I was under the impression that they got that shape because the bees will push the wax outwards as they work, and so over time, as many bees push the perimeters of the wax outwards, they behave a lot like bubbles being pushed by air pressure.
I got really confused by your argument about the natural numbers "If the biggest natural number existed, it'd have to be one because I can make the other ones bigger" Probably it needs to be phrased in another way? Take another example. Imagine the most awful car that is so bad nobody is willing to bet on its price, which is $1 to begin with. Then you see other cars that are more expensive already, and imagine ways on which they can become even more expensive. Your conclusion is that the crappy car must be the most expensive of all of them?
Maybe swap "I can make the other ones bigger" with "I can find a number bigger than each of the other numbers". x^2 is bigger than x for every natural number x except for 1, and if there is a number bigger than x, x can't be the biggest number. The only option we're left with is 1!
@@Danyel615 You're not missing anything, the point is that this "proof" that 1 is the biggest number is clearly incorrect because a "biggest number" doesn't exist. Just like we found a way to get a bigger number for every number except 1, Steiner found a way to get a smaller perimeter shape for every shape except a circle. Naively, that might seem like a proof that a circle has the smallest perimeter, but this analogy with numbers demonstrates that it isn't a complete proof unless we also prove that a shape with minimum perimeter exists.
@@physicsforthebirds sorry for being stubborn. I think I get all of that and the extra subtle detail in Steiner's proof. For every other shape he found a way of getting one with a smaller perimeter, thus getting closer and closer *to the circle*---- that is almost enough. But, as you mention, one needs the extra step of proving that there is something to reach at the end of the road to really complete the proof. In the number analogy, for all of the natural numbers except 1 you can make them bigger, so that might makes us believe that there is such a thing as the biggest one. And that is the point of Steiner's extra step, that you are not guaranteed that such a thing actually exists even if everything is pointing in that way. Up to that, the analogy seems fine to me. But then you bring up this extra statement that we could naively suspect that one is a potential candidate for the biggest number. But that's doesn't even seem naively coherent from the previous statements, because all of the 'making bigger' processes are pointing *away* from the number one. In the circle case, all of the other processes tended towards the circle, and you just need that extra step about the circle. That's a big difference. Maybe I misinterpreted, but it sounded like you were making the point that in the analogy, the number one was taking the place of the circle in Steiner's case, but that is clearly not true.
@@Danyel615 Okay, I think I understand you. Correct me if I'm wrong, but I think the reason you don't like my sentence "If the biggest natural number existed, it'd have to be one because I can make the other ones bigger" is because that sentence can _never_ be right. Like you said, the "making bigger" function always points away from 1. My sentence makes it sound like I think that 1 is in someway special like the circle is, but the reality is that 1 is only special because of the operation I chose (x^2). If I would have chosen 2(x-2)^2+2, then now 2 is the only number that could possibly be the biggest number. I could now say the same sentence: "If the biggest natural number existed, it'd have to be two because I can make the other ones bigger". I completely agree with you that it's silly that I can logically say both sentences!
Water absolutely can be blown into bubbles. The issue is that in a gravitational field there is a preferred direction for the surface tension to force the water, so it rapidly flows downward and the film squeezes a hole in itself. However, in an inertial reference from (i.e. in space) pure water bubbles are extremely stable.
Gotta be careful with the definition of "bubble". There are *solid* bubbles (air bubble rising in a glass of water; also a drop of water in air (while falling). There are *hollow* bubbles (a soap bubble drifting in air; also a rare "anti-bubble", a hollow shell of air that sits underwater with water inside it). There are solid bubbles of water that "float" on top of water (tricky to produce; they don't last long; an electrostatic field helps). There are solid bubbles of air that sit just under the surface in your glass of water (they don't last long). It's hard or impossible to "blow" *a hollow bubble of water in air;* it breaks before it forms. You can't even make a film by lifting the bubble wand out. Things might change if the wand is very small (microscopic films and microscopic bubbles?) or in *zero-g.* It all depends what is really happening. In *zero-g,* released water sticks together as a blob. The blob tends toward the shape of a solid sphere (a *ball* ). At first it will be oscillating, but in time the waves damp out (unless you blow on it). (A spinning blob will tend toward an ellipsoid.) With a straw, you can blow a solid air bubble inside the water bubble, yielding a thick-walled *hollow bubble of water in air.* What happens next? (Assume the air bubble is not centered.) Without forces, the air bubble will stay where it is. Do forces like surface tension exert a directional force on the air bubble? If forces push the air bubble to the center, you got it right. If forces push the air bubble to the edge and then the air bubble exits the water bubble, you got it wrong. In *zero-g,* an anti-bubble *(a hollow bubble of air in water)* might persist longer, because there is no buoyancy to drive it to the surface.
@@kashu7691 The response to the 'Billionaire Propaganda' allegations was quite interesting, I'm not sure if you've seen it. Kurzgesagt opened up on how they are funded and money from the Gates fundation came down to only 4% I think. Not sure if that changes your mind or anything but I think it's worth a read. Being skeptical is of course not a bad thing no matter who is talking.
@@EliStettner That's like... the exact opposite of their content though? All of their space technology content is the definition of 'Here's cool shit we could perhaps do one day' or 'heres a cool way the world will definitely never end'. All of their videos on real world problems tend to take cautiously positive stances, always ending with the message that although things aren't perfect we can definitely make a difference and that we can come out the other side. The recent immune system videos are just 'Hey look at how cool our human bodies are'. Hell, go watch the The Human Era
You get a sub. Been watching for a while but what’s pushed me to push the button is that you are tackling real world phenomena in a way that both me, an engineer, and my 6 year old can watch and both be totally engrossed. It’s like 3Blue1Brown but more relevant to non-maths nerds and more approachable for little ones. Thank you!
EVERY TIME YOU MAKE A VIDEO IT ABSOLUTELY MAKES MY ENTIRE DAY!! your style is so friendly that i almost don't notice you're combining advanced maths from MULTIPLE disciplines (still can't stop thinking about the jazz video). Thank you for what you make!!
At first I thought "isn't it obvious that since the circle's perimeter could not be reduced, it must have the smallest perimeter?". But then the example using the reasoning that "1 is the biggest number since every other number could be made bigger by squaring" clicked and instantly made me understand your point. Amazing!
One thing that always interested me is when you make a double (or higher) bubble the internal walls aren't actually flat (most of the time) but will curve convexly into the larger bubble. I'm not sure if it is a parabolic curve or if it is the curve of a larger theoretical sphere whose radius is based on setting the larger bubble's radius to 1 and and then dividing that by (1-the radius of the smaller bubble). Either way, I have boned light off them just right on to a wall to get some pretty sharp images of the light source. I kind of thought if gravity could be taken out of the equation the internal dividing walls of bubbles could make excellent optical surfaces (especially for how cheap and easy they are to make and even adjust on the fly.
Here's something about curvature. P is pressure, T is surface tension, R₂ and R₁ are the radii of the larger and smaller bubble respectively, R₃ is the radius of the wall or intermediate film between them. "The pressure in a bubble is inversely proportional to its radius since P = 4T/R. The radius of the intermediate film is dictated by the difference in the pressures on either side of it. These pressures are 4T/R₁ and 4T/R₂ respectively. It immediately follows that P₃ = 4TR₃ = 4T/R₂ - 4T/R₁. So finally we have the simple equation 1/R₃ = 1/R₃ - 1/R₁." (From Gems of Geometry by John Barnes)
The internal pressure of the bubble scales inversely with radius (crude idea: smaller bubble = higher SA/vol ratio = more surface tension per volume = higher pressure; more exactly: P = 4*gamma/R) so a smaller bubble will bulge slightly into a connected larger bubble. But that bulge may be difficult to see because two bubbles of similar size will have a minimal pressure difference (minimal bulge) while a duo of widely different sizes may have more of a bulge but less of a connecting surface to see it (unless one of the bubbles is huge)
@@alberthung6191 Yes, the radius of the face between two bubbles is dictated by the difference in the pressures on either side of it. Let P be pressure, T surface tension, R1 ,R2, and R3 the radii of the smaller bubble, the bigger bubble, and connecting or intermediate surface respectively. The pressures are 4T/R1 and 4T/R2. So P3 = 4T/R3 = 4T/R2 - 4T/R1. So finally 1/R3 = 1/R2 - 1/R1. Must be tricky to verify in some cases though. Photographs?
I didn’t learn much more than the basics of surface tension until I took thermodynamics in grad school, and then I understood why they waited so long to teach it haha. The coolest thing I learned in that class was that the vapor pressure inside of a bubble is proportional to its curvature and the difference in pressure that caused provided some the driving force behind smaller bubbles combining to make larger bubbles in a foam.
Physics for the Birds is seriously growing to be one of my favorite science channels Everything just makes sense, from prerequisite knowledge to the more complex things it all just makes sense and is simple AND listing all the sources? Seriously, such a good channel
Do we know how close to a perfect sphere a real soap bubble is? Has anyone actually done measurements on a real bubble to see how close to the math it is?
In theory it should be as close as possible, but there is a finite smallest edge size due to the minimal distance between molecules in the Lennard Jones potential. But they are arguably the closest things to a sphere we have on Earth
With no wind or external forces, bubbles should be as close to perfect spheres as protons I’m sure in real life, the bubbles are slightly bottom-heavy due to gravity. You could confirm this experimentally through high-optic photography from multiple angles
3:05 This argument immediately falls flat because there's no reason why the density or pressure has to decrease as you approach the surface from the inside of a volume. It also doesn't explain how water rises up the sides of hydrophilic surfaces or up through materials like paper. Also, surface tension works in vacuum, where there's no gravity to generate a pressure differential. Your explanation is seriously flawed. Now I haven't exactly worked out how surface tension works myself, but I know roughly how the negative surface tension of NaK droplet explosions works thatnks to Thunderf00t and co.'s experiments. In those NaK explosions, and sodium, potassium, rubidium, and cesium explosions, too, the chemical reactions of the alkali metal with the water generate a positive charge on the surface of the metal droplet. the charge remains on the surface of the droplet because of repulsion from the positive charge on the other side of the droplet. This positive charge overrides surface tension and drives the surface to expand in a wrinkly, spiky fashion. The new surface also reacts with the water, generating more positive charge and creating a feedback loop that turns the metal droplet into a hedgehog in a fraction of a fraction of a second, then the kinetic energy of the surface expansion becomes very large and you have an explosion. Water surface tension obviously isn't like that because there is no net charge. However, I think the surface tension has to do with how water molecules are repelled only by other water molecules within a short range, and attracted by water molecules in a larger range. Imagine water molecules inside of a u-shaped valley. Molecules at the bottom are repelled primarily by molecules below them, but attracted by molecules up the sides of the valley. molecules at the bottom of the valley accelerate upwards. Meanwhile, molecules on the side of the valley are repelled by molecules on their own side, but attracted to molecules on the other side due to the extra distance. Therefore, molecules on either side of the valley accelerate to close the gap. The net effect looks like surface tension as the valley closes itself. If there's a peak, molecules on the side of the mountain are repelled outwards, and their increasing distance from the peak increases their attraction, pulling molecules down from the peak. Of course, I just came up with this on the fly, but I think I'm already close to accurate on the real interactions that cause surface tension.
I wonder how much of the difficulty in some areas of math comes down to lacking notation or representation of functions, etc. Often, when something is discontinuous, it feels abnormal to treat it mathematically, as if "math didn't like it", and yet nature has no problem with those. Like trying to model someone kicking a ball before learning about Dirac's delta.
It's been amazing watching your channel grow from just 20k subs not too long ago to 80k now! I think that you'll hit 100k in no time. I think that no matter what, given your content's extraordinarily high standard of quality and interesting and highly researched topics, you're severely underrated.
When one say s they don't let out air on either parallel side of the tongue. Otherwise they'd lisp. Same goes with sh-sounds. I'm a bit into tongue placement since i went to speech therapy for a few months when i was a teen. Then i gave up. The therapist just gave me homework like 'say sun 20 times a day until we meet next week'. But a while later my mother told me to smile with my teeth 😁 while saying s. Turned out i just had to put the tip of my tongue behind my teeth. Your s' are beautiful btw. I hope my advice will help. Thank you for videos, especially this one. I fucking love bubbles
it is because the real physical bubble is NOT a problem it IS A SOLUTION. the physical reality is a solutions generating machine. whereas your math.... is a crutch.
It would be interesting to hear you talk about Ken Brakke's "Surface Evolver" - a program that solves complicated minimization of surface problems. And how about the packing of spheres? Another problem with a long history and recent progress.
Wasn't the double bubble conjecture proven in 1995 by Hass and Schlafly? Edit: apparently that was for the special case of both bubbles having the same volume. Also, a third author (Hutchings) was involved in one of the papers.
WAIT I don't think what you said at 6:16 is correct. The perimeter is STILL the same..of the shape youbdraw around the trapezpods hasn't thanked, why would.the perimeter be any different? See what zi mean? You said something about balancing the trapezoidal, but I don't know what thst means..the sides of the trapezpids are not part of the perimeter anyways so isn't what you said wrong?? Or is it because tounare rotating the ship to fit the new configuration of the trapezoids wirhin since nkq they are cnetralozed and when you rotate it then the oerimeter adjjsts to the new vroder kf the trapezpid somehow?? If not i dont see how its correct. Thanks for sharing
I'm not sure if this comment will be seen considering the video was uploaded 2 months ago, but the captions on this video don't work. There's just a huge block of text at the start.
There was a part of my mind: When i was under the influence of certain substance's.. My mind hypothesized about what if the properties of bubble's is a HUGE aspect factor in the underlying structure's & mechanisms of our Universe? In way's that we haven't even considered yet?
The point at the end of the video is the center of a lot of philosophical debate in computational complexity theory (e.g. the field that asks questions like P vs. NP). We have the conception of problems which are inherently *hard* to compute (say NP-hard problems), and we think of different computation models being roughly the same power (Church-Turing Thesis). However, we see a lot of examples of those problems in nature being computed all the time. Oftentimes, the hard problems we see being solved in nature are examples of "easy instances" of broader hard problems. This helps us dig down deeper about what the hard part of a problem really is. Most of this is still pretty up in the air and I think our organization of complexity theory will change a lot in the coming decades.
If you do this in 4D won't you get the most compact 4D structure? 😁 (I think that'll be either icositatrachora or tesseracts). Should be easy enough to stimulate eh, has anyone even done that? When doing research I did think it's amazing how much stuff has never been done.
At 7:12, didnt youbmean to say its not a proof that 1 is tbe smallest number since 1 doesnt increase qhen you square it and we are dealing with minimizing surface areas, not maximizing..even if you didn't mean minimum, i think youd admit i still.made a very valid argument for why youncouldve said minimum there too! lol
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Interesting, thank you. Greetings from Popayan, Colombia.
I don't understand the comparison at @3:26. The vast majority of attraction in water is from hydrogen bonding. Both this and the attractive dispersion/LJ potential are interactions only with nearest-neighbor molecules, with hydrogen bonding being more directional. What is the attractive force at 3:26?
incredible video as always - this has become one of my fav channels on youtube. Are you a berkeley physics student? just noticed one of the birbs in your header has a cal hat. if so, go bears
2:17 I've never heard surface tension explained like this in all my years as a "science-boy" and as a private tutor. I really curious if I simply have never heard of it or if it's really just taught in American schools (not sure of your nationality, sorry)
"I study bubbles for a living" strikes me as someone that had a question at age 1 and has simply refused to give up on answering it. Talk about persistence!🤣
If surface tension is what keeps a drop of water spherical, what happens to water with a low surface tension in zero gravity? Would a large "blob" of water break apart into smaller spheres that the surface tension could contain?
Boy am I glad to have learned about surface tension and even how the tension in a single bubble due to the pressure inside and outside the bubble causes it to be spherical with the derivations and the math.
the gravity surface tension analogy doesn't work for an upside down item, like a spout with a mesh on top of it, or a straw with your thumb on it. it's sometimes upside down.
Bees don't actually make a honeycomb shape; they make them circular and heat transforms them into hexagons.
who cares? nerd
holy shit i never knew that. thanks for sharing
They settle into hexagons, because of course they're the bestagons!
@@faytaliti why do you hate nonagons?
I was under the impression that they got that shape because the bees will push the wax outwards as they work, and so over time, as many bees push the perimeters of the wax outwards, they behave a lot like bubbles being pushed by air pressure.
this channel is gonna take off really fast
the analogy at 6:50 makes my head turn inside out
oh, the guy that pronounces "sh" weird is back.
Good vid!
It's interesting to me that the shape of a bubble is not differentiable. Not sure I understood correctly what you were saying there
How much matj background do you have im curious?
Double the bubble, double the trouble~
saddle-shaped bubbles; helical bubbles; ...
Honeycombs aren't even optimal-there are better 3d cell configurations for storage.
Except water molecules are all zipping around at 1000 mph+ and rotating super fast almost randomly :/
I got really confused by your argument about the natural numbers
"If the biggest natural number existed, it'd have to be one because I can make the other ones bigger"
Probably it needs to be phrased in another way?
Take another example. Imagine the most awful car that is so bad nobody is willing to bet on its price, which is $1 to begin with. Then you see other cars that are more expensive already, and imagine ways on which they can become even more expensive. Your conclusion is that the crappy car must be the most expensive of all of them?
Maybe swap "I can make the other ones bigger" with "I can find a number bigger than each of the other numbers". x^2 is bigger than x for every natural number x except for 1, and if there is a number bigger than x, x can't be the biggest number. The only option we're left with is 1!
@@physicsforthebirds but I can find a number greater than 1---all of the rest ... What am I missing?
@@Danyel615 You're not missing anything, the point is that this "proof" that 1 is the biggest number is clearly incorrect because a "biggest number" doesn't exist. Just like we found a way to get a bigger number for every number except 1, Steiner found a way to get a smaller perimeter shape for every shape except a circle. Naively, that might seem like a proof that a circle has the smallest perimeter, but this analogy with numbers demonstrates that it isn't a complete proof unless we also prove that a shape with minimum perimeter exists.
@@physicsforthebirds sorry for being stubborn. I think I get all of that and the extra subtle detail in Steiner's proof. For every other shape he found a way of getting one with a smaller perimeter, thus getting closer and closer *to the circle*---- that is almost enough. But, as you mention, one needs the extra step of proving that there is something to reach at the end of the road to really complete the proof.
In the number analogy, for all of the natural numbers except 1 you can make them bigger, so that might makes us believe that there is such a thing as the biggest one. And that is the point of Steiner's extra step, that you are not guaranteed that such a thing actually exists even if everything is pointing in that way. Up to that, the analogy seems fine to me.
But then you bring up this extra statement that we could naively suspect that one is a potential candidate for the biggest number. But that's doesn't even seem naively coherent from the previous statements, because all of the 'making bigger' processes are pointing *away* from the number one. In the circle case, all of the other processes tended towards the circle, and you just need that extra step about the circle. That's a big difference.
Maybe I misinterpreted, but it sounded like you were making the point that in the analogy, the number one was taking the place of the circle in Steiner's case, but that is clearly not true.
@@Danyel615 Okay, I think I understand you. Correct me if I'm wrong, but I think the reason you don't like my sentence "If the biggest natural number existed, it'd have to be one because I can make the other ones bigger" is because that sentence can _never_ be right. Like you said, the "making bigger" function always points away from 1. My sentence makes it sound like I think that 1 is in someway special like the circle is, but the reality is that 1 is only special because of the operation I chose (x^2). If I would have chosen 2(x-2)^2+2, then now 2 is the only number that could possibly be the biggest number. I could now say the same sentence: "If the biggest natural number existed, it'd have to be two because I can make the other ones bigger". I completely agree with you that it's silly that I can logically say both sentences!
Water absolutely can be blown into bubbles. The issue is that in a gravitational field there is a preferred direction for the surface tension to force the water, so it rapidly flows downward and the film squeezes a hole in itself. However, in an inertial reference from (i.e. in space) pure water bubbles are extremely stable.
Lol "however, because in a gravitational field the preferred direction of......"
But I get what you mean tho, and that's really cool actually
168th like
Thanks. What should I look for with/involving water bubbles?
Gotta be careful with the definition of "bubble". There are *solid* bubbles (air bubble rising in a glass of water; also a drop of water in air (while falling). There are *hollow* bubbles (a soap bubble drifting in air; also a rare "anti-bubble", a hollow shell of air that sits underwater with water inside it). There are solid bubbles of water that "float" on top of water (tricky to produce; they don't last long; an electrostatic field helps). There are solid bubbles of air that sit just under the surface in your glass of water (they don't last long). It's hard or impossible to "blow" *a hollow bubble of water in air;* it breaks before it forms. You can't even make a film by lifting the bubble wand out. Things might change if the wand is very small (microscopic films and microscopic bubbles?) or in *zero-g.* It all depends what is really happening.
In *zero-g,* released water sticks together as a blob. The blob tends toward the shape of a solid sphere (a *ball* ). At first it will be oscillating, but in time the waves damp out (unless you blow on it). (A spinning blob will tend toward an ellipsoid.) With a straw, you can blow a solid air bubble inside the water bubble, yielding a thick-walled *hollow bubble of water in air.* What happens next? (Assume the air bubble is not centered.) Without forces, the air bubble will stay where it is. Do forces like surface tension exert a directional force on the air bubble? If forces push the air bubble to the center, you got it right. If forces push the air bubble to the edge and then the air bubble exits the water bubble, you got it wrong.
In *zero-g,* an anti-bubble *(a hollow bubble of air in water)* might persist longer, because there is no buoyancy to drive it to the surface.
Kurtsgezart? Never heard of them, this is the superior "cool things + birds" channel.
@@channelknightfadran7901 they are just billionaire propaganda, sorry bro
Kurtzegat is really depressing, hopeless and inhuman.
@@kashu7691 The response to the 'Billionaire Propaganda' allegations was quite interesting, I'm not sure if you've seen it. Kurzgesagt opened up on how they are funded and money from the Gates fundation came down to only 4% I think. Not sure if that changes your mind or anything but I think it's worth a read. Being skeptical is of course not a bad thing no matter who is talking.
@@nive7299 thank you for the info =)
@@EliStettner That's like... the exact opposite of their content though?
All of their space technology content is the definition of 'Here's cool shit we could perhaps do one day' or 'heres a cool way the world will definitely never end'.
All of their videos on real world problems tend to take cautiously positive stances, always ending with the message that although things aren't perfect we can definitely make a difference and that we can come out the other side.
The recent immune system videos are just 'Hey look at how cool our human bodies are'.
Hell, go watch the The Human Era
You get a sub. Been watching for a while but what’s pushed me to push the button is that you are tackling real world phenomena in a way that both me, an engineer, and my 6 year old can watch and both be totally engrossed. It’s like 3Blue1Brown but more relevant to non-maths nerds and more approachable for little ones.
Thank you!
I feel like getting compared to 3b1b is every math ed channels dream come true. This channel is truly marvelous.
EVERY TIME YOU MAKE A VIDEO IT ABSOLUTELY MAKES MY ENTIRE DAY!! your style is so friendly that i almost don't notice you're combining advanced maths from MULTIPLE disciplines (still can't stop thinking about the jazz video). Thank you for what you make!!
This feels like a Numberphile / Matt Parker video and I’m all for it!
Yet another great video - hope to watch you on Nebula some day🤞
*me, secretly not a bird:* _"I'm in"_
At first I thought "isn't it obvious that since the circle's perimeter could not be reduced, it must have the smallest perimeter?". But then the example using the reasoning that "1 is the biggest number since every other number could be made bigger by squaring" clicked and instantly made me understand your point. Amazing!
One thing that always interested me is when you make a double (or higher) bubble the internal walls aren't actually flat (most of the time) but will curve convexly into the larger bubble. I'm not sure if it is a parabolic curve or if it is the curve of a larger theoretical sphere whose radius is based on setting the larger bubble's radius to 1 and and then dividing that by (1-the radius of the smaller bubble). Either way, I have boned light off them just right on to a wall to get some pretty sharp images of the light source. I kind of thought if gravity could be taken out of the equation the internal dividing walls of bubbles could make excellent optical surfaces (especially for how cheap and easy they are to make and even adjust on the fly.
Here's something about curvature. P is pressure, T is surface tension, R₂ and R₁ are the radii of the larger and smaller bubble respectively, R₃ is the radius of the wall or intermediate film between them.
"The pressure in a bubble is inversely proportional to its radius since P = 4T/R. The radius of the intermediate film is dictated by the difference in the pressures on either side of it. These pressures are 4T/R₁ and 4T/R₂ respectively. It immediately follows that P₃ = 4TR₃ = 4T/R₂ - 4T/R₁. So finally we have the simple equation 1/R₃ = 1/R₃ - 1/R₁." (From Gems of Geometry by John Barnes)
I always found it interesting that the face between 2 bubbles is more or less flat. Which makes sense if both bubbles have the same internal pressure
The internal pressure of the bubble scales inversely with radius (crude idea: smaller bubble = higher SA/vol ratio = more surface tension per volume = higher pressure; more exactly: P = 4*gamma/R) so a smaller bubble will bulge slightly into a connected larger bubble. But that bulge may be difficult to see because two bubbles of similar size will have a minimal pressure difference (minimal bulge) while a duo of widely different sizes may have more of a bulge but less of a connecting surface to see it (unless one of the bubbles is huge)
@@alberthung6191 Yes, the radius of the face between two bubbles is dictated by the difference in the pressures on either side of it. Let P be pressure, T surface tension, R1 ,R2, and R3 the radii of the smaller bubble, the bigger bubble, and connecting or intermediate surface respectively. The pressures are 4T/R1 and 4T/R2. So P3 = 4T/R3 = 4T/R2 - 4T/R1. So finally 1/R3 = 1/R2 - 1/R1. Must be tricky to verify in some cases though. Photographs?
I didn’t learn much more than the basics of surface tension until I took thermodynamics in grad school, and then I understood why they waited so long to teach it haha. The coolest thing I learned in that class was that the vapor pressure inside of a bubble is proportional to its curvature and the difference in pressure that caused provided some the driving force behind smaller bubbles combining to make larger bubbles in a foam.
Physics for the Birds is seriously growing to be one of my favorite science channels
Everything just makes sense, from prerequisite knowledge to the more complex things it all just makes sense and is simple
AND listing all the sources? Seriously, such a good channel
Blub Blub is the sound they make
unproven conjecture
Never knew how similar bubbles were to the phospholipid bilayer in biology
Do we know how close to a perfect sphere a real soap bubble is? Has anyone actually done measurements on a real bubble to see how close to the math it is?
In theory it should be as close as possible, but there is a finite smallest edge size due to the minimal distance between molecules in the Lennard Jones potential. But they are arguably the closest things to a sphere we have on Earth
@@rafaelalmada723 “in theory” that’s why we should actually measure it, maybe learn some new stuff by how much it is off from a real sphere
@@crsmith6226 there may be some way of measuring it through Mie scattering, but I am not an experimentalist so it's out of my expertise 😔😔
With no wind or external forces, bubbles should be as close to perfect spheres as protons
I’m sure in real life, the bubbles are slightly bottom-heavy due to gravity.
You could confirm this experimentally through high-optic photography from multiple angles
Well you can “see” the thickness of a bubble from the diffracted colors, so it must be aspherical by at least a couple 100nm
3:05 This argument immediately falls flat because there's no reason why the density or pressure has to decrease as you approach the surface from the inside of a volume. It also doesn't explain how water rises up the sides of hydrophilic surfaces or up through materials like paper.
Also, surface tension works in vacuum, where there's no gravity to generate a pressure differential.
Your explanation is seriously flawed.
Now I haven't exactly worked out how surface tension works myself, but I know roughly how the negative surface tension of NaK droplet explosions works thatnks to Thunderf00t and co.'s experiments. In those NaK explosions, and sodium, potassium, rubidium, and cesium explosions, too, the chemical reactions of the alkali metal with the water generate a positive charge on the surface of the metal droplet. the charge remains on the surface of the droplet because of repulsion from the positive charge on the other side of the droplet. This positive charge overrides surface tension and drives the surface to expand in a wrinkly, spiky fashion. The new surface also reacts with the water, generating more positive charge and creating a feedback loop that turns the metal droplet into a hedgehog in a fraction of a fraction of a second, then the kinetic energy of the surface expansion becomes very large and you have an explosion.
Water surface tension obviously isn't like that because there is no net charge. However, I think the surface tension has to do with how water molecules are repelled only by other water molecules within a short range, and attracted by water molecules in a larger range. Imagine water molecules inside of a u-shaped valley. Molecules at the bottom are repelled primarily by molecules below them, but attracted by molecules up the sides of the valley. molecules at the bottom of the valley accelerate upwards. Meanwhile, molecules on the side of the valley are repelled by molecules on their own side, but attracted to molecules on the other side due to the extra distance. Therefore, molecules on either side of the valley accelerate to close the gap.
The net effect looks like surface tension as the valley closes itself.
If there's a peak, molecules on the side of the mountain are repelled outwards, and their increasing distance from the peak increases their attraction, pulling molecules down from the peak.
Of course, I just came up with this on the fly, but I think I'm already close to accurate on the real interactions that cause surface tension.
0:04 Wait there's such thing as a bubble stacking competition?! 😱
A great theologian named Sir mixalot spoke a lot about the double bubble back in 1992 A.D.
I am a stable configuration of bubbles
1:05i see so the stacking guy was before that cuz everyone knows that physics don't apply until someone discoveres them
It’s insane how much I love this channel!
I'm curious how do you find all the research papers to make the timeline at about 9:00 how are you sure that nothing has been missed?
Thank you for including your sources in the description!!!
Actually it’s just because the hexagon is the Bestagon
I wonder how much of the difficulty in some areas of math comes down to lacking notation or representation of functions, etc. Often, when something is discontinuous, it feels abnormal to treat it mathematically, as if "math didn't like it", and yet nature has no problem with those. Like trying to model someone kicking a ball before learning about Dirac's delta.
While I'm not a bird, I always enjoy learning these neat little parts of physics.
Bro is the type of guy to find out and prove his shower thoughts 💀
The CONCEPT is simple, the MATH is hard. That's why they're difficult to prove, but very intuitive to understand at a conceptual, high level.
This channel makes me like physics and birds.
3:14 hmm but isnt the density of water always constant only the pressure changes?
It's been amazing watching your channel grow from just 20k subs not too long ago to 80k now! I think that you'll hit 100k in no time. I think that no matter what, given your content's extraordinarily high standard of quality and interesting and highly researched topics, you're severely underrated.
When one say s they don't let out air on either parallel side of the tongue. Otherwise they'd lisp.
Same goes with sh-sounds.
I'm a bit into tongue placement since i went to speech therapy for a few months when i was a teen. Then i gave up. The therapist just gave me homework like 'say sun 20 times a day until we meet next week'. But a while later my mother told me to smile with my teeth 😁 while saying s. Turned out i just had to put the tip of my tongue behind my teeth.
Your s' are beautiful btw.
I hope my advice will help. Thank you for videos, especially this one. I fucking love bubbles
it is because the real physical bubble is NOT a problem it IS A SOLUTION.
the physical reality is a solutions generating machine.
whereas your math.... is a crutch.
Evolution is the best optimizator.
It's just horrendously, terrifyingly, apocalyptically inefficient.
It would be interesting to hear you talk about Ken Brakke's "Surface Evolver" - a program that solves complicated minimization of surface problems. And how about the packing of spheres? Another problem with a long history and recent progress.
Wasn't the double bubble conjecture proven in 1995 by Hass and Schlafly?
Edit: apparently that was for the special case of both bubbles having the same volume. Also, a third author (Hutchings) was involved in one of the papers.
WAIT I don't think what you said at 6:16 is correct. The perimeter is STILL the same..of the shape youbdraw around the trapezpods hasn't thanked, why would.the perimeter be any different? See what zi mean? You said something about balancing the trapezoidal, but I don't know what thst means..the sides of the trapezpids are not part of the perimeter anyways so isn't what you said wrong?? Or is it because tounare rotating the ship to fit the new configuration of the trapezoids wirhin since nkq they are cnetralozed and when you rotate it then the oerimeter adjjsts to the new vroder kf the trapezpid somehow?? If not i dont see how its correct. Thanks for sharing
I'm not sure if this comment will be seen considering the video was uploaded 2 months ago, but the captions on this video don't work. There's just a huge block of text at the start.
There was a part of my mind: When i was under the influence of certain substance's.. My mind hypothesized about what if the properties of bubble's is a HUGE aspect factor in the underlying structure's & mechanisms of our Universe? In way's that we haven't even considered yet?
The point at the end of the video is the center of a lot of philosophical debate in computational complexity theory (e.g. the field that asks questions like P vs. NP). We have the conception of problems which are inherently *hard* to compute (say NP-hard problems), and we think of different computation models being roughly the same power (Church-Turing Thesis). However, we see a lot of examples of those problems in nature being computed all the time. Oftentimes, the hard problems we see being solved in nature are examples of "easy instances" of broader hard problems. This helps us dig down deeper about what the hard part of a problem really is. Most of this is still pretty up in the air and I think our organization of complexity theory will change a lot in the coming decades.
What I don't get is why the bubbles don't just merge to make a single larger (more efficient) sphere...
If you do this in 4D won't you get the most compact 4D structure? 😁 (I think that'll be either icositatrachora or tesseracts).
Should be easy enough to stimulate eh, has anyone even done that? When doing research I did think it's amazing how much stuff has never been done.
As a kid I had a phobia of double bubbles
great channel! subscribed.
and remember, nature does NOT owe you an explanation. it exists.
it's up to us to understand it
Try beatboxing bro, it fixes the tsch sound - speaking from experience. NICE VIDEO.
At 7:12, didnt youbmean to say its not a proof that 1 is tbe smallest number since 1 doesnt increase qhen you square it and we are dealing with minimizing surface areas, not maximizing..even if you didn't mean minimum, i think youd admit i still.made a very valid argument for why youncouldve said minimum there too! lol
Interesting, thank you. Greetings from Popayan, Colombia.
This channel is consistently wonderful, thanks for the great content.
I don't understand the comparison at @3:26. The vast majority of attraction in water is from hydrogen bonding. Both this and the attractive dispersion/LJ potential are interactions only with nearest-neighbor molecules, with hydrogen bonding being more directional. What is the attractive force at 3:26?
I'm here because of that joe Rogan and Terrance Howard podcast. I think he's onto something
incredible video as always - this has become one of my fav channels on youtube. Are you a berkeley physics student? just noticed one of the birbs in your header has a cal hat. if so, go bears
Yep, I graduated from Cal's physics department. Go Bears!
2:17 I've never heard surface tension explained like this in all my years as a "science-boy" and as a private tutor. I really curious if I simply have never heard of it or if it's really just taught in American schools (not sure of your nationality, sorry)
"I study bubbles for a living" strikes me as someone that had a question at age 1 and has simply refused to give up on answering it. Talk about persistence!🤣
dude i was searching for why bubble are spherical and i got a much more interesting subject than the one i was looking for thanks.
Do you not learn about polar molecules in chemistry where you live? It's a pretty basic part of chemistry here.
A Double Bubble Blowing Baby doesn't belong out here.... in BIRD country!
Just add frequency and vibration? And let’s watch those bubbles move
If surface tension is what keeps a drop of water spherical, what happens to water with a low surface tension in zero gravity? Would a large "blob" of water break apart into smaller spheres that the surface tension could contain?
Boy am I glad to have learned about surface tension and even how the tension in a single bubble due to the pressure inside and outside the bubble causes it to be spherical with the derivations and the math.
i know this is irrelevant, but i absolutely love your voice, especially when you say "double bubble"
10:50 Song name?
11:27 Song name?
I make all of the music just for these videos!
@@physicsforthebirds Can you upload the music, so we can listen to it, please?
@@physicsforthebirds I searched the whole comment section for this. The music was lovely and made me happy. Thank you for this little musical gem
10:45 dont bees just make circles?
If you stack them in 2d and apply pressure, they end up hexagonal
Excelente video, era justo lo que estaba buscando!! felicitaciones!
Surface tension is why your bones break when you hit water at high speed, ie stupid Tick tok challenges.
You call it a double bube i call it a bubble butt, we are not the same. 🚶♀️🚶♀️🏃♀️🏃♀️
the gravity surface tension analogy doesn't work for an upside down item, like a spout with a mesh on top of it, or a straw with your thumb on it. it's sometimes upside down.
I think I remember that I used to call double and triple bubbles “livers” for some reason when I was in like grade 1.
I did not know there were theorems and math equations or rules for…A bubble I guess I’m just simple minded
How did we not solve þe question of "I wonder why bubbles connect in þe way þey do" until þe 2000's
Man I love your videos, but that outro music is kinda unsettling.
At 8:20 WHY donmutliple esges meet in fours because in 3d soace yiu csnt fit mlre than four or is something else going on?
Fantastic Work, but how does this fit into the “4th Phase of Water” and the science behind it?
just eat one sugar cube anytime he mentions "bubble" or "bubbles", you will have a sugar rush xD
Does that mean that hydrogen atoms have similar surface tensions to oxygen atoms because that's a watermolecule
videos spongebob would make after taking the limitless pill
Bubbles are just good analogs for electron fields in atoms and molecular configurations
the bees don't know, they do circles and it just ends up being hexagon.
Calculus of variations can handle non differentiable solutions if you ask an engineer.
thank you for your's gorgeous videos, huge hugs from russia
Just last night I re-rewatched most of the videos, who'd ave thought that that today would give me another
"it's clearly physics" no, it's clearly chemistry :)
All I could think about the whole video is "Double bubble disco queen headed to the guillotine"
So bubbles are fuzzy on a microscopic level? Creepy.
The standard double bubble is such a powerful phrase
I am fascinated and awed, thank you for sharing this!
fun fact. cells are basically just bubbles with stuff in em and on em.
im sorry, bubble stacking competitions?
How can we apply this to the multiverse bubble theory?
w video idea
How would the rules change, if the ruble is inside a liquid?