A world from a sheet of paper - Tadashi Tokieda

Starting from just a sheet of paper, by folding, stacking, crumpling, sometimes tearing, Tadashi will explore a diversity of phenomena, from magic tricks and geometry through elasticity and the traditional Japanese art of origami to medical devices and an ‘h-principle’. Much of the show consists of table-top demonstrations, which you can try later with friends and family.
So, take a sheet of paper. . .
Tadashi Tokieda is a professor of mathematics at Stanford. He grew up as a painter in Japan, became a classical philologist (not to be confused with philosopher) in France and, having earned a PhD in pure mathematics from Princeton, has been an applied mathematician in England and the US; all in all, he has lived in eight countries so far. Tadashi is very active in mathematical outreach, notably with the African Institute for Mathematical Sciences.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

[@JAG_2023]

It’s both humbling and reassuring to know that there are still professors who truly embrace the idea that they exist to advance their area of expertise and to educate others. What a privilege it is to be able to access content like this. Thank you.

[@blackawana]

That is the truth!

[@imnotlettingyouseemyname]

Which professors don't do either one of those? 🤔

[@Coolcmsc]

⁠@@imnotlettingyouseemynameThis is a good question. It has an easy answer. And, I’m wondering if you are a maestro of irony.

[@DerSaa]

Ok. And do you have kids? Because THAT is your purpose in life. You live because all your ancestors had children they took care of.

[@ashadowawhisper]

@@imnotlettingyouseemynamethere are many in the great institutions of the west who have taken to activism using their lecterns as a platform to push agendas or politics, its more prevalent amongst the most prestigious institutions of academia now unfortunately… Yale, Berkeley, Harvard, Stanford, Oxford, etc., the supermajority of which are in the social “sciences”.

[@michaelsohocki1573]

When he was talking about isometrics and the Miura Ori, I couldn't help but think about baby plants. When you watch grass grow (yes, you can watch grass grow too), there is an outer sheath that bulges, cracks down a seam, and it's fascinating to see how nature has packed its long, slender, almost full-size member into that tiny space: it's folded, like tiny little accordion squares. Ferns are also encase in unimaginably tiny geodesic curled patterns, palmetto leaves packed so tightly that you can scarcely imagine that inside that compact waffle of greenish gold, there are over a hundred perfectly straight leaves waiting to unfurl. I feel certain that Miura was outside sitting in front of a garden one day, staring at a lead coming of out its tightly packed chute. It's just really beautiful and intriguing. I LOVED this lecture--thank you so much!

[@Gamerock82]

The same for moth and buterfly wings when they first emerge from their chrysalis. As I recall, they inflate their wings with a tiny amount of fluid. This transforms the wings from super compact and unrecogniseable to fully unfurled and quite rigid, complete with the necessary aerodynamic curvature.

[@Berend-ov8of]

The only 'walking' plant I'm familiar with, Avena Fatua, proceeds across the ground as a seed on the basis of a folding pattern similar to the Miura Ori shown at 54:55. This shape folds and unfolds powered by changes in humidity, enabling the seed to 'walk' in order to find a good place to root.

[@davemarx7856]

Seeds themselves.

[@murrygreenlaw6522]

Far more interesting is to discover who created those folded parts so small in the first place. There are too many, 100s, of folds to have happened perfectly, without even one being off. Most people will look at this and say it all happened by chance mutations over millions of years' time. Really? No. What has then stopped the evolutionary process now? If the evolutionary hasn't stopped then we should see imperfections in these plants as they change into their next form. But we don't see this. Why not?

[@Gamerock82]

@@murrygreenlaw6522 I'm inclined to agree with you but the usual response is that, human lifespans are but a blink, in evolutionary time - that all of recorded history of our species, is nothing more than the last few minutes of deep time. My response is usually something along the lines of, intelligent design is apparent and being willfully blind to it changes nothing.

[@robjohnston1433]

Wow! It takes TRUE talent and genius to be able to teach, demonstrate and JOKE in another language! And he is GREAT ... in teaching, demonstrating and being funny -- all at the same time! I wish I had discovered him earlier, but NOW I will seek out EVERYTHING he has made!

[@graymouser1]

And not just one other language, since he dipped into Greek at points as well. (And probably another language or two when I wasn't paying close enough attention.) A chem prof at my local U went on sabbatical for 4 months, to guest at a lab in Germany and then Italy. Now, he was Polish and so already spoke a smattering of eastern European languages to begin with, but in that 4 months he went from nothing to being able to function in a lab in both of those languages. Plus, he was there to participate in some research so it's not like all he did was study language. Wild!

[@justyoutubin]

On an episode of Numberphile, he revealed that English is actually his EIGHTH language!

[@frechjo]

The way he crumbled the paper between the cans, reminded me of crushing an aluminium can of soda or beer. I do the same twisting and pushing together, but I never thought about the Poison (🐟) ratio involved in that, haha.

[@WammesWaggel-ep1en]

Beautifully done. It surprised me, though, that he didn't mention why the symbol for the Poisson ratio is so perfect. Many native speakers of English don't know any other language, and may not know that the name Poisson is the French word for 'fish'. So the alpha with the dot is a visual representation of a fish, of a Poisson.

[@Lolleka]

I kinda have the impression that there is a high chance that people watching this content actually do know about Poisson = Fish.

[@j0k0m0]

And you would be wrong. Speak to me like an elementary school student. This lecture opens doors Of understanding to fellows Like me … make it simple. That’s what professor means.

[@NickC_222]

That's fantastic. I didn't know that!

[@martnal]

It didn't NEED an explanation. Watch again, and listen at 27:20. It's also used a religious symbol all over the world.

[@Kargoneth]

I love professor Tokieda.

[@benji104]

As a mathematician I have to say this was the most entertaining and creative math talk I have seen!

[@ArtistDiwakar]

This lecture is really brilliant. Specially who love to see the practical application alongwith mathematical concept

[@ClassicalMontessori]

This is a fantastic professor! He must leave the students with a sense of exciting curiosity!

[@mvlad8725]

Though my career is in literature/art, I am fond of this professor's passion and humor. I would gladly sit in on all of his lectures, especially after his mention of Galois.

[@helenscoffield]

I remember as a four year old my father came home with a great big fish and when I asked where he brought it, he told me in a little box. Since then my mind began churning. I found crushed hosepipes, accordeons, smocked dresses, yards of vaporous dress material twisted into a bodice and flowing skirt, and proteins folding in fantastic ways. Anatoly Fomenko did a series of illustrations you math people would love!

[@purelyconstructive]

This is brilliant! I already love math, but he has a very fun and interesting way of presenting things.

[@jarredmattingly5369]

Pppeeeeeehhhhh....You're telling me, for 41 years I've been using a compass, and divider, and protractor, and rubbing my stomach, and simultaneously patting my head, while jumping on one foot, and repeatedly singing "rubber baby buggy bumper" just to come up with something that looks close to a pentagon, and all I had to do the whole time was tie a strip of paper into an overhand knot, and then tighten and flatten it? There's no way.... I'll be right back. Gotta check something unrelated...... ..... Well, I'll be damned! I'm subbing!

[@matthewziemba7526]

Is you continue wrapping the paper with the tail after flattening, you can press in on all edges at once to create a three dimensional puffed star!

[@genixia]

What a wonderful, entertaining and educational lecture. A true joy. I idly noticed towards the end that his attire was somewhat crumpled, and several thoughts went through my mind. First, I found it bizarrely reassuring that professors like this still exist today, a beautiful mind not caring so much about the external packaging. Next, I wondered why, despite that, someone wouldn't make an extra effort for a special invitational lecture anyway. If traveling all day why wouldn't someone just pack an ironed shirt to change into just before the lecture? Then I realized that it was the perfect natural instantiation of everything that he'd just spent an hour telling us about, and all was well with the world.

[@segamai]

I loved this lecture, so full of simple marvels and humor

[@MagicOfAM]

Just landed on the channel and I am already addicted to watching those wonderful lectures.

[@JJ-fr2ki]

Tokieda is amazing. This should have 1m+ views.

[@wandiloch]

Know him from Numberphile, one of the best teachers

[@SaveSoilSaveSoil]

Same. Have been a fan since.

[@Psi_Fan123]

Same found him from the perplexing paper clips video

[@crashpodROCK]

Brilliant man, wonderfully inspiring and passionate lecture

[@brittanyoleyar4649]

Most enjoyable lecture ive ever seen. A passionate professor makes all the difference.

[@blacklabela]

Wow! So much mathematics and science can be explained with just one piece of paper. 😮

[@RaindropsBleeding]

A whole world, you might say 😉

[@JJ-fr2ki]

25:01 This is incredible.

[@lukeves]

i love how he's just casually redesigns stents and feeding tubes, he like "hey kids if you want to make a 10 million dollars go prototype this"

[@mghemke]

He only solved the problem of getting a stent installed, I will be really impressed if he explains how to get it back out.

[@remuladgryta]

@@mghemkePut a string inside the tube so that you can pull it back out under compression.

[@oat1000]

​@@remuladgryta I had the same thought, but mine might be overengineered. You could use two concentric tubes, with the inside being an "accordion" tube. Have it so the accordion tube can only expand in diameter, not in length. There might be a good reason to do this over a simple string but idk what it would be

[@vincentcleaver1925]

That's the first thing I thought, like a Chinese finger trap now locked in place inside the body. Maybe a double walled tube which inflates and deflates, going from skinny and semirigid for placement and opens up as pressure pushed the folds in the double wall open, to increase cross section and flow rates and also keep it in place

[@benruniko]

Twist it. Make sure the folds follow a helical pattern so that rotating in one direction has the same effect as compressing it. So inserting can happen straight and twisting can release it.

[@ZoonCrypticon]

A great professor with a great teaching style!

[@primenumberbuster404]

A lot of teachers/educators have stopped to develop the concept of teaching and actually Engineer the "Teaching" to be more practical and efficient. I am tired of hearing that students are silly or dumb. Glad that Professors like Tadashi exist and we are proud to have a legend like him to preserve this culture of creative teaching.

[@samrobbins5665]

I suppose I am not the first to note that Prof Tokieda had an active folding experiment on display throughout the whole lecture which he never mentioned once - his shirt!

[@shennyboi110]

Nice, this has been one of my favourite Maths Lectures

[@Stormrider-Flight]

No matter which subject he talks about, he always will be known as the man who held a mobius loop with his feet.

[@TruthOfZ0]

Wow Origami is like getting the solution on a hard problem ...without goin thru the tedious equations that required for solving it!! I liked the elasticity part ..it remind me that each folding is like a round of coil in a spring that also does the same but its metallic!!

[@antoninbesse795]

1 hour of totally engaging content, Tadashi Tokeieda is at once a genius communicator and teacher and a genius full stop.

[@gabriellebaalke6704]

I am absolutely in love with this. I was told in my formative years that I wasn't 'good at math' but I love math. I think what I wasn't good at was the inane way that math is taught in the US. This is gorgeous. It's like poetry. And I was good at poetry.

[@samuel.00]

The proof of the equality of the sum of opposing angles at 18:35 is wonderful.

[@gblackhead]

Mr. Tokieda, Thank you! That openned my eyes.

[@eeleye1624]

yeah but did anybody notice you can make an extremely durable paper by rubbing it with a persimmon? incredible

[@nojavascript]

man what I would give to attend one of his lectures live.

[@michaelschabow2911]

Amen!

[@rougesunset]

Idk who this lecture is primarily for but as someone who is long done with college (math minor tho!) and loves origami, it seems that the algorithm got me good 🖤 Also when he was demonstrating the paper squished with two cans, he mentioned nature and now I can’t stop thinking about how flower petals fold 🌺

[@ClockworkAvatar]

this was an amazing watch.

[@pontusforsman6561]

Very much thanks for this. It was more then 20 years ago I was at school reading mathematics and now being shown how interesting it can be is really fun.

[@sieglindesmith9092]

What a great teacher!

[@materionline6720]

wonderful lecture.

[@jamcarr1073]

Clicked on video out of curiosity and could not stop watching.

[@jacobsims5848]

This guy is a good teacher. Who knew Oxford had it in them

[@ptrckqnln]

He teaches at Stanford.

[@joshsblee]

a gifted lecturer

[@SierraNovemberKilo]

I have accidentally come across this presentation. Hiw marvelous- such wide ranging ideas from a simple observation. TY. Really appreciated this.

[@justicewillprevail1106]

Thank goodness for captions ...

[@johnappleton3382]

Very well presented and informative. I am sharing this with my non-math friends.

[@jballenger9240]

Imagine Prof Tokieda would be a fascinating Christmas Lecturer at The Royal Institution. Domo Arigato Gozaimus!

[@JaapvanderVelde]

What a masterful swift ending to an incredibly engaging talk. I love listening to Tokieda-sensei. There's amazing videos with him on the Numberphile KZbin channel.

[@dinosauralan.9486]

What a fascinating and humorous video, extremely well done. Again, one learns (myself in particular) something every day. It never fails and thus I wish to learn more as to in keeping those little grey cells alive. Thank you, Mr Tadashi, thank you, take care.

[@mugogrog]

I've always been very interested and fascinated with origami and especially repeating shapes that gain new characteristics. If only I had know the connection between mathematics and how origami works I would have been less disinterested in mathematics.

[@marshallnoel2045]

Amazing mesmerizing satisfying lecture

[@dwdei8815]

Enthralling. Sublime. And it explains the Tardis!

[@blackawana]

Awesome! So inspiring and enlightening to this below-average math mind. I always like the nature references.

[@agrajyadav2951]

WHAT? This is awesome!

[@MagnusWissler]

I love this lecture! As I am slightly hard of hearing, I enjoyed it the most at 0.75x

[@stevesloan6775]

Over the last six months, I’ve been shaping thick 14 gauge(1.9mm) cold rolled steel. It’s amazing how mailable cold rolled steel is when you use thousands of strikes with a light hammer. You almost got to ask it to move nicely.😑 Time is a definite factor in how accurate you can form 2mm steel over a shaped die. 💙

[@theshire9173]

I’m so glad Morning Brew recommended this

[@AnnihilatorX3000]

Marvellous!

[@raphaellasne3609]

Brilliant.

[@user-nc4fb2hb9f]

I love Oxford mans!

[@samnelson2343]

I'll sadly admit that my mathematical talents are woeful. It's 4am and im only 20 minutes in to this lecture. But its so wonderful that i know I'll be back. Thakk you the prof and the uploader...

[@maxpercer7119]

the pentagon origami trick is pretty cool

[@mcnichollsdj]

This guy is amazing. This video is so much better than the Tadeshi recordings at the Institute of Advanced Studies. Same genius on show, but this time I can hear and see him!

[@bennoarchimboldi6245]

Nope it’s garbage

[@SchutzmarkeGMBH]

A wonderful lecture, captivating, informative and funny. But my favourite part is the noise Prof. Tokieda makes at 37:28

[@user-sk4kg4hr3k]

Pressed like button after presentation of almost Pi. I guess it's already deserved on that mark

[@EmperorLuxury]

I wish this guy taught me math in..., well all my life.❤️

[@kaltkalt2083]

Always liked this guy, and for some reason it makes me sad that more Japanese people don’t speak English. I don’t know if it’s true but I’ve heard it’s because they fear speaking with an accent. But anyway love his Numberphile videos. I think the gist of some of these "interdimensional" concepts explain the apparent impossible movement of UAPs.

[@wPeniSwiadomy]

I didn't think that a lecture on paper folding would make such an impression on me.

[@dougr.2398]

Excellent talk

[@dougr.2398]

When I was at Yale’s Gibbs Symposium and New York Academy of Sciences meetings back in the 1980s, the only scientists present who were polite to me and complimentary or interested in what I had to say and my background were Japanese

[@dougr.2398]

To be more accurate, C. N. F. Yang was also very polite to me, circa 1979, but what I had attempted to present to him was totally idiotic nonsense

[@HaileISela]

a very good demonstration of geometry as a set of behaviors of bodies of spacetime. this is indeed very synergetic in nature. however, synergetics would not call Origami 2.5 dimensional because it would not abstract the sheet of paper (a flat body) into a 'purely two dimensional plane'. to quote synergetics directly: " 966.12 In synergetics, all experience is identified as, a priori, unalterably four- dimensional. We do not have to explain how Universe began converting chaos to a "building block" and therefrom simplex to complex. In synergetics Universe is eternal. Universe is a complex of omni-interaccommodative principles. Universe is a priori orderly and complexedly integral. We do not need imaginary, nonexistent, inconceivable points, lines, and planes, out of which non-sensible nothingness to inventively build reality. Reality is a priori Universe. What we speak of geometrically as having been vaguely identified in early experience as "specks" or dots or points has no reality. A point in synergetics is a tetrahedron in its vector-equilibrium, zero-volume state, but too small for visible recognition of its conformation. A line is a tetrahedron of macro altitude and micro base. A plane is a tetrahedron of macro base and micro altitude. Points are real, conceptual, experienceable visually and mentally, as are lines and planes. 966.20 Tetrahedron as Fourth-Dimension Model: Since the outset of humanity's preoccupation exclusively with the XYZ coordinate system, mathematicians have been accustomed to figuring the area of a triangle as a product of the base and one-half its perpendicular altitude. And the volume of the tetrahedron is arrived at by multiplying the area of the base triangle by one-third of its perpendicular altitude. But the tetrahedron has four uniquely symmetrical enclosing planes, and its dimensions may be arrived at by the use of perpendicular heights above any one of its four possible bases. That's what the fourth-dimension system is: it is produced by the angular and size data arrived at by measuring the four perpendicular distances between the tetrahedral centers of volume and the centers of area of the four faces of the tetrahedron." www.synergetics.info/s09/p6300.html#966.12 the Poisson effect described here is an expression of the generalized principle of precession, as described by synergetics and the negative ratio behavior strongly resembled the so called Jitterbug transformation, one of the most essential wave propagation patterns within spacetime. thank you for the fabulous lecture🙏

[@jazznomad]

Great presentation. Funny, precise and informative. Regards negative poison ratio and the illustrations of the momotani carpet , I am reminded of those "Chinese finger trap" toys that require a push to expand your trapped finger. Of course they're not of a single sheet ..

[@daineminton9687]

Very nice, yet on drawing a crumpled piece of paper being extremely difficult... An camera lucida is very useful.

[@user-hq9rb2dz3s]

BRAVO, BRAVO, BRAVOS..!

[@Achrononmaster]

For a minute around @56:00 I thought he was going to finish with the cosmological constant problem (aka. positive vacuum energy density, or "dark energy"). The more matter tries to pull together the entire cosmos (gravity), the more it expands. Negative Tokieda ratio ⋈.

[@oopsadaze]

This has so many applicable applications in medicine, space exploration, gravity, etc...There has to some connection between folding and fractals ( 46:00 )

[@oopsadaze]

MY FAVORITE LINE..." All my my demos start with the phrase...Take a sheet of paper." ( 46:33 )

[@robotech2566]

5:44, put perpendicular to one of leg of angle intersecting other leg,so use inverse trignometry to find angle,as we have ruler, usetrig to find opposite side of 1/3rd angle, no need of compass : )

[@marklundeberg7006]

46:55 This reminds me also of the skin buckling seen on some airplanes like the B52 and 757.

[@padraighill4558]

The thing about the toilet paper is so true :) Whenever you want to rip a section of the paper in the Maths Institute you get a useless long narrow piece wrapped around your hand

[@suindude8149]

Really I appreciate how the art in case of creation of Origamy gives the most 3D shapes,can anyone think of all dimension and equivalent angular cut so that a 3D may appear yields something unknown,while everything stops,the theorems and riders and the graphics work yielding lot.

[@jackykong6000]

Someone's Tiktok made me search you.. I am not a student anymore. But this is pretty interesting!

[@fngrusty42]

Only one question . Where were you when i used maps all the time dang i learned how to fold them but never that push together trick ... enjoyed thank you

[@WhyWhatWhoWhenWhyAgain]

Black holes show us the poisson ratio when a galaxy surrounds it and we can see the negative poisson ratio of the warping of space by the layout of the stars.

[@beautifulsmall]

I wonder if Earwig wings are mathematically impossible to get stuck, folded many times. love the knots in flat paper. Became fascinated with Knots since a vertasium, Is sphere a 3d unknot.can you tie a knot into a sphere. Just made the paper hole coaster trick. Some things you have to feel. I wonder if thats why origami flourismed. Can you start an origami with a knotted plane.. Beauty is all around. Inspiring and absorbing . UMIST.

[@jazznomad]

The trick with the stent origami proposed would then be how to pull it out since pulling causes expansion and pushing sends it deeper.. not so easy.

[@earthbound9381]

Wow. This video was so long I skipped to the last 10-15 mins and became so utterly absorbed I just did not want it to end.

[@highseassailor]

"Negotiate" the corners! 😂

[@MrLuigge]

51:25 would be useful but then how would you remove the tube since when you pull it, it stretches and then would became hard to pull 🤔

[@MeredithAvila]

I would like to know how to fold the paper that he did on the plane

[@Xubono]

Instructions can be found on youtube: look for Yoshihide Momotani’s “exploding brick wall tessellation”.

[@sheikyerbouty2926]

Would water have a negative poisson when freezing? Explaining why it expands when frozen while other materials contract.

[@johnscovill4783]

Só, can this be applied to the expansion of the fabric of space.

[@maciej12345678]

55:49 what if universe have only one point of freedom and you can fold it it to one point easy and with minimal energy that exist -- and universe is by axiom homogenie right, and this is very interesting how ball is squiz with minimal energy in black hole

[@Maxander2001]

Yes! T- squared!

[@somebodyoncetoldme1704]

woop woop

[@DivineMisterAdVentures]

Ion's Law: "Extra Freedom" of the next higher dimension, at least partially and irrationally (non-linearly) overcomes the limits of the lower dimension, as a purposeful system crosses the bridge. Sub-corollary: Biology and Evolution are, of course, purposeful by their outcome. Meta-corollary: this holds true for every bridge between a lower to higher system. Sub-corollary: Pauli-Brain is created skeptical of the influence of the higher dimension(s) (Pauli after Pauli-Exclusion Principle, referring to the human mind occupying one or another dimension but not two at once, following the same theory of "enthalpy" applied there.) Sub-corollary: absent the restraint, it is difficult for the system to function. (Example shown has displays greater utility but requires special circumstance than in either separately.) ETC. a few dozen more.

[@Hunne2303]

a real life example already in use of that tube would be a stent...a small tube that get´s inserted into your aorta (me thinks) while it is compressed, then gets pulled and expands to widen your clogged up bloodvessel

[@Strontyum]

He said this

[@samhavholm]

paper is forgiving...u cant see it, but if your the holder of the paper you can feel it!

[@PrabhakarKumar]

Nice

[@richardfredlund8846]

would be nice if someone could invent a tent that folds that way, getting them back in the bag isn't so easy.

[@RichardBiggind]

This is a really compelling lecture, but I couldn't help but perpetually wonder "Who hosted this lecture," and also "Who sponsored this lecture?" I wish there were some kind of jarring blue banner for the entire video which took up approximately 1/6th of the screen but with only approximately 1/10th of that space actually being used to answer those questions. That would be really helpful and not at all distracting, and I'm sure the bright blue light wouldn't cause any weird brightness issues while I'm trying to watch before bed at night.

[@dedge8425]

Zoom is your friend.

[@helenscoffield]

Wish he'd been my maths teacher.

[@PhilipChandler]

I almost understood some of that...

[@orgildinho]

I think it is a mathematical trick. None of us can find two-dimensional objects in the universe; everything has a volume. I wonder what is the calculation of start ironing that wrinkled paper