The Remarkable Way We Eat Pizza - Numberphile
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- Опубликовано: 25 окт 2024
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Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza.
More links & stuff in full description below ↓↓↓
Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature."
Animation by Pete McPartlan.
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I didn't even know that a person could even be this excited.
i think he's mad or something....
See his klein bottle videos...
Wait till you see him talk about Klein bottles.
OOOOH BOY!
A friend just linked me to the Klein Bottle video... he got even more excited there, lol
The Klein bottle video was great.
"Mum, Grandad is drawing on the food again!"
+ 😂😂👏
Doug Las Lol, not again!
Said no math enthusiast grandchild ever
i laugh so harddddddd
"MUUUUUUUM, GRANDAD'S BLOWING MY MIND AGAIN! I JUST WANTED SOME PIZZA!"
I absolutely love this guy. His passion can make you feel excited about any topic. I really really enjoy watching him.
+jgallantyt thanks. More with Cliff coming soon
he was just a little bit much for me. I feel exhausted
+Smokestacks Not me, I'm exited about pizza maths now!
Everyone seems to love this guy. I am with this group too!
I would support a channel that was nothing but Cliff Stoll being excited about things. Stollophile?
I have seen this man, who is reportedly a physicist, work as a mathematician, robotics engineer, computer programmer, historical restorationist, knitter, weaver, amateur glassblower, and businessman. I don't even have a proper response to that, except that I'm not sure I'd be surprised if it turns out he was also a master thief or astronaut or anything else, too.
If you count hacking as theft?
Jack of all trades idk
He also speaks Chinese lol
A true Renaissance man
jbt 7493 Given those skills, he’s essentially already a master thief.
This saved my degree in pizza engineering.
Yes i got my phd on biomedical quantum pizza engineering and now work at Domino's
@@James-le8gd Did your PhD include the Domino Effect?
OrangeC7 omg that hurt my mental health
Cool. The university I'm working in is developing the technology outpizza the hut.
@@youngflamer1667 but... you can't outpizza the hut! it's impossible!
This guy is so entertaining! I want more of him!
Me too. What I like about him is he is always so excited about whatever he's talking about.
He seems like a happier version of doc brown.
"I want more of him!"
I agree. I also want pizza.
You should watch his movie "The KGB, the Computer, and Me".
It is about him catching hackers in the late 80s
+DeDeNoM I studied Artificial Intelligence and Computer Science, because I love Math and Computers! I have my own company developing as a Software Developer! I will watch it asap!
"Pizzas don't like to do that."
Thank you for letting me know.
pizzas dont wanna disappoint gauss
Pizza harassment is a serious crime
1000th like yayyy, btw what does the comment say?
gauss knocked at every door and slapped everyones pizza out their hand til they ate it right. a real hero that guy
Yeah but his curvature would need to be at Italy
If you ever want to be happy in life, find something and love it as much as this guy loves geometry.
topology
Cant agree more
... or get a pizza. Pizza is disk-shaped happiness!
experiment506 True😂😂
George Higgins klien bottles
"Honey, why does all the food have sharpie marks on it?" - "Gauss..."
legend has it that 2 years after this comment was posted he's still going on about gauss
@@pluff. and 2 months after that
@@LumenArty and 2 weeks after that
and 23 hours after that
@@VeryUniqueUsername And 3 days after that
Why can't all math teachers be as hyped as this guy?
Because most math teachers failed at being something else so they became math teachers. You have to wonder what the world would be like if math teachers, at every grade level, were more similar to this guy and the others featured on this channel.
+Taco Jiminez I feel like you have had bad math teachers, because I have had math teachers who are as excited as the guy.
Pay them more than retail workers and they'll be much more hyped.
+Antonio Lewis Truth
They can't be as hyped as him because they aren't Cliff Stoll...This man was the first person to ever track down and catch a hacker. Dozens of dial up proxies spanning the globe and he caught the guy!
He in college when his campus broke out in anti-Vietnam war protests. The police were teargasing the crowd... and he was climbing the stairs inside the campus's clock tower to get above the fray...
He's seen and done so many things. When your life is full of excitement, how can you not be excited about life?
This enthusiastic math grandpa made my day.
But can you make a pizza in the shape of a Klein Bottle?
I'll immediatly try this at home
A klein bottle has only one side. So then you'd have cheese and toppings on every side whereas a normal pizza has cheese and toppings on 'top' but crust on the 'bottom'. I could see how this might become a messy dilemma.
+nairbil Not in 3D though, his Klein bottles have two sides.
No, there's still only one side, but it has one self-intersection.
+Hundersoft thank you
I think this also sums up the reason why the spherical Earth cannot be straightened out into a rectangular map without tearing or warping.
actually all "rectangular" shaped maps have quite a lot of scaling issues. i.e. Greenland looking to be the same size as Africa when in reality ther are not the same sizes
Tom Latz Yeah. The scaling you are talking about falls under what I called "warping" above.
i think i misread yours sorry for the confusion haha
Tom Latz No problem! I think we meant the same thing, but just said it in slightly different ways.
I thought the same thing!
this guy seems absolutely crazy and it's amazing
In my mental list of best people on earth (includes bob ross and Bill nye) Cliff stoll is in that list too.
@@apothecurio
How many people are on that list?
I like how he just calmly pulls out:
A Bagel
A Banana
An Orange
Do you freak out when pulling
Bagels
Bananas
Orange
?
enzo queijão
You
Don’t?
And draws on them
@@darylcatpiss 4 years later
And a marker
An orange is an orange, a banana is a banana, but a bagel is a torus.
He said sphere for orange >D
Yeah, he did.
+Isu Asenjo Haha I didn't notice that
racism
#BagleLivesMatter
For him
math is
meth.
Hmm this is meant to represent something
Cliff is just…the greatest :)
Meth error
he never forgets to carry the toke.
Rumor is he once got fired from a job for coming tp work with algebra on his breath.
This man does two things to me.
1. I become hungry.
2. I experience joy.
+Ivan Rodriguez if Marijuana makes you interested in math, yes
mathrijuana
+agustin venegas it definitely does
Try studying on a smaller dose.
Reece983
can you send me some of that? i'd find it useful now as the semester its about to end
All the people on numberphile love math but this guy is different. He loves math so much that some might call it crazy. I call it smart.
Numberphile is the only channel that can make going simple maths on a banana logical
Going---> * doing
"Why do we eat pizza the way we do?"
Starts explaining negative and positive curvature.
Makes sense
An orange = A sphere
A bagel = A torus
A pizza = A flat surface
A banana = A banana
Banana is the mathematical term for the shape.
Banana is maybe a deformed sphere? Or a deformed cylinder?
you could model the inside of a banana as a hyperbolic paraboloid... i think. my degree was a while ago now.
This guy is our dimension's Rick
To be fair...
But what happened to his Morty?
Average Geek rick isn't excited about science thougj
He doesn't seem depressed enough to be a Rick.
The Green Llama ^^
The second I saw the thumbnail...
"IS THIS THE KLEIN BOTTLE GUY!?"
same😂😂
His happiness has no flipside
and then click into the video and hear this excited guy talk about pizza... Yep, definitely him!
I was hoping it would be Carlos Séquin.
My thought process exactly!
Props to Germany for putting Gauss on their money.
John Chessant
10 Mark
Before there was euro
The Gaußian Bell Curve is on it as well :) Sad we don't have it anymore
It also helps that they put their money on Gauss.
@@aryanparikh9085 underrated comment of the century
The orange and banana made me hungry. He drew on them. I said, "No problem, I wouldn't eat the peel anyway". Then he pulled out the yummy looking bagel....
workhardism Yall eat the bagel peel?
@@brockbierly wait you don't eat the peel of the bagel?????
LogicA002 Why would i it got sharpie all over it
@@brockbierly Bro, sharpies are the best part of a bagel
@@brockbierly I cannot express in words how much I love this reply.
Find someone who loves you the way this man loves math
Wow
I could not handle that amount of love.
Find someone who loves you the way Cliff loves both Möbius strips and Klein bottles.
@@conde_bathory and stopping hackers
I love this man's enthusiasm :D
I do too. Him as a math teacher... = GREAT GRADES
MrSheepFetus Exactly! And even better, he would even motivate me to learn math or physics! That's already something in my case, as I'm not motivated at all.
this guy is Awesome!! I wish all math teachers were like this
Garcio ツ yaaas so true
A class taught by Cliff Stoll and Richard Feynman would blow my mind.
I love this guy. I could watch him draw on bagels all day
Today, a bagel got ruined, for mathematics.
I came to the comments solely to find this comment, and it was first. Thank you for understanding my pain.
Today his lunch got ruined, for mathematics
Some sacrifice is necessary
It was probably stale.
Sometimes, you have to make sacrifices...
I love how he starts whispering "Curvature stays the same" XD
5:15
They need to make this into merch
Watching this at 2x speed, it's about a crazy old man scribbling on food
just watched it at 1x speed, and i've got something to tell you
pinkgnu I literally just laughed for 3 mins straight
I'm laughing without even trying it
Why adjust the speed? It's the same at 1x.
How do you adjust the speed?
I love the massive amounts of wet cat food cans Albert Catenstien has at 3:05
Als Mathematiker würde ich sagen, auch beim kleinen Hunger zwischendurch ist alles
eine Frage der Definitionsmenge. Kennst du Mad Max2?
Wow this comment got a lot of likes...
maybe he has a lot of cats. I like cats too.
I have a sudden urge to grab a marker and mark curvature in any object...
It's very normal after watching videos about how curvatures can be used to eat pizza more easily. It seems that drawing curvatures on food is more satisfying than on other objects
Sometimes I wonder what math would look like without Gauss.
btw:
He reminds me of Doc Brown from Back To The Future.
Me too but the mathematician version well he's our dimensions version of him. But sadly he doesn't have a time travel car or a Portal gun but he still has his inventions and Kline bottles
This guy is incredible. Do they have a Cliff Stoll playlist on Numberphile yet??
+littleblu33 it's in the description
I don't see any mention of a Cliff Still playlist in the description
No it's not. :-\
Smit Ramteke
Awwww :(
Max Warner how is it going?
1 AM, somehow ended up watching this video, now want pizza.
sounds like a typical day with the late night munchies XD
Alexander Krikorian 1AM and 3AM browsing is the best
how funny... 1 month later it happened again
The only thing that didn't get drawn on. Lol.
Same
RUN FOR IT MARTY!!
HAHAHAHAHAHAHA😂
Great Scott!
I never thought I would enjoy watching somebody drawing lines on random foods
This guy is nuts. I like him
he is probably the founder of tha gauss fan club
+Villager Number 35 Klein Bottle*
I consider Gauss one of the greatest mathematicians. And back then, mathematicians usually contributed to other sciences, and Gauss was pretty prolific it seems like
BUT is this a causal relationship, or merely correlated?
This guy is nuts. I don't like him.
I only watch this channel for this dude
Same
Exactly
Him and Hannah Fry.
this man looks like maths
Best comment ever!
what does this mean im so confused
This is so entertaining
An old man filled with so much energy talking about random stuff, No fillers, no silence just straight to the point, ITS EVEN ENJOYABLE FOR A TEENAGER
Numberphile: Back to the Future Edition
THAT"S EXACTLY WHAT I WAS JUST THINKING!!!!
Hahaha glad I'm not the only one...
brought to you by bernie sanders
lol
1.21 Klein Bottles! Great Scott!
How can there be so much war and hatred in the world when we have people - heck, even one is enough - like this?
probably because there are many many other kinds of people that could care less about learning and only act impulsively.
PapaKay damn, you couldn't be more right.
+ericsbuds educating everyone wouldn't help violence and terrorism. We are emotional beings.
MillerTurk forcing people to be educated wouldn't work, no. notice I said the lack of interest in learning was an issue. so you said what I said. we are also a social species. enough people do something and it will become popular.
Xyko It's a rhetorical question, not a joke.. regardless.. if it was meant as a joke.. that's sad..
the kids in Africa could've eaten that marker...
Yours too.
The Sauce The kids in Africa could've eaten you...
+Ash Ketchum racism never stops ash, neither does your odd age stunt
leave
+Ash Ketchum its not exactly racist. more like.. continentist.
Cliff: watch this
Cliff: flips over banana
My baked self: woah
I have no empathy for the fruits, but I was very worried he would draw on the pizza
It wouldn't work because the sauce will jam the marker. Pizza saved!😃
An intrinsic property of pizza.
food racist.
Peel the crust off of the bagel where the marks were, problem solved. How is it wasted?
Because, gee, you're still throwing perfectly edible pieces away? Also, did you see how much he scrawled on it? You'd need to cut like half of the crust :|
math + pizza + this guy = Amazing Video!
Everybody agrees.
I think.
And by negative something we mean the absence of that something, or one negative unit of that something?
If it's the first one then we can conclude that the most amazing video is the one that only shows pizza!
+Murariu Ciprian it means its on thr opposite side of the number line, you only get positive or negative when you/someone decides a origin. Its affine, just cause i say something is one jas no meaning to the object its just properties of the object we can describe mathematically.
There was really no point or purpose to this video. People eat pizza like that so that the contents don't fall, not because of the Gaussian curvature.
+Saeed
You've missed the point entirely. This video is explaining that the _reason_ the contents don't fall is _because_ of Gaussian curvature.
Isn't that the Klein bottle guy?
yep
+Numberphile he's awesome
+Kitsuneoni klen pizza
I love this guy
Think so
“Honey.... why is there sharpie on all our groceries?”
*G A U S S*
This man right here is the ideal image of a mathematician in my head. I feel like this is me in the future.
I wish for you and the people around you that you're right :D
People who can excite themselves and use that to inspire are invaluable to students of all kind :)
3:03 cracks me up."I'll draw a line here. Zzzzzzzyooop!" This guy is always so excited!
"BUT WHAT ABOUT A BANANA!" 1:18
"I'll draw a line here! BJOOP!" 3:02
"Pizzas don't like to do that" 5:42
Kid -Grandpa why are there lines on the..
Grandpa - CURVITURES
I love the way he says 'the curvature of a banana' (1:55)
He just says it so nonchalantly with his fun voice like that's just the kind of thing you would talk about when it comes to bananas.
5:17
CURVATURE STAYS THE SAME
this guy is just a pure ray of sunshine, i love it!
also im sure your wife's homemade pizza is superior too😂
Can you imagine being the wife of this guy? I wonder what she's like.
"Honey, why are there Sharpy marks all over our food?"
+Dlee645 exactly like him, and they get together and fangirl about theorems constantly
Hopefully, because that would be adorable
+Jonathan Pesek You made me so happy for a second
+mebthegirl ♥️
It's nice to see that Doc Brown is still going strong these days...
he could of written on the crust
+Canatime *semantics
"I'll draw a line here: *ZHHHHHHUUUUUUUUUUUUUP*."
I love him. He brings me joy every time.
all i get from this is a guy tat looks like a crazy scientist that is eating pizza and drawing on food
this guy is doc brown IRL
He's the crazy topologist.
I love his videos
I was like "don't you dare draw on that pizza". Then, they showed animation instead. Now I'll be thinking of the guy every time I eat pizzas.
Quick, tem pay 4 colleg!
As an engineer I 'd say that by flipping it a little you just increase the moment of inertia of the piece's cross section, and by that you increase it's bending moment load capacity... You mathematicians see things so differently...
Well that is because the pizza dough has a elastic modulus. So for our engineering theory to work it would have to be a material with non zero elastic modulus. Gaussian curvature theory is not dependent on thickness or elastic modulus, so maybe it is a more generalistic description.
Yes this is very Mesopotamia indeed
Ιωάννης Βουβάκης Μανουσάκης what does that even mean
I'd*
its*
@@debayanbanerjee And all this time I just assumed we eat the pointy bit first because we hold the crust, in order to keep our fingers clean.
Clicked on a random RUclips video, accidentally learned math.
You're more effective than any teacher I've ever met.
I always love this guy. He's always so happy to talk about anything. He could tell me my whole family died in a fire and I'd ask him to go bowling.
KIDS IN AFRICA COULD'VE EATEN THAT POSITIVE CURVATURE
Don't forget the negative curvarure
@@barrytone6581 bruh the negative curvature would just make them more hungry
@@gramptbeele1966 that's the point, make their expectations greater for negative curvature!
All they do there thanks to Western aid and medicine is producing ever more kids they cant feed, so I guess the meme is here to stay...
@@barrytone6581 curvature*
Cliff Stoll is the best person ever I love watching the videos he's in
It is always either Gauss or Euler! (a throwback to Dr.Grimes' video on "e")
If you ever need to fake mathematical knowledge, just say "Gauss" or "Euler". Probably like 85% chance it's the right guy.
I love this guy's enthusiasm towards all maths, from Klein bottles to pizza. More, please! :)
This man needs his own Math TV show. He makes this stuff really interesting.
"Well pizzas don't like to do that".. you obviously haven't met a Swedish pizza.. it defys gravity..
True that haha
A real life Doctor Emmet Brown
I would give a thousand likes to this video. Love this guy and want to see him more often here!!! Sooo expressive :D
I've been seeing you on just about every RUclips video I've watched this week
I hope he left some pizza for Brady!
+beeble2003 yep
haha Just go round a guys house, do some maths, film a video and then eat pizza.
You're living the life right there
+Lewis Massie I know just dont forget to eat all the food
Did he just paint a bagel with a sharpie
"torus" XD
I hope they ate the fruit at least
Yes he did! And the orange and the banana! But not the pizza.
Seeing him draw on food with a Sharpie was shocking, something I would never do... except for the sake of explaining maths.
Why do so many people have a problem with this?
+Madra Because
1) So many other people don't have food, so it's not the best thing to waste it with a sharpie
2) It's just annoying because they can't eat it anymore
0:09 I didn't knew that lol
i guess u dont know grammar either
Start to live
I knew it but I never think of it when eating pizza, lol.
But I'm eating pizza this evening so I'm gonna try to think about it
@@CommissarIbramGaunt yeah, fork and knife was invented for a reason
@@シロダサンダー who eats pizza with a fork?
It's like someone eating KFC with a fork.
You ever been so excited you WROTE ON A BAGEL WITH A MAGIC MARKER
I have an idea for a video: asking the Numberphile mathematicians what they think is the most boring number, meaning one that doesn't have any special properties or anything like that.
Of course, there's a well-known proof that there cannot be a most boring number.
I actually didn't! I'll look into that now.
By saying a number has the least/no unique properties, you have just given it one and made it more interesting :P This question is paradoxical.
From what a math professor told me, complex numbers are fairly useless in that they have very few practical purposes. Then again, I think their mere existence is really interesting.
+mightyNosewings Right, it's the very concept of subjectivity, haha
i wsh i had a professor like Clff
Love that beginning. Why do we eat pizza like this? Gauss!
And then he starts drawing on a banana. With no context, this word be very strange.
And then a bagel. FFS.
Holy sh*t! I thought this was boring video until he said why a pizza doesn't fully flop.
If every Maths teacher was like this, there wouldn't be any angry tweets from 16 year olds about hating maths.
This guy is insane and I love it.
But if the perpendicular lines on the inside of the banana are diagonal to it, it will have a positive curvature.
Edit: I just learned that you have to pick the minimum and maximum curvature.
It makes sense to pick the directions of extrema because otherwise you could always find a flat curve in the negative curvature regions.
If there's a curve A with negative and curve B with positive curvature passing through a point, then you can go through all possible curvatures between the two (including a flat curve) by rotating around that point from A to B.
Pizza is weird, we put it in a square box, made into a circle, cut it into cones/triangles and we eat it inside out!
And some people (heathens) don't even eat the outermost edge, which is an edible, built-in handle.
Square boxes are easier and cheaper to make than a round box. "Cheaper" is the key reason for why.
+Gustavo XD plus they are easier to pack and ship.
+ElTurbinado oh man wow that was cool so awesome man
And the crust makes a torus!
Thank you for not ruining the pizza. Even bad pizza is better than a bagel. :)
I am a bagel and I find this offensive.
LOL, I wasn't expecting see your comments here Lift xD
I'm still pretty sad that he rekt the bagel.
George Higgins Be glad it wasn't a doughnut
I was sad about the bagel until I remembered that he is on the West Coast and so it probably tastes like bread.
I don't eat pizza like that. I support the pizza's tip with my finger such that only a small part has the chance to flop down.
I also usually choose thicker based pizza because it flops less.
I'd guess pretty much everybody not using the zero-on-the-radius technique supports the tip with their finger :D
That was just to illustrate the point - and that you don't have to make that effort (which is of _course_ a non issue IRL) - by simply applying a Gaussian curvature perpendicular to the radius
*****
So you're saying that you don't eat pizza?
I DON'T CARE
+OriginalPiMan Yes, I eat pizza the same way too. Gaussian curvature just does not hold against heavy toppings and long radius. And I like my pizza large and meaty!
+enchiladaplatter1 Thanks for your insight.
+681726 thats not the only thing you like large and meaty. 😉
I saved this video just so I can watch cliff eat pizza whenever I want
4:36 I find it hilarious when he does stuff like that.
This guy is fantastic at teaching things, he's so into it. I've never actually been able to comprehend someone so well, most people who teach are dull and don't even care about what they're teaching. But, this guy? He's actually a lot of fun to listen to.
Yeah, this guy is genuine fun to watch.
In Gauss I trust
In Cliff Stoll I trust to build a time machine
I like how instead of simply drawing on the pizza he made an animation with sound effects and everything
I love how usually it's done in a classroom or something, but this guy's like, "Just come on over to my house, I got pizza in the oven! Bring your Sharpies!"
OMG WE NEED MORE FROM THIS LOVELY MAN!
I like the theorem in the video. I dislike the fact that you wrote on a bagel with a magic marker. I get the point of doing that, but the poor bagel can't be eaten now. It spent it's entire shelf life and its time on your countertop waiting to be eaten, now it just gets thrown away.... #BagelsHaveFeelingsToo #SaveOurBagelPopulationFromTrashCans
What do you mean, _can't be eaten_?
I'll sacrifice myself, I'll do it, so the bagel shall have his life purpose fulfilled!
"but the poor bagel can't be eaten now. "
Well, not with that attitude it can't.
But the sharpie said "Non-Toxic"...
I guarantee he still ate that bagel.
When you tell everyone you're trolling, you're not trolling.
I love how my professor gives us extra credit in quizzes for watching these videos lol
This guy is amazing! He's so enthusiastic!
I'm old enough to remember the DM (Deutsche Mark) but I never knew that Gauss was on the 10DM note.
Cliff Stoll sells them as "portraits of Gauss" at his Acme Klein Bottle website.
Like the proper real things? Or just replicas? Surely can't be real DM notes. Especially the one on his fridge. It looks so crisp and new.
DM were around till 2002 so I'd say a lot of people still remember them.
From his website:
Although it would be much cheaper to make these ourselves, we have imported these portraits directly from a trusted manufacturer in an Important First World Country. But on Dec 31, 2001, the factory stopped printing them, so our supplies are very limited. NEVER-AGAIN-AVAILABLE!
The ones he has left are uncirculated. His website worth visiting just for the amusement value (at least if you have a certain kind of sense of humour.)
I wish Cliff become my grandfather one day.
Me too!
Even though that's not how either genealogy or grammar works :P
Sorry, bro, english is not my first language :3
Oh, I see where I did it wrong; it was Google's fault though LOL I wasn't right about it, so I put it on Google to check it, but actually it turned a correct sentence into a wrong one.
Jorge Augusto Santos
:D No worries - I mainly just thought the answer was kind of funny
(And I'm not a native speaker either)
+Jorge Augusto Santos I'm curious now, what did you mean to say
Always happy to see Clifford Stoll.