The Nescafé Equation (43 coffee beans) - Numberphile

Featuring Cliff Stoll. Check brilliant.org/... for Brilliant and get 20% off their premium service (episode sponsor)
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Cliff scrutinizes the lyrics of a Nescafé advertisement dealing with the brand's famed 43 beans.
Alternative ending to this video: • 43 Beans (Alternative ...
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[@numberphile]

Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) Alternative ending to this video: kzbin.info/www/bejne/nmrWnZyjYp6ZsLc

[@rajeevk440]

"4 beans times 10 beans and add 3 more beans equals 43 RICH BEANS" Ans : beans = 0 ,1 , (( (( -1 )) )) 43 RICH BEANS 😂🤣

[@TheInselaffen]

One fell out... So there are 42 beans. If that is the answer then what is the question?

[@Mr.Beauregarde]

Beans is a name, 2, John, times 2, John, is 4, John. Or rich coffee is a function taking the argument "beans" yielding a quadratic

[@harrytsang1501]

So the roots of beans are 0, 1 and -1

[@johnjeffreys6440]

So 2 beans times 2 is four beans. I don't think I would have picked up on that.

[@TheWalkerboh65]

I love how Cliff is now too chaotic for the brown paper

[@Sauvenil]

it's still brown paper, just glued together in layers with a rippled layer for strength. ;)

[@alfastur6833]

Given his energy the additional strength of the cardboard is a must for Cliff.

[@ilRosewood]

He always was

[@wobblysauce]

Sturdy paper

[@davidsmith8384]

The box is Brown Paper cubed (asumming brown paper is brown paper squared). Obviously, this has far reaching applications.

[@2Cerealbox]

This man really held a 60 year pedantic grudge against this commercial and he's finally got it off his chest.

[@gjfjfgjdhjd1303]

I'd be jumping up and down too

[@Triantalex]

false.

[@DasGanon]

The editor had way too much fun adding that little jingle riff to all of Cliff's lines. It's great

[@keithmills778]

What bothered me is that the tape recorder had the sound of a film projector when it was running.

[@francogonz]

@@keithmills778 thats the best thing!

[@jwolfe01234]

@@keithmills778 That's because it's a reel-to-reel tape machine. It has exactly the same mechanism as a reel-to-reel film projector. You're hearing it drive the reels to transfer the medium from one reel to the other. In one case, it's film, and in the other case it's audio, but it exactly the same principle.

[@harriehausenman8623]

@@francogonz *dingelingding* 🛎

[@cliffstoll568]

@@jwolfe01234 You betcha, Jeff. I dragged that ol' machine out of the attic. And the tape? It's from when I was like 11 years old. Retro-rocket time...

[@andyking894]

Technically, the units on the right side of the second equation are "rich coffee beans," which would change the maths a bit.

[@nickfifteen]

Exactly! This mean the equation should be: 10 "Beans" × 4 "Beans" + 3 "Beans" = 43 "Rich coffee beans" Or simply: _10B × 4B + 3B = 43R_ It's too early in the morning for me to work out the ratio between B and R, however.

[@miorioff]

Exactly, bean math is getting deeper

[@platypi_otbs]

Whoa. I'm going to have to rethink this whole thing.

[@modernkennnern]

I was thinking that myself. Was hoping he'd catch onto that. We need a continuation of this story

[@IanWilkinson]

@@nickfifteen No, no, no - you're missing the first equation - 2 Beans × 2 Beans = *4 Beans ²* Therefore: 10 Beans × *4 Beans ²* + 3 Beans = 43 "Rich coffee beans"

[@hicksyfern]

“I put 43 beans into a Klein Bottle” said Cliff, surprising exactly no-one

[@TranquilSeaOfMath]

He put coffee beans into a zero volume container! There is something to that. ☕

[@artembaguinski9946]

could have easily placed 43 beans in 43 klein bottles

[@TranquilSeaOfMath]

@@topherthe11th23 There is no inside to a Klein bottle, it does not enclose a volume. The glass bottles that he designed are a representation, not a true mathematical Klein bottle. Your Shakespeare idea is interesting; I was not familiar with it. Do you know which play it is in?

[@TranquilSeaOfMath]

@@topherthe11th23 When you color your Möbius strip, do you color the geometric space it is embedded in?

[@Fred-tz7hs]

@@TranquilSeaOfMath yes

[@SufferingPlanet]

This is ridiculous, and I love it. Never a dull video with Cliff.

[@VikingTeddy]

This is the kind of pedantry I can appreciate! I hope I'm half as enthusiastic when I get older, it's so infectious.

[@Dragoninja26]

Yeah Cliff videos are probably my favorite ones

[@Triantalex]

false.

[@PC_Simo]

@@Triantalex Just like your existence.

[@ablebaker8664]

Nescafe apparently uses beans from coffee bushes with square roots.

[@crkmt]

🤜🤜🤜

[@blakeytv]

Straight cash homie

[@prof.keebler]

I just love this comment

[@gr329]

Now that was pure cleverness

[@alveolate]

some may even have cubic roots... and they all have real roots for sure! ...altho i have no idea how a root of 0 would work on a coffee plant...

[@spyguy318]

The moment he said “two beans times two beans is actually four beans squared” the engineer side of me instantly screeched and recoiled in horror at what he had just implied and I knew instantly where this video was going

[@paulvangemmeren9351]

I remember using the unit "square kilopeople" in a geography class once. My professor looked about ready to give up

[@mattbox87]

Yes! Take comfort that you're not alone, Sam. ... I mean I loved the s**t out of the vid but I totally reacted the same way.

[@julesk1088]

@@paulvangemmeren9351 HAHAHAHA What was the context

[@minerscale]

@@paulvangemmeren9351 Otherwise known as a megasquareperson

[@artembaguinski9946]

at 0:00 we've all knew instantly this video was going into a klein bottle

[@yevhenkuzmovych4494]

"I've put 43 beans into a Klein bottle". That's all I needed to hear today

[@trueriver1950]

Isn't there something odd about putting anything _in_ a Klein bottle?

[@lacuentadevideos]

@@trueriver1950 yea, I thought you can´t put a lid to that coffee jar

[@HaloInverse]

@@trueriver1950 I was thinking the same. In a sense, he just put 43 beans in _contact_ with a Klein bottle (or with other beans in the set). That being said, "43 beans _in_ a Klein bottle" is possibly less incorrect than the Nescafé jingle.

[@vigilantcosmicpenguin8721]

43 rich coffee beans in a Klein bottle, 43 rich coffee beans...

[@alveolate]

btw... wouldn't klein bottles make a great container if you just wanna smell coffee beans?

[@zeppelins4ever]

I absolutely adore his enthusiasm for the math in something as simple as a coffee advertisement!

[@Triantalex]

??

[@zeppelins4ever]

​@@Triantalex!!

[@royalninja2823]

Cliff Stoll is a treasure. He so clearly takes great joy in everything he does.

[@Marconius6]

Come now Cliff, we both know there is no such thing as "inside" a Klein Bottle.

[@FrankenSteinsGate]

My favorite videos on the internet are when people take things that were never meant to be taken seriously, and take them _way_ too seriously. Add in Cliff's natural chaotic energy, and this is one of the best videos I've watched in a long time

[@Triantalex]

??

[@debblez]

this is by far the most chaotic numberphile video and im all for it

[@javacofe]

Whoever animated this was definitely living their best life. Love it!

[@RobertoMariani]

I've always had similar issues with Ferrero's Pocket Coffee, which is advertised as "la carica del caffè più l'energia del cioccolato" [coffee's charge plus chocolate's energy], which of course should instead read as ”coffee's charge TIMES THE VOLTAGE AT ITS END plus chocolate's energy.

[@vigilantcosmicpenguin8721]

It's like coffee companies don't realize they're alienating mathematicians, which should be their target audience.

[@alveolate]

@@vigilantcosmicpenguin8721 we need a numberphile coffee brand!

[@Triantalex]

false.

[@Kram1032]

5:45 technically this doesn't mean you get one bean, it means that the concept of "bean", the unit called "bean", is identical to having no units at all. You also dropped, at that point, the possibility that it's just 0, meaning it's both unitless *and* sizeless! (Though you get to that later)

[@gfrank98]

Thank you! I was going to complain you can't divide by B because it might be 0.

[@Bleighckques]

You could say that, of all the beans that exist, Nescafe beans are the unit beans.

[@Kram1032]

@@Bleighckques units still usually square. Unless they happen to be idempotent. Like, you could introduce a special value with the rule b²=b and then follow the logic like with complex numbers: (w+x b)(y +z b) = w y + (w z+ x y+ x z) b Such a number system has a variety of interesting properties, but most importantly you get: b² = b (1 - b)² = 1 - b b (1 - b) = 0 which means you can decompose any number x + y b as x (1 - b) + (x + y) b And with that you can very easily show than (x + y b)^n = x^n (1 - b) + (x + y)^n b or if you want it in the regular form, x^n + ((x + y)^ n - x^n) b This formula holds without issue for all n≥0 and if x ≠ -y, I think it holds for all n in R. (x - x b) or x (1-b) doesn't have an inverse but aside of that line, every other element can be divided by. All that and more follows directly from just the rule b²=b It's not even very difficult to show. For instance, if your want to find division, try solving for y and z in (w+xb)(y+zb) = 1 Exactly like you'd do with complex numbers Anyway, with a number system like that, any polynomial in b becomes linear by construction, making that song 100% correct

[@Bleighckques]

@@Kram1032 I meant that all beans would be measured against the Nescafe beans (the Nescafe bean represents 1 essentially), in the same way that a "unit circle" is a circle with radius 1 for example.

[@GenericAnimeBoy]

Clearly they're using dimensionless coffee, which explains why instant coffee is blah.

[@sushantmanandhar1387]

Cliff Stoll is one of my favorite humans ever

[@mastershooter64]

same!

[@PC_Simo]

Same here!

[@bradmiller2725]

That was the most fun! The asides and little details were a pleasure to behold. Inspired joyful editing was brilliant for such a joyful man! Thanks!

[@nintendold]

I loved the movie More-beus, especially when he said "it's more-bean time"

[@lapetitecuillereetlepaindo3005]

wackadoo ?

[@JorgetePanete]

I loved the part where the protagonist got nescafé-mored

[@stefansamoyloff3866]

My goal ... no, my DREAM in life is to be as happy doing literally anything as this man is singing a 60 year old jingle.

[@Arx_724]

Great editing, love the little sound effect every time.

[@danielepicone1480]

The equation is not necessarily inhomogenous if the "rich coffee bean" is a separate entity from just a "bean".

[@nickfifteen]

I wanted to point this out as well... the equation---assuming the second was on its own---is: 10 "beans" × 4 "beans" + 3 "beans" = 43 "rich coffee beans", or: _10B × 4B + 3B = 43R_ It's too early in the morning for me to work out the ratio of B(eans) to R(ich coffee beans), however.

[@feedbackzaloop]

Been thinking about it the whole video. Clearly "rich coffee bean" is some function of "coffee bean" and they would explore it's properties

[@QuantumHistorian]

Adding beans to beans^2 is still inhomogeneous, no matter what you equate it to.

[@fahrenheit2101]

@@QuantumHistorian Yes, that's what I thought too

[@neilgerace355]

Oh no, please don't go there :) It sounds like the imperial system of beans, which has different beans for measuring different things. Like the mile or ounce :)

[@morscoronam3779]

Cliff Stoll Numberphile videos are the best, and I dare say this is the best of the best. The editing complements Cliff's general attitude just perfectly.

[@mystuhree8827]

Can't help but grin this whole video, Cliff is an incredible human and his excitement is infectious

[@josephjohnherbert]

Cliff Stoll is by far Numberphile's greatest asset - what a pleasure it is to watch this guy in action!

[@giannotti7777]

I think James Grime would have a say in that regard ;)

[@Triantalex]

false.

[@josephjohnherbert]

@@Triantalex what a well articulated retort 😄

[@mattricks21]

My favorite part was when Cliff proclaimed "It's More beans time!", and proceeded to add more beans all over the floor

[@TheSabian321]

Truly one of the numberphile videos of all time.

[@charlieb8735]

I’d love to see bean math extended to a Mörbean-us strip. That’d be be a morbillion dollar equation

[@harriehausenman8623]

As a kid, I threw a huge tantrum when I found out, that it was considered ok to lie in advertisements. I was furious. 😂

[@SpooNFoy]

This man is a treasure and must be protected at all costs.

[@mastershooter64]

yes!!

[@sternmg]

By all beans!

[@thea.igamer3958]

Nescafé: Hold by beans. Cliff: I won’t hold them, they are dimensionally inhomogeneous.

[@lynk_1240]

THANK YOU FOR POINTING OUT THE PROBLEM IN THE UNITS!!!!!!!!!!!!!! It drives me absolutely wonkers whenever anyone doesn't pay attention to dimensionality.

[@BurnieBaker]

As a video editor - Cliff must be a BLAST to edit for. If you don't mind my asking, Bradyz who does the editing for these pieces? I would love to pick their brain, or at least give them some personal props. Keep up the fantastic work

[@pmcpartlan]

I do :). And yes, Cliff Episodes are especially fun, it's the only time I think it's appropriate to add more jump cuts

[@franghigli]

For some reason "I put 43 beans into a klein bottle" has the same energy as "I sawed this boat in half" and I'm all for it

[@TheRubySpider]

That little “doodledoodledoo” made me smile every single time.

[@IcecalGamer]

and the fact that the animator animated bean characters dooooing stuff, reflected in what was happening; like lights going off or door bells ringing :D

[@cliffstoll568]

Sigh - for sixty years, that "doodledoodledoo" has been wasting space in my all-too-limited brain. So I'm happy it brings a smile after half a century...

[@manu-4601]

The editing fits Cliffs energy hilariously perfectly. I was laughing throughout the entire video, thanks for uploading.

[@alminhelex]

I love how one of the solutions of the full song is -1 beans for every cup. Sounds like a great cup of jo!

[@fv9422]

Not -1 beans. Just -1.

[@alminhelex]

Well if b is beans then it would be beans= -1. How many beans per cup? -1 XD

[@EebstertheGreat]

No, we get the solution B = -1, but there are 43 beans in every cup, so that means each cup contains -43. Not -43 beans, just -43. The number.

[@hughcaldwell1034]

@@EebstertheGreat Do not ingest the number -43. Much like 2, it's lethal to humans.

[@bozo5632]

That's the decaf.

[@faastex]

The energy of this video is so chaotic, I love it

[@tomer.solberg4445]

I think it makes perfect sense if you look at coffee beans in measure theory. Put beans on a line at equal intervals - the number of beans is proportional to the total length. Put them on a 2d square lattice, the number of beans is proportional to the area (and so on). Now if you look at a 2d lattice set on a rectangle with 4 beans on one side, and 10 beans on the perpendicular side, it has an area of 40 beans (add 3 more beans and you indeed get 43 beans).

[@mikew6644]

The soundscape for this video was an absolute chef kiss 👌😂

[@HolyGiraffeMapleStory]

Cliff Stoll is such a sunshine of a person. I can't get enough of him

[@maxdudek4911]

The first result of B=1 or 0 makes perfect sense regardless of the equation! Nestlé is treating B^2 as equivalent to B, which can only be true when B=1 or 0

[@mrhalfburnttoast]

The equation of B^3 - B = 0 has solutions at B = 0, 1, and -1. This means that Nescafe could use negative beans in their coffee, and it'll still be fine!

[@tomdekler9280]

Nope, that doesn't work. For the song to work lyrically, word for word, it needs to work for 40 cubed beans but also for 40 squared beans. Otherwise 4 beans times 10 beans plus three more beans cannot equal 43 beans, even if 4 beans is equal to 4 square beans.

[@Gimpy2K5]

What a fantastic human and wonderful edit!

[@Seth_Campbell]

“I put 43 beans in a Klein bottle” is the perfect summation of Cliff

[@GLF-Video]

This one jumped the shark. Just stupidly.

[@Dreamprism]

This is the most pedantic complaint about a radio jingle I've ever heard, and I'm here for it.

[@1.4142]

There is more math you can do with beans: - Rooted beans - Lemma beans - Taco bell distribution curve

[@ronumpleby3517]

I wish I would have had Cliff as a professor in freshman algebra!

[@thekaxmax]

He took up teaching highschool kids for some time, to keep grounded in young students

[@stephenbeck7222]

@@thekaxmax science class. Great video a few years ago on some of his experiences doing that.

[@SteveGuidi]

This is so ridiculous, I love it! It reminds me of one of my university calculus professors who routinely stressed the importance of dimensions and accurate communication during his lectures. Rest in peace, Frank Goodman (f o g) -- your lessons are not forgotten!

[@paulw987]

Perhaps we should consider the possibility that bean is a contraction of boolean (so it really should be b’ean). In Boolean algebra anything squared is just itself (including variables… and perhaps units, too). So b^2 = b (and also b^3 = b). So in the end it’s just all beans. Of course, in the Boolean world 43 beans is just 1 bean…(still better than nothing (40 beans)).

[@sabinrawr]

I love that you applied boolean algebra to this system of equations to show that the answer is the same as in Cliff's solution: Bean = 1.

[@aaronwelther3536]

I thought similar when I saw that b^2 = b, so a square bean is just the same as a bean (and the jingle isn't wrong after all?)

[@jellymath]

​@@aaronwelther3536 No... what? I'm not sure if you're saying some kind of joke here, but "B^2 = B" is probably not true, its roots are 0, 1 and beans definitely aren't real numbers don't trust the equality of "B^2 = B" - the point is, it is false ultimately it depends on what you believe a bean is, if you believe that B = bean = 0 or, alternatively B = bean = 1 then "B^2 = B" is true So the jingle isn't true unless we think a bean is 0 or 1 It's funny to think of bean^2 because it just doesn't make sense. If you define a bean to be a bean's 3D volume, B^2 would be some 9D volume squaring a square's area is crazy enough (you'd get a 4D hyper-volume from it), let alone squaring a bean that doesn't have just its volume, but also a shape, a surface area, a taste and a smell - it all, when combined together to create a satisfying description of a bean, is mathematically inexpressible!

[@Leedramor]

As a math teacher, I wish my students to get half excited... tenth get excited to see me as to seeing Cliff here in Numberphile. He brings up the student who I was in highschool, inventing my own math, loving every each way.

[@sublimeade]

Your students would have to be the kind of people in the comments section. Statistically unlikely

[@Simoss13]

I just admire that you have kept the original tape of the commercial after all this time

[@alanjhargreaves]

I love Cliff's improv. I have a fond memory of him running around at a Unix Conference in Darling harbour Sydney, showing people in the theatre his slides (viewgraphs) because the overhead projector had been unplugged next door.

[@cliffstoll568]

Yikes - I remember that! Must'a been 20 or 25 years ago!

[@alanjhargreaves]

@@cliffstoll568 Keep going, it would have been the very early 90's as I was still working for The University of Newcastle at that point. I finished there at the end of '92. Actually,now I think more, Imay have been at CSIRO at that point, so maybe 93/94ish. I *think* it may have been the same year that Lunus Released Linux 1.0 from that conference.

[@SolinoOruki]

This video and what the editor did just made my day

[@lost_actuary8084]

"Let's take Nescafe word by word lyrically" This is great! 😂

[@charlieb8735]

This is where the möbius obsession came from, the prospect of an infinite recording strip must’ve seemed like the philosopher’s stone to a young Cliff. Perhaps the definition of bean^2 is a rich bean

[@OmnipresentPotato]

Why don't we consider "rich coffee beans" to be another variable? We'd have a system of two equations, one of which is linear and the other is quadratic, as follows: 2B×2B=4B 10B×4B+3B=43R, And then solve for B and R

[@deyesed]

B and R both equal 1 then

[@SZ-xd3vw]

Or both zero :)

[@gregiles908]

That's why they are called "Beancounters".

[@ricdavid]

"I put 43 beans into a Klein bottle"... of course you did, Cliff; it'd have been weird if you didn't.

[@davidfinch7418]

I really think the heading should be "Cliff Stoll on Coffee Beans"... except you probably couldn't distinguish that from any other Cliff Stoll video. (Yes, we love Cliff, and his seemingly neverending energy!)

[@tlou34]

I think that thisis the best Numberphile video I've ever watched! Easy to understand even though I'm bad at math, it has coffee and that crazy guy in it and it got me nostalgic.

[@salaufer]

maybe i'm not a space wizard super genius like cliff, but when i heard the commercial, the first thing i thought was "YOU CAN'T MULTIPLY BEANS" also about halfway through writing this comment i realized who this is and omg the cuckoo's egg is like my favorite book ever that changed the trajectory of my life

[@konungredocsil657]

Cliff is the quirky mathematician we all need in our lives.

[@chadoftoons]

Holy moly cliff at 11 years already has the shine in his eyes like everything in life is a wonder

[@helvio89]

This is just plain genius. Great editting!

[@lumotroph]

That’s just the best video I’ve seen all day

[@friiq0]

Perhaps a “rich coffee bean” is a different unit from an ordinary “bean”

[@zlatanibrahimovic8329]

Rich coffee bean := (40/43 beans^2+ 3/43 beans)

[@friiq0]

@@zlatanibrahimovic8329 LOL YES

[@pjn7136]

Thank you for publishing my favorite Numberphile of all time!

[@tiberiu_nicolae]

Cliff is back!!!

[@justsomeguy5628]

The release of these vids should become national holidays.

[@PokeCastle]

@@justsomeguy5628 someone make a petition for it

[@Mutual_Information]

This is my first time seeing Cliff Stoll.. and I like him very much. And I’ll now always make sure to square my units, whether they’re coffee beans or not

[@garr_inc]

Watch more of the guy. He is hands down my favourite mathematician on this channel, and it has Matt Parker!

[@cloud_tsukamo]

He also did the conic loaf one, which is so much fun.

[@miorioff]

@@garr_inc yeah Cliff and Matt are both the best

[@platypi_otbs]

Cliff is one of my all time favorite presenters. Every so often I go back and watch all his videos again. His enthusiasm is infectious.

[@stephenbeck7222]

@@cloud_tsukamo conic loaf isn’t even in my top 4 Cliff Stoll moments, which is not an insult at all to the conic loaf.

[@ElCapAddict]

The care Nestle put into making that song is probably congruent with level of regard they had for infants fed with their formula.

[@trollme.trollmehard.9524]

-formula- coffee :)

[@ch48_]

@@trollme.trollmehard.9524 You better not give your infants Nestle coffee, they'll get sick

[@antman7673]

I actually enjoyed the old advertisement. So silly.

[@bozo5632]

And their employees.

[@mrnicomedes]

Chaotic brown cardboard boxes > brown paper. Thanks, Dr Cliff!

[@Spicarium]

One of the best Numberphile episodes ever, love it :)

[@Kahedro]

The editing is delightfult

[@andytheaardvark1]

oh yea, it's morbean' time

[@666xMajor]

Paul Erdos turned a lot more than coffee into theorems if you catch my drift 💊

[@ChristainGuyOfAction]

Watching Cliff trying to wrench apart a cardboard box was funnier to me than it should have been. :P

[@TheyCallMeNewb]

Nice era-appropriate foot tapping on that bean person.

[@mrxmry3264]

10:04 you started with 43 beans and one fell out, that leaves you 42. the meaning of life 🙂

[@zaraak323i]

So, The Meaning of Life, The Universe, and Everything, is... One less coffee?

[@mrxmry3264]

@@zaraak323i LOL!

[@Xormac2]

That's funny because in "La Smorfia" which is the book used to traslate dreams into numbers you can play in lottery in Neaples folklore, the number of Coffee is 42

[@nishandevkar2709]

Wait a minute, let me just grab my towel.

[@happysprollie]

Nope. Remember what Cliff said about watching your units. The answer to life etc is 42 ... not 42 beans.

[@Dac_vak]

This may B my favorite Numberphile video to date

[@Rubrickety]

I don’t think I’ve ever loved Cliff more, which is saying something.

[@johnchessant3012]

dang that jingle is gonna be stuck in my head all day now

[@cliffstoll568]

Silly jingle stuck in my head for sixty years. Don't get that ear-worm started!

[@javik9165]

Of course he put 43 beans in a Klein bottle.

[@jellymath]

This is probably my favorite Numberphile video!

[@lars3509]

5:33 dividing by B means that B=0 must be excluded. But B=0 is also a valid solution of 40 B^2 = 40 B.

[@vsm1456]

There's one mathematical trick (you know, the ones where you eventually get 4=5 or 0=1 or whatever) where division by zero is hidden in division by X. So yeah, that stuff is important. :D

[@lars3509]

@@vsm1456 yeah, a better way would be to factor out 40 and B, 40B^2 - 40B = 0 40 * B * (B-1) = 0 Which leads directly to the factored form and thus the solutions

[@yppahpeek]

This is exactly the content I required after a mind numbingly boring day of work

[@Marguerite-Rouge]

I was anxiously waiting for the apparition of the Klein bottle! I love Cliff's videos!

[@oenginz]

Love the detail of 10 Turkish Liras with Ord.Prof.Cahit Arf on it.

[@TominiOfficial]

I am really happy that Doc Brown solved the great mystery of the universe and moved on to studying coffee.

[@donfabian1542]

This is what makes time travel possible...43 rich coffee beans 🙃

[@chance1986]

Love the Klein bottle twist. But the damn jingo. I can't get it out of my mind!

[@Tarsonis42]

This guy originally looks like Doc Brown from Back to the Future. And he not only looks like him... he also has the same energy!

[@boopis-]

this video felt like a dream

[@platypi_otbs]

I think since we are counting physical objects which exist therefore non-zero, 1 bean or portion thereof would have to be a positive number so we would have to reject 0 and -1 just as we reject negative distances. I love the way Cliff poses such interesting questions. His videos are truly multidimensional. Pun intended. Cliff videos are an absolute treat.

[@bongo50_]

@@topherthe11th23 I think Bryan might have meant to say negative length? You couldn't have a square with a side length of -2.

[@tomkerruish2982]

Apply the Dirac equation and derive the existence of anti-beans.

[@platypi_otbs]

@@bongo50_ You're right, I meant length. Oops.

[@redpepper74]

Negative distance is a thing when you consider 1-dimensional vectors

[@stephenhicks826]

I'm just glad we weren't dealing with complex roots or we may have ended up with imaginary beans.

[@RedRad1990]

All those smart people working on clean energy sources and not a single one of them thought about Cliff Stoll

[@aikumaDK]

If anyone is going to remember a coffee commercial from 60 years ago, it's Cliff. Matt Parker did a video about the math in a mnemonic meme to easily-ish remember something about the sine function. I think those two would get along well

[@zeikjt]

I love that it's "easily-ish remember something about the sine function" because if it were easy you'd have been able to write it out completely.

[@ulfy01]

This is probably my favourite Numberphile video.

[@lafcursiax]

I could not stop laughing! You have really outdone yourselves. This might be the best Numberphile of all time!

[@kngofwrld]

2x • 2x = 4x squared 2x • 2 = 4x "Watch those units!" He's right. 😮