Looking Glass Universe
Looking Glass Universe
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How AlphaFold solves protein folding
AlphaFold paper: www.nature.com/articles/s41586-021-03819-2
The original paper about transformers (the technology behind GPT), Attention Is All You Need: arxiv.org/abs/1706.03762
*Helpful videos and blogposts about attention and AlphaFold*
3blue1brown's video on transformers: ua-cam.com/video/eMlx5fFNoYc/v-deo.htmlsi=V5k3r6sc5NSMhFt0
Nazim Bouatta's talk on AlphaFold: ua-cam.com/video/ri39B0Voujc/v-deo.htmlsi=JpFOlxrVIm0wfmsZ
Simon Kohl's talk on AlphaFold, (he is one of the coauthor's of the algorithm): ua-cam.com/video/tTN0MM2CQLU/v-deo.htmlsi=x7I5muFg0lm0VDy3
A very thorough blogpost about the algorithm from UV-Bio: www.uvio.bio/alphafold-architecture/
The Openfold github + paper: github.com/aqlaboratory/openfold + www.biorxiv.org/content/10.1101/2022.11.20.517210v2.full.pdf
Переглядів: 10 541

Відео

What *is* a photon?
Переглядів 164 тис.2 місяці тому
This video was supported by Screen Australia and Google through the Skip Ahead initiative. Animations by the extremely talented Kathy Sarpi: kathysarpi.com Link to the full series: ua-cam.com/play/PLg-OiIIbfPj3mDFx5zjVPtgiGwZMM4Erw.html Links to other photoelectric effect videos: This one has a very simple at home set up: ua-cam.com/video/A9SSfZBMaH8/v-deo.html For this one you'd need to buy th...
What can my homemade quantum computer do?
Переглядів 328 тис.4 місяці тому
This video was supported by Screen Australia and Google through the Skip Ahead initiative. Part 1 is here: ua-cam.com/video/muoIG732fQA/v-deo.htmlsi=_vFy9siMqkOdO1xV f you want to do this experiment at home, you can! It's very simple. All you'll need is: - a weak red laser pointer (the type in cat toys are generally safe) - polarizing film or polarizing filter. If you have polaroid glasses or c...
I made a (useless) quantum computer at home
Переглядів 194 тис.4 місяці тому
This video was sponsored by Screen Australia and Google Australia through the SkipAhead Initiative. Thank you Kathy for the beautiful animations! kathysarpi.com Part 2: ua-cam.com/video/tHfGucHtLqo/v-deo.html If you want to do this experiment at home, you can! It's very simple. All you'll need is: - a weak red laser pointer (the type in cat toys are generally safe) - polarizing film or polarizi...
I don't know why light slows down in water. (part 2)
Переглядів 68 тис.5 місяців тому
Supported by Screen Australia and UA-cam through the Skip Ahead initiative. Links to the other videos mentioned: Part 1 of this story: ua-cam.com/video/yP1kKN3ghOU/v-deo.html 3Blue1Brown's explanation of Feynman's proof: ua-cam.com/video/KTzGBJPuJwM/v-deo.html Experiment: If you’d like to try the experiment I did at home then you’ll need a phone with Lidar or you can get a laser meter quite che...
I didn't believe that light slows down in water (part 1)
Переглядів 96 тис.5 місяців тому
Supported by Screen Australia and UA-cam through the Skip Ahead initiative. 3Blue1Brown's video: ua-cam.com/video/KTzGBJPuJwM/v-deo.html Part 2: ua-cam.com/video/uo3ds0FVpXs/v-deo.htmlsi=zW8nyuZpn8NshfqC Experiment: If you’d like to try this experiment at home then you’ll need a phone with Lidar or you can get a laser meter quite cheaply. The app I found most reliable for the measurement was th...
I did the double slit experiment at home
Переглядів 1,8 млнРік тому
I did the double slit experiment at home
"bad at math" is a myth
Переглядів 45 тис.Рік тому
"bad at math" is a myth
It's possible to prove the Born Rule of quantum mechanics
Переглядів 14 тис.Рік тому
It's possible to prove the Born Rule of quantum mechanics
The biggest problem in the Many Worlds theory of quantum mechanics
Переглядів 19 тис.Рік тому
The biggest problem in the Many Worlds theory of quantum mechanics
How is energy conserved in Many Worlds?
Переглядів 29 тис.Рік тому
How is energy conserved in Many Worlds?
If there are “Many Worlds" why don’t you experience it?
Переглядів 48 тис.2 роки тому
If there are “Many Worlds" why don’t you experience it?
"Many Worlds" is a simplification of quantum mechanics
Переглядів 125 тис.2 роки тому
"Many Worlds" is a simplification of quantum mechanics
Making a mathematical mural
Переглядів 16 тис.2 роки тому
Making a mathematical mural
This calculation tells you your chances of being sick
Переглядів 49 тис.2 роки тому
This calculation tells you your chances of being sick
Is entanglement the key to quantum computing?
Переглядів 61 тис.2 роки тому
Is entanglement the key to quantum computing?
What math research feels like (for me)
Переглядів 57 тис.3 роки тому
What math research feels like (for me)
Should you do a PhD? | PhD in theoretical physics at the University of Cambridge
Переглядів 316 тис.3 роки тому
Should you do a PhD? | PhD in theoretical physics at the University of Cambridge
🎄 Making an overly math-y (ugly) Christmas tree 🎄
Переглядів 12 тис.3 роки тому
🎄 Making an overly math-y (ugly) Christmas tree 🎄
Coronavirus: why you should stay home
Переглядів 62 тис.4 роки тому
Coronavirus: why you should stay home
How to learn Quantum Mechanics on your own (a self-study guide)
Переглядів 1,7 млн4 роки тому
How to learn Quantum Mechanics on your own (a self-study guide)
Electrons aren’t actual waves
Переглядів 107 тис.4 роки тому
Electrons aren’t actual waves
From being terrible at math to a quantum physicist - my journey
Переглядів 705 тис.5 років тому
From being terrible at math to a quantum physicist - my journey
How to take a scientific approach to charity
Переглядів 18 тис.5 років тому
How to take a scientific approach to charity
The meaning of the dot product | Linear algebra makes sense
Переглядів 71 тис.5 років тому
The meaning of the dot product | Linear algebra makes sense
Change of basis explained simply | Linear algebra makes sense
Переглядів 60 тис.5 років тому
Change of basis explained simply | Linear algebra makes sense
A simple condition for when the matrix inverse exists | Linear algebra makes sense
Переглядів 27 тис.5 років тому
A simple condition for when the matrix inverse exists | Linear algebra makes sense
Matrices, matrix multiplication and linear transformations | Linear algebra makes sense
Переглядів 36 тис.5 років тому
Matrices, matrix multiplication and linear transformations | Linear algebra makes sense
Vector addition and basis vectors | Linear algebra makes sense
Переглядів 73 тис.5 років тому
Vector addition and basis vectors | Linear algebra makes sense
Comment response video for Understanding Quantum Mechanics
Переглядів 32 тис.6 років тому
Comment response video for Understanding Quantum Mechanics

КОМЕНТАРІ

  • @rudde7251
    @rudde7251 18 годин тому

    Tsk. Didn't even teach us how to get rid of the interference pattern. That's like the most important part.

  • @saaalaka
    @saaalaka 22 години тому

    Haven't they included this home experiment in a journal yet

  • @BenjaminOwenSlattery
    @BenjaminOwenSlattery День тому

    Using beams of light as qubits, can you entangle those qubits? How?

  • @ernestschoenmakers8181
    @ernestschoenmakers8181 День тому

    Well you say that it's not a wave/particle duality a light ray but somehow it has particle character cause the way a photon goes thru a double slit it interferes with itself and ends up somewhere on the screen, the way the interference pattern builds up can be calculated by wave properties but it's not a real wave more like a probability wave. One can see that the pattern is built up by dots which are single photons.

  • @brstudio7768
    @brstudio7768 День тому

    “How to learn quantum mechanics on your own” Don't

  • @YoutubePremium-cf5le
    @YoutubePremium-cf5le 2 дні тому

    Im amazed how you simplified the not so simple concepts especially for a beginner like me. Appreciate your channel and content.

  • @resmaurow
    @resmaurow 2 дні тому

    Isn't the fact that when light's position gets measured it can change its colour in agreement with Heisenberg 's uncertainty principle? Position and momentum are complementary and momentum is proportional to wavelength so, as you reduce the uncertainty of the position through a measurement, the uncertainty of momentum (and so of wavelength) should increase. I might be wrong, but that made quite a lot of sense to me! Anyway great channel! I'm gonna try and reproduce some of your experiments with my students!

    • @lepidoptera9337
      @lepidoptera9337 День тому

      No, that is not a fact. The wavelength/energy uncertainty depend on the duration of the measurement. It does not change with the precision of the position measurement. Strictly speaking the interpretation of Heisenberg in terms of measurement is 100% false, anyway. Heisenberg predicts that the localization of the entire wave function raises the energy levels of the system. In other words, the lowest energy a quantum can have in a box potential rises to infinity as the size of the box goes to zero. That is NOT how a measurement works. The measurement device does NOT localize the wave function to the size of the measurement device. A wave function scattering off a small measurement device is a non-unitary process in which some of the quanta get absorbed while others are being scattered back into the remainder of the entire system volume. In practical terms this means that smaller measurement devices have very low quantum efficiency while they are violating Heisenberg. The actual physical behavior is NOT covered by the naive application of the unitary theory.

  • @lene6641
    @lene6641 2 дні тому

    Wow, these two videos and the one by 3Blue1Brown taught me to understand something really deep which I thought I had down, but... understood as little as apparently almost everybody else. What I find most awesome about them is how you included all the wrong turns and frustrations on the way to figuring this out instead of just presenting the result. That is not just only a great way to teach, but also gave the videos an emotional depth that had me absolutely gripped while watching them... or maybe the emotional depth is just the thing that makes your teaching style so great.

  • @PP-pq2sk
    @PP-pq2sk 3 дні тому

    Why does light speed up when it comes out of the water?

  • @FunnyMarshmallow-ne2bz
    @FunnyMarshmallow-ne2bz 3 дні тому

    You find the answers see David LaPoint you will bee a little be surprised 🥰

  • @rvscript
    @rvscript 3 дні тому

    I saw another video and watched their reason.The speed of Light does not change. The issue is how we understand light. Light is interpreted as both a light and a wave. The “slowed down” light is an average of different waves . That is why light seems to regain its speed when light exits water into air.

  • @mjasper87
    @mjasper87 3 дні тому

    Sadly I disagree a lot ☹️. The Hong-Ou-Mandel effect is pretty good evidence that photons ARE finite wave packets. Friends don't let friends believe in the existence of plane waves..........

    • @lepidoptera9337
      @lepidoptera9337 День тому

      There are no photons in that scenario. As soon as light interacts with a physical mirror it turns from a free field into a quasi-excitation of a solid. Photons are, by definition, the quanta of the free field.

  • @easyerthanyouthink
    @easyerthanyouthink 3 дні тому

    because the problem is your focusing on space time as we know it and the photon as a discreet part of it and also that the properties of photon just wavelength/frequency ? ,! its what we cant detect or measure that is the key. The fabric of space time is considered 3d more or less in a simplistic way. Space time is just the tip of the iceberg!!! but we have been taught it is all there is !!! its a big lie . Im in Aus BTW. thanks for nice video and your humble attitude! you will go far with that for humility and curiosity is the key to to penetrate the barrier of future knowledge. dont forget me !

  • @Lukasz3332x
    @Lukasz3332x 3 дні тому

    We simply dont know how to use it. What is for sure is that one particle sends an impulse to the second one faster than light.

  • @kenlong9363
    @kenlong9363 3 дні тому

    Couldn’t you have a large amount of particles up is yea down is no. If it isn’t the answer you want you do it again until it is or you run out in witch case the other measured would assume it is whatever they haven’t seen.

  • @karnaghose4784
    @karnaghose4784 3 дні тому

    Should've found this vlog earlier

  • @hitoshiyamauchi
    @hitoshiyamauchi 3 дні тому

    Thanks! It was fun to watch.😀

  • @mw9297
    @mw9297 4 дні тому

    We live in a simulation.

  • @LarryErb-gs9fm
    @LarryErb-gs9fm 4 дні тому

    All wrong ...not a particle or a wave

  • @drewprof
    @drewprof 4 дні тому

    Well presented!

  • @dmartin23
    @dmartin23 4 дні тому

    yeah you really missed the most amazing part of this experiment. The fact that firing one particle through the slit still produces a wave pattern..but when you try and observe what slit the particle went through with a detector, the pattern disappears and you get the expected result as if you just had one slit. The fact that you have observed has interfered with the wave function.

  • @rominiyi1385
    @rominiyi1385 4 дні тому

    I genuinely could never imagine myself doing a PhD ... never ever! I would rather do three different thorough two year taught master's degrees. My field is an applied field ... so I believe I would learn a lot more from all the knowledge that is already out there ... rather than focusing on one very narrow field ...

  • @BooleanDisorder
    @BooleanDisorder 4 дні тому

    Attention is truly all you need

  • @angelgallardo9612
    @angelgallardo9612 5 днів тому

    I was wondering if the air in the atmosphere has to do somerthing with the light taking a wave pattern. Like the light is particles are bouncing in the air maning it behave like a wave.

  • @hansisbrucker813
    @hansisbrucker813 5 днів тому

    I remember playing Fold-it years ago to help scientists figure out proteine folding as computers couldn't do it. Glad to see that computers *can* do it now 😊

    • @LookingGlassUniverse
      @LookingGlassUniverse 5 днів тому

      I remember that!! Crazy isn’t it that computers are now good at this problem?

  • @sukitrebek
    @sukitrebek 5 днів тому

    Wonderful video, thank you. The photon-particle aspect of light hit me when I learned about the photoelectric effect, and the fact that low frequencies of light will never reach the threshold energy to eject an electron from a metal. This implies that light is not simply a wave, but has to be also thought of as quantized into discrete packets of energy, i.e. photons. Only photons of sufficient energy can activate the photoelectric effect!

  • @lbgstzockt8493
    @lbgstzockt8493 5 днів тому

    The triangle inequality is the kind of mathematical construct that, when learning about, seems kind of useless or obvious but then shows up everywhere.

    • @LookingGlassUniverse
      @LookingGlassUniverse 5 днів тому

      Right? I remember thinking, “why are we bothering to learn this?” When it first came up.

  • @charlesprabakar
    @charlesprabakar 5 днів тому

    Very informative -and equally good to know this algorithm uses the attention factor idea used by large language models of AI as well. This brings me to our firm’s latest research of integrating genetics/neuroscience with quantum mechanics including economics and AI etc with a common threading factor called attention factor, that has been derived straight from fine structure constant (FSC aka alpha) of quantum mechanics Interestingly enough this model has been named as alpha-fold as well Rightfully so, we have hypothesized that FSC mechanics is the one that is causing this folding logic What do I mean by that? For example, the four fundamental bases that make up the gene segments of DNA follow our quadrupled DNA rotaxane model, with an mechanically interlocked architecture consisting of a circular DNA molecule threaded onto a linear DNA axle, holding the four bases ( I.e. adenine (A), cytosine (C), guanine (G), and thymine (T) to A. Turns out, a similar Stoddart-Leigh's light sourced mech-interlocked rotaxane ring(lnkd.in/g6re2Nx6) is experimentally proven to be adhering to a thermodynamics equilibrium rule of FSC’s 2/3:1/3 ratios This is where we have hypothesized that this 2/3:1/3 rule caused thermodynamics imbalance of dipole must be one controlling the genetics mechanics at large, including this algorithm at a quantum level. For example, as you know as well as I do that the height of one unit of the DNA helix showing the Golden ratio pattern, the flip side of FSC(α) - which then goes back to our firm’s 5 FSC-GR driven 5 AITGE formulas of TOE, including our consciousness model as well as explained in my articles Again, having not read the paper yet , something intuitive tells me that the triangular inequality geometrical formulas that are used to calculate the molecular distances perhaps can be fine-tuned with our r=αR dipole logic guided 2/3:1/3 rule driven CP-Yang-Mills-Koide-Descartes-Kocik formulas" of n+2 spherical dipoles in 'n' dim-spaces can "explaining" the “mass and radius gap” existing in the Yang-Mills and Koide equations (lnkd.in/dxnNs_Xf). My rationale here is this dipole geometrical logic comes straight from our firm’s proof of solving the century old unsolved Riemann hypothesis including its related 10 proofs as explained in my recent post (facebook.com/share/p/7ePMsccWSoMTxwAq/?) Simply Put Our Riemann hypothesis proof (CP-function) has "Symbiotic FSC/GR Fractal Causality" to these 10 proofs (5 Clays + Gauss + Collatz + Maxwell's Daemon + Einstein-Bohr Hidden Variable and last but not the least our firm’s TOE/SOE Engine itself. Once we grasp this, then everything will fit perfectly like a jigsaw puzzle using this "Symbiotic FSC/GR Fractal Causality" This is where we have hypothesized that during this precise sub moment of conception, the unique Higgs dipole/quadrupole fields of both sperm and egg must be colliding to create the so called integrated Higgs field of the zygote with a zinc spark - which then start serving as the “dipole nanoantenna”, with a predetermined wavelength/frequency/angular momentum , as per the probability of the 2/3 rule of FSC & its flip-sided 1/3 rule of golden ratio, similar to BBN/stellar synthesis This brings us to our TOE Engine (aka CONSCIO-SCOPE), that has been developed by solving these 10+ century-old unsolved problems (i.e. including 5+ $5MM prized problems from Clay institute) -- which brings us to our TOE/SOE thought experiment (TE) -- What if the "fundamental frequency of QVF/ZPE and FSC(α)-Einstein-Bohr-HV-Maxwell Daemon governed TOE Engine" is nothing but the fundamental frequency of Riemann's zeta function Ζ(S) with a singularity of S=1+0i, that is made up of his harmonic oscillating zeros(S=1/2+it stacked on his 1/2 critical line (as per Gauss's/Euler product primes), before being transformed as a 137 frequency-spin momentum matched dipole, using our FSC(α)-GR-PLA+5 AITGE origin formulas? In other words, our TOE/SOE engine is the one that is transforming the Riemann's zeros into an artistic unit charge dipole(see visual), by contracting/expanding its electric flux as the center of mass (as r = αR), before rotating its magnetic flux by 90 in such a way that it can be extended into the left plane as a paired unit charge, using the "only possible analytical continuation of Zeta" -- which brings us to our proof This "one & only allowed analytically continued Zeta dipole" is what limits/constrains the ∞ pole of Riemann sphere to a value of 137 cycles( per Laurent/Cauchy residue including the α=r/R,=fe/fp=we/wp logic of our CP function as explained in my post (www.linkedin.com/posts/charlesprabakar_sovereign-ocean-w-its-10-toe-proofs6-clay-activity-7189304893994614785-vUjQ?) lim t→ ∞ CP(1/2 + ti) = 1/α cycles of dipole This is where we have also hypothesized that this toggle also lands as a dipole/quadrupole using the very same Riemann zeta function logic (z=1/2+it), in perfect alignment with the 4 gene segments of the quadrupled DNA rotaxane model, with an unique S-number, thus deciding our unique genetic code perfectly like a jigsaw puzzle! Hope it helps

  • @nataliaquenmaz2097
    @nataliaquenmaz2097 5 днів тому

    Holy moly!!

  • @MelindaGreen
    @MelindaGreen 5 днів тому

    The triangle inequality went a long way towards understanding for me, thanks

  • @JeanYvesBouguet
    @JeanYvesBouguet 5 днів тому

    How is it possible that it is the first time I see a video in your channel? I absolutely love this. You are amazing and deserve a much much larger audience! Thank you for being here on UA-cam and sharing your love for science.

  • @Killer_Kovacs
    @Killer_Kovacs 5 днів тому

    I think photons are hollow

  • @user-oz8eo6cm1f
    @user-oz8eo6cm1f 6 днів тому

    Wow, great video! I will read the books you mentioned. Thank you!!!

  • @TOOJOHNBLAZE
    @TOOJOHNBLAZE 6 днів тому

    Intelligent, Beautiful, and Wise. I'm tuned in 💪🏼

  • @CodepageNet
    @CodepageNet 6 днів тому

    all the math in the world do not convince me that many worlds is reality. if it's a simplification mathematically and potentially a useful way to look at it, fine, good for you. but i refuse to believe it represents reality. i don't think the theory is useful in the long run, because it keeps you away from the truth. it's one thing that always bothered me a bit about Sean Carroll.

  • @BrianHickmanMilitaryBrat
    @BrianHickmanMilitaryBrat 6 днів тому

    With videos like this I learn a lot. As someone that never studied science in school but out of school have an interest in science, I enjoy this. Clear explanation. Your animation is a lot better in this video as well.

  • @MrofficialC
    @MrofficialC 6 днів тому

    So do the experiment with an L bracket and find out if the particles will travel backwards. To the base of the L |_ . . .

  • @thunderlifestudios
    @thunderlifestudios 6 днів тому

    Why not try this: You have particles A and B. If particle A is untangled, it will cause the other B particle to untangle also, assuming they can then have particle B interact with a non-interference detector (this detector does not interact with the particle, but rather, the B particle interacts with it once it has been untangled, this assumes that an untangled particle can have behaviors that can thus cross into the non-interference detector e.g. if it could begin moving towards the detector as an example, I am not saying that an untangled particle moves in anyway). Assuming this is in a binary system of yes or no: Particle A is observed to determine a "Yes" (state is not important) Particle B then untangles to the opposite state and then interacts with the non-interfering detector giving Observer B the "Yes" response. The downside to this system is that it essentially creates 4 states (yes, no, false yes and false no) due to potential malfunction of the systems. The next caveat is that you would have to create timeframes at which these states should be expected to occur (maybe not since the detector doesn't actually activate unless the particle is untangled). So in a more complex system your only limiting factors would be malfunction and number of entangled particles. In a large scale you could create FTL computers that communicate fast, however, the limitation is the amount of entangled particles you can have. And how would they even be able to determine you have entangled particles in the first place?

  • @MarkKirschnerMelbourneFL
    @MarkKirschnerMelbourneFL 6 днів тому

    Excellent demontration for the casual physics hobbyist. Bravo!

  • @checkm8606
    @checkm8606 6 днів тому

    Awesome animations. Really nicely done :)

  • @bryalee2782
    @bryalee2782 6 днів тому

    i have something to add about this whole thing that I can explain something on one is saying

  • @sebastianweissbarth3385
    @sebastianweissbarth3385 7 днів тому

    maybe its just my headphones but your audio sounds vaguely like Robert Kennedy, like, but as though its an electronic effect.

  • @AdityaMehendale
    @AdityaMehendale 7 днів тому

    There is a philosophical dilemma here - would you give credit for "solving" a protein-folding to alphafold itself or the architects who baked-in the various sequences, loops, inequality-checks, pairwise modifiers, etc. into the basic design of alphafold? A "vanilla" model would have been inadequate to solve the problem, right? Alphafold "just" does the number-crunching.

  • @michaelm358
    @michaelm358 7 днів тому

    We missed you!!

  • @ThePowerLover
    @ThePowerLover 7 днів тому

    I hope you can catch up with the bleeding edge in public AI very soon, at least with its capabilities. Thanks for your videos.

  • @kricketflyd111
    @kricketflyd111 7 днів тому

    God's geometry of creation is waiting for you, your Esoteric studies will be realized in Time. ❤

    • @das_it_mane
      @das_it_mane 4 дні тому

      Please take this nonsense elsewhere. Smug theists always show their whole ass when they can't understand something. Go read a book. Try and learn.

  • @purezero23
    @purezero23 7 днів тому

    Top tier content right here

  • @zachatomata9168
    @zachatomata9168 7 днів тому

    It's interesting to see some AI topics on your channel. I find quantum physics interesting, but a lot of it goes over my head admittedly. AI/ML is more in my wheelhouse, so I'm excited for the follow up video on this. I think a lot of the more interesting AI algorithms are those like AlphaFold which combine some expert/domain knowledge to provide structure to more numerical machine learning algorithms. If you're starting to explore more AI literature, do you think you would try to create a video combining your own domain knowledge of physics plus AI to solve something new?

    • @LookingGlassUniverse
      @LookingGlassUniverse 7 днів тому

      Thank you! I’m very interested in the intersection of quantum physics/ chemistry and AI. I’d love to make more videos about it!

  • @philochristos
    @philochristos 7 днів тому

    I don't know much biology, but isn't it the case that not all amino acid sequences are capable of folding into a stable shape? I wonder what AlphaFold would say about those. Would it say, "I mean, like, we can fold parts of it, but we can't get the whole thing to fold into a stable shape"?

    • @LookingGlassUniverse
      @LookingGlassUniverse 5 днів тому

      That’s so interesting! I might give it a go. My guess is that it just takes a stab at it and gets it wrong

  • @dibenp
    @dibenp 7 днів тому

    Come for the animation. Stay for the content. ❤