Queen: "They don't have bread? Why don't they eat cakes?" Attributed to Marie Antoinette, but, traced back to Rousseau. Well, I'm not a historician. And as always, thanks for the video. P.
best way? ask my mother to make the cuts. I still wonder how she manages to make them so perfect. as far as I know, never has anybody complained about it.
@@McFrax we're talking about very small numbers here. For n=2 already, lower bound is 4 but 2^2^2^2^2 already is a number with 19729 digits. I think you can see, that upper bound=2^(number with 19729 digits) is gonna be very large compared to 4. Also, upper bound grows much much faster... btw, the number of atoms in the known Universe has about 80 digits.
When I was studying Mathematics at Adelaide in the 1960s, this problem was posed in a paper for our Measure Theory course. After all, this problem is about the gastronomic value measure each of the eaters apply to different parts of the cake. A cutter, who may be one of the eaters, makes a radial cut in the cake and poises the knife over slowly rotating it, keeping the point in the centre, so sweeping out a sector of cake. The scrupulously honest eaters continuously integrate their measure of the value of the sector and call out when it reaches their fair share, i.e., 1/nth of the cake. The first to call out obviously values the piece more than the others, so there should be enough for the others to get at least their fair share. The cut is made, and the piece handed over, and the process is repeated to satisfy the desires of the remaining eaters.
This is logically equivalent to (and physically less messy than) the solution in my comment, which I also remember from the 1960s (no later than 1966). Jade, your history does not go back far enough!
@@johnbonnett5746: My reply was later than your comment by about a day; it looks like you noticed it as soon as was reasonable and there's nothing to be sorry about. I'm glad our memories line up on the general nature of the proof and the approximate time period. If only we could find some actual documentation to cite from that period -- but probably neither of us had any reason to preserve bibliographical notes on the subject.
So it only works if people are honest. So maybe at a birthday party where all people are friends, but definitely not when dividing resources as claimed in the video.
I am glad you mentioned about the metaphor thing. In one of the previous videos about a goat grazing half of the field, I made a joke about the engineer's approach and thousands of people seem to have taken it seriously and called mathematicians stupid 🤦♂️ Dear Mathematicians (And other scientists in general), as an engineer, I can not be more grateful for the foundation that you that you lay for us to build upon!
A cake is a metaphor for all the resources my mother has given me. And when she isn't looking, I take an extra slice, symbolizing my dissatisfaction with being fair.
Maybe instead of cutting the cake, we should cut one of the people. That reduces the number of people you need to cut cake for, therefore simplifying the problem.
you can remove the human factor. For example, you want to draw a blueprint for a new bedroom with bathroom and balcony in your house, but you have to decide three shapes to "cut" the floor on the second story, to strike a balance between the three areas. No ones being difficult there, and you want to make the best use of your hard earned money.
I think you need to make a full length video about this. What are the limitations for the scenario? Does everyone value a different aspect of the cake or can they all value the same thing?
This is so interesting and humorous for me, because I recently saw this diagram about how to cut cake in an equal way so that the cake (from a circle) equally can be distributed to how ever many people there are lol actually was really interesting imo. Basically it showed the cake being cut by circles, from the inside to out or whichever, then having those rows be individually cut to a specific size
When I was a kid, my parents always made sure that kids got the pieces they wanted. For example, we had a rectangular sheet cake and a kid at my birthday party wanted this very specific piece right in the middle. So, my mom cut the piece right out from the center. She always said “What’s more important: a neatly cut cake or a happy kid?”
Thanks for this... This question has haunted me since I was a young boy, so always refused to let anyone bake me a cake for my birthday. Finally, I can get my own birthday cake.
I too, as a philosopher, take the problem seriously. I recommend the "Quit whining & enjoy what you get" philosophy & applying it to all cake people! 😂
Now I'm imagining the absolute scene when it's somebody's birthday in the maths department and one of the juniors/grad students naïvely brings in a cake to celebrate 😂
A diplomat could have solved this problem in a heartbeat. Former German chancellor Ludwig Erhard is quoted by saying: "A compromise is the art of dividing the cake so that each person thinks they got the biggest part." I was tasked this as a kid regularly. I was given a bag of assorted candy, and I needed to divide it three ways between my dad, baby sister and I. Inknew what candies they liked, so I was usually left with the set I planned on having. Same with portioning ice cream into bowls. I think this made me who I am currently. Or messed me up, or both. 😂
I know how to solve this problem. Invite a bunch of Mathematicians to a party and get a really nice cake. Ask the smartest Mathematician to cut the cake perfectly, watch them all argue, then steal the cake and leave.
You explain things beautifully! It must be hard to explain this problem and find ways to summarize the assumptions (if the weight on the cake is continuous or not, if it depends on the participant, if cuts are restricted somehow, in which order participants cut and choose, if they can skip choosing, blah blah...) and not bore your audience. I would like to have the skill to do that graphically and just saying the bare minimum, as you do. A follow up on that "it's more complicated but it can be done in 5 cuts" would be nice.
Wow, what a simple recepe for 2-person case. Never occured to me before. I will suggest this now to my children next time they need to share something (fortunately, I only have two!)
A mathematicians birthday party must be a very complicated affair.
Ha ha. Yes indeed :-)
That's why mathematicians should have at least 56 friends, so the probability of at least two people sharing the birthday is nearly 1.
Depends on the mathemetician. The most elegant solution in this circumstance is just have nearly no friends. xD
cuz 50% of the time, theyre sharing the bday with 100 other people :P
@@limitingchaosand then we can add the extra complexity of multiple cakes, with potential for flavor preference too
Just put the cake in a blender and give everyone an equally full glass of cake.
tf
No fair, mine was half empty but hers was half full
@@WyzrdCat You got the wrong address, the Philosophers' birthday party is next door
Drinkable cake (for consumption at the pink lake, with Sam Denby).
The cake's real mother will not agree to that
There is no fair way to divide a cake as no matter how it's divided, I want everything
*soviet anthem plays*
I guess fairness has different meanings for different people :D
@@Lattamonsteri There is no sich thing as fairness when it comes to sharing cake - or bacon
i guess we just need to buy the bakery instead
As above comment said , put it in a mixer/grinder
Give everyone glass of cake😂
Oppenheimer tried to cut the cake down to the atomic level back in the 1940's. He realized it isn't a good idea.
"I am become death, destroyer of cake"
It was yellowcake
@@georgewang2947that is an Iranian specialty 😂
I thought Japanese loved it
@@anonymouscode1635the cake division ceremony was held there but they were not informed. I assume they don't like it
Queen "Let them eat cake"
Masses: Well that's just not gonna cut it"
Queen: "They don't have bread? Why don't they eat cakes?" Attributed to Marie Antoinette, but, traced back to Rousseau. Well, I'm not a historician. And as always, thanks for the video. P.
Sounds like an Adrian Bliss Skit lmao
... that's just not going to cut it. However, we found something that will. It's called a guillotine.
@@irfaanfarhat100% immediately imagined him saying it
Cut
best way?
ask my mother to make the cuts.
I still wonder how she manages to make them so perfect. as far as I know, never has anybody complained about it.
Well, what if nobody's complained and lived to tell the tale...
I have absolutely been the one to cut the cake and then still envy the piece the other person chose lol
Skill issues.
@@trucid2 human error, 100%
@@SteveJubsGrass is always greener… even when perfectly cut 🙃
@@J-sv9dp best reply
me every time coz i hope they don’t notice ones slightly bigger
Now, that's a "sweet" math problem, LoL 😂😂😂😂
I’m un-liking, only because I was 70th
@@jameswilkerson4412 LoL😂😂😂
Of course, now it has 163 ‘Likes’
@@jameswilkerson4412 yea😂😂
you had my attention at "imagine you have a cake"
Jade should have hearted this one, too.
The best part is while the upper bound in n^n^n^n^n^n while the lower bound is just n^2
when mathematicians have skill issue
Frankly, n^2 is still a lot.
@@McFrax we're talking about very small numbers here. For n=2 already, lower bound is 4 but 2^2^2^2^2 already is a number with 19729 digits. I think you can see, that upper bound=2^(number with 19729 digits) is gonna be very large compared to 4. Also, upper bound grows much much faster...
btw, the number of atoms in the known Universe has about 80 digits.
"skill issue", he says! @@cubing7276
Wait didn't 3 people do if in 5 cuts or less than n^2 (9)
If you are at a mathematical festival, always choose the first toilet. No-one else will.
Ye Olde' Secretary Outhouse Problem
"Mathematician festival" makes them sound like they have an entire culture lol
I'm going to need to buy quite a few cakes to really get to the bottom of this.
I'm impressed that mathematicians have abstracted that problem in the first place, let alone solved it.
When I was studying Mathematics at Adelaide in the 1960s, this problem was posed in a paper for our Measure Theory course. After all, this problem is about the gastronomic value measure each of the eaters apply to different parts of the cake. A cutter, who may be one of the eaters, makes a radial cut in the cake and poises the knife over slowly rotating it, keeping the point in the centre, so sweeping out a sector of cake. The scrupulously honest eaters continuously integrate their measure of the value of the sector and call out when it reaches their fair share, i.e., 1/nth of the cake. The first to call out obviously values the piece more than the others, so there should be enough for the others to get at least their fair share. The cut is made, and the piece handed over, and the process is repeated to satisfy the desires of the remaining eaters.
This is logically equivalent to (and physically less messy than) the solution in my comment, which I also remember from the 1960s (no later than 1966). Jade, your history does not go back far enough!
@@larrykuenning5754 That sounds right to me. The last year of my formal mathematics was 1967. I'm sorry I did not notice your reply before.
@@johnbonnett5746: My reply was later than your comment by about a day; it looks like you noticed it as soon as was reasonable and there's nothing to be sorry about. I'm glad our memories line up on the general nature of the proof and the approximate time period. If only we could find some actual documentation to cite from that period -- but probably neither of us had any reason to preserve bibliographical notes on the subject.
now, apply that to warfare responsibilities amongst the U.N.
So it only works if people are honest. So maybe at a birthday party where all people are friends, but definitely not when dividing resources as claimed in the video.
I am glad you mentioned about the metaphor thing.
In one of the previous videos about a goat grazing half of the field, I made a joke about the engineer's approach and thousands of people seem to have taken it seriously and called mathematicians stupid 🤦♂️
Dear Mathematicians (And other scientists in general), as an engineer, I can not be more grateful for the foundation that you that you lay for us to build upon!
I tried this with my wife and she ate up the whole cake. Thank you Jane!
A cake is a metaphor for all the resources my mother has given me. And when she isn't looking, I take an extra slice, symbolizing my dissatisfaction with being fair.
This is why cupcakes are awesome. Everyone just picks one and the leftovers go home with the birthday child.
It doesn't matter how accurately or fairly you cut the cake; someone will always complain
Maybe instead of cutting the cake, we should cut one of the people. That reduces the number of people you need to cut cake for, therefore simplifying the problem.
But then you have the problem of dividing the person among the others.
That escalated quickly
Step 1: assume the cake is a sphere. 😂
Step 2 : And let the volume of of cake is infinite, problem solved
My goodness... to be able to listen to you while eating your cake sounds like a dream 😜
That way I eat whole cake 😂
Now I want cake :(
The cake is a lie.
And there is no spoon.
Cutting it in atoms and divide it 😅
I love the simplicity of “one person cuts, the other chooses.” Immediate incentive for the cutter to make the cut as fair as possible.
This sounds like less of a maths problem and more like humans being difficult.
you can remove the human factor. For example, you want to draw a blueprint for a new bedroom with bathroom and balcony in your house, but you have to decide three shapes to "cut" the floor on the second story, to strike a balance between the three areas. No ones being difficult there, and you want to make the best use of your hard earned money.
The accountants are getting their slice first and leaving us with the crumbs
Parent: Here's your cake. If you don't want it, I will eat it for you.
The team of researchers still wasn't able to enjoy a meal together.
Ah yes, math and its importance displayed in full power
Siblings will cut the cake in an infinite number of pieces to make it fair
I think you need to make a full length video about this. What are the limitations for the scenario? Does everyone value a different aspect of the cake or can they all value the same thing?
There is a good video from RUclips channel Numberphile titled " Equally sharing a cake between 3 people'
I kinda want to know how to cut the cake when there are 3 people
I recall a numberphile video on exactly that. I forget what it's called, but I'm sure you can find it!
Let's hope Graham's number of people don't want to share a big cake equally then.
Mathematically correct. Technically the best kind of correct.
That was much clearer than the first short on the envy-free-cake-cutting. Great job!
one of my favorite things about mathematicians is how they will come up with the most unhinged way to cut something and it's always so much fun
This is so interesting and humorous for me, because I recently saw this diagram about how to cut cake in an equal way so that the cake (from a circle) equally can be distributed to how ever many people there are lol actually was really interesting imo.
Basically it showed the cake being cut by circles, from the inside to out or whichever, then having those rows be individually cut to a specific size
When I was a kid, my parents always made sure that kids got the pieces they wanted. For example, we had a rectangular sheet cake and a kid at my birthday party wanted this very specific piece right in the middle. So, my mom cut the piece right out from the center. She always said “What’s more important: a neatly cut cake or a happy kid?”
my mom would say the neatly cut cake
I love this channel bc you tell us problems that have been solved but nothing about the solution, not even the equation
I have pondered this problem for many years. Thank you for talking about it!
I never realized cake cutting was a metaphor, I’ve always thought mathematicians were just interested in ways to cut cake
Ah yes, the cake smoothie. Perfectly devided and distributed.
Always have an engineer cut the cake. They know how to round up and down.
The only thing about the two person cutting of the cake is that the two people tend to argue on who will cut and who will choose
when people are jobless enough to write such complex pieces of code
Hey I think this re-upload is much clearer in explaining the concept.. Thank you for introducing a new concept for me...👌
Thanks for this... This question has haunted me since I was a young boy, so always refused to let anyone bake me a cake for my birthday. Finally, I can get my own birthday cake.
I too, as a philosopher, take the problem seriously. I recommend the "Quit whining & enjoy what you get" philosophy & applying it to all cake people! 😂
One moral of the lesson: Just bring plain cakes with no decorations on it to a gathering of mathematicians.
Forget the cake , I just fell in love with her
three mathematicians are having a party and a fourth walks in…
I eat entire cakes alone sometimes.😂
Now I'm imagining the absolute scene when it's somebody's birthday in the maths department and one of the juniors/grad students naïvely brings in a cake to celebrate 😂
Thing is, everyone will still be envious because everyone always want more cake.
I am glad they solved it. Been sitting here with this cake for the past 40 years. I can finally move on to doing laundry.
My immediate question was "how many dimensions do we have to work with?"
I love the little hair flick at the start of every video lol
More people need to watch Labyrinth. "Life isn't and will never be fair."
"for two people, it's a cakewalk"
😂
so that's why mathematicians have only three people in birthday parties.
It's always the computer scientists.
That’s why the best outcome is achieved by mutual compromise.
Ah so this is how old Marie Antoinette trolled the masses and lost her bonnet in the process
"Why do u want her slice?? theyre all mathematically calculated and perfectly cut"
"I want 2"
I, for one, remember the Numberphile Cake Video Incident.
A diplomat could have solved this problem in a heartbeat. Former German chancellor Ludwig Erhard is quoted by saying: "A compromise is the art of dividing the cake so that each person thinks they got the biggest part."
I was tasked this as a kid regularly. I was given a bag of assorted candy, and I needed to divide it three ways between my dad, baby sister and I. Inknew what candies they liked, so I was usually left with the set I planned on having. Same with portioning ice cream into bowls. I think this made me who I am currently. Or messed me up, or both. 😂
"Imagine you have a cake..."
Hold that thought, I'm making a quick run to the bakery.
You know, you could just... not share the cake. That's an option.
"You'll get nothing and like it. Now who else wants to complain?" This solves the problem.
Me buying a cake with just frosting 💀💀
Thanks for teaching us maths in an easy to understand way ❤❤
Is this what computer scientist really does?
haha yeah :)
Call me when mathematicians discover how to have your cake eat it too.
I am standing there with a twelve-inch chef's knife, you aren't. You will take the slice I give you.
Mathematicians will do anything but figure out how to communicate lol
I know how to solve this problem. Invite a bunch of Mathematicians to a party and get a really nice cake. Ask the smartest Mathematician to cut the cake perfectly, watch them all argue, then steal the cake and leave.
The best way is to give everyone a full cake
You explain things beautifully! It must be hard to explain this problem and find ways to summarize the assumptions (if the weight on the cake is continuous or not, if it depends on the participant, if cuts are restricted somehow, in which order participants cut and choose, if they can skip choosing, blah blah...) and not bore your audience. I would like to have the skill to do that graphically and just saying the bare minimum, as you do.
A follow up on that "it's more complicated but it can be done in 5 cuts" would be nice.
RNG fixes everything.
Instructions unclear. Now I have a smoothie
Sometimes i think mathematicians are insane, just cut the cake
Love your videos. Momentarily I am back at university. Thank you.
Solved by the axiom ‘you get what you get and you don’t throw a fit’.
Sounds so interesting! Would definitely love to see a full video on this :)
It's weird to imagine that working on the collatz conjecture is thought to be more silly than this.
Brilliant discussion! 👍🏽♥️
One of the nicest math books I've ever read was called precisely that "How to cut a cake (and other mathematical conundrums)" 😄
Mathematicians must have run out of problems to solve
When I see someone cut a round cake not towards the center I almost have an aneurysm.
I always wondered how to fairly divide which countries' military duties in war.
She got me in the beginning 😂
"I was told there would be cake." ~Milton
"Hey, no fair! I wanted that atom of the cake!"
I quote from the TV show Numb3rs, "What's wrong with you mathematicians? Cake is never a problem."
*Casually Divides up chores to the billionth power* 💀
The ham sandwich theorem sounds like a better solution to this. Just add more cuts (and more spatial dimensions) for each person
I was happily studying Gaussian Kernel distribution, and here we are. Right then, back to studying.
Wow, what a simple recepe for 2-person case. Never occured to me before. I will suggest this now to my children next time they need to share something (fortunately, I only have two!)