Corrections and FAQ in this comment! 0) If you want to see the ink machine ideo about turbulent and laminar flow in a tube: th-cam.com/video/qm5AHAb0SmY/w-d-xo.html and if you just want to watch it go, I have a 45 minute single cut: th-cam.com/video/DtYVYfOvgKE/w-d-xo.html 1) I'm a little loose with the definitions when I get to the interchangeability of entropy and energy, but that's because it gets really complicated in a hurry - maybe a topic for a future video. What I'm referring to is "thermodynamic free energy", which is not conserved like "real" energy. If you have a bucket of water on a ladder and you let the water pour out of it into a bathtub, you could extract energy from that process with a paddlewheel or something - that's "free energy" being spent. Once the water lands in the bathtub, the kinetic energy of it falling goes into heating the water, so now the energy of the water is in heat, and there's nowhere to put the waterwheel, so the energy, although it's still there, is kinda useless. Entropy is exchangeable with "thermodynamic free energy", not "real energy". 2) 5:05 "proobability" 3) When talking about osmosis, I intentionally swept enthalpy of mixing under the rug. there are other (real, non-entropic) forces that can increase osmotic pressure in certain cases en.wikipedia.org/wiki/Enthalpy_of_mixing 4) my “push the marbles to one side” demo may LOOK like the classic “maxwell’s demon” hypothetical, but it’s supposed to represent what’s actually happening near a REAL semi-permeable membrane. I think the ideal “demon” would not produce osmotic pressure, but even in this demo of 20 marbles, there was some measurable osmotic pressure 5)
The initial example of the marbles assumes a perfectly elastic collision. In real life some of the kinetic energy at the initial conditions is permanently lost to heat, sound, deformation etc
It is insomuchas the reverse clock could theoretically cool and undeform the marbles and fully absorb the sound waves. It's highly unlikely to happen because this would reduce entropy
But "real" energy is conserved in the process, right? Does that mean that, during the osmosis when the sugar water is being pushed up, the fluid cools down? If not, where does the energy come from?
And with that, wouldn’t entropy be the “useless” part of the energy, i.e. the less “free energy” (as a proportion of total energy in a system) the higher the entropy of that system?
He already did that, in his "10 coin flips in a row" video, with the small modification of letting the first two throws dictate the pattern he's going to go with (effectively reducing this to a problem of 8 coin flips). Whatever arrangement of HHHH..., TTTT..., HTHT... or THTH... he got, he just ran with.
There is version of this that actually helps to remember the physics as well as being funny: 1. You can never win, you can only break even. 2. You can only break even at absolute zero. 3. You can never reach absolute zero.
As a Physics TA this is absolutely GOD tier Physics education. You've perfectly communicated the basics of undergrad-level Statistical mechanics and Thermodynamics and given a solid foundation for the rest of the math and equations without using ANY Jargon. Like Einstein said, if you cant teach it to a 6 year old you don't understand it well enough.
haha thanks! I did also take graduate thermodynamics for a few classes but I can’t claim to remember any of it… way too abstract. Base level statmech is just so wonderfull because it’s just probabilities. (I actually took thermo from the engineering dept. and the physics dept. in adjacent semesters in undergrad. the MSE side was like "hey here's an equation for the Gibbs, go use it, and the physics side was like "go count dots in boxes" and see what happens. I liked the physics one more. Thanks Dr. Daniels!
Einstein obviously didn't have kids when he said that.. six year olds listening is highly contingent upon snacks, naps, and other more mysterious factors we can't possibly fathom. You can do EVERYTHING right and that kid may very well be like "vroom vroom, rocket go fast!"
@@idontwantahandlethough "if you can't teach it to a 6-year-old who is currently curious about specifically this" That's one of the things my mom taught me about parenting that's proven pretty useful already and my kids are only two: you might be able to get them interested in what you wanna teach them or what you want them to do... but you'll never make them pay attention or learn things they're not interested in. That's just how the human brain works, and small children are even less capable than most of us of self-regulating their focus. Okay, to be fair that's me extrapolating what my mom taught me to make it fit what we're talking about in a little more useful way. What my mom taught me is "When they ask the question is when they'll learn it. You can't set it aside for later and expect them to care." and that's apparently why she ended up explaining sex to my brother in the middle of a crowded public bus.... cause that's when he asked about it, and she figured it was important he understand it. Absolute legend of a woman; lifelong inspiration to be sure.
I like to use this example when someone says “well it’s possible.” For an extremely extremely unlikely event. “Yes, it is possible, it is also possible for every molecule of oxygen in the room to shift up 6 feet, but I’m not about to spend my whole life standing on chairs to avoid suffocating.”
I like to say that it is possible to pass through walls. Particules do teleport with the tunnel effect, you just need to have all your particules teleporting at the same time, in the same direction, for the same distance.
I LOVE the overall explanation, but I have a little nitpick about the sugar/water example: At sufficiently high sugar concentrations, statistics is not the only force driving the dilution, but energy (mixing enthalpy) will be released by changing the intermolecular interactions between sugar and water (there will be "free" water instead of only "hydration shell" water touching other "hydration shell" water). By chance we actually produced a physically-chemically better, albeit less tangible, example, when decommissioning an NMR magnet a few months ago: We closed the helium pressure sensing line at the magnet cryostat, but left the pressure sensor at the other end connected. Because the line (plastic hose) was more permeable to helium than to air (as most things tend to be), the pressure inside the hose actually decreased by some 200 mbar below ambient pressure over a few weeks. Helium diffusion from the inside to the outside was more likely than the other way round due to the concentration gradient, and air diffusion in the other direction was hindered by the material of the hose. However, there are no relevant interactions between the different gases that would contribute to this, at least not at the pressures and temperatures we are talking here.
There's a similar example to this on Cody'sLab, Cody filled a set of balloons with different gases and the balloons with heavy gases that diffuse poorly through latex actually self inflated a bit by absorbing air
There is a consequence of entropy we deal with in our day-to-day lives at the macroscopic level: tangled wires. There are so many configurations where wires are tangled compared to the few configurations where they're neatly separated that they have a tendency to become tangled with the energy input from random jostling.
You can do a kind of reverse osmosis on them too, usually. Grab two tangled bits, apply tension (analogous to pressurizing the filter) and jiggle them around (analogous to increasing the temperature). Make entropy work for you, instead of the other way around.
@@jamesgebhardt6175 but making entropy work for you requires energy, meaning at the end of the day, you are still working for entropy. Entropy is like a loan shark that gives you work but at an exorbitant interest rate
As a biologist I'd never really looked in to why osmosis happens just knew that if different concentrations of fluids are separated by semi permeable membranes it occurs, thanks for showing me why
when life (aka cells) look like they're "cheating" entropy, isn't it just using osmosis + some energy? that seems true at least at the cellular level right?
@@alveolateYes and no. Yes, cells use osmosis to a great extent. No, cells use "pumps" to actively work against entropy and osmotic balance. The most well known in high school text books is one that pumps sodium and potassium to different sides of the synapse membrane so they can be reused as neurotransmitter.
@@SojournerDidimus I thought electromagnetism is involved too, no? Like salty water is charged differently than non salty water so that can create some work too.
As a high school physics teacher I am often frustrated by poor explanations or loose definitions of entropy. This is outstanding! You have explained it in a way that non-physics students can understand. This is extremely helpful for understanding biological systems, heat transfer and the universe in general.
This made me think of another way of explaining why a systems entropy increases with the coinflips : If you have a random system of coins, lets say 6 head and 4 tails, and you have to randomly pick one coin to flip, you are more likely to pick a coin showing head since there are more of them, then when you flip that coin, you can either land on head and nothing changes, or land on tails and entropy increases. This makes it clear why any system tends to entropy. In your example at 9:16 you flip all the coins at once instead of picking one at random to flip which made it less clear to me why it would tend to increased entropy. Thanks for another great video :)
I guess a non circular way of phrasing the second law is "physical distributions of things will resemble statistical distributions, and those distributions get narrow if you have enough things"
That still winds up circular though, because the human bias is also the reason those statistical distributions occur, our tendency to consider 9 heads plus one tail to be the same thing as 4 heads, one tail then 5 heads.
@bosstowndynamics5488 Except we made those choices because they match what we see in reality and because considering every single coin flip that has ever happened is ridiculous.
Amazing. I finally found someone doing the things I think about on the tram but never have the energy to delve deeper into. I love that you bring simulations and other things to the table. Best channel I’ve come across in a long time. Keep it up!
12:30 this is a great visualization why it's /theoretically/ possible to throw a tennisball at a brickwall and have it quantum tunnel through. But the /chance/ that every single particle of the ball dodges every single particle of the wall in it's path is less likely than the ink reversing out of it's "spike". 14:30 I was already wondering why osmosis filtering requires pressure to work. Now I know. Because without the pressure, the water would "prefer" to become dirtier instead of cleaner.
Nah. There are forces holding the ball together, so the ball would never pass through the wall... you could argue maybe that it would integrate into the wall, but not pass through. Like a fishing net passing through another fishing net.
They way I think about it is that the dirty water wants to become cleaner (i.e. wants the concentration of impurities to be lower) by pulling in the clean water.
@@mina86 The molecules are moving around more or less randomly. So if there is a greater concentration of something on one side of some arbitrary boundary and one particle from each side swaps places, the "dirty" side had a higher likelihood of sending a "dirty" particle than the clean side just by virtue of there being more. This probability imbalance means that every interaction works to reduce the gradient. Imagine a 10x10 grid where the 10 cells on the right edge are black and the rest are white. Every second, for every pair of adjacent columns, a random cell on the right will swap places with a random cell on the left. On the first swap for the last two columns, the last column MUST send a black cell because it only has black cells. More swaps between those columns will equalize the number of black/white cells until the probability of sending a black cell is equal on both sides. Since all column pairs are swapping, this will result in a gradual migration of the 10 black cells until they are roughly equally distributed. So if you had to assign "desire", you'd have to say that the "dirt" in the water wants to go where there is less dirt, while the pure water wants to go where there is less pure water.
Thank you for explaining this! Everyone has always explained entropy to me as a definite thing not a statistical thing. They always said "Your laundry will never be perfectly folded after a trip through the dryer" when it is *possible*, but just insanely unlikely. Your explanation actually makes sense!
Yeah, it's frustrating that I had a couple degrees in engineering and still didn't understand this. I had to think about it on my own for a while before I understood. I believe it was always explained to me very poorly.
This is why production of industrial chemicals often runs at high temperatures and pressures, often in a gas phase. It's basically to beat unfavorable chemical equilibria... Sometimes heat is used just to speed things up if the product formation is thermodynamically favourable but kinetically unfavourable. The product is often continually separated from the reaction mixture to keep its concentration low which favors more production as the system continually approaches chemical equilibrium. One of the oldest of such processes is the production of quicklime in a lime kiln. Here calcium carbonate is roasted at high temperatures give off carbon dioxide, leaving behind highly reactive calcium oxide melt used for making cements. The quicklime "wants" to turn back into calcium hydroxide or carbonate once it cools down, because different conditions favor different products. This is why it's so hard to make pure chemicals, especially organics - sometimes it's super tricky to separate a single compound and this explains why 98% purity costs $10, 99.9% purity costs $100 and 99.99% purity costs $10,000+
Perfect timing! Our undergraduate thermodynamics final exam is tomorrow, and I just shared this to channel on our student discord. Already helped a couple people remember how entropy works.
That’s great! Apparently I just missed someone else’s exam last week… I did sit down like a month or two ago while writing this script and try to rederive the entropy of mixing from n choose k and stirlings approximation, but nothing lined up and I never actually found my mistakes… turns out I did remember the correct starting point but I’ve lost the ability to do the math - good luck tomorrow!
@@AlphaPhoenixChannel I'm fairly certain we actually did that derivation during an early homework or lecture, but honestly probably couldn't do it off the top of my head rn, and I'm still in the course! So don't worry about it. And thanks! I'm pretty confident, thankfully, it's my quantum 2 and E&M2 exams I'm worried about. 😅
Here's an interesting fact: a microstate is mathematically identical to a function, and the collection of all possible microstates is the same thing as a function set. So the configuration of a system with n-many particles where each particles can be in one of m-many states is mathematically equivalent to a function f:n→m. There are exactly m^n possible functions/microstates.
This video finally made me understand entropy. When you said it was more of a statistical law than a physical one, I understood it a lot better, “technically” you can have certain things happen, but it isn’t practical to base your rules and laws around that
By far the best video for understanding entropy from scratch that I've ever seen. I had a lot of these thought experiments bouncing around in my mind for years. Awesome to see them manifest in a video that's so well made and intuitive.
This is legitimately like one of the best educational TH-cam videos I’ve seen in my entire life (and I’ve seen a lot). Hats off to you for explaining so so well and so thoroughly.
This is so cool, I have never really considered that "entropy always increases" is not as much a physical law as just a restatement of the law of large numbers in an unbounded universe.
@@rr.studios Because if it did, the Universe would not have started with a Big Bang, but would have only existed for less than a picosecond before becoming a black hole.
@@denelson83 Is that an assumption you've made based on studying other celestial bodies or are you a physicist? That kind of sounds like the process of how black holes are thought to come into existence.
TH-cam says no. TH-cam's saying your reply to yourself came before the post you replied to (59 minutes ago for the OP, 1 hour ago for the reply). Sure, it's different, but if YT allows effect to occur before its cause, it can do all sorts of things.
@@Splarkszter but what makes you say that the way we are is "order"? Wouldn't it be much more likely that the way we are is disorder? (we are not 10 heads, but instead 5 heads and 5 tails?)
@@Splarkszter vortices in turbulence are structured, but they stir up the fluid surrounding them a lot so they can happen spontaneously. Life is also a structure that increases the entropy of its surroundings. The fact that life exists is not improbable, it's inevitable! :)
Love the discussion with the osmotic membrane. This helps explain 'reverse osmosis' desalination plants. It takes high pressure pumps to 'push' seawater against the membranes to get freshwater on the other side. Without the external source of pressure, we wouldn't get nearly as much freshwater because it 'wants' to go dissolve back into the seawater side. (edit: wrote this before the end of the video where you explain just this. I guess I jumped to this conclusion from the first part of the video)
This is the best explanation of entropy I've ever seen. There was a Steve Mould video that was also really good and explained things well, but the dive into statistics in this video really tied everything together and made things make a lot more sense to me.
While i learned about entropy at university, I really appretiate the effort you put into these low-level, tangable examples and models! The time you put into making sure that this concept of entropy is well explained for nearly everybody to understand is astonishing! Love your work, keep on doing great stuff!
Graduated from MIT, and NEVER understood the concepts of the relationship between entropy and energy. You are brilliant. Thank you for your efforts to make a difference
I like the video. You managed to find a sweet spot with not too much oversimplification. Maybe you can do a follow up on how temperature can actually be defined from the entropy and how system with a negative absolute temperature like a laser is effectively hotter than any positive temperature system. Also the entropy being a logarithm makes it additive when two systems are joined but the multiplicity of the combined system is a product of multiplicities of its parts. That makes it very clear as to why the logarithm.
I appreciated it the final connection between entropy and energy. I didn't see that crucial step in other similar videos. I'll have to watch this one again a few times until I really understand everything that's going on.
the reverse implication is also true though, the smaller the system, the more likely you going to get "ordered" outcome. theoretically if a hypothetical spatial divider were to subdivide the state space into many sub space, you get more reversal.
This guy is like a less evil version of Veritasium. To be clear, I'm not implying Veritasium is evil, I'm just taking a 50/50% chance this guy's less evil, and when it comes to making defamatory statements, I like those odds.
All these YTers giving everyone free science educations online are doing good work.. but they all generally fail to disclose that they're sharing knowledge right out of the textbook and not actually *discovering* anything. I wish they'd share some citations at the end of the videos like the professors do.
@@Paul_Bedfordyeah, I kind of soured on Veritasium with the whole "switch, light bulb a meter away, and light-second long wire" thing. Incidentally, that is also how I discovered THIS channel. Which I like much more.
I thought I had a pretty solid grasp on basic thermodynamics and entropy from university-level chemistry, but your explanation and demonstrations take it to a whole new level!
I never like the concepts “evolving from ordered to disordered” because ordered can be subjective. I tend to think “evolving toward more likely arrangement”. A classic example from microbiology is the formation of micelles, which appear more “ordered” than a complete mixture; it’s actually more likely for the micelles to form because of the way the polar molecules interact.
DNA is an entropy reducing device, but it requires energy to do so. Animals eat living things, so they first increase entropy before decreasing it. Plants get energy from the sun as its entropy increases via nuclear fusion.
@@litigioussociety4249 Clearly, I was describing the sun's entropy increasing by nuclear fusion, not the plant. However indirectly, nuclear fusion powers photosynthesis.
It may be useful to compare extreme improbably to other things that we're familiar with: getting struck by lightning 3 times the same day, earth being hit by a devastating meteor, etc. At some point, it becomes much more likely that earth will end than a fluid and ink arranging to spell your name.
Great explanation, like usual. This ties into the feasibility and promise of high entropy alloys of 5 or more equi-molar elemental constituents (affectionately called chaos alloys). With enough heat and time in the right closed environment during smelting/forging and subsequent cooling, quenching, and tempering procedures, you are almost guaranteed to be able to predict with high probability the possibility of some sort of stable metallic crystal or amorphic structure at room temperature from basic information of the target constituents off the periodic table and some surprisingly simple formulas and macroscopic intuitions. And although you'll never be able to even remotely predict the exact properties of the resulting alloy without an expensive amount of compute because of the computational irreducibility of the massive entropy, with some careful consideration you can nudge the phase space of possibilities to at least narrow a bit in on some pretty exciting exotic properties which could revolutionize entire industries practically overnight. Room temperature superconductivity and the like are obviously enticing possibilities, but I've already seen demonstrated in a paper last year a high entropy alloy that demonstrated the unique and potentially quite useful property of actually getting harder and tougher as it was heated. The possibilities for meta materials approached by the method of multiplicative equi-molar elemental formulation is quite possibly the most exciting and likely branch of science to give us a concrete technological leap in the near term future (imho).
Another aspect of entropy WRT to the current state of the universe which is often glossed over: Take a pebble being dropped into a body of water, for example. The reason why you never see a stone being randomly spit out of a lake is not merely due to the fact that such a thing would be "unlikely", but quite simply because gravity cannot be reversed! And it is worth mentioning, because a lot of people seem to think time reversal to be a "fairly trivial" affair. Which is of course rather irritating, considering that it is in fact not. Great video, by the way! I love these kinds of deep-dives into the world of physics.
You don't really need to reverse gravity. You just need to have all atoms interacting with the rock to produce a net force that opposes gravity. Imagine every atom simultaneously pushing up on the rock.
Every time I see a new video on this channel I'm more and more convinced that I'm watching a future star in the realm of popular science. Keep giving your videos the same amount of care you're giving them here, and success will be beating down your door.
I'm almost done with a bachelor's degree in biology. I've watched so many lectures about entropy. I understood enough to get the grade, but I never understood why those equations etc work. This video makes it all make sense, thank you!
Very well done video! One of the cool things about entropy is that it operates at lots of different scales and in lots of different settings, from fundamental particles to human societies. It's also, so far as we know, the only fundamental law of nature that distinguishes between past and future.
PBS Spacetime has a great episode (I think? I don't remember exactly where I heard this actually) where they posit that life is purely a consequence of the Universe's march towards higher entropy. Life's "purpose" is basically just to increase entropy if you look far enough down; all we really are is walking chemical reactions, and in the case of intelligent life it's even more true because we consume at a greater rate than life would otherwise. By this line of thinking it is essentially guaranteed that more intelligent life exists, isn't it?
Imagine what technology exists out there given that space and time are both never ending ! It's hard to except or conceive that there is life trillions of light years away from us
shuffle sort, once quantum computers work, we can basically sort anything in one iteration, by having "unlimited" shuffles at the same time and one of them will be sorted after :D
I don’t think this explains why and what direction time flowing. I once said a white hole(time reversed black hole) is not white, because light is coming out from eyes back to the white hole. It doesn’t even have colour. Same can apply to your idea, still nothing restricting time to go backwards.
@@name-nam I think you get it wrong. While hole do emit everything without any absorption, under the perspective of time goes forward. Respectively, if time goes backward, a white hole becomes sort of like black hole. It’s just matter of relativity.
Dude, I've been through tertiary science education and ALWAYS been confused by people insisting entropy is a physical law in the absolute sense, rather than a statistically emergent one as my mind would have me understand it. I assumed I had to be missing something, and it's always made me feel stupid. You're the FIRST PERSON I've ever seen to confirm this; THANKYOU!
Well done, great video! One of the best I have seen on entropy, and really shows the statistical nature of it - that as the number of particles increases, the likelihood of them all separating out on their own quickly gets very close to zero. Not zero, it COULD happen, but it just never will. This just reminded me of the infinite improbability drive in Hitchhiker’s guide to the galaxy. In that book, you had the room full of monkeys at typewriters who came up with the complete works of Shakespeare. Again, great job!
I love the explanation that entropy isn't some law governed by some convoluted physical process... It's just the fact that the math in such huge systems of particles demands it. I've always seen where someone will say that in an infinite universe every possible combination will occur an infinite number of times and that thought kinda hurts my brain lol. I like the idea here more that if we're just limiting ourselves to a finite system, like the observable universe, those extremely unlikely combinations will never happen. Great vid as always!
Well now I need to look up how 3-angstrom pores for RO filters are manufactured.. Amazing video as always AP. You share the pinnacle of science education on TH-cam with a very, VERY small crowd. Your effort is much appreciated!
Does it feel awesome that with this video you hsve lowered the entropy in many thousand brains by teaching (adding structure) us something? Its somehow neat that learning about entropy actually _reduces_ entropy within your own mind! How very cool. Thank you
The last time I felt so enthralled by a subject but also needed to rewatch the video again and again was Vsauce’s “What is down?” video. This is amazing, thank you
Thank you so much for this demonstration! As ever, you really got me thinking about something I already "understood." This time just thinkin about how it's funny that we describe a perfect equillibrium as "more disordered" than an "unstable/unlikely" arrangement
You just gave me an 'aha!' moment when you're separating the ink from the water. That's exactly what is also being done in a desalination plant, as seen in Practical Engineering's video.
Ignore Boltzmann's Constant. Fact: the sum of p(k)*ln(1/p(k)) over N microstates indexed by k is maximized when all p(k) are the same, and thus equal 1/N. Then the entropy (modulo B's constant) is ln(N). Made a quick program in Mathematica to calculate entropy for a biased coin with probabilities p and q. Entropy is maximized at p=q=1/2. But it is unbounded with n= number of coin flips. n = 33; p = 0.75; q = 1 - p; Sum[Binomial[n, k]*(p^k)*(q^(n - k)), {k, 0, n}]; s1 = Sum[k*Binomial[n, k]*(p^k)*(q^(n - k))*Log[p], {k, 0, n}]; s2 = Sum[(n - k)*Binomial[n, k]*(p^k)*(q^(n - k))*Log[q], {k, 0, n}]; s3 = -(s1 + s2) // returns 18.5571 n=49, p=0.75 returns 27.5544 As n increases without bound, so does the entropy. But for any n, the return is 0 when either p=0 or 1.
Fascinating! Givin infinite time, even the statistically improbable outcome of a completely sorted system is possible. But on a cosmological scale, infinite time means an infinitely expanded universe, so does that mean a completely "smooth" energy state? I.e. absolute zero? And in that state, does time exist?
One thing I've begun to appreciate is that a lot of the supposed "weirdness" of quantum mechanics is attributable to: 1) Most of the entropy of small quantum systems being in different variables than in systems approaching the classical limit. 2) Most of the entropy of quantum systems at the classical limit being in different variables than in the original classical theory (and in variables that aren't even in the classical theory). Complex quantum systems have a ton (nay, a solar mass!) of phase entropy.
Damn I love this channel! At the end when you said you might shake the system for a very long time and cause the ink and water to separate, but that it's just not gonna happen in reality, we could say instead that it is not gonna happen 'in the lifetime of the system' since the wood, glass, etc. will deteriorate before the ink and water separate. You could also say 'in your lifetime' but humans live such a short time I'll go with the system's lifetime. (Yeah, with infinite time and a never deteriorating system it will, 100 percent, separate.) I know you know ALL OF THIS but I wanted to state it for the record!
Great video! Food for thought: The way to show osmosis is using different size balls. You could even build a 2D semi-permeable membrane by having little wooden blocks with appropriate spacing to let small balls pass but trapping the bigger balls on one side.
Oh, nice! And reading your description, I realized that a possibly-even-better way to make a semi-permeable membrane for this case would be to put a bar across the box, raised to a height where the small balls can easily go under it while the large balls can't.
Having three of one outcome and 1 of the other IS the most likely outcome for 4 coins. There are 6 permutations of HHTT vs 4 of HHHT and 4 of HTTT for an 8 total. And this holds for larger sets. If you have an even number of coins, being 1 flip away from perfect 50/50 split is the most likely outcome, and it is nearly twice as likely as an even split for large number of coins. The reason is that having N+2 heads and N-2 tails is almost exactly as likely as having N heads and N tails, but now we also have N-2 heads and N+2 tails as the second option, giving you nearly double the odds of not being perfectly even.
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Corrections and FAQ in this comment!
0) If you want to see the ink machine ideo about turbulent and laminar flow in a tube: th-cam.com/video/qm5AHAb0SmY/w-d-xo.html and if you just want to watch it go, I have a 45 minute single cut: th-cam.com/video/DtYVYfOvgKE/w-d-xo.html
1) I'm a little loose with the definitions when I get to the interchangeability of entropy and energy, but that's because it gets really complicated in a hurry - maybe a topic for a future video. What I'm referring to is "thermodynamic free energy", which is not conserved like "real" energy. If you have a bucket of water on a ladder and you let the water pour out of it into a bathtub, you could extract energy from that process with a paddlewheel or something - that's "free energy" being spent. Once the water lands in the bathtub, the kinetic energy of it falling goes into heating the water, so now the energy of the water is in heat, and there's nowhere to put the waterwheel, so the energy, although it's still there, is kinda useless. Entropy is exchangeable with "thermodynamic free energy", not "real energy".
2) 5:05 "proobability"
3) When talking about osmosis, I intentionally swept enthalpy of mixing under the rug. there are other (real, non-entropic) forces that can increase osmotic pressure in certain cases en.wikipedia.org/wiki/Enthalpy_of_mixing
4) my “push the marbles to one side” demo may LOOK like the classic “maxwell’s demon” hypothetical, but it’s supposed to represent what’s actually happening near a REAL semi-permeable membrane. I think the ideal “demon” would not produce osmotic pressure, but even in this demo of 20 marbles, there was some measurable osmotic pressure
5)
The initial example of the marbles assumes a perfectly elastic collision. In real life some of the kinetic energy at the initial conditions is permanently lost to heat, sound, deformation etc
@@i_am_lambda That isn't really relevant to the entropy
It is insomuchas the reverse clock could theoretically cool and undeform the marbles and fully absorb the sound waves. It's highly unlikely to happen because this would reduce entropy
But "real" energy is conserved in the process, right? Does that mean that, during the osmosis when the sugar water is being pushed up, the fluid cools down? If not, where does the energy come from?
And with that, wouldn’t entropy be the “useless” part of the energy, i.e. the less “free energy” (as a proportion of total energy in a system) the higher the entropy of that system?
Matt Parker would have filmed coin flip attempts until he got 10 tails in a row, then just casually throw the footage in without further comment.
He already did that, in his "10 coin flips in a row" video, with the small modification of letting the first two throws dictate the pattern he's going to go with (effectively reducing this to a problem of 8 coin flips). Whatever arrangement of HHHH..., TTTT..., HTHT... or THTH... he got, he just ran with.
Ya
Yeah, but he's a mathematician, they're not the most mentally sound of people.
@@AlucardNoirHe's "Parker Sane"
@@AlucardNoiras a math guy I 111% agree 😂
The three laws of thermodynamics:
1. You can't win.
2. You can't break even.
3. You can't even quit the game.
Worst casino in history smh
Get it twisted, you will win, you will break even, 99% of gamblers quit before their cup of cold coffee spontaneously becomes warm
@janoycresva9941 i think it’s a little more than 99%😉
I lost the game
There is version of this that actually helps to remember the physics as well as being funny:
1. You can never win, you can only break even.
2. You can only break even at absolute zero.
3. You can never reach absolute zero.
As a Physics TA this is absolutely GOD tier Physics education. You've perfectly communicated the basics of undergrad-level Statistical mechanics and Thermodynamics and given a solid foundation for the rest of the math and equations without using ANY Jargon. Like Einstein said, if you cant teach it to a 6 year old you don't understand it well enough.
haha thanks! I did also take graduate thermodynamics for a few classes but I can’t claim to remember any of it… way too abstract. Base level statmech is just so wonderfull because it’s just probabilities.
(I actually took thermo from the engineering dept. and the physics dept. in adjacent semesters in undergrad. the MSE side was like "hey here's an equation for the Gibbs, go use it, and the physics side was like "go count dots in boxes" and see what happens. I liked the physics one more. Thanks Dr. Daniels!
Einstein obviously didn't have kids when he said that.. six year olds listening is highly contingent upon snacks, naps, and other more mysterious factors we can't possibly fathom. You can do EVERYTHING right and that kid may very well be like "vroom vroom, rocket go fast!"
@@AlphaPhoenixChannel thanks for showing me a physical not reversed video showing of kinda like bogosort.
you can't
@@idontwantahandlethough "if you can't teach it to a 6-year-old who is currently curious about specifically this"
That's one of the things my mom taught me about parenting that's proven pretty useful already and my kids are only two: you might be able to get them interested in what you wanna teach them or what you want them to do... but you'll never make them pay attention or learn things they're not interested in. That's just how the human brain works, and small children are even less capable than most of us of self-regulating their focus.
Okay, to be fair that's me extrapolating what my mom taught me to make it fit what we're talking about in a little more useful way. What my mom taught me is "When they ask the question is when they'll learn it. You can't set it aside for later and expect them to care." and that's apparently why she ended up explaining sex to my brother in the middle of a crowded public bus.... cause that's when he asked about it, and she figured it was important he understand it. Absolute legend of a woman; lifelong inspiration to be sure.
I like to use this example when someone says “well it’s possible.” For an extremely extremely unlikely event.
“Yes, it is possible, it is also possible for every molecule of oxygen in the room to shift up 6 feet, but I’m not about to spend my whole life standing on chairs to avoid suffocating.”
They might shift down instead, after all.
I like to say that it is possible to pass through walls.
Particules do teleport with the tunnel effect, you just need to have all your particules teleporting at the same time, in the same direction, for the same distance.
My dad always says: I won 6 bucks in the lottery. I did not play.
@@NaridaXGet low, get lowww, to the window, to the wall, til en-tro-py makes us crawl
Stealing that
I LOVE the overall explanation, but I have a little nitpick about the sugar/water example: At sufficiently high sugar concentrations, statistics is not the only force driving the dilution, but energy (mixing enthalpy) will be released by changing the intermolecular interactions between sugar and water (there will be "free" water instead of only "hydration shell" water touching other "hydration shell" water).
By chance we actually produced a physically-chemically better, albeit less tangible, example, when decommissioning an NMR magnet a few months ago: We closed the helium pressure sensing line at the magnet cryostat, but left the pressure sensor at the other end connected. Because the line (plastic hose) was more permeable to helium than to air (as most things tend to be), the pressure inside the hose actually decreased by some 200 mbar below ambient pressure over a few weeks. Helium diffusion from the inside to the outside was more likely than the other way round due to the concentration gradient, and air diffusion in the other direction was hindered by the material of the hose. However, there are no relevant interactions between the different gases that would contribute to this, at least not at the pressures and temperatures we are talking here.
There's a similar example to this on Cody'sLab, Cody filled a set of balloons with different gases and the balloons with heavy gases that diffuse poorly through latex actually self inflated a bit by absorbing air
Interesting.@@bosstowndynamics5488
There is a consequence of entropy we deal with in our day-to-day lives at the macroscopic level: tangled wires. There are so many configurations where wires are tangled compared to the few configurations where they're neatly separated that they have a tendency to become tangled with the energy input from random jostling.
You can do a kind of reverse osmosis on them too, usually. Grab two tangled bits, apply tension (analogous to pressurizing the filter) and jiggle them around (analogous to increasing the temperature). Make entropy work for you, instead of the other way around.
@@jamesgebhardt6175 but making entropy work for you requires energy, meaning at the end of the day, you are still working for entropy. Entropy is like a loan shark that gives you work but at an exorbitant interest rate
Even weirder is I can put them in a drawer, not touch that drawer again for weeks, come back to get one and they are tangled.
@@LouisNothing That's just gremlins
a loose floppy string can tie better knots than I can
As a biologist I'd never really looked in to why osmosis happens just knew that if different concentrations of fluids are separated by semi permeable membranes it occurs, thanks for showing me why
when life (aka cells) look like they're "cheating" entropy, isn't it just using osmosis + some energy? that seems true at least at the cellular level right?
Are you aware of Maxwell's Demon? It's a thought experiment based on this sort of scenario
@@alveolateYes and no. Yes, cells use osmosis to a great extent. No, cells use "pumps" to actively work against entropy and osmotic balance. The most well known in high school text books is one that pumps sodium and potassium to different sides of the synapse membrane so they can be reused as neurotransmitter.
@@SojournerDidimus I thought electromagnetism is involved too, no? Like salty water is charged differently than non salty water so that can create some work too.
I get very excited when biology and physics explicitly overlap.
As a high school physics teacher I am often frustrated by poor explanations or loose definitions of entropy. This is outstanding! You have explained it in a way that non-physics students can understand. This is extremely helpful for understanding biological systems, heat transfer and the universe in general.
This made me think of another way of explaining why a systems entropy increases with the coinflips :
If you have a random system of coins, lets say 6 head and 4 tails, and you have to randomly pick one coin to flip, you are more likely to pick a coin showing head since there are more of them, then when you flip that coin, you can either land on head and nothing changes, or land on tails and entropy increases. This makes it clear why any system tends to entropy.
In your example at 9:16 you flip all the coins at once instead of picking one at random to flip which made it less clear to me why it would tend to increased entropy.
Thanks for another great video :)
Of the coins that weren’t “excess” heads or tails, the expectation value is still 50:50
So you're telling me there *is* a chance?
Yes
"I get that reference!" :)
No. Statistics is a scam created by the shadow government.
Smart & Smarter
Ms. "Samsonite" 😉
I guess a non circular way of phrasing the second law is "physical distributions of things will resemble statistical distributions, and those distributions get narrow if you have enough things"
That still winds up circular though, because the human bias is also the reason those statistical distributions occur, our tendency to consider 9 heads plus one tail to be the same thing as 4 heads, one tail then 5 heads.
@@bosstowndynamics5488 oh god, it's circles all the way down. I'M SPIRALING!
*SPIRALING!*
@@bosstowndynamics5488that's just combinatorial probability.
@@lvlinty Yes, but the choice to combine some outcomes and consider them the same is still a choice humans made when developing these concepts
@bosstowndynamics5488 Except we made those choices because they match what we see in reality and because considering every single coin flip that has ever happened is ridiculous.
Amazing. I finally found someone doing the things I think about on the tram but never have the energy to delve deeper into. I love that you bring simulations and other things to the table. Best channel I’ve come across in a long time. Keep it up!
Imagine the ink in the water system shot out and the ink cloud spelled out *“Entropy, pfft”* and then dissipated- but the camera broke.
12:30 this is a great visualization why it's /theoretically/ possible to throw a tennisball at a brickwall and have it quantum tunnel through.
But the /chance/ that every single particle of the ball dodges every single particle of the wall in it's path is less likely than the ink reversing out of it's "spike".
14:30 I was already wondering why osmosis filtering requires pressure to work. Now I know. Because without the pressure, the water would "prefer" to become dirtier instead of cleaner.
I ran into this topic couple days ago and apparently that theory is abandoned and more "advanced" quantum theories are used
Nah. There are forces holding the ball together, so the ball would never pass through the wall... you could argue maybe that it would integrate into the wall, but not pass through. Like a fishing net passing through another fishing net.
They way I think about it is that the dirty water wants to become cleaner (i.e. wants the concentration of impurities to be lower) by pulling in the clean water.
@@mina86 The molecules are moving around more or less randomly. So if there is a greater concentration of something on one side of some arbitrary boundary and one particle from each side swaps places, the "dirty" side had a higher likelihood of sending a "dirty" particle than the clean side just by virtue of there being more. This probability imbalance means that every interaction works to reduce the gradient.
Imagine a 10x10 grid where the 10 cells on the right edge are black and the rest are white. Every second, for every pair of adjacent columns, a random cell on the right will swap places with a random cell on the left.
On the first swap for the last two columns, the last column MUST send a black cell because it only has black cells. More swaps between those columns will equalize the number of black/white cells until the probability of sending a black cell is equal on both sides. Since all column pairs are swapping, this will result in a gradual migration of the 10 black cells until they are roughly equally distributed.
So if you had to assign "desire", you'd have to say that the "dirt" in the water wants to go where there is less dirt, while the pure water wants to go where there is less pure water.
@@DanKaschel, there is a membrane which doesn’t allow ‘dirt’ to pass through.
Dude is actually Maxwell's demon with balls.
Maxwell's demon cosplay
Maxwell's demon has balls?
@@thevikingwarriorno, but this guy is Maxwell’s demon but *with* balls.
Thank you for explaining this! Everyone has always explained entropy to me as a definite thing not a statistical thing. They always said "Your laundry will never be perfectly folded after a trip through the dryer" when it is *possible*, but just insanely unlikely. Your explanation actually makes sense!
Yeah, it's frustrating that I had a couple degrees in engineering and still didn't understand this. I had to think about it on my own for a while before I understood. I believe it was always explained to me very poorly.
Depends on the dryer.
This is why production of industrial chemicals often runs at high temperatures and pressures, often in a gas phase. It's basically to beat unfavorable chemical equilibria... Sometimes heat is used just to speed things up if the product formation is thermodynamically favourable but kinetically unfavourable. The product is often continually separated from the reaction mixture to keep its concentration low which favors more production as the system continually approaches chemical equilibrium.
One of the oldest of such processes is the production of quicklime in a lime kiln. Here calcium carbonate is roasted at high temperatures give off carbon dioxide, leaving behind highly reactive calcium oxide melt used for making cements. The quicklime "wants" to turn back into calcium hydroxide or carbonate once it cools down, because different conditions favor different products. This is why it's so hard to make pure chemicals, especially organics - sometimes it's super tricky to separate a single compound and this explains why 98% purity costs $10, 99.9% purity costs $100 and 99.99% purity costs $10,000+
Biogenesis, evolution... !?
Much of practical bench biochemistry is learning ways to separate mixtures of biomolecules without destroying the molecules you want to study.
@@zanicar4087 Is that a question?
so this is what made walter white's meth so special
Perfect timing! Our undergraduate thermodynamics final exam is tomorrow, and I just shared this to channel on our student discord. Already helped a couple people remember how entropy works.
That’s great! Apparently I just missed someone else’s exam last week…
I did sit down like a month or two ago while writing this script and try to rederive the entropy of mixing from n choose k and stirlings approximation, but nothing lined up and I never actually found my mistakes… turns out I did remember the correct starting point but I’ve lost the ability to do the math - good luck tomorrow!
@@AlphaPhoenixChannel I'm fairly certain we actually did that derivation during an early homework or lecture, but honestly probably couldn't do it off the top of my head rn, and I'm still in the course! So don't worry about it. And thanks! I'm pretty confident, thankfully, it's my quantum 2 and E&M2 exams I'm worried about. 😅
Here's an interesting fact: a microstate is mathematically identical to a function, and the collection of all possible microstates is the same thing as a function set.
So the configuration of a system with n-many particles where each particles can be in one of m-many states is mathematically equivalent to a function f:n→m. There are exactly m^n possible functions/microstates.
You’re thinking about bijections, no?
This video finally made me understand entropy. When you said it was more of a statistical law than a physical one, I understood it a lot better, “technically” you can have certain things happen, but it isn’t practical to base your rules and laws around that
By far the best video for understanding entropy from scratch that I've ever seen. I had a lot of these thought experiments bouncing around in my mind for years. Awesome to see them manifest in a video that's so well made and intuitive.
This is legitimately like one of the best educational TH-cam videos I’ve seen in my entire life (and I’ve seen a lot). Hats off to you for explaining so so well and so thoroughly.
This is so cool, I have never really considered that "entropy always increases" is not as much a physical law as just a restatement of the law of large numbers in an unbounded universe.
Except the universe does not have an infinite amount of energy.
@@denelson83How do you know that?
@@rr.studios Because if it did, the Universe would not have started with a Big Bang, but would have only existed for less than a picosecond before becoming a black hole.
@@denelson83 Is that an assumption you've made based on studying other celestial bodies or are you a physicist? That kind of sounds like the process of how black holes are thought to come into existence.
@@rr.studios Well... It seems there is no scientific consensus on whether or not the universe has infinite energy.
Veritasium level explaining + >steve mould level demonstrating. Very well done, immediately saved to my physics playlist!
Oh cool. So "Do you know why is it hard for things to be 'in order'? It's not because it's hard, it's actually because it's very improbable!"
There are way more instances of disorder than of order. The fact that we exist, we are so improbable that we must be unique!
TH-cam says no.
TH-cam's saying your reply to yourself came before the post you replied to (59 minutes ago for the OP, 1 hour ago for the reply).
Sure, it's different, but if YT allows effect to occur before its cause, it can do all sorts of things.
@@Splarkszter but what makes you say that the way we are is "order"?
Wouldn't it be much more likely that the way we are is disorder? (we are not 10 heads, but instead 5 heads and 5 tails?)
@@Jehty_ I'm pretty sure we're 1 head and 4 limbs
@@Splarkszter vortices in turbulence are structured, but they stir up the fluid surrounding them a lot so they can happen spontaneously. Life is also a structure that increases the entropy of its surroundings. The fact that life exists is not improbable, it's inevitable! :)
i feel like alpha phoenix has gone from "applied science" channel to a more "steve mould" type explainer. im here for it
Applied Science > Steve Mould
@@TheMetalButcher hmmmmm you make an excellent point sir
@@TheMetalButcher applied science dont do kiwico crates
Love the discussion with the osmotic membrane. This helps explain 'reverse osmosis' desalination plants. It takes high pressure pumps to 'push' seawater against the membranes to get freshwater on the other side. Without the external source of pressure, we wouldn't get nearly as much freshwater because it 'wants' to go dissolve back into the seawater side.
(edit: wrote this before the end of the video where you explain just this. I guess I jumped to this conclusion from the first part of the video)
I believe this is also the same forces that cause excess salt in our diet to be fatal, salt water pulls the water out of our cells and destroys them.
There is an infinite number of monkeys outside that wish to speak with you about a script for Hamlet that they've worked out.
can't wait to hear about the tiny pig
And they're all dead...
This is the best explanation of entropy I've ever seen. There was a Steve Mould video that was also really good and explained things well, but the dive into statistics in this video really tied everything together and made things make a lot more sense to me.
12:10 Nice to see "10 billion human second century" as a unit :)
10 billion human seconds for a century?
@@AarushA.San activity that takes 1 second, being performed by 10 billion humans, for a century
While i learned about entropy at university, I really appretiate the effort you put into these low-level, tangable examples and models! The time you put into making sure that this concept of entropy is well explained for nearly everybody to understand is astonishing!
Love your work, keep on doing great stuff!
5:30 I love that you KNOW there are thermodynamicists watching...
Huh, that's a word?
It’s me :)
Graduated from MIT, and NEVER understood the concepts of the relationship between entropy and energy. You are brilliant. Thank you for your efforts to make a difference
I like the video. You managed to find a sweet spot with not too much oversimplification. Maybe you can do a follow up on how temperature can actually be defined from the entropy and how system with a negative absolute temperature like a laser is effectively hotter than any positive temperature system.
Also the entropy being a logarithm makes it additive when two systems are joined but the multiplicity of the combined system is a product of multiplicities of its parts. That makes it very clear as to why the logarithm.
In my opinion this is the best science channel on youtube. Consistent quality, with great demonstrations and approachable explanations!
wait. you're not styropyro
Pretty cool, right?
No thats his shorter clone whos not scared of death or electrons
I appreciated it the final connection between entropy and energy. I didn't see that crucial step in other similar videos. I'll have to watch this one again a few times until I really understand everything that's going on.
For a split second ALL the air molecules in my room gathered in one corner and my head 🤯..
Boltzman has left the chat.
Watching you is the best thing that I have going for me in my life right now.
Thanks for sharing your work!
the reverse implication is also true though, the smaller the system, the more likely you going to get "ordered" outcome. theoretically if a hypothetical spatial divider were to subdivide the state space into many sub space, you get more reversal.
love this video . im in hvac industry and this brought back the studies in entropy we did way back then .great to watch
This guy is like a less evil version of Veritasium.
To be clear, I'm not implying Veritasium is evil, I'm just taking a 50/50% chance this guy's less evil, and when it comes to making defamatory statements, I like those odds.
Veritasium is extremely evil
All these YTers giving everyone free science educations online are doing good work.. but they all generally fail to disclose that they're sharing knowledge right out of the textbook and not actually *discovering* anything. I wish they'd share some citations at the end of the videos like the professors do.
With Veritasium, I say it is a higher than 50/50 chance because Veritasium uses science to flex his smarts and learning happening is a side effect
@@Paul_Bedfordyeah, I kind of soured on Veritasium with the whole "switch, light bulb a meter away, and light-second long wire" thing. Incidentally, that is also how I discovered THIS channel. Which I like much more.
The Man Who Accidentally Killed The Most People In History. Yeah, "Accidentally"
I thought I had a pretty solid grasp on basic thermodynamics and entropy from university-level chemistry, but your explanation and demonstrations take it to a whole new level!
Thank you for making such high quality awesome entertaining educational content.
I never like the concepts “evolving from ordered to disordered” because ordered can be subjective. I tend to think “evolving toward more likely arrangement”. A classic example from microbiology is the formation of micelles, which appear more “ordered” than a complete mixture; it’s actually more likely for the micelles to form because of the way the polar molecules interact.
DNA is an entropy reducing device, but it requires energy to do so. Animals eat living things, so they first increase entropy before decreasing it. Plants get energy from the sun as its entropy increases via nuclear fusion.
Life doesn't actually reduce entropy, it increases the overall entropy in order to decrease entropy in a smaller environment
@@ExylonBotOfficial True. To be precise it's a "local-entropy reducing device".
That’s why you get more calories per acre farming vegetables than raising animals for meat.
@@litigioussociety4249 Clearly, I was describing the sun's entropy increasing by nuclear fusion, not the plant. However indirectly, nuclear fusion powers photosynthesis.
The only video I've seen in the whole TH-cam that talks correctly and without unnecessary bells and whistles about entropy. Congratulations
It may be useful to compare extreme improbably to other things that we're familiar with: getting struck by lightning 3 times the same day, earth being hit by a devastating meteor, etc. At some point, it becomes much more likely that earth will end than a fluid and ink arranging to spell your name.
Great explanation, like usual. This ties into the feasibility and promise of high entropy alloys of 5 or more equi-molar elemental constituents (affectionately called chaos alloys).
With enough heat and time in the right closed environment during smelting/forging and subsequent cooling, quenching, and tempering procedures, you are almost guaranteed to be able to predict with high probability the possibility of some sort of stable metallic crystal or amorphic structure at room temperature from basic information of the target constituents off the periodic table and some surprisingly simple formulas and macroscopic intuitions. And although you'll never be able to even remotely predict the exact properties of the resulting alloy without an expensive amount of compute because of the computational irreducibility of the massive entropy, with some careful consideration you can nudge the phase space of possibilities to at least narrow a bit in on some pretty exciting exotic properties which could revolutionize entire industries practically overnight. Room temperature superconductivity and the like are obviously enticing possibilities, but I've already seen demonstrated in a paper last year a high entropy alloy that demonstrated the unique and potentially quite useful property of actually getting harder and tougher as it was heated. The possibilities for meta materials approached by the method of multiplicative equi-molar elemental formulation is quite possibly the most exciting and likely branch of science to give us a concrete technological leap in the near term future (imho).
Another aspect of entropy WRT to the current state of the universe which is often glossed over: Take a pebble being dropped into a body of water, for example. The reason why you never see a stone being randomly spit out of a lake is not merely due to the fact that such a thing would be "unlikely", but quite simply because gravity cannot be reversed! And it is worth mentioning, because a lot of people seem to think time reversal to be a "fairly trivial" affair. Which is of course rather irritating, considering that it is in fact not.
Great video, by the way! I love these kinds of deep-dives into the world of physics.
You don't really need to reverse gravity. You just need to have all atoms interacting with the rock to produce a net force that opposes gravity. Imagine every atom simultaneously pushing up on the rock.
Every time I see a new video on this channel I'm more and more convinced that I'm watching a future star in the realm of popular science. Keep giving your videos the same amount of care you're giving them here, and success will be beating down your door.
maxwell's demon casually boiling me using a door
This is absolutely the best explanation and demonstration of entropy I've ever seen! Thank you! ❤
3:21. Hold my beer. I will put myself in 100 mllion debt to win lotery and off myself the same day I won it. This will technically count.
I'm almost done with a bachelor's degree in biology. I've watched so many lectures about entropy. I understood enough to get the grade, but I never understood why those equations etc work. This video makes it all make sense, thank you!
first 🎉🎉 btw, I love your videos ❤
Very well done video! One of the cool things about entropy is that it operates at lots of different scales and in lots of different settings, from fundamental particles to human societies. It's also, so far as we know, the only fundamental law of nature that distinguishes between past and future.
PBS Spacetime has a great episode (I think? I don't remember exactly where I heard this actually) where they posit that life is purely a consequence of the Universe's march towards higher entropy. Life's "purpose" is basically just to increase entropy if you look far enough down; all we really are is walking chemical reactions, and in the case of intelligent life it's even more true because we consume at a greater rate than life would otherwise.
By this line of thinking it is essentially guaranteed that more intelligent life exists, isn't it?
Imagine what technology exists out there given that space and time are both never ending ! It's hard to except or conceive that there is life trillions of light years away from us
Absolute banger, your intelligence and passion is on full display, again. Award worthy content.
shuffle sort, once quantum computers work, we can basically sort anything in one iteration, by having "unlimited" shuffles at the same time and one of them will be sorted after :D
Lol bogo sort ftw
@@jamesyoungquist6923 yeah thanks for the correct name :D
@@Marco-xz7rf 🤜🏻🤛🏻
the real question now is how do you get the right result
@@OSrBurns you shuffle once, then run through the list and only return true, if the list is sorted :D
Cute visuals. I love using excel too for things like this. But you gave me some inspiration on some number theory. Funny how things can tie together.
I don’t think this explains why and what direction time flowing. I once said a white hole(time reversed black hole) is not white, because light is coming out from eyes back to the white hole. It doesn’t even have colour. Same can apply to your idea, still nothing restricting time to go backwards.
light cannot come back to the white hole, its literally impossible
@@name-nam I think you get it wrong. While hole do emit everything without any absorption, under the perspective of time goes forward. Respectively, if time goes backward, a white hole becomes sort of like black hole. It’s just matter of relativity.
Dude, I've been through tertiary science education and ALWAYS been confused by people insisting entropy is a physical law in the absolute sense, rather than a statistically emergent one as my mind would have me understand it. I assumed I had to be missing something, and it's always made me feel stupid. You're the FIRST PERSON I've ever seen to confirm this; THANKYOU!
Well done, great video! One of the best I have seen on entropy, and really shows the statistical nature of it - that as the number of particles increases, the likelihood of them all separating out on their own quickly gets very close to zero. Not zero, it COULD happen, but it just never will. This just reminded me of the infinite improbability drive in Hitchhiker’s guide to the galaxy. In that book, you had the room full of monkeys at typewriters who came up with the complete works of Shakespeare. Again, great job!
I love the explanation that entropy isn't some law governed by some convoluted physical process... It's just the fact that the math in such huge systems of particles demands it.
I've always seen where someone will say that in an infinite universe every possible combination will occur an infinite number of times and that thought kinda hurts my brain lol. I like the idea here more that if we're just limiting ourselves to a finite system, like the observable universe, those extremely unlikely combinations will never happen.
Great vid as always!
your explanations and examples are extremely well done and thought through - AWESOME!!
Awesome work. Thank you for the lesson. It has taken me many years to understand entropy. Excellent methodology to expose nature of entropy. Well done
Well now I need to look up how 3-angstrom pores for RO filters are manufactured..
Amazing video as always AP. You share the pinnacle of science education on TH-cam with a very, VERY small crowd. Your effort is much appreciated!
Thank you! Finally, I understood exactly how trees pump water to a height! They have membranes in each cell, and the juice contains sugar.
Does it feel awesome that with this video you hsve lowered the entropy in many thousand brains by teaching (adding structure) us something? Its somehow neat that learning about entropy actually _reduces_ entropy within your own mind! How very cool. Thank you
god this channel is so underrated it’s insane; your videos are amazing
THE single best concrete explanation of entropy I've ever seen, hands down. Thanks!
So many good maths and science channels comment on these videos, he really is your favorite TH-camrs favorite TH-camr
Your second example with the 10 balls was a beautiful example of entropic action and probability… loved it.
12:03 absolutely amazing visual illustration of the difference in the distributions of outcomes as the system grows larger!
This is the best demonstration and explanation of entropy I've ever seen. Thanks!
The last time I felt so enthralled by a subject but also needed to rewatch the video again and again was Vsauce’s “What is down?” video. This is amazing, thank you
Thank you so much for this demonstration! As ever, you really got me thinking about something I already "understood."
This time just thinkin about how it's funny that we describe a perfect equillibrium as "more disordered" than an "unstable/unlikely" arrangement
The best explanation of entropy I have ever seen. Thank you!!
I want u as a professor, i absolutely love this kind of videos and the way u can go Deep with thinghs explaining the Essence of all
You just gave me an 'aha!' moment when you're separating the ink from the water. That's exactly what is also being done in a desalination plant, as seen in Practical Engineering's video.
Congratualitions for the great video, it's one of the best explanations on entropy I've ever seen.
Ignore Boltzmann's Constant. Fact: the sum of p(k)*ln(1/p(k)) over N microstates indexed by k is maximized when all p(k) are the same, and thus equal 1/N. Then the entropy (modulo B's constant) is ln(N). Made a quick program in Mathematica to calculate entropy for a biased coin with probabilities p and q.
Entropy is maximized at p=q=1/2. But it is unbounded with n= number of coin flips.
n = 33;
p = 0.75;
q = 1 - p;
Sum[Binomial[n, k]*(p^k)*(q^(n - k)), {k, 0, n}];
s1 = Sum[k*Binomial[n, k]*(p^k)*(q^(n - k))*Log[p], {k, 0, n}];
s2 = Sum[(n - k)*Binomial[n, k]*(p^k)*(q^(n - k))*Log[q], {k, 0, n}];
s3 = -(s1 + s2)
// returns 18.5571
n=49, p=0.75 returns 27.5544
As n increases without bound, so does the entropy. But for any n, the return is 0 when either p=0 or 1.
This is the best video I've ever seen on entropy
This is the best video on entropy that I have ever seen! It was a joy to watch
Fascinating! Givin infinite time, even the statistically improbable outcome of a completely sorted system is possible. But on a cosmological scale, infinite time means an infinitely expanded universe, so does that mean a completely "smooth" energy state? I.e. absolute zero? And in that state, does time exist?
i think thats pretty much the heat death of the universe
Really excellent explanation of some pretty counter-intuitive stuff. Top tier physics communication!
This is the most unique way I've ever seen entropy explained. And I love it!
Really high-quality video. Still trying to wrap my head around parts and really understand them, but it's getting there. Thanks!
This is the best video on entropy so far, ig , better than the veritasium one, every high schooler should watch this
I love this guys exccentric ADHD style enthiusism.
And his mad videos.
Nice geezer.
this is a really great companion piece to Angela Collier's recent video on entropy
How fitting that this video came out exactly while I have entropy and all things around it in school XD
One thing I've begun to appreciate is that a lot of the supposed "weirdness" of quantum mechanics is attributable to:
1) Most of the entropy of small quantum systems being in different variables than in systems approaching the classical limit.
2) Most of the entropy of quantum systems at the classical limit being in different variables than in the original classical theory (and in variables that aren't even in the classical theory). Complex quantum systems have a ton (nay, a solar mass!) of phase entropy.
Damn I love this channel!
At the end when you said you might shake the system for a very long time and cause the ink and water to separate, but that it's just not gonna happen in reality, we could say instead that it is not gonna happen 'in the lifetime of the system' since the wood, glass, etc. will deteriorate before the ink and water separate.
You could also say 'in your lifetime' but humans live such a short time I'll go with the system's lifetime.
(Yeah, with infinite time and a never deteriorating system it will, 100 percent, separate.)
I know you know ALL OF THIS but I wanted to state it for the record!
This is probably the most clear explanation of entropy I have ever heard
Pov : You couldn't figure out the first clip of the video but you found it incredibly to identify the forwards video in the second clip
Great video! Food for thought: The way to show osmosis is using different size balls. You could even build a 2D semi-permeable membrane by having little wooden blocks with appropriate spacing to let small balls pass but trapping the bigger balls on one side.
Oh, nice! And reading your description, I realized that a possibly-even-better way to make a semi-permeable membrane for this case would be to put a bar across the box, raised to a height where the small balls can easily go under it while the large balls can't.
Having three of one outcome and 1 of the other IS the most likely outcome for 4 coins. There are 6 permutations of HHTT vs 4 of HHHT and 4 of HTTT for an 8 total. And this holds for larger sets. If you have an even number of coins, being 1 flip away from perfect 50/50 split is the most likely outcome, and it is nearly twice as likely as an even split for large number of coins. The reason is that having N+2 heads and N-2 tails is almost exactly as likely as having N heads and N tails, but now we also have N-2 heads and N+2 tails as the second option, giving you nearly double the odds of not being perfectly even.
95% ink and 5% water isn’t the same as 5% ink and 95% water, but they both have the same entropy of mixing