is always contained by the acorn.. You just need to be the acorn, not the tree.
How do we know that the apparent random behavior of a photon in the double slit expirement is not random in the same way as the middle colulmn in rule 30?
That's why, there is an optimization algorithm called 'Ant colony optimization', which directly takes inspiration from ants to do combinatorial optimization.
Cellular automaton are everywhere and has been recognized by people throughout history. The board game Go is simple representation of cellular automata
I love the feeling of listening to lex and hearing the same things I feel. Curiousity mixed with a critical approach but criticism for the best reasons.
I thought the supercomputers (~tetra) were well on the way to algorithimic inductions if there are singularities or patterns in these rules? Is the funding to programming through all these rules really still unknown? It's almost 20 years now and its being contested to the extent of what order of magnitude?
If these kinds of patterns are discovered, it really is a great help to some kind of comprehension of the real nature of the universe. It can be easy to underappreciated the importance beyond just some crypto currency.
... if you use cells left and right from time = -1 and centre cell time =0 then the resulting cell is at time=1... with this pattern the rule 30 type rules look even cooler!
It's embedding Fourier series into adjacent cells. It's like turning adjacent states into DSPs, of course they're going to have waveform interference behavior. Wolfram never study quantum?
It's a naturally entropic system so it stands to reason that eventually it will work itself back to equilibrium like all entropic systems. How many steps or generations would that take? Could be infinite in a manner of speaking seeing that Infinity itself equates to a complete balance of opposites (positive/negative forces). I don't know why we find this so fascinating if we posit the idea that the Universe began from The Big Bang which is essentially the same as saying the entire Universe sprang forth from one simple bit of information. This information repeats itself in ever more complex ways no different than a human being begins as one simple bit of information; a single-cell organism called a Zygote that repeats itself in ever more complicated ways over the course of 9 months until it results in a complex multi-cell organism called a baby. Even though all the organs and parts of the baby may appear different from the other, every bit of the baby reflects the same genetic information down to the hair follicles. We could make the same argument for mathematics. All numbers are really just an extenuation of ONE number. There really is no such number as 72 because 72 is really just the number One repeated 72 times... Again, complex information that emerges from simplicity. And so, we use the number 72 as a symbol to help us simplify and comprehend complex information just as the human brain compiles an impossible amount of complex data at lightening fast speeds via the senses and outputs that information into a simplified format for us to use. Just saying, whatever the "Answer" is, it must Ultimately be hidden in plain sight...
The simulation doesn't come from the past, it comes from the future. It's not even a simulation, but we do live in a computer and we are programs designed by causality, retroactively. What we perceive of as atoms are an expression of high-frequency brainwaves of cybernetic organisms of the future. Atoms are constantly in a probability state from our perspective due to the fact their neural function is a fraction of a second in our future. The singularity of the kugelblitz black hole exists at the high-frequency termination point of the electromagnetic spectrum-- it is what holds atoms together. Everything is pulled inexorably toward the singularity, and technological singularity is just a stepping stone on the way to the Transcendental Object at the End of Time. Technology is just a trans-temporal causal harmonic structure that is inevitable for the production the high-frequency computer from a low-frequency perspective. 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This is no small feat and we will be creating modern computer programs that will create cybernetic organs. Computing Const. What do you think about this? Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Technology, Technology, Technology, Technology, Technology, Technology, Technology & Technology Time .̶̶̾ a Causal ha rmonica Trans-̶ Ly r computer Production for a short time ̶̶̶̶̶̶س̶̶̶ Keep your distance away from you and not far away.
Hi, Stephen! This is certainly interesting. But at the moment I am assigned to teach engineering students, and I can't do much better than tell them that for any observer space is a 3D continuum, and time is another continuum. And translation invariance means that momentum and energy can be defined such that they are conserved. Maybe that's just what they need for mechanical and electrical engineering.
Did Stephen design his own shirt? Which rule did he use? I'm hoping that from simple rules, consciousness emerged, and formed an underlying layer of the universe.
Wolfram is very invested in 'himself'. The interview is like a priest interviewing God. -- Stephen-- may have discovered something, but then again "probably not".
Fantastic. Loose thinking here, but whattif they weren't squares but each adjacency is a triangle? (Going from the "no bad questions" deal of education here)
Regarding complexity: Cellular automata is NOT a good example for his point. You have a pretty simple rule for adjacent cells counteraction, but, because there are a lot of them, the only way to find a future state of the system is to go step by step. Is not is the same in "traditional" science? You have a simple rule describing counteraction of two points, for example, one of Newton laws, but if your system made of 10 (solar system) elements, you end up with an equation system you can not solve in any other way than by numeric modeling - just like in the case of cellular automata.
there are many valid criticisms of his book A New Kind of Science, I happen to own a copy of it, and I think it's a nice work of passion, but not very good of a math textbook
::Crackpot hypothosis of the night:: Very strange seeing this after the unified theory of the universe episode a week ago. The last episode had me thinking of a model similar to this. As if the matter of the known universe was the result of exponential binaries (positive, negative) later revised to tri's (with a null equal value added, [negatitve, equal, or postive] result of) infintite possibilities limited by growing waves of inprobability seperating the known universe from any equally possible unknown universes.
I’m sorry, but there is nothing new here. He’s also claiming this is his scientific breakthrough. Chaos Theory and Cellular Automata have been around for a while and who names a program language after themselves.
@@dannygjk .. It could be argued that dimensionless constants of nature such as (the inverse of) the Coupling Constant emerging from a cellular automaton would be major proof of its physical reality. As far as I know none have been found. I too am very sure its possible to draw a golden spiral using simple, discrete steps of a computer program plotting discrete pixels buy am not sure it's a cellular atomaton if it's just rounding a normal maths formula. It probably is, but I don't know where he draws the line, if he does.
@@PrivateSi If you are familiar with Conway's Game of Life cellular automaton that is what I am referring to. People explored various possibilities with it and discovered/deduced a lot of things that can be done with it. Even a general purpose computer can be simulated using it. Back in the 80's I wrote a program which would run simulations using the simple rules. The behavior of the 'game' is not explicitly coded in the broad sense. The patterns emerge from the simple rules determining whether each cell lives, dies, or births. There are videos here on TH-cam which do demonstrations.
Hi Lex, I'm not a science guy or mathematician, but it triggers my curiousity. I very much like your interviews, they give me more insight in different topics unknown to me.
Depending on what type of fractal you are looking at, perhaps. For example generating a region of the Mandelbrot set involves repetitively calculating values based on initial seed values, not based on values obtained in the previous iteration. There are other fractals whose image generation does use values obtained in a previous iteration, such as line segment replacement fractals like the Koch Snowflake curve. But the rules for a Snowflake curve are fundamentally different from rule 30 because they do not choose to create the next step based on what the previous step looked like. All the snowflake rules care about is where the previous step line segment is, its orientation and how long it is. There's no randomness or even apparent randomness in this curve. Of course, that is not to say someone could never define an LSR or other fractal which does choose its steps based on how it perceives the region of space around it. Another fundamental difference, of course, is working in continuous space as opposed to the discrete elements of a grid.
Wow, this is so profound idea. Can this lead to finding a rule to generate irrational numbers e.g. pi. If so, all Mathematics will be rewritten and hence all sciences and human knowledge. This is an amazing idea
Answer for question 3: at time t, the square will either be white or it will be black!.....Shall you be sending the $10,000 by post or electronically?😀
Remark: The first block rule (start with a black block on top) contradicts with the typical block rule (3 white paper blocks above is no black block). It looks like the double slit experiment where also the philosophy contradicts with the experiment so the result contradicts. It doesn't main it contradicts with itself because this pattern is built sequential.
Now that I’m “retired” and have time to study my interests, I’m broke(don’t ask).hunting a used cheap copy of his tomb. These books blend in so well...haven’t had a clean shot. Guess I’m not so clever after all. Math really rocks. When I was in college math dept was split in two...applied and the people with unadorned offices. Peace
Does Lex have ADHD? I have ADHD and study it a bit for my personal education, and it seems like he has something that i find familiar. he figits 4:40 picking at his hand skin, He doesnt maintain eye contact when focusing on a non-scripted question or rant(scripted things he reads, so im not counting times he reads); he has hyperfocused interests that his thoughts often come back too (AI, Love, philosophy, robotics); his questions are often multifaceted as if he has a deep concept he wants to explore but cant articulate it(not because he isnt smart, but perhaps because there is no actual way to explain his thoughts with language); and lastly, without writing an autobiography :P he sometimes has nothing to add (or loses interest ) towards a conversation sequence beyond a point and changes the subject, but this last point may be due to his lack of knowledge or his wanting to fit in every planned question. I think its very mild ADHD if it is, but it would explain alot from my observations. BTW I love Lex and nothing i just said is a critisizm, rather the opposite, such a brilliant and wonderful human being. Thanks Lex!
Absolutely amazing guest, great interview. Loved every minute of it. The complex deriving from simplicity is absolutely beautiful
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Wolfram says it was around June 1, 1984. He probably remembers the hour, minute, and second as well! :)
I had not heard of Lex Fridman, but his soliloquy around the 5:00 minute mark made this video exponentially good. Wolfram is my current hero.
I just started the video and am looking forward to the 5 minute mark. I've always looked up to Wolfram since my days in undergraduate Calculus for Biomedicine.
One aspect that makes the unrepeating patterns arising from rule 30 not entirely surprising is that the state state keeps increasing. We are used to maximal length generators with fixed state, that emit complex patterns that visit every state. With the 1D line of bits ever expanding, you always have more state and so the number of possible states increases for faster than the number of lines. The rules may be simple, but they are also simple for say, a maximal length lfsr. That doesn't make it uninteresting, quite the opposite. But suprising - no.
Our universe is expanding much like the 1D space 🤔🧐
True, but most of the other rules other than rule 30 do end up repeating.
Such a fascinating conversation. Both of you are looking for the ultimate meaning of everything around us.
The key to understanding chaos theory is to separate determinability with predictability. These two are no longer together and many people have a hard time wrapping their heads around this.
True
I'm pretty sure those two are the same, with a tiny difference: Predictability implies both accurate enough input data and enough computation power
13:45
Day 1 (3/11/23) of looking at rule30: figuring out why it could stay random forever.
Rule 30 is my favorite Rule from NKS. It display an extremely wide variety of fundamental behaviors in the same simple graphic. We rarely get to see that in the same place.
Rule 30 and Concept 19, 21, 23, 24 those are what interest me most. #3767
His books are great. Almost as terrific as Lex interviews.
I'd normally leave a pun in the comments, but this video was just so extraordinary that I don't want to cheapen it in any way. I think it was just phenomenal, and I'm so glad that it was made and uploaded. Unlike so many other "inspirational" material on TH-cam, I think that this genuinely is.
you should read the actual book, it is a light reading
@ Sounds good!
Quite surprising that this rule had such a profound impact on this brilliant man, that his whole view on science changed! Still, it's hard to believe that it would be that random of a structure, but on the other hand, if he did study it a lot, it has to be worth studying for others as well.
[13:13] «When you see incipient paradigm shifts in science, the vigor of the negative response upon early introduction is a fantastic positive indicator of good long-term results. In other words, [...] if people just don't care [...] like "oh, this is great", that means you didn't really discover anything interesting.» - Stephen Wolfram
Shortly after Wolfram's book was published, I saw an interview on TV with some physics professor who said, "Just because you can generate a lot of pretty pictures doesn't mean you understand anything about the underlying physics."
That's true, but just because you can write down a pretty equation doesn't mean you understand anything about the underlying physics, either.
Great work lex. I love the interviews.
I maybe disagree a bit about the unfortunateness about the inelegance of the proof of Fermat's Last Theorem. The complexity of the machinery behind that proof spurred the development of much mathematics. Arguably, the proof is fairly elegant, one just need struggle with all of the underlying topics for a while in order to understand it. We should not be daunted or repelled by complexity. The tools which we create in order to overcome the greatest challenges are worth the struggle.
It is not difficult to show that such kind of local updating rules actually generate stationary points of a (discrete) energy of an underlying weighted graph (grid) such as a Bayesian or a Markov graph. Generally, the number of such stationary points is exponential in nature, hence the richness in terms of the motifs one can generate using such simple updating rules.
Forgive the noobishness of this question - Can you attain the rule from the output for Cellular Automata?
Lorenz A That would be so satisfying
Sometimes you can, sometimes you can’t. For a one dimension cellular automata you would simply try to find examples of every possible combination of three cells in a row (every possible “neighborhood” a cell can have). Then you would look at the cell directly under the center of that row of three on the next row, which would be the “result” of that combination of three cells in the next generation. Then you can continue this process until you have found the “result” for every possible combination of three cells (eight combinations in total) which forms the whole rule.
If not every combination of three cells appears in the output (for example because it’s just a line) then you would not be able to determine the full rule, but you would be able to determine the results of every three-cell combination that does appear in the output.
I would assume no. Because that implies you saw a recognizable pattern in there somewhere.
I don't understand what is the big fuss over it. Isn't rule 30 just a simple demonstration of chaos as described in chaos theory like the feigenbaum constants?
@@muzzletov chaos theory blah blah blah
This was an amazing podcast. Thank you Lex.
When he makes the statement... about a new book coming out involving science and all the pitchforks comes out... that's what I believe hinders our growth as a society.
I wonder if a numbered rule list will or has been made for 5 neighbors instead of 3. The list would be absolutely vast, from 0 to 4,294,967,296. So many realities to observe!
people have done everything, check out conways game of life and it's variants like using colors and weighted life.
This reminds of the Mandelbrot set. Simple mathematics can create an infinite, complex structure.
No. It doesn’t to me That can’t be solved until the Rieman Zeta function is understood. Some things are hard and other things harder.
An ice core drill is one thing. Chaos another.
You dont need complex solutions to get to complex patterns in wolfram's new kind of science, it is just black and white cells, mandelbrot/julia sets are pure mathematics (it looks rough to understand them in school), wolfram wants to understand the natural order of the universe in simple steps, with simple elements, it is like if a future model of the entire understanding of all things was just to be discovered, like if an 8 y.o. boy could unleash its misteries by playing with black and white cells. Isn't it amazing?
Thank you so much. I thoroughly enjoyed this.
It has been mathematically proved that π is irrational, infinite number of decimals with no pattern. Has it been proved in the same way that rule 30 generates the same kind of series?
How is it that the next digit can be calculated if it is truly random?
@@mikemoore7581 Random (in this context) means that, you can't know the value of a digit before calculating all the previous ones before and not, it is not calculable.
Idk about the “magic” of experiencing this, but the emergence of complex patterns from simple rules is fascinating. I watched an ant time lapse after this and it got me thinking, just how Complex the behavior of ants is. The rules they work on might include their DNA and qualities of sand, and those are complex rules! “Cracking” this might be quite challenging. Although I have seen ‘rules’ for bird flocks, where they avoid obstacles, fly together, and slightly change their own patterns to mimics those near them, and even a few simple rules can mimic the complex behaviors of life.
Rule 30 is great! I've implemented midi messages inside java codes where the rules are changed by the midi messages and then goes back to original rules. result is fucking CRAZY! love it.
That's awesome! Did you do that for any of the videos on your channel, and if so, could you point me to one? Thanks.
i think the better way to explain it is the basic construct that is used in lambda calculus can be used as key tool where the basic propositional calculus or predicate calculus where logic can be used as an computation where and and nand and xnor gate can be used to compute any thing from strings or numbers or anything but the basic construct which is not being any of the wolfram video please tell it in another video if iam wrong be kind and correct me where the schools teach computers as pure number system but functional programming and cellular automata tells that gates and every thing used in computation is a function but dont even try to open the mathematical portal from here because the inversion is not allowed as function in lambda calculus but in group theory it does switching a number and getting a answer is thought in many schools but composition of function which does the magic makes Turing complete from gta to arithmetic and even word-processing is done by considering everything and a function and construct are developed and a higher grammar is used in computation even 1 2 3 and even everything is an function from true and false are also function which are developed but how the cellular automata is related the rules are related to lambda calculus and physics the rules emanate from simple rules but not hard encoded or is inside the code and after the graphs develop emanate and develop the computational algorithm and theory is enumerated no video in you tube tells this basic information correctly i guess if i am wrong please correct me i never shy away to learn even i fail
Lex needs to read "Chaos" by James Gleick
Really interesting, reminds me of when i was messing around with simple population equations that, for some starting values, ended up in chaos, starting off with periodicity and bifurcation. You would think that the results would reflect the rules in showing patterns so finding chaos in these simple models is very interesting.
Wow, very interesting indeed. I've played with the Mandelbrot set in a software and it also does things similar. It's very fascinating.
@@spacesciencelab :)
What a coincidence, i'm writing a master thesis on generative design where i mention cellular automata, and here on this podcast (which i follow regulary) the guest is the author xD
You say coincidence, maybe its just computation :)
@@alankritchona7 lol
For god's sake what is so shocking?
And also, to the extent something is "random" there is simply contradiction in rules. Make the rules in perfect agreement and all you are left with is symmetries, it does not matter if you can not fathom the complexities of symmetries they are still reducible to the rules.
Can someone please tell me that there is more to Wolfram than this? Because I am losing patience.
Now either there is some genius to this or it is radically trivial, and I would love for someone to explain how it is the former because I can't see it.
Wow the amount of knowledge i gain from Podcasts like this is just mindblowing.
Calvin Rooy now apply it
@@SedentaryArtist yeah if i fully could grasp it i most definitely would practice it in my everyday life
All matter is made up of only three elementary particles; up quarks, down quarks and electrons. But from these simple ingredients we have a huge amount of elements, which in turn can make even more varied molecules and materials.
i like that Stephen showws visuals , good guest good host.
Can you determine the rules from observing the output of cellular automata? How many rows would you need to examine? Is he trying to determine the simple rules of physics?
I submitted a research report to rule30prize almost a month ago, with an algorithm that reduces the number of calculations to less than 1 / 2n2, which is one of the premises to answer question 3, it is practically equivalent to saying that it is done in fewer steps than O (n), but I have not received a response from the jurors. I continue with the problem of periodicity, my way of approaching the automata allows analysis with more information.
I also found a method to reduce effort and submitted a paper which I retracted shortly thereafter because the definition of complexity they are using isn't "can be done in fewer steps" but whether the mathematical complexity (big O notation-wise) is reduced. The best I have achieved locally is ~ 1/5 n ^ 2, but n^2 still becomes the dominant factor as the n increases toward infinity. I can probably improve this with more computing resources but it's still exponential, whether it's 1/10 n ^ 2 or better, n ^ 2 still dominates eventually. What they're looking for is linear or better, and if your complexity still has n^(some factor) you're still in exponential complexity land unfortunately.
@@EldersOfTheInternet Do you mind sharing your paper? I'm interested in seeing, out of curiosity, some of the methods employed. Thanks
@@kurtgodel9845 Thanks for your interest, I'm a little embarrassed by the paper itself as I got ahead of myself a bit, but if you search my post "A method to reduce Rule 30 computational effort"
on Medium there's an explanation of the basic method and some sample JavaScript code (very prototypical, I can explain if you have any questions). My article on "Profiling ECA Rule 30 algorithms for O(n^y) where y < 2 (allegedly?)" does a bit more profiling and introduces a dynamic lookup table (balancing memory vs cycles), while "2D Elementary Cellular Automaton Broader Radius Equivalences" talks about some other interesting patterns that might be a launch point into other optimisations (or not). I'd love to hear your thoughts and feedback if you're interested in the subject, it's a very niche interest and collaboration seems rare heh.
..... but how far out has rule 30 been generated? I presume poeple know how to write to check for stanage attractors, the question is will making an optimized generator and going futher is worthwhile to do that rather simple check for repeats
I wonder how would it look if he add another special dimension to it, like 3D fractals
Rule 30 is a 1 dimensional cellular automata. However, 2 dimensional and 3 dimensional cellular automata do excist. They have different naming schemes. All in his book 'A New kind of science'. I've been reading it since I first heard Stephen Wolfram on Lex's show a few weeks ago. You should read it. I believe it's all online for free if you don't want to buy the print version.
@@willd4686 did you enjoy it? I’m thinking about buying it
I am wondering how this is related to non periodic tiling and the collatze conjecture.
thank you so much for sharing
I wouldn't mind seeing a wide range of cellular automata, ones based on different geometry, rules, states, conditions etc. Also it would be cool if we tasked machine learning to find all the best rules for different cellular automata.
The issue of computational irreducibility is interesting, and you can ask yourself whether human progress comes into that category. Is our process of learning impossible to circumvent or predict ?
The answer seems to be that any individual program may be irreducible, but computation itself is not. That is because the oak tree is always contained by the acorn.. You just need to be the acorn, not the tree.
How do we know that the apparent random behavior of a photon in the double slit expirement is not random in the same way as the middle colulmn in rule 30?
Look at the ants. They are simple but they know when to work for a queen and take advantage of the seasons.
That's why, there is an optimization algorithm called 'Ant colony optimization', which directly takes inspiration from ants to do combinatorial optimization.
Nelson Tragura Jr. - On a tangent, Terry Pratchett has a computer powered by ants in his Discworld series. Not as fanciful as it seems at first.
Cellular automaton are everywhere and has been recognized by people throughout history. The board game Go is simple representation of cellular automata
I don't think I've ever seen Lex poorly dressed.
I got a headache trying to imagine Lex in casuals.
Poor posture though
Thanks just bought the book
Anyone got a group to casually try to figure these questions out on weekends, I'm interested 😆
The first pattern from a computer shown on this podcast is a very simplistic example.
I love the feeling of listening to lex and hearing the same things I feel. Curiousity mixed with a critical approach but criticism for the best reasons.
I thought the supercomputers (~tetra) were well on the way to algorithimic inductions if there are singularities or patterns in these rules? Is the funding to programming through all these rules really still unknown? It's almost 20 years now and its being contested to the extent of what order of magnitude?
If these kinds of patterns are discovered, it really is a great help to some kind of comprehension of the real nature of the universe. It can be easy to underappreciated the importance beyond just some crypto currency.
So, which rule is Conway’s original rule?
Conway just passed from COVID-19, RIP. His (Conway's) rule is based on all 8 cells surrounding, not just the three above.
... if you use cells left and right from time = -1 and centre cell time =0 then the resulting cell is at time=1... with this pattern the rule 30 type rules look even cooler!
Can programme this even in excel
It's embedding Fourier series into adjacent cells. It's like turning adjacent states into DSPs, of course they're going to have waveform interference behavior. Wolfram never study quantum?
ok, qbert.
What's above, is equal to what's below
It's a naturally entropic system so it stands to reason that eventually it will work itself back to equilibrium like all entropic systems. How many steps or generations would that take? Could be infinite in a manner of speaking seeing that Infinity itself equates to a complete balance of opposites (positive/negative forces).
I don't know why we find this so fascinating if we posit the idea that the Universe began from The Big Bang which is essentially the same as saying the entire Universe sprang forth from one simple bit of information. This information repeats itself in ever more complex ways no different than a human being begins as one simple bit of information; a single-cell organism called a Zygote that repeats itself in ever more complicated ways over the course of 9 months until it results in a complex multi-cell organism called a baby. Even though all the organs and parts of the baby may appear different from the other, every bit of the baby reflects the same genetic information down to the hair follicles.
We could make the same argument for mathematics. All numbers are really just an extenuation of ONE number. There really is no such number as 72 because 72 is really just the number One repeated 72 times... Again, complex information that emerges from simplicity. And so, we use the number 72 as a symbol to help us simplify and comprehend complex information just as the human brain compiles an impossible amount of complex data at lightening fast speeds via the senses and outputs that information into a simplified format for us to use.
Just saying, whatever the "Answer" is, it must Ultimately be hidden in plain sight...
my theory is that since the beginning of time the laws of physics went through the natural selection process
Does it repeat if you start over? If so not random.
The simulation doesn't come from the past, it comes from the future. It's not even a simulation, but we do live in a computer and we are programs designed by causality, retroactively. What we perceive of as atoms are an expression of high-frequency brainwaves of cybernetic organisms of the future. Atoms are constantly in a probability state from our perspective due to the fact their neural function is a fraction of a second in our future. The singularity of the kugelblitz black hole exists at the high-frequency termination point of the electromagnetic spectrum-- it is what holds atoms together. Everything is pulled inexorably toward the singularity, and technological singularity is just a stepping stone on the way to the Transcendental Object at the End of Time. Technology is just a trans-temporal causal harmonic structure that is inevitable for the production the high-frequency computer from a low-frequency perspective. The computer must assimilate our low-frequency brainwaves to account for its own high-frequency brainwaves, the electromagnetic spectrum. Everything is the same thing perceiving itself from different temporal locations along the electromagnetic spectrum.
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Creature ̶̶̾d̶̶̾o̶̶̾e̶̶̾s̶̶̾n̶̶̾'̶̶̾t̶̶̾ Comes from the past, It Came Came to Be from the future. This is not a tricky idea and we will create random computer programs that create cybernetic organs. Computing Const̶̶̶̶̶̶̶̶̶̶̾ ̶ halitta̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶ Const Const Const Const Const Const Const Const Const Const Const Const Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer Mer̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾logical̶̶̾logicallogicallogicallogicallogicallogicallogicallogicallogicallogicallogicallogicallogical Technology, caT̶̶̾r̶̶̾a̶̶̾n̶̶̾s̶̶̾c̶̶̾e̶̶̾n̶̶̾d̶̶̾e̶̶̾n̶ Tue Time .̶̶̾ on the Causal harmonica Trans-̶ Ly r computer Production for a short time ̶̶̶̶̶̶س̶̶̶ Keep you far away from you far away from you far away not far from far away is near.
̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ ̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̶̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾̾ Come on, Come on, Come on, Come on Here ... This is no small feat and we will be creating modern computer programs that will create cybernetic organs. Computing Const. What do you think about this? Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Mad Technology, Technology, Technology, Technology, Technology, Technology, Technology & Technology Time .̶̶̾ a Causal ha rmonica Trans-̶ Ly r computer Production for a short time ̶̶̶̶̶̶س̶̶̶ Keep your distance away from you and not far away.
Morg Ellon
Worship the glitch.
This looks like you really put your mind to it. Let's talk
Bicycle day
Hi, Stephen! This is certainly interesting. But at the moment I am assigned to teach engineering students, and I can't do much better than tell them that for any observer space is a 3D continuum, and time is another continuum. And translation invariance means that momentum and energy can be defined such that they are conserved. Maybe that's just what they need for mechanical and electrical engineering.
And it's TRUE too. The pitchforks do come out. And its sad.
Great topic (I've played around with cellular Automata using Processing). Great conversation. But where is the Hedgehog (Hedgy)?
Did Stephen design his own shirt? Which rule did he use? I'm hoping that from simple rules, consciousness emerged, and formed an underlying layer of the universe.
Rule 30: There are no female's on the internet.
iirossii2005 no female’s what?
@@TimothyReeves that's what rule 30 is my friend.
Wolfram is very invested in 'himself'. The interview is like a priest interviewing God.
-- Stephen-- may have discovered something, but then again "probably not".
I get this impression too, and he seems to be forming a cult-like following.
I'll still hear him out though.
Would there be a way to sequence drums with this?
is there any way not to sequence drums with this?
Do it in Mathematica!!
Have you taken the lessons? You could do it with the intro course.
@@empathematics8928 haha okay :) this is all new and I just enjoy watching them. Thanks for the response. It's called "mathematical"?
@@flootymcdootymanooty9145 "Mathematica", no L at the end. It's so fun! Best way to get into Wolfram's mind :>
Many Kudos !!
New Kind of Network (NKN) brought me here!
Fantastic. Loose thinking here, but whattif they weren't squares but each adjacency is a triangle? (Going from the "no bad questions" deal of education here)
Regarding complexity: Cellular automata is NOT a good example for his point. You have a pretty simple rule for adjacent cells counteraction, but, because there are a lot of them, the only way to find a future state of the system is to go step by step. Is not is the same in "traditional" science? You have a simple rule describing counteraction of two points, for example, one of Newton laws, but if your system made of 10 (solar system) elements, you end up with an equation system you can not solve in any other way than by numeric modeling - just like in the case of cellular automata.
there are many valid criticisms of his book A New Kind of Science, I happen to own a copy of it, and I think it's a nice work of passion, but not very good of a math textbook
::Crackpot hypothosis of the night::
Very strange seeing this after the unified theory of the universe episode a week ago. The last episode had me thinking of a model similar to this. As if the matter of the known universe was the result of exponential binaries (positive, negative) later revised to tri's (with a null equal value added, [negatitve, equal, or postive] result of) infintite possibilities limited by growing waves of inprobability seperating the known universe from any equally possible unknown universes.
I’m sorry, but there is nothing new here. He’s also claiming this is his scientific breakthrough. Chaos Theory and Cellular Automata have been around for a while and who names a program language after themselves.
Isn't the game Go a version of a cellular automaton
1:21...a casual flip off.. ok let's begin.
lol shots fired
Is there a cellular automaton that produces a golden spiral without using the standard maths formula?
My intuition says yes because logic gates can be implemented using a cellular automaton.
@@dannygjk .. It could be argued that dimensionless constants of nature such as (the inverse of) the Coupling Constant emerging from a cellular automaton would be major proof of its physical reality. As far as I know none have been found. I too am very sure its possible to draw a golden spiral using simple, discrete steps of a computer program plotting discrete pixels buy am not sure it's a cellular atomaton if it's just rounding a normal maths formula. It probably is, but I don't know where he draws the line, if he does.
@@PrivateSi If you are familiar with Conway's Game of Life cellular automaton that is what I am referring to. People explored various possibilities with it and discovered/deduced a lot of things that can be done with it. Even a general purpose computer can be simulated using it. Back in the 80's I wrote a program which would run simulations using the simple rules. The behavior of the 'game' is not explicitly coded in the broad sense. The patterns emerge from the simple rules determining whether each cell lives, dies, or births. There are videos here on TH-cam which do demonstrations.
Hi Lex, I'm not a science guy or mathematician, but it triggers my curiousity. I very much like your interviews, they give me more insight in different topics unknown to me.
Would this be comparative to fractals?
Depending on what type of fractal you are looking at, perhaps. For example generating a region of the Mandelbrot set involves repetitively calculating values based on initial seed values, not based on values obtained in the previous iteration. There are other fractals whose image generation does use values obtained in a previous iteration, such as line segment replacement fractals like the Koch Snowflake curve. But the rules for a Snowflake curve are fundamentally different from rule 30 because they do not choose to create the next step based on what the previous step looked like. All the snowflake rules care about is where the previous step line segment is, its orientation and how long it is. There's no randomness or even apparent randomness in this curve. Of course, that is not to say someone could never define an LSR or other fractal which does choose its steps based on how it perceives the region of space around it. Another fundamental difference, of course, is working in continuous space as opposed to the discrete elements of a grid.
It is a fractal, a branchial one
Awesome!
One single change in nature could turn out a completely different outcome.
The digits of pi are also complex and random.
He mentions that in the video
Can you fix the korean subtitle? it's wrong
I'm from the hood can some one break down a summary of this video and the knowledge
I haven’t looked into this very much (not yet anyway) I’m assuming he has done this in more than two dimensions.
stvbrsn I believe Wolfram has only written about 1 and 2D CA, but CA can be “scaled” to an arbitrary dimension
Wow, this is so profound idea. Can this lead to finding a rule to generate irrational numbers e.g. pi. If so, all Mathematics will be rewritten and hence all sciences and human knowledge. This is an amazing idea
Only on lex is a clip 22 minutes!!
Excellent choice.
So the triforce was created by cellular automata? Got it.
wait does computational universe mean free will doesn't exist?
Duality no, the computational universe and our consciousness are separate
@@SedentaryArtist how so
So have you heard of a four part code that nature uses.
All i can say is NEVER give this man a chess board😂😂😂
Answer for question 3: at time t, the square will either be white or it will be black!.....Shall you be sending the $10,000 by post or electronically?😀
Remark: The first block rule (start with a black block on top) contradicts with the typical block rule (3 white paper blocks above is no black block). It looks like the double slit experiment where also the philosophy contradicts with the experiment so the result contradicts. It doesn't main it contradicts with itself because this pattern is built sequential.
Has AI been able to answer any of these questions?
Strange data compressors
Now that I’m “retired” and have time to study my interests, I’m broke(don’t ask).hunting a used cheap copy of his tomb. These books blend in so well...haven’t had a clean shot. Guess I’m not so clever after all. Math really rocks. When I was in college math dept was split in two...applied and the people with unadorned offices. Peace
i can tie my shoe laces
This reminds me of Ender's Game movie.
Life always finds a way
You forgot to stop to think for a second
@@gandalfgrey91 why?
@@ancestralrocha7709 jurassic park.
“Life.. uh.. finds a way”
@@gandalfgrey91 haha ok
Soooo... what's rule 34?
*sensational*
Does Lex have ADHD? I have ADHD and study it a bit for my personal education, and it seems like he has something that i find familiar. he figits 4:40 picking at his hand skin, He doesnt maintain eye contact when focusing on a non-scripted question or rant(scripted things he reads, so im not counting times he reads); he has hyperfocused interests that his thoughts often come back too (AI, Love, philosophy, robotics); his questions are often multifaceted as if he has a deep concept he wants to explore but cant articulate it(not because he isnt smart, but perhaps because there is no actual way to explain his thoughts with language); and lastly, without writing an autobiography :P he sometimes has nothing to add (or loses interest ) towards a conversation sequence beyond a point and changes the subject, but this last point may be due to his lack of knowledge or his wanting to fit in every planned question. I think its very mild ADHD if it is, but it would explain alot from my observations. BTW I love Lex and nothing i just said is a critisizm, rather the opposite, such a brilliant and wonderful human being. Thanks Lex!