Running back in time is *not* recalling the past

Running back in time is not recalling the past

Рет қаралды 59,333

Күн бұрын

This follow-up discusses fluid simulation related information reduction in view of time irreversibility of the governing evolution equations.
We gain an overview of a statistical perspective on the microscopic motion and highlight the implied time irreversibility as well as the exclusion of anti-dissipation.
Topics covered/used: Kinetic Theory of Gases, Boltzmann Equation, One-Particle Phase Space Density Function, Information Reduction, Laws of Evolution, Microscopic and Macroscopic Perspective, Laws of Motion, Time Reversibility vs. Time Irreversibility, Dissipation.
Timetable:
-----------------
00:00 - Microscopic Motion vs. Macroscopic Experience
01:33 - Macroscopic Influence on Microscopic Motion and Dissipative Tendency
04:38 - Statistical Perspective on Microscopic Motion and Information Reduction
08:54 - Time Irreversibility of the Statistical Perspective
10:13 - What's coming next? (Fluid Simulation Series!)
Important Note:
-----------------
I recommend exploring the literature further (see a few selected references below), as there are many more aspects necessary to fully understand the nature of time irreversibility, which may be covered in an extended version of this part. In particular, for brevity, I have chosen not to introduce the n-particle phase-space density perspective here, useful to talk about densities of (anti-)trajectories what could be done to define dissipation and related concepts probabilistically. This is addressed more verbally by saying things like "some anti-time behavior", implying that probabilities should not be attached to individual trajectories, but rather that one should think in terms of probability densities. For the short version, I have tried to convey such aspects at least verbally, but if you are interested, you should know that there is of course much more to say.
Selected Papers and Learning Resources:
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Book: Evans, Denis James, Debra Joy Searles, and Stephen Rodney Williams. Fundamentals of classical statistical thermodynamics: dissipation, relaxation, and fluctuation theorems. John Wiley & Sons, 2016.
Book: Hoover, William Graham, and Carol Griswold Hoover. Time reversibility, computer simulation, algorithms, chaos. Vol. 13. World Scientific, 2012.
Paper: Lebowitz, Joel L. "Boltzmann's entropy and time's arrow." Physics today 46 (1993): 32-32.
Paper: Ardourel, Vincent. "Irreversibility in the derivation of the Boltzmann equation." Foundations of Physics 47.4 (2017): 471-489.
Paper: Maes, Christian, and Karel Netočný. "Time-reversal and entropy." Journal of statistical physics 110.1 (2003): 269-310.
Lecture Notes: from "volkov.eng.ua.edu/ME591_491_NE..." to "NEGD-06"
Lecture Notes: "Kenkre, V. M.. Statistical Mechanics. www.unm.edu/~aierides/505/" specifically ".../bbgky2.pdf" & ".../bbgky3.pdf"
Lecture Notes: "Cerfon, Antoine. Mechanics (Classical and Quantum). www.math.nyu.edu/~cerfon/mech..."
Disclaimer:
------------------
This series focuses specifically on the aspect of information reduction in dynamical systems. For the sake of clarity, I had to omit many interesting aspects of the topics addressed in the video. So, the video itself is a reduction. :-)
I hope you enjoyed this little braintruffle!
If you like this series and want to support my work, you may consider subscribing to the channel and support me on Patreon.
/ braintruffle

Пікірлер: 151

@antoniobaianosvizzero764 2 жыл бұрын

This series is going to be a masterpiece

@fburton8 2 жыл бұрын

The definitive guide, yes!

@maxjost9266 2 жыл бұрын

It already is a masterpiece.

@braintruffle 2 жыл бұрын

I'm so happy you like it! Thank you!

@ecicce6749 2 жыл бұрын

it's already a masterpiece. It was pure joy to watch and follow along

@firstnamelastname3367 2 жыл бұрын

@@maxjost9266 A phdpiece then

@DerName2 2 жыл бұрын

I love the clarity of the shown thought process. Many others would have covered the entire video in 1-2 sentences, omitting all this detail. Thank you!

@braintruffle 2 жыл бұрын

Scripting indeed takes the most time. Hearing it being appreciated makes me happy! :)

@wolfyklassen 2 жыл бұрын

Perhaps the best series of videos about statistical mechanics I've ever seen, and it's not even about statistical mechanics. Waiting for the algorithm to pick this one up!

@braintruffle 2 жыл бұрын

I like your comment so much because it captures so well how I feel about this whole series. As we accidentally understand the different topics we encounter, we hopefully recognise the underlying patterns of approaching such topics and develop the necessary mindsets to tackle different problems in the future that seem to be unrelated to fluids.

@starrmont4981 Ай бұрын

@@braintruffle Peak big brain behavior. Please reproduce.

@Lukegear 2 жыл бұрын

Awesome! This series is probably the best I've seen when it comes to understanding fluid simulations. I'm a chemical engineering graduate and I've always wanted to program a simulation as a hobbyist but I've never quite had enough of a solid grasp on the concepts to proceed with the implementation. I could've simply followed some random tutorial but I'd rather develop an understanding of the concepts being applied to able to code my first simulation. Can't wait for the next part!

@braintruffle 2 жыл бұрын

Thank you for taking the time to write such a kind comment! I'm glad you like the general approach. Personally, I focus a lot on the conceptual side (maths, problem setting, changing perspective, asking the right questions, things like that ...) and it helps to see that others share these thoughts. I hope to see you in the next part!

@tamashamas6193 2 жыл бұрын

Really respect the thought you put into now just the how but also the why to your methodology. Super excited for the rest of this series!

@galzajc1257 2 жыл бұрын

One of the most underrated channels on yt

@astrogabba1190 2 жыл бұрын

This is shaping to be one of the most exquisite series on youtube. Outstanding work so far, truly.

@braintruffle 2 жыл бұрын

Thank you soo much! I'm glad you like it. :)

@matjesmeister2403 2 жыл бұрын

This has to be one of the best educational series of videos I have ever seen! Right up there with 3Blue1Brown and others

@braintruffle 2 жыл бұрын

Thank you for the appreciation! I feel honored. :)

@ntt2k 2 жыл бұрын

I hope this channel gains more popularity. The videos are visually stimulating. And you learn a lot in the process

@estebanmarco8755 2 жыл бұрын

Hell yeah, more fluid dynamics

@problemecium 2 жыл бұрын

This is making me have deep thoughts about the nature of time and determinism in the real universe.

@raghavendradheeraj7445 2 жыл бұрын

Just discovered this channel and spent 2 hours watching one of the more precise and lucid explanations on the internet. As a graduate on these topics, I find your perspective is incredibly unique and worth sharing with everyone. Keep up the great work! Waiting for your next upload!

@tfs711 2 жыл бұрын

Your videos has simulations as exactly how I think and they completely present my imagination which is so beautiful. Thanks a lot for this wonderful work. I liked and subscribed already. Wonderful Channel!

@braintruffle 2 жыл бұрын

I'm very happy that it fits to your imagination! I hope you like the next parts too :)

@luislindgren5615 2 жыл бұрын

The clarity of your explanations and the beauty of your animations are admirable. Thank you so much for this!

@luislindgren5615 2 жыл бұрын

As a side note, do you use manim for the animations?

@lucaslemos2037 2 жыл бұрын

Amazing job. Never stop the channel. Congratulations from Brazil.

@EggCess 2 жыл бұрын

Fantastic video again, I'm in love with this series. Thank you so much!

@vitorheitorcardosocunha3843 2 жыл бұрын

I'm dazzled and speechless with your amazing video. I'm a fluids engineer working with statistical thermodynamics and your video made me recover my energy and motivation towards my daily routine. Damn!

@mistertheguy3073 2 жыл бұрын

Such an interesting way of thinking, wanting less information to be able to simulate faster

@Modalitony 2 жыл бұрын

Absolutely brilliant! As a chemical engineer I am delighted with this series. This is the most intuitive derivation of how macroscopic properties are derived from microscopic states. It took some years of studying to develop this picture for myself. And here you derive it all in a visually intuitive way, in such a short period of time. Masterfully beautiful. Your videos fill me with joy. I have a newfound appreciation for having studied this field.

@MMT--Games 2 жыл бұрын

You have only 13k subs and this video only has 22k wiews? im really expecting you to blow up very very soon, you have big potential

@guylaingreer4190 2 жыл бұрын

Geez your visuals are stunning! Loving this series! Thanks :D

@graycat7777 2 жыл бұрын

This is the top tier of KZfaq. Congratulations!

@t.nicklasson6906 2 жыл бұрын

Extremely interesting! Very much looking forward to the next episode in those series!

@Lukilliano 2 жыл бұрын

So exited for that series! Have fun creating it!

@jaredjones6570 2 жыл бұрын

This is amazing! I've watched all the videos in the series so far and I'm excited for the future videos. I would love to build my own CFD.

@hieule8575 8 ай бұрын

Amazing videos! Can’t wait for the next ones

@neocortical451 2 жыл бұрын

Thank you for giving us hope for the next parts!

@literallyagalaxy7789 2 жыл бұрын

10:17 when your microscopic simulation tells you your full legal name and address

@ansonhaniwalt4806 2 жыл бұрын

Outstanding video as usual, and the thumbnail this time is a significant improvement! I'm so glad to see that your videos are starting to get the attention they should. Also good to see you made a Patreon! I imagine over time you'll reach many people who will be very happy to support novel content like this :)

@braintruffle 2 жыл бұрын

I'm happy to hear from you. :) Thank you again for addressing the thumbnail issue last time. I thought carefully about your comment when creating this one! :) And of course, thank you for your support!

@ranglurofrivia5985 2 жыл бұрын

Phenomenal video, exited for the next one already!

@tommclean9208 2 жыл бұрын

ive never heard of this cfd method and its absolutely genius

@AK56fire 2 жыл бұрын

All your videos on a whole another level.. It's beyond awesome.. Great animations and great in depth explanation.. Great work through and through.. Loved it..

@hermanthenakmuaygerman 5 ай бұрын

Great videos, great channnel. 🙌🏻 Thank you for your good work. 🙏🏻

@gutzimmumdo4910 2 жыл бұрын

incredible quality of teaching and animation

@ScrantonpaperCo 2 жыл бұрын

This man DELETING TIME for better sims. This series is awesome!

@karllundgren 2 жыл бұрын

Amazing! Looking forward to the following episodes!

@KMPR40 2 жыл бұрын

Absolute master class. This is exquisite content.

@RealMarciBE 2 жыл бұрын

Your videos are amazing! Keep up the good work!

@Zandario 2 жыл бұрын

Can't wait to see more! I absolutely adore this kind of stuff

@Guitareben Жыл бұрын

This channel is incredible.

@RTDAVIDgamer 2 жыл бұрын

simply beautiful, great work!

@bregottmannen2706 2 жыл бұрын

This is the best youtube series on youtube, making 3b1b look like a fool

@skep2825 2 жыл бұрын

Loving this series!

@HUEHUEUHEPony 2 жыл бұрын

One of the best simulation animations I've ever seen but the voice is good for sleeping. Sleep is a good thing tho

@Life_42 2 жыл бұрын

Great channel! Subscribed!

@mraxilus 2 жыл бұрын

I'd love if you could do a video solely about how you go about making these videos (research process, tools used, etc.). The pacing, colours, animations; all fantastic!

@Petch85 Ай бұрын

Absolutely beautiful

@entertainmentupdates5730 2 жыл бұрын

awesome, mind blowing , marvellous kindly keep it up

@hansiboy5348 2 жыл бұрын

This is criminally underrated

@Nithaelilluvatar 2 жыл бұрын

I want more of that thank you for this video i love your voice is so relaxing

@jpk8588 2 жыл бұрын

fantastic animations :)

@oUncEblUnt420 2 жыл бұрын

This is the type of in-depth thinking I've been missing

@balajisriram6363 2 жыл бұрын

please make sure to discuss both space and time discretization methods in detail. We would love such a video

@y5mgisi 2 жыл бұрын

Can not wait for the next episode!

@loukitmyname 2 жыл бұрын

Waiting for the next video eagerly. Very very eagerly.

@kevin-jm3qb 2 жыл бұрын

Amazing video please keep making moar!!

@boomiboom3900 2 жыл бұрын

I think its time to revisit my patreon account now :D I would easily pay for a full fluid simulation course of this quality! Thanks for the effort to create this

@braintruffle 2 жыл бұрын

Thank you very much for your support! It helps a lot! :)

@alan5506 2 жыл бұрын

The legend has returned!

@mindprobe3587 2 жыл бұрын

Love your videos

@thewiseturtle 2 жыл бұрын

The real laws of motion always include both *repulsion* and *attraction* which is why the normal curve of probability in entropy (probably) makes all possible microstates actually happen. That's why so many folks get confused by entropy, and think that it means that things only ever fall apart, and it's why these computer models are not especially accurate to real life, because entropy actually means that things fall apart and form new things, over and over. Entropy is the same as evolution, with that messy sexual reproduction via natural selection (things coming together) and random mutation (things coming apart).

@88Magician88 2 жыл бұрын

Sorry but no. Entropy is not evolution. If you look at each state of a time crystal you can say it evolves into the next state but yet time crystals have 0 entropy, they are non-entropic processes. Entropy is often misunderstood because it is just that, a hard concept to understand. Look up Shannon entropy to get a better understanding. Essentially entropy is the limit of energy transfer of the microstates. Very, very few things in this universe have 1:1 energy transfer, there is usually a resistance. (Time crystals are the only example I can think of) Hence, entropy increases for most systems. Essentially entropy means things lose energy over time. Hence why you can't have perpetual motion. I think what you mean is that like evolution, entropy is a quantity which exists ONLY for the system. If you take the particle out of the box there is no entropy. Which is true!

@thewiseturtle 2 жыл бұрын

@@88Magician88 Yeah, it's unfortunate that so many kids were taught such a weird, old fashioned, backwards idea of what entropy (the laws of reality) is. Shannon entropy is what I'm talking about, which is evolution, as in the process of generating a family tree, where individual patterns combine and then divide, over and over again. As you say, it's the number of possible microstates in a system (macrostate). Pascal's triangle models this nicely, or a Galton board, if you're curious about what it looks like. What something appears as to an observer (anything that can change, and have multiple states) will vary based on what the observer is (how it's observing). So some things seem to not be changing (matter), and others seem to change rapidly (energy). If you experience things "losing energy over time" that's because you, as an observer, are focusing on the matter-like elements of it. In reality, the universe never creates, nor loses, energy or matter. It's always the same amount. Just differently distributed. Like how a fractal keeps changing while staying the same. Reality is just one massive family tree of patterns of varying stability and change branching and recombining, to evolve all possible states of existence. Stephen Wolfram is starting to explore this if you want a different approach then my own.

@88Magician88 2 жыл бұрын

@@thewiseturtle I agree! (kind of) Whenever I heard entropy being described by a prof I always had to sort of tune it out because they would say something like "this isn't really how it is but it's an analogy to help you understand", if it isn't how it is don't teach it to me, ya know? I hesitate to say I fully agree because you use evolution, which is loosely defined. Time crystals evolve over time (yes they repeat, hence the crystal but they do evolve) but are non-entropic. So I can't say I agree that entropy IS evolution but I will say they are analogous. I do love the way you think about the universe. Not many people see it like you but I think your picture is a lot closer to reality than others! Well done!

@oUncEblUnt420 2 жыл бұрын

Dont gravity and electromagnetism work thru the move along spacetime=attract, move opposite to=repel? Wonder if the notion of electrons being one-handed has anything to do with this asymmetry? I forget what I'm referring to, but something about them not being reflected in a mirror

@88Magician88 2 жыл бұрын

@@oUncEblUnt420 I think you are talking about electron chirality. Electrons are left-handed (spin) and positrons are right-handed (spin). The Stern-Gerlach experiment was what they used to figure this out. Spin has nothing to do with gravity or E and M. Spin has to do with angular momentum. (If the electron was a macroscopic object then it would be spinning. It's not, therefore, spin is an objectively confusing name.) The "notion of electrons being one-handed" has to do with this chirality. The claim is that there should be an even amount of left-handed electrons (electrons) and right-handed electrons (positrons). We don't see this though, we see mostly left-handed electrons. Thus you could say that chirality symmetry is broken by electrons. However, there is nothing that states the universe must have chirality symmetry. We assume it does because then we can say the universe has parity symmetry, which would be nice mathematically but there is no physics that demands this, thus things that break parity symmetry (probably) aren't paradoxical.

@visualgebra 2 жыл бұрын

Great Explaination❤❤❤❤

@s1l3nttt 2 жыл бұрын

This was epic!!!

@mawillix2018 2 жыл бұрын

Great animation quality.

@cretinobambino 2 жыл бұрын

OH BOY! HERE WE GO!

@doBobro 2 жыл бұрын

So good!

@leonard2000s 6 ай бұрын

The video is super beautiful :) I'm wondering about one thing though: When simulating fluids with those SPH-particles the SPH equations (in the zero viscosity case) are (although derived from Euler equations which are derived from the Boltzmann equation which is irreversible) time reversible and using a reversible integrator and fixed point arithmetic, we can actually see the particles forming up again if we reverse the velocities after coming from such a formed state, as done in Globally time-reversible fluid simulations with smoothed particle hydrodynamics - that we can do this, however, comes from knowing the exact particle positions and velocities - only from the 1- particle density, it is as in the colliding spheres case - just unlikely to find this behaviour. The Boltzmann entropy (based on the 1-particle phase space density) increases (statistically) while the Liouville entropy remains constant. Edit: Actually forming a dam again and clumping up are very different phenomena. For a non / weakly compressible fluid to form a dam again is quite plausible, but the system will not clump up again working against pressure forces which normal particles - not our SPH particles - could do.

@faresabbasi2613 6 күн бұрын

Waiting for upcoming videos :)

@frostygecko 2 жыл бұрын

Where is the next part?! I miss this series so much, even if it only has 3 videos

@goodstuffhappyshare 2 жыл бұрын

Set up a particle simulation and witness energy un-dissipate? I have tried that too ;D When I learned about Poincaré recurrence theorem as a student, I thought to myself, doesn't this destroy the 2nd law of thermodynamics? You sir, have a very satisfying answer.

@apocalypt0723 2 жыл бұрын

Can't wait

@Zeno2Day 2 жыл бұрын

Nice simulation

@mahxylim7983 2 жыл бұрын

Amazing script!

@Michallote 2 жыл бұрын

Yooooo this is amazing!!!!! I really appreciate how KZfaq has become a platform that shares knowledge that bewilders my understanding of the world. I've always been a keen learner but holy cow. This is beyond that, eye opening tbh. Sir I want some advice. I already am somewhat familiar with coding and programming. I don't know OOP but i do know the use of structures in MATLAB and fairly complex stuff in Wolfram Mathematica. I want to learn how to build my own simulator of fluids so I can play around see what I discover. Which language would you recommend me? What are it's advantages and what's the main framework I need to understand to make it become a reality? I'm curios about C# as Sebastian Lague seems to use it. Python I'm familiar but not proficient. I am willing to really take the dive into it. But I don't know where to start!

@sasucarefree4694 2 жыл бұрын

Agree with all the other comments here! What tools do you house for your simulations and animations?

@damirtenishev6874 2 жыл бұрын

Thank you for another great masterpiece! One question: should we consider this as a part 3 of the Understanding Fluid Simulation series? I see your comments below the video and asking because: (1) The video name doesn't start with the "Understanding Fluid Simulation" prefix and (2) title picture is different. Should we expect part 3 as a separate video or this is it?

@braintruffle 2 жыл бұрын

Thank you very much! This part is meant to be a short follow-up, as it addresses things that I couldn't fit into part two. So it's kind of part 2.5, if you will. I plan to make the next part (3) more in line with the first two parts.

@PaulanerStudios 2 жыл бұрын

LETS GOOOOO!

@DyegoMiranda 7 ай бұрын

Sorry if this is a stupid question (since I am not a physicist, just a curious man), but don’t you need to add gravity? In zero gravity, fluids tend to stay in their lower energetic form, which is a spherical shape. If your model doesn’t include gravity, will the particles eventually acquire a less energetic formation? Or maybe this doesn’t apply to single atoms, but only to molecules with more complex interaction such as hydrogen bonds? Anyway, congratulations to your series, it is truly amazing!! You should keep the channel active! Thank you for all the effort you put in it!

@SirTravelMuffin 2 жыл бұрын

Could you help me to understand what program/libraries you used to make this? I really like the visualizations you use and want to start making physics education videos

@Tonjevic 2 жыл бұрын

Are there delicate fluid phenomena other than time-reversibility that are lost in this approach?

@Alexander_Sannikov 2 жыл бұрын

when you are going from a lower-level model to a higher-level model, do you rigorously derive how their coefficients are connected so that they produce the same results, or do you approximate them until they sort of match? for example, in this case did you derive the macroscopic parameters such as viscosity from the microscopic parameters such as particle freerun length and radius or did you just tweak them until they sort of match?

@braintruffle 2 жыл бұрын

Personally, I like the fact that there are different approaches that can be used depending on the main objective of the analysis. Your comment addresses this aspect perfectly! Since this series is about giving structure and looking conceptually at problems, knowing that there are different ways is a good placeholder for further discussion if needed.

@miguelc.8153 2 жыл бұрын

Great

@mateuszbugaj799 2 жыл бұрын

While watching this I got hit by the brick of solid nitrogen that improbably materialized above my head.

@thewiseturtle 2 жыл бұрын

Most everything that happens in our animal level of the universe is pretty improbable. This is what we call free will. It might be deterministic, but it's also (likely) pure randomness. So everything that possibly can happen does happen, somewhere, somewhen. Of course, not everything is possible. But nitrogen glass does happen here and there. And so does your head. So while improbable, it's not impossible. Just like falling in love, or winning the lottery.

@TheQxY 2 жыл бұрын

@@thewiseturtle That's not how probabilities work.

@thewiseturtle 2 жыл бұрын

@@TheQxY What's the probability that that's not how probabilities work? Also, which isn't how probabilities work. I said several different things.

@12kenbutsuri 2 жыл бұрын

Amazing tutorial. What do you use to animate so fluidly?

@bernardobritto8352 2 жыл бұрын

Which software/library do you use to generate these amazing demonstrations?

@dimadima5298 13 күн бұрын

Hello Braintruffle . Can you please suggest what you consider as the best fluid mechanics books (videos ) for a mathematician and a hydraulic engineer , and I need also books on the subject of Numerical Analysis ... thanks in advance

@alienmoonstalker 2 жыл бұрын

Wouldn't intermolecular forces introduce dissipation and prevent time direction effects? Or are you only interested in perfect gases, based on kinetic theory?

@aniksamiurrahman6365 2 жыл бұрын

Reminds me of early 2-minutes paper video.

@alfchemy 2 жыл бұрын

Awsome. What rendering technique do you use? Blender + python?

@manishvarshney5571 2 жыл бұрын

I also want to know the same thing.

@MikeFico998 2 жыл бұрын

These blue light dots make my brain white hot

@michaelzumpano7318 2 жыл бұрын

I’m sure you’re familiar with the SINDy work they’re doing at UW. Is the average probability density and dissipation already built-in to SINDy by the nature of sparse optimization? I’m wondering if explicitly incorporating this probability average could be used algorithmically to reduce the cost of hunting for sparse matrix coefficients, or if it is just as costly?

@WelshGuitarDude 2 жыл бұрын

Is there a 4th video planned ? :)

@SuperExodus13 2 ай бұрын

I like this video but when you say "reversing" it initially confuses me. Obviously, if you could magically pause a flow and reverse all the particles, that new flow cannot defy laws of thermodynamics. But that is not usually what reversal means. If you were to simply run back the clock and track the particles in a simulation (not the real world) they would go back to the initial conditions. Anyway, thank you for the very insightful video.

@ebakes 2 жыл бұрын

Isn’t the energy collecting effect just the pendulum synchronization thing

@lucasnoetzold 2 жыл бұрын

hmmm, so destroying localized information restricts the arrow of time 🤔 that got me a philosophical epiphany on the nature of our own reality... if quantum fluctuations are truly random, they do destroy localized information, and that would explain the "only forward" nature of time. Either that or I already drank too much

@ecicce6749 2 жыл бұрын

or the statistical nature of quantum mechanics is already hiding an underlying deterministic concept that doesn't really have a forward time direction. Maybe "forward" or "backwards" has no meaning at all its just happens to be either case (not both) which doesn't really effect anything as particles behave the same either way. macroscopically it's just statistic so certain unlikely low entropy states like sudden perfectly straight towering atoms or every particle accumulating in the corner of a room or similar meaningful stuff just don't occur or at least extremely rare.

@raghavendradheeraj7445 2 жыл бұрын

@@ecicce6749 great answer. i'll add my 2 cents here. evolution laws do not require a definitive arrow of time to work, since they are symmetrical. I don't know if that's relevant, but I felt like I should say it.

@ARBB1 2 жыл бұрын

You produce the simulated graphics with a mix of Blender and Python I suppose?

@saigonpunkid 8 ай бұрын

Is this like a microscopic time machine?

@macprofire 2 жыл бұрын

Beautiful and instructive video but any encoder’s worst nightmare ^^

@enginsci8307 2 жыл бұрын

Disappointed by this TIME this video is published because i wish it was earlier that i can now find the future parts in the channel

@manishvarshney5571 2 жыл бұрын

From which software you are making these simulations?

@irri4662 8 ай бұрын

Randomness, viscosity ,'nothing is entering or exiting in such a pure and sealed box.', .This was left out. Tending to an unrealistic odds of system development. Seemingly breaking law of entropy.