An unexpected way to inflate a balloon - Numberphile

Using a kamifusen (a Japanese paper balloon). Featuring Tadashi Tokieda.
More Tadashi videos: bit.ly/tadashi_vids
More links & stuff in full description below ↓↓↓
Objectivity (videos by Brady about science objects): bit.ly/Objectivity
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Videos by Brady Haran
Editing and animation in this video by Pete McPartlan
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A NOTE ON THIS VIDEO:
A few of our Tadashi videos blur the already blurry line between mathematics and physics... Some people suggest they may be a better fit on Brady's dedicated physics channel (called Sixty Symbols).
In response, the reasons they are on Numberphile are:
1) Tadashi, while certainly a modern polymath, is based in a mathematics department.
2) This sub series (with its animation and extra production work) has been supported by the Mathematical Sciences Research Institute, a Numberphile collaborator.
3) Some of the previous and future Tadashi videos are more math-oriented than physics - and it just makes sense to put them on one channel rather than dividing the series between two channels on an ad hoc basis.
In a multi-disciplinary world, it is challenging to run KZbin channels which people come to associate with just one discipline.
That said, feel free to go over and watch hundreds of physics videos on Sixty Symbols --- / sixtysymbols

[@RobertMilesAI]

I love the way Tadashi is just batting the thing around casually while also explaining how it works, and then in the slow-mo Brady's face is like [MAXIMUM CONCENTRATION]

[@numberphile]

+Robert Miles in his defence, Brady was also operating a slow motion camera!!! ;) And slow motion makes everything look more intense anyway.

[@RobertMilesAI]

It's more a comment about Tadashi's skills, I expect I'd look the same as Brady!

[@harryandruschak2843]

At age 73, I doubt if I could do the trick at ANY pace :)

[@josgeerink9434]

IKR!!

[@16montana24kobe]

Well if it isn't a Miles Robert impersonator

[@ThaNinjazTube]

I was waiting for him to drop it... but he got skills

[@mosk11tto]

Asians

[@pluto8404]

If he dropped it, his kung fu master would see it that his head sliced off.

[@Kyurem97]

And his father would have degraded him

[@robertofontiglia4148]

I think the correct spelling is "skillz"

[@Xnoob545]

@@robertofontiglia4148 no it's NUT

[@keenantroll5151]

when i see a new numberphile video, i get excited... when I realize it's a new Tadashi Tokieda episode, it's like christmas

[@maldoran9150]

Can't get enough videos with this guy, great teacher! Reminds me a lot of Feynman, always curious about why things behave the way they are.

[@maldoran9150]

you mean bedroom eyes, I suppose.

[@wierdalien1]

mal doran nah he looks tired.

He's japanese -_-

[@wierdalien1]

andrecampana_ you dont say. But he also looks tired.

[@xeli3046]

mal doran the physicist who made the diagrams of particle interaction?

[@noahzuniga]

the way he drew that hand is amazing

[@WashingtonThwackhurst]

he has skillz with that keepy-uppy

[@noobnoobyify]

The scientific term is throwing-hitty-keepity-in-suspension.

[@RWBHere]

Complete with a header!

[@mathsmoica]

*Numberphile - an unexpected way to love mathematics !*

[@bigboysteen7638]

Ce pseudo tho >~

[@nytmare3448]

The folding of the paper is partially elastic and partially inelastic deformation. Its like stretching a metal spring a little too much. It will compress back a little, but not all the way.

[@-danR]

As I see it, the probability of hitting a convex fold is (much) greater than hitting a concave fold. each time a convex fold is struck, the inertia of the ball will cause the the fold to _un_ fold ever so slightly. After repeated impacts and all the convex folds flattened out, the ball assumes a more spherical shape. I haven't watched the full video, I don't know if that's the explanation. Edit: OK, that's not his theory. There may be a bit of both. It may be a complex phenomenon. I think my theory is more _mathematically_ parsimonious. Edit2: Actually the dynamics and geometry of impact will also slightly unbend the concave as well as the convex folds.

[@tylerm442]

I thought it also had to do with the decreased air pressure inside the ball the instant after crumpling. When the ball is initially crumpled/hit two things happen. 1) air inside is jettisoned out through the hole, slightly decreasing number of air molecules inside relatives to outside, which would cause an immediate influx of air to balance out the system. 2) more surface area is present inside the ball after immediate deformation, therefore more force should be present because increased impacts from the air. I don't think this effect, even if my thinking is right, could explain the phenomenon fully but I also think that it does have an impact. Feel free to scrutinize and challenge lol

[@ilmanowar]

I think it has a paper valve, each hit generates a pressure wave in the compression phase changes the shape of the ballon in the non hit side and in the expansion phase shape the hit one.

[@RWBHere]

Tyler, the surface area does not change.

[@tylerm442]

RWBHere I understand that. Surface area may not have been the term I was looking to use lol. My idea was more like effective surface area I guess with the idea about how since the terrain is more uneven and jagged, the air will interact with the surface more so. Thanks for pointing that out tho, wasn't really considering that until you said it lol.

[@raimundozubelzu2794]

Tokieda is amazing, he always come up with great stuff!

[@numberphile]

thanks - and thanks for watching

[@bscutajar]

The explanation is simpler. The material wants to be in a state of least internal stresses which is the spherical shape in this particular case. When you hit it arbitrarily you are altering it's shape in several places. If the alterations are ones which increase stress, the material fights back, otherwise it goes along with it. And thus eventually it reaches the spherical shape. An analogy would be a heap of sand in a pan where shaking the pan moves the grains arbitrarily but they want to go down in an even distribution so that's where they will end up even if your movements are not specifically targeted to move them down.

[@MechaKillWhitey]

I like your explanation better.

[@Davidbasque15]

Yes indeed, I knew from his explanation that the push back he was talking about accounts for not much. It's hard to explain into words but your explanation is what I couldn't find a way to express.

[@-danR]

Also the convex folds are the most likely part of the ball to contact on a strike. The deceleration of the local paper at that region is going to un-fold that convex bend ever so slightly. But the impact will also slightly unbend the con _cave_ folds.

[@swunt10]

nonsense

[@_t03r]

Thanks, I wanted to write almost the same :D As a physicist, this seems to be the most intuitive explanation. Though I would describe it rather as the ball being in a local energy minima in the configuration space of the possible crumpled states of the ball. By hitting it, you put some energy in the ball. Basically a shock wave passing through the surface, which allows it to move closer towards the global minima (the state with least tension, which is close to being completely round) before falling into another local minima. I think it's basically the same idea as yours.

[@donotfeedthebirds7305]

Love vids with him

[@achu11th]

Great slow mo.

[@EPMTUNES]

achu11th MElonS

[@achu11th]

EPMTUNES I hope, you mean Kamifusen.

[@Npvsp]

Yes you can see Brady’s ugliness and reflexes absence!

[@MalcolmCooks]

Tim from Grand Illusions would love this

[@trobin]

Finally a reward for getting up at 6

[@numberphile]

Good morning!

[@yousorooo]

CDT huh

[@trobin]

Derek Leung est

[@lelouchyagami703]

He looks like he's having so much fun hitting the balloon and that's why I really enjoy his videos

[@chicoktc]

Lelouch Yagami he's always having fun, isn't he? Passionate about his craft, I suppose. Lucky man

[@Rhino123freak]

I love this man.

[@cheem2952]

RhinoFreak 100LIKE!!!

[@henridelagardere4584]

The state of being hit hard *by* inflation I know only too well, but the concept of hitting hard *to* inflate is genuinely new to me.

[@ashboon1625]

*Tadashi Tokieda!*

[@Doc_Fartens]

Really enjoy the videos with Tadashi.

[@jeremyshaferorigami]

I wonder if the centrifugal force of it rotating plays some role as well.

[@chicoktc]

Yes, Tadashi is back! Love him, great video once again!

[@syvisaur7735]

Pr. Tokieda you are just amazing, please make more videos, I love them !

[@timseguine2]

I love your interviews with Tadashi

[@thrillscience]

I always love Dr. Tokieda's videos! He's got a great style.

[@vdang6592]

Gosh I love Tadashi. He shows you can be enthusiastic about shapes without appearing like a lunatic with a Klein bottle!

[@nerminkurtic8546]

Marvellous once again! Love this guy!

[@feynstein1004]

Hey Brady. I just wanted to say that while this is a newer account, I've been subscribed to Numberphile since 2011. Back then, my internet connection was kinda weird in that downloading KZbin videos was faster than buffering them. So I downloaded the videos that I really liked. I had Numberphile, Vsauce and minutephysics. :)

[@kindoflame]

I love Tadashi's Toys. They are always the best videos.

[@llamafromspace]

Tokieda is awesome, love his voice and explanations.

[@DekarNL]

Tadashi has this infectious curiousness about the simplest of things. A great characteristic to have!

[@zippymax1]

Okay, now *_THAT_* is metaphorically and metaphysically profound.

[@epicormic_bud]

Tadashi's Toys is my favourite Numberphile series! His voice and personality are so soothing, and the predicaments he presents are always sort of taken for granted real-world phenomena at play :)

[@felix2315]

Braidy asks a question, "interresting question, i have to think about this", 5 years later warp drive

[@magre9656]

The videos with Tadashi are my favorite.

[@tracyhouser3138]

There's something really captivating and attractive about a person who speaks English as a second language and with a notable accent like his, yet has a certain eloquence in vocabulary and etiquette. I see it often in informative videos likes this and I dig it quite a bit. Intriguing video for sure. Thanks for sharing (:

[@DarkestValar]

Boss: Are you playing in the office? Me: No!, im proving a math theorem

[@samseidel9917]

What a delightful man. Excellent and entertaining explanation.

[@BenjaminGatti]

Two additional principles: 1. Centripetal force favors the sphere, so any induced rotation helps, 2. The dome is a stronger geometry than a folded surface, so once formed, the dome will be more resistant to collapse than it's crinkled neighbors.

[@Folko]

Tadashi videos are always the bomb

[@SidV101]

Thanks, this hit me right in the nostalgia feels

[@ProTayToeGamer]

S C I E N C E

[@Blazico]

Tadashi's back! YAY

[@maltezachariassen7496]

This guy is my favorite! More with him please!

[@ShifterPEE]

Those japanese words literally means "paper wind boat" in chinese, amazing how chinese and japanese language share the same words, but have different meaning edit: added wind

[@SeanKD_Photos]

Having learned both languages, I agree it's really interesting

[@DarkAngelEU]

You should look into the history between China and Japan if you're so interested in the development of both languages. Japan used to be ruled by China for quite some time and they were forced to take over their alphabet which is why one of their alphabetical systems is still quite identical to Chinese ;)

[@DarkAngelEU]

I think the Chinese even brought writing to the Japanese but I might be mistaken about that one.

[@akuyume7]

As info, 風船 in Japanese I believe was originally used to mean balloon like an airship, but the meaning drifted to mean small, toy balloons.

[@MMrandomdude12]

Tadashi's voice is so soothing.

[@Nf6xNet]

I love all of Tadashi's videos, but this one is even better because it includes a cameo appearance by a small dog.

[@geethag696]

Awesome video! Please post a follow up on why the balloon tries to fight back.

[@charlesdaugherty7780]

Professor Tadashi is probably my favorite professor of all time! He really enjoys the maths as well as the explanations of them!

[@KhalilEstell]

I love this professor sooo much!!!!

[@hirakmondal6174]

2:12 question.... The answer is *_ELASTICITY_* elasticity is observed on a very small amount as the material has passed it's breaking point and there is no way to get it exact shape back..and shaping the balloon is done by the air particles which pushes the molecules of the paper to inflate up to a certain limit..and get its highest accomplish-able shape i.e. the *_SPHERE_*

[@limbridk]

Tadashi has such a nice and pleasant way about him. Seems like a great person to be around.

[@josepharmstrong6852]

love his voice this is an unintentional ASMR video.

[@kkme7]

Really nice animation too!

[@ColynBowman]

More Tadashi pls!

[@anaussiebloke3309]

That slow-mo game bois! On point

[@PaltryPete]

I totally appreciate Tadashi's sense of order at the brown paper. Good idea to use a fine pen rather than a Sharpie

[@eldsdrak]

His sketches are so neat and beautiful. (:

[@-.._.-_...-_.._-..__..._.-.-.-]

Nice animations!

[@001100AAAEA]

Great animation

[@Ruminations09]

I love Tadashi. Just like with James Grime and Cliff Stoll, he has an infectious love for what he does that just makes me want to learn from him.

[@dcpngn3740]

I love him and his voice, and yes I do think his voice is a separate entity

[@codingphysics695]

The spherical shape of the ball is that shape for which the elastic strains and stresses are minimal. As with an elastic spring, which has a preferred length and returns to its original shape after stretching and oscillation, the ball will again assume its spherical shape over time. However, in the case of the ball, the driving forces are minimal and are largely compensated by frictional forces. The path of the crumpled ball to its energy minimum is very complicated as there are so many kinks and bumps that all have to be smoothed out without creating new kinks and bumps. On the way to a global energy minimum, the ball will often get stuck in a local energy minimum, causing the healing process to stop. The blows on the ball help him to overcome such local minima in the energy landscape and to get closer to his optimal form. Another example is heat treatment from metallurgy, which can be used to heal crystal defects such as grain boundaries and dislocations in metals. In this case, an annealing of the metal at high temperatures causes the atoms to be excited to thermal vibrations. In itself, these vibrations lead to more disorder in the crystal, because the atoms no longer sit well in their places. But large defects in the crystal structure decreasing over time due to the heat treatment, so that the order in the structure increases if the crystal is slowly cooled down at the end.

[@rastrisfrustreslosgomez544]

Aha! this is a very well tought explanation. I do believe this to be the case, but I have a little issue regarding the second law of thermodynamics. Wouldn't each successive iteration of the hitting actually increase the entropy of the ballon? I mean, we are adding energy after all. After an indeterminate number of hits, wouldn't the folds of the paper be so microscopic that the energy gap between local minimuns becomes arbitrarly large? What I'm trying to say is that altough we can inflate a ballon using such a method, we can never achieve perfect roundness, as entropy doesn't allow the system to reach global energy minimum

[@codingphysics695]

I basiscally agree with you. Inside the crumpled a small amount of elastic energy is stored. By rounding the ball this energy is released and converted into heat, so that entropy is increased a litte bit due to the rise in temperature. But at a certain point the ball is almost spherical, so that the stored energy becames negligible small. Therefore, there is no driving force to round the ball beyond that point, because the tiny energy release is overcompensated by the entropy increase of the ball, since the perfect round shape would be a highly ordered structure. In the same way, you cannot grown a crystal without imperfections. You will alway have a tiny amout of impurity atoms, even if the elements tend to segregate, because few imperfections make up for a large entropy contribution.

[@stvltn]

Yeah, his description of "fighting back" is not very precise. Yours is much better. But to be honest, before reading your comment I wasn't sure about the english vocabulary for this phenomenon either.. Also, this is numberphile not physicsphile :D

[@BLenz-114]

I am also thinking that when you hit it, you are never hitting it at a point where the crumple is "in" because your hand encounters the "out" part first. So, the inertia of the "in" part makes it come to be more in the plane with the "out" part. I guess that's only true while it's more crumpled, though. Once it starts to take on a more rounded shape, you're striking the "out" more than the "in". Hmmmm. A second mechanism may be that when you strike it, you compress the air inside, which only has a small hole to escape, and the hit happens quickly, so not as much air is expelled as it might if the hit were slower. This is the "puff" as he says. Then it has a relatively greater amount of time to pull air in. I'm kinda just repeating what he said, but what I think I'm adding is that the small hole acts a bit like a one way valve that lets more air in than out because of the fluid dynamics of the air. ???

[@flamencoprof]

I agree there re pressure, see my slightly more recent comment, but I also like your approach re the most likely strike points.

[@longcat]

i now realise that this is the same process that's going on when i plump a cushion by turning it over and dropping it many times... ... thanks x lots of love for Tadashi x

[@johnredberg]

Tadashi is so instantly likeable. I think what makes him so enjoyable is seeing an adult who managed to never lose the curiosity we all experienced as children. Brady, thanks for introducing him to the world!

[@suprguy]

another video with tadashi!! yeeeee

[@AeroNest5]

This guy is simply brilliant!!!

[@helgefan8994]

Fascinating! I think the centrifugal force from making the ball turn after hitting it might also help it to "fight back".

[@tomwhitington8737]

There is nothing more wholesome than Tadashi.

[@imdeadserious6102]

2:10 the reason it bounces back slightly after being crumpled is the resting elasticity and spring like tensions aren't equal after being forced into a specific shape so when you let go it equalized the forces.

[@justindie7543]

No matter what the subject is, Tadashi can explain it and everyone will understand.

[@liewwh]

He is impossibly amazing!

[@MK-13337]

The balloon is like a spring when it's "over compressed" and the tension in the balloon "fights back"

[@pintohoareau579]

great stuff..

[@kjk5736]

Haha amazing!!! Great video

[@PetAnimalCareReptilesandmore]

I've always used this to make pillows more fluffy. Nice!

[@inchinaxp8663]

Tadashi has got some mad skills!

[@jacquesfall8117]

Quite amazing

[@ryanhollander7474]

I would’ve LOVED this guy teaching me. I had this guy who taught us how gps satelites image the surface of the earth. He was approachable and explained the content so you would understand. It was so interesting even if I don’t work with gps in my everyday job. On second inspection it seems a lot of people are a fan of his teaching style.

[@RogueCulture]

Tadashi has tremendous handwriting and drawing skills.

[@jtveg]

Very interesting and so counterintuitive. 🤔

[@theclarinetjooddsandends3753]

"Oops", indeed. Very cool and enjoyable !

[@timedebtor]

This feels like it could be used as an approach to a solve some classes of optimization problems

[@duncanurquhart5278]

This is too adorable!

[@KamiInValhalla]

Just looking at that curly bracket he drew makes me jealous. Beautiful.

[@GerikDT]

It helps me to think of it in terms of which side of the balloon is easier to deform by putting pressure on it. Since it's round, the convex shape as seen from the outside will have a naturally higher rigidity to it, and will not as easily buckle. However, the inside, wanting to return to its normal state, will have a far easier time buckling in the opposite way. So the direct pressure from your hand will not buckle the balloon that much, but the residual pressure that then carries over to the opposite side (from the inside) will have a greater effect, so it eventually returns to its original shape...more or less.

[@invisi.]

Paper ASMR Love it

[@tacobor]

Tadashi was having so much fun batting that ball around. A lot of physics at work here.

[@lohphat]

It also seems the material is under tension and wants to resume its inflated form too. Crumpling it basically compresses the fibers like a spring and hitting it releases the compression so the fibers straighten out again.

[@nicholasball1119]

We all just got pranked by mathematicians into watching a video of grown men batting around a wad of crumpled paper.

[@RafidW9]

oh how I have missed Tadashi's videos...

[@mumu22mumu22]

That bracket was smooth

[@7markhunter]

Crumpling the ball is akin to folding, which is also akin to compressing springs. When you wack the ball around you are adding energy which has the effect of unfolding the folds on the far side, and the effect of over-folding or compressing the hit side, the potential energy stored by compressing the hit side tends to be released just like a compressed spring does. When you continue this process you gradually at random unfold all the "sides" of the formerly crumpled/folded ball. It may also be similar to the effect of untying a knotted chain through vibrations (in that case the story is told through entropy).

[@TheMullerClan]

Very fun to watch, especially the explanation part while juggling the paper ball! :) While watching I was thinking about the point that, by hitting it repeatedly and randomly by all sides, the force of the impact would be transferred even all across its spherical surface over the time, well, relatively. Isn't this also an important thing to consider?

[@goboogsiego]

he explains it very well

[@seikeshklerns]

Thought he would inflate the ball by juggling it with his bare feet.

[@numberphile]

Maybe next time

[@iliasasdf]

No.

[@nymalous3428]

One of my favorite Numberphile videos involved Tadashi holding a Moebius loop with his toes... it was the most interesting use of fingers and toes during mathematics I had ever seen.

[@jimday666]

Very nice drawings!

[@BenjaminGatti]

As pointed out below, bent paper partly recovers because it is a collection of fibers in various stages of deformation, it is largely impossible to bring all fibers simultaneously to the point of plasticity, some will remain in an elastic state.

[@Ed__Powell]

Tadashi is a rock star

[@whiterottenrabbit]

3:10 Beautiful curly bracket, expertly executed!

[@lachlangreenbank9031]

the shape of the graphed curve, losing volume when hit but regaining more as it waits for next hit reminds me of that bitcoin things price when graphed on a chart over the long term. intresting video!