Yes we should have used greater/equals symbols at around 5:15, but the meaning pretty clear and Brady and Simon live about 10,500 miles apart --- so not worth a re-shoot!
Naa, it was actually fun, the people, even your fans are idiots... 3 is just a constant, yes, it's not that interesting, but is not always gonna be a super algorithm that creates planets -_-
The whole "3 friends or 3 not friends" thing is just like the riddle "How far can you go into a woods? Half way because then you are walking out of it."
I have a maths exams next week and this is surprisingly relevant to the course. This is actually a question that can come up. Now this counts as part of my revision :D
I kept waiting for there to be more to this one. It was just so intuitive I was waiting for another step that would make me think. I guess they can't all be winners.
This video is an icebreaker! Tried the whole day to understand Ramsey's Theory from my university literature, without any succes. Thanks to this video I understand everything. Thanks!
Sometimes if find myself wondering what application some of these mathematical principals have. Then, I'll either do the research or accept the fact that sometimes it's simply about finding order out of chaos. Thanks guys!
@@erek pigenhole principal is basically if there are more numbers of pigeon than hole than one hole should have more than one pigeon. So n>m where n is number of pigeon and m is number of holes than one hole will fundamentally have more than one pigeon it's simple. Lol
That graphic at the end showing how you inadvertently made a group of strangers by trying not to make a group of friends makes it look like it's possible to do this with 4 or 5 people. I had to actually draw my own diagram with 5 people to reaffirm what you showed earlier with it mattering how many connections they each have.
This entire video sounded simple as he explained it. Intuitive, even. So I tried to derive the conclusion on my own, starting with conclusions one can make about groups of three people, then four people, and hey, why not seven... By the time I got to ten my head was fried. I'm beginning to see why Graham's Number is used in Ramsey Theory.
I once read that there is a way to calculate that you know everyone on earth within like 15 corners. So with only around 15 relations you are connected to everyone on earth. An explaining video to that would be really cool :) Numberphile
What about higher numbers? If you have more friends, does the minimum number of people in a friendship group increase? Or is it always 3? If you have 8 people does it change to 4? Or was the fact that 3=6/2 a coincidence?
Hi Brady , I know you work very hard doing these videos and I´m sure you take the time to check every single one of them to deliver them the way you want , but, I´m from argentina and do enjoy your videos a lot only when they come with the sound. I´ve seen literaly hundred of videos and I´m sorry to tell you that only half of them have sound in all your channels , sixty simbols , periodic videos , veritasium, etc. unfortunately this is one of those videos without sound and I can´t let it pass thanks for all your good work, I learn new things every day with this videos, cheers
For anyone interested in this topic this comes from an area of mathematics known as Ramsey Theory. In Ramsey Theory we ask ourselves, "How big must a system be before we can always find a certain pattern?" The problem shown here is the most classical example and is actually just a simple example of a much broader theorem known as Ramsey's Theorem. I invite all the intrepid minds to look a little deeper into the subject. You may enjoy what you find.
Its popular name is ramsey problem. R(n,m) is the minimum number k such that any red and blue coloring on Ck (complete graph of k vertices) always contains Cn red or Cm blue. Here, R(3,3)=6. This problem is so hard as Erdos said like "if alien invade us and they give us option to answer R(6,6) or war, it's better to choose war"
I like to think this might be laying the ground work for the awesome upcoming Graham's Number videos! ...I _like_ to think this, but I have a very weak grasp of the problem that Graham's Number is the solution for. But it involves 2 colours :D
It is strange... I saw many of these things in math class back in high school. Back then I assumed it was normal but it seems like I just had a really really awesome math teacher.
Wednesday would be a scary friend to have on facebook. You'd say something similar to, "My grandma passed away..." and then there would be a singular 'like'...
Brady, thanks for giving me Simon Pampena on UA-cam. That makes his appearances on Outrageous Acts of Science more exciting to me. (And Matt Parker too.)
IMHO though the "triangles" should have been introduced right in the beginning in order to make even more clear what was meant with three people all being or not being friends.
Exactly, in the first drawing, they show triangles, and then when Simon explains it with the table, he just shows the possible combinations out of 5 connections. But these combinations do not necessarily form triangles because you don't know what the other guys are doing. And then he shows the proof. To me it seems like the middle part does nothing to aid in proving it, they might as well have left that out. Still a cool video though.
@TijnvanBoekel follow the video more closely, he needs the middle part to prove that for any one person, the minimum number of friends or not friends is three. Only because of this can he say that in all situations is there a triangle. If he didn't do the middle bit consider this - I can say "what if the first person (with three friends) were to have only two friends with those people then we can avoid the triangle. I.e. Turn the third line red". I agree it is obvious this is just displacing the problem, but if he is being mathematically rigorous (despite 3 > 3) then he should prove it.
Just in case anyone else was wondering how he gets the 15: With 6 people: Person 1 can have 5 unique connections. (Person 2, 3, 4, 5, 6) Person 2 can have 4 unique connections. (Person 3, 4, 5, 6) Person 3 can have 3 unique connections. (Person 4, 5, 6) Person 4 can have 2 unique connections. (Person 5, 6) Person 5 can have 1 unique connections. (Person 6) Person 6 can have 0 unique connections. 5+4+3+2+1 = 15 This can be mathematically modeled as: .5(n^2 - n) or .5n(n-1) In my field we refer to this at Metcalfe's Law (specifically referring to telecommunications)
Question for Simon, what do you do in your spare time, and how easy is it for you to think and see the problems that you are explaining. It would be fascinating to think like a mathematician, could you describe?
I have a strong penchant and absorption for mathematics, and, reading the comments, should this build into something larger and more foreign to myself (it appears the Ramsey Theorem is what this builds into), it would greatly satiate my thirst for being able to better understand maths when I cannot afford to take classes on it all. Thank you, Brady and Simon! :)
The conclusion is the same as the introduction. He proved a theorem. It's the theorem that's interesting. There are thousands of possible combinaisons that have seemingly nothing in common and yet you can find a quite strong property that they all share. By itself it's something even if this theorem didn't have that many application in maths and computer science (being the basis of Ramsey theory and whatnot).
That a "huge" chaos can be comprehended by a "small" rule. That you don't need to verify every single one of the many possibilities to realize there is a pattern. In a concept more simple to grasp: you don't need to analise all grains of sand in a desert to understand the desert. Just a few. If you drop a little bit of water in a bit of sand, you'll see that it dries out really quick, so you know why the desert is so dry. If you heat it up, you'll notice that sand doesn't hold the temperature for too long, and then you understand why the desert gets so cold at night. Take a fill grains and you notice how small and light-weight they are, so you comprehend why dunes are so instable, why the wind changes the geography of the region so quickly and why sandstorms happen. The human beign may never be able to comprehend the universe as a whole, but he can understand it by analysing phenomenons in a small scale that are repeated trough space.
Hi Brady, Is there a way to know what that magic number will be given the number of elements in the group? In this case it was 3 friends or 3 not friends given a total group size of 6. Given a group size of n, is there a mathematical way to say what the number of connected or not connected group members will be? Obviously the most immediate answer is n/2, but that seems like it might be too simple of an answer. Any thoughts?
There is a result in graph theory that states that if G is a graph on 6 vertices, then either G contains a triangle or G'(complement of G) contains a triangle.
This is called the game of Sim. Players 1 and 2 have 3 vertices each and you take turns drawing edges. The first person to complete a triangle loses. Ransey theory guarantees the game can never end in a draw.
It gets even better: every combination in a six person's game had 3 connected people by the same kind of line, red or green, then does it mean that for a N person's game we get N/2 people are always connected by the same kind of line? I think so, but haven't been able to show it.
2^15 derivation is simple: there are 15 "connection" lines, and each has a possibility of 2 states (friends or not friends). If you want to think of it like a tree diagram, connection 1 has two states, and from each of connection 1's states connection 2 has two states, and so on (2 x 2 x 2....), or 2^15 for short because there are 15 connections.
Fun fact: Graham's Number, the former largest number ever used in a mathematical proof, actually stems from this fascinating 'order out of chaos' theory, also known as Ramsey theory!
Why wasn't the term Ramsey Number mentioned? In the video you showed that R(3,3) = 6. "Paul Erdős asks us to imagine an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5,5) or they will destroy our planet. In that case, he claims, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they ask for R(6,6). In that case, he believes, we should attempt to destroy the aliens."
A number of commenters are saying that this is obvious because if less than half the group are friends, more than half will be strangers and vice versa. This is not true because you cannot neatly classify a whole group of people into friends and strangers. You may have two friends who don't know each other, and two people you don't know may be friends. In a group of eight, for example, you may say that there must be at least one group of four that all know each other or are all strangers to each other. That is not true. Imagine (or rather try graphing it out because it is probably hard to visualize) eight people, numbered one to eight. In this group, two people know each other if they're separated by one or two, otherwise they're strangers. Also, we're using modular arithmetic, so 1 and 8 know each other, and so do 1 and 7. In this group of eight there is no group of four people who all know each other and there is no group of four people who are all strangers. (If you find any, please let me know.) I hope this helps.
It is worth noting that in a group of six there can be a situation were there are no 'triangles' of friends/not friends, but in those cases there is a 'loop' of 4 people which does count for this theorem. In those loops, however, the people across from each other are of a different relation than what makes up the loop. Easy example: take people {1,2,3,4,5,6} with friend connections between 1-2 2-4 4-5 5-1 3-6 and fill the rest with not friends. Here you have a loop of friends in 1-2-4-5 and not friends a couple of ways but 0 triangles of either type.
Isn't it easier to just say 6(people) / 2(choices) = 3(minimum of one choice). If you just take six and split it in half, you get 3. If you take a smaller group (any 2 or 1), then the opposite group becomes larger than 3. Thus, with 8 people and 2 choices (friends or not), at least 4 people would know each other or not. With 10 people, at least one of the two groups would be made up of 5 or more people.
to know the number of possible connections(c) between dots(n) you can use c=(n*(n-1))/2 wich would be p=(6*5)/2=15 you can try is with 3 or 4 or 5 dots on paper and you will see its true. And for every line there are 2 options, a connection or no connection. Thats why he uses 2^15
If you know "Combinatorics", 15 is simply (6 choose 2), but if you don't, you just have to manually count the possible number of unique "links" between any two people from amongst a group of 6 people. An efficient way to do that would be counting all the links of one person and then not include that person in any further counting. e.g For six people named p1,p2...p6 1) Number of links involving p1, is (6-1) = 5 (he can have a link with any of the six people excluding himself) 2) Number of links involving p2, is (6-2) = 4 (he can have a link with any of the six people excluding himself *and p1*, because then the link p1-p2 would be counted twice) 3) Similarly Number of links involving p3 = (6-3) = 3 ... 6) Number of links involving p4 = 6-6 = 0 and so we get the total number of unique links to be 5 + 4 + 3 + 2 + 1 + 0 = 15. Another clever way would be counting all possible links (not only unique), that would be (6 people) x (5 links for each) = 30 and then dividing this number by 2 because each *unique* link has been counted twice (i.e. once for each person involved in that particular link e.g the link p1-p2 would be counted twice, once for p1 and once for p2) which yields 30/2 = 15.
NotTheRealBassKitten take one person as a reference point: he is directly connected to the 5 other people there are six people so 6 different reference points to consider however for the second reference you have to take away that person's connection to the first reference: so you count 4 connections to other people... for the third, you take away his connections to the first two references, so you count 3 connections, and so on and so on you get 5 + 4 + 3 + 2 + 1 = 15 overall connections
If points could connect to themselves the number of connections would be the sum of 1 to n, since they cannot, it is the sum from 1 to n-1. 1+2+3+4+5=15.
The question then leads to why 3? In a group of 6, you always have at least one trio that are all green or all red. Does this hold true for higher group sizes? In a group of 20 people, is it still trio, is it a tensome, is it a different size, etc?
is about ramsey's theorem, R(3,3) is 6 ,r(4,4) is 18(means in a 18 people group ,there will always be a square,"four-some") and thats it , we dont know how many people is needed for pentagon(or "five-some)
🤯 that I randomly watch this video 7 years after it’s been uploaded and I literally know the couple whose photo was used. Lol. Friends and strangers for real.
The first person can has exactly 5 connections with the 5 other people, obviously. The second person has 5 connections as well, but one of those connections is with the first person, which we don't need to count twice, so we get 4. The third person has 5 connections, 2 of which we counted already, and so on. By the time we get to the sixth person, there are no more connections left that we didn't count yet, so the number of connections between 6 people is 5+4+3+2+1=15.
7:44 Did he said 3 people that are your mom and dad? "Three people that are friends with one another, or three people who can't stand each other, or don't know each other, or are your mom and your dad."
They never really talked about any application for this theorem. I get that not every proof is directly applicable to real life, but sometimes these simpler proofs are useful for complex proofs. So what's the potential usefulness of this theorem?
It is the begining of the ramsey theory wich can be then apply to conbinatorics wich is used in computer science,... An graph theory, wich also is use in computer science. Also, but i really dont know if its related, there is this problem relating facebook,which wonders: if you can view the profile of the n friend of a friend, how big must be n so you can see all the profile of facebook.
i would have to echo this.....it makes it have a 0% interest factor...they took a interesting concept and just applied a equation....boring....but its a math show, i cant expect philosophy.....
Jaime Cernuda Isn't that last just a Facebook specific restating of the small world problem? In most contexts where that comes up the mean value of n is 6.
vlademir1 Yeahh basicly, but most of the people had heard about this problem through the facebook problem so thats why i mention it. Ans also because it related to the application of this video.
Look up Ramsey Theory which is a sub-field of Combinatorics, I'm not sure if the Computational Complexity required of an algorithm to solve problems within the field can be applied yet or not? Anyhow, I guess you wouldn't like Pure Mathematics?
Can you guys do a video about essential singularities in complex analysis and Picard's Theorem? It's my single favorite Theorem just because of how awesome it is to imagine. Thanks :)
I have to say though, it was a quite complicated explanation. I'm not sure I totally understood it all, but from what I can make out, I'm pretty sure, Bredy is my mother.
I feel like I should know this; what's the math to get 2 to the power 15? So the math to get that it's power 15. Now that I've typed this up ... is it because 5+4+3+2+1=15? Right? (Start with one person who has 5 people that they can be connected to in one of two ways. Move to the second person who has 4 people remaining that can be connected to in one of two ways. Etcetera.)
What about people who quite facebook entirely? If you have a group of 6 people who quit facebook, is it possible to have less than 3 of those people either be friends or not be friends? Cuz i quit it, and i know a large number of people who have as well.
Yes we should have used greater/equals symbols at around 5:15, but the meaning pretty clear and Brady and Simon live about 10,500 miles apart --- so not worth a re-shoot!
hi
Naa, it was actually fun, the people, even your fans are idiots... 3 is just a constant, yes, it's not that interesting, but is not always gonna be a super algorithm that creates planets -_-
Reply becasue else it is red line and i will be sad 😔 😂
Numberphile who’s the person who writes UA-cam comments? Just asking...
The whole "3 friends or 3 not friends" thing is just like the riddle "How far can you go into a woods? Half way because then you are walking out of it."
FFS Brady! DO NOT ROUND IT UP!!!!
Don't round it up, Brady.
Don't ever round it up.
and today we learned, that 3 > 3 = true
yep, he said "at least" so he should have written ≥3 instead
minauras yeah I know, I was just referring to what he wrote :3
Brandan09997 not if he takes it lightly
Brandan09997 and you're a piece of shit :3
and i learned that
(3 > 3 = true) = true
Note to self: avoid threesomes at all costs.
nah fam
"There are more than six people on facebook. You know that, right?"
I mean, there must be at least 10 if you round up.
You can tell this video is old b/c it features a positive reference of Facebook
Three people who are my mom or my dad? That does make for one very awkward christmas party.
It is time we tell you about the flowers, the bees and the Turtle.
You'd be the third person, mate.
Cheer up mate, LOTS of presents :)
Psykodamber.dk Surely you mean tortoise, bees don't swim very well ;-)
I have a maths exams next week and this is surprisingly relevant to the course. This is actually a question that can come up. Now this counts as part of my revision :D
Å
me too,
combinatorics for computer science
i got a test in a week, this can totally be one of the questions!
I'm doing the D1 paper too! This exact question actually came up on a mock I did yesterday!
what the hell is albert neville is talking about?
Albert Neville Chill out you worthless goat.
The one direction example of the connections would now have 5 red lines 😂
TOO SOON
@@alexsawyer8467 what do you mean, you commented 3 years later hahah
I kept waiting for there to be more to this one. It was just so intuitive I was waiting for another step that would make me think. I guess they can't all be winners.
This video is an icebreaker! Tried the whole day to understand Ramsey's Theory from my university literature, without any succes. Thanks to this video I understand everything. Thanks!
1:53 😂😂 I love how much offense he takes to the approximation
Shouldnt be ">=" instead of ">"?
Sometimes if find myself wondering what application some of these mathematical principals have. Then, I'll either do the research or accept the fact that sometimes it's simply about finding order out of chaos. Thanks guys!
A popular application of the pigeonholes theorem. Well explained!
can you please explain?
@@erek _"And ever since, Louis-Math had not explained"_
@@fantiscious lol
@@erek pigenhole principal is basically if there are more numbers of pigeon than hole than one hole should have more than one pigeon. So n>m where n is number of pigeon and m is number of holes than one hole will fundamentally have more than one pigeon it's simple. Lol
@@arpitdhukia9026 i know what it is. How is that related to this video?
That graphic at the end showing how you inadvertently made a group of strangers by trying not to make a group of friends makes it look like it's possible to do this with 4 or 5 people. I had to actually draw my own diagram with 5 people to reaffirm what you showed earlier with it mattering how many connections they each have.
Good thing I have no friends
Simon is one of my favourite people in these videos.
This entire video sounded simple as he explained it. Intuitive, even. So I tried to derive the conclusion on my own, starting with conclusions one can make about groups of three people, then four people, and hey, why not seven...
By the time I got to ten my head was fried. I'm beginning to see why Graham's Number is used in Ramsey Theory.
This is my favourite problem! I am so excited that they have done this!
This reminds me of when someone said to me that no person is more than 6 relationships away from any other person.
"There is exactly 32,768 different ways...don't round it up" hilarious!
I once read that there is a way to calculate that you know everyone on earth within like 15 corners. So with only around 15 relations you are connected to everyone on earth. An explaining video to that would be really cool :) Numberphile
What about higher numbers?
If you have more friends, does the minimum number of people in a friendship group increase? Or is it always 3?
If you have 8 people does it change to 4? Or was the fact that 3=6/2 a coincidence?
This is simply amazing, both the concept and your explanation
Since when is 3 > 3?
Cuz no one wants 3
Gotta love how 8 years ago, Facebook was considered a hip thing for the kids, now only boomers use it
Hi Brady , I know you work very hard doing these videos and I´m sure you take the time to check every single one of them to deliver them the way you want , but, I´m from argentina and do enjoy your videos a lot only when they come with the sound. I´ve seen literaly hundred of videos and I´m sorry to tell you that only half of them have sound in all your channels , sixty simbols , periodic videos , veritasium, etc.
unfortunately this is one of those videos without sound and I can´t let it pass
thanks for all your good work, I learn new things every day with this videos, cheers
I saw a question where you had to explain this in a D1 A Level maths paper (which I'm taking on Tuesday).
"Sorry I don't want to be friends with you don't try it and just stop requesting to be friends, I don't want to be friends with you ok? No." lol
This is such an amazing way to learn math at master's level.
For anyone interested in this topic this comes from an area of mathematics known as Ramsey Theory. In Ramsey Theory we ask ourselves, "How big must a system be before we can always find a certain pattern?" The problem shown here is the most classical example and is actually just a simple example of a much broader theorem known as Ramsey's Theorem. I invite all the intrepid minds to look a little deeper into the subject. You may enjoy what you find.
Simon is just amazing :) Great video!
Its popular name is ramsey problem. R(n,m) is the minimum number k such that any red and blue coloring on Ck (complete graph of k vertices) always contains Cn red or Cm blue. Here, R(3,3)=6. This problem is so hard as Erdos said like "if alien invade us and they give us option to answer R(6,6) or war, it's better to choose war"
I watched this whole video wondering what the point of this video was until the end where it all made sense.
I like to think this might be laying the ground work for the awesome upcoming Graham's Number videos!
...I _like_ to think this, but I have a very weak grasp of the problem that Graham's Number is the solution for. But it involves 2 colours :D
Yeah, I thought that too :D Then after a quick google it turns out they're both part of Ramsey Theory, so I think that's quite probable!
They did a Graham's Number video already: v=XTeJ64KD5cg
***** Can't quite say they did a very good job of explaining the problem that led to Graham's number, though. Would be nice to seem them return to it.
Guess what...
I lawled so hard when he said: Dont round it up. He was so serious:DDD
It is strange... I saw many of these things in math class back in high school. Back then I assumed it was normal but it seems like I just had a really really awesome math teacher.
Wednesday would be a scary friend to have on facebook. You'd say something similar to, "My grandma passed away..." and then there would be a singular 'like'...
Thought he was gonna talk about the "At least through 7 strangers, you'll meet someone you know" thing.
Brady, thanks for giving me Simon Pampena on UA-cam. That makes his appearances on Outrageous Acts of Science more exciting to me. (And Matt Parker too.)
IMHO though the "triangles" should have been introduced right in the beginning in order to make even more clear what was meant with three people all being or not being friends.
Exactly, in the first drawing, they show triangles, and then when Simon explains it with the table, he just shows the possible combinations out of 5 connections. But these combinations do not necessarily form triangles because you don't know what the other guys are doing. And then he shows the proof. To me it seems like the middle part does nothing to aid in proving it, they might as well have left that out. Still a cool video though.
I think it's pretty self explanatory.
@TijnvanBoekel follow the video more closely, he needs the middle part to prove that for any one person, the minimum number of friends or not friends is three. Only because of this can he say that in all situations is there a triangle.
If he didn't do the middle bit consider this - I can say "what if the first person (with three friends) were to have only two friends with those people then we can avoid the triangle. I.e. Turn the third line red". I agree it is obvious this is just displacing the problem, but if he is being mathematically rigorous (despite 3 > 3) then he should prove it.
Malkitasoman that makes sense, thanks :)
bloody triangularists
Just in case anyone else was wondering how he gets the 15:
With 6 people:
Person 1 can have 5 unique connections. (Person 2, 3, 4, 5, 6)
Person 2 can have 4 unique connections. (Person 3, 4, 5, 6)
Person 3 can have 3 unique connections. (Person 4, 5, 6)
Person 4 can have 2 unique connections. (Person 5, 6)
Person 5 can have 1 unique connections. (Person 6)
Person 6 can have 0 unique connections.
5+4+3+2+1 = 15
This can be mathematically modeled as: .5(n^2 - n) or .5n(n-1)
In my field we refer to this at Metcalfe's Law (specifically referring to telecommunications)
I like how you try to make it relevant and then use the Addams family for the diagram...
Now I feel like adding Simon Pampena up on Facebook, just because of his hilarious reaction when he says he doesn't want to be friends with anyone.
Best phrase ever "there's more than 6 people on Facebook"
Question for Simon, what do you do in your spare time, and how easy is it for you to think and see the problems that you are explaining. It would be fascinating to think like a mathematician, could you describe?
This has to do with a fabulously mysterious area of mathematics called Ramsey numbers
I have a strong penchant and absorption for mathematics, and, reading the comments, should this build into something larger and more foreign to myself (it appears the Ramsey Theorem is what this builds into), it would greatly satiate my thirst for being able to better understand maths when I cannot afford to take classes on it all.
Thank you, Brady and Simon! :)
very cool explanation and very well explained in simple language thanks numberphile 😀
Great video! Do more about this!
what is the conclusion of this? '-'
Plot twist: There is no conclusion.
that 3 > 3
None ;p
The conclusion is the same as the introduction. He proved a theorem. It's the theorem that's interesting.
There are thousands of possible combinaisons that have seemingly nothing in common and yet you can find a quite strong property that they all share. By itself it's something even if this theorem didn't have that many application in maths and computer science (being the basis of Ramsey theory and whatnot).
That a "huge" chaos can be comprehended by a "small" rule. That you don't need to verify every single one of the many possibilities to realize there is a pattern.
In a concept more simple to grasp: you don't need to analise all grains of sand in a desert to understand the desert. Just a few. If you drop a little bit of water in a bit of sand, you'll see that it dries out really quick, so you know why the desert is so dry. If you heat it up, you'll notice that sand doesn't hold the temperature for too long, and then you understand why the desert gets so cold at night. Take a fill grains and you notice how small and light-weight they are, so you comprehend why dunes are so instable, why the wind changes the geography of the region so quickly and why sandstorms happen.
The human beign may never be able to comprehend the universe as a whole, but he can understand it by analysing phenomenons in a small scale that are repeated trough space.
"There are exactly 32,768 different ways to do that, Brady. Don't round it up." LOL
Not only that, but most of your friends have more friends than you do!
Hi Brady,
Is there a way to know what that magic number will be given the number of elements in the group? In this case it was 3 friends or 3 not friends given a total group size of 6.
Given a group size of n, is there a mathematical way to say what the number of connected or not connected group members will be? Obviously the most immediate answer is n/2, but that seems like it might be too simple of an answer.
Any thoughts?
Look up ramsey numbers. Very interesting
There is a result in graph theory that states that if G is a graph on 6 vertices, then either G contains a triangle or G'(complement of G) contains a triangle.
Great explanation, really!
This is called the game of Sim. Players 1 and 2 have 3 vertices each and you take turns drawing edges. The first person to complete a triangle loses. Ransey theory guarantees the game can never end in a draw.
It gets even better: every combination in a six person's game had 3 connected people by the same kind of line, red or green, then does it mean that for a N person's game we get N/2 people are always connected by the same kind of line? I think so, but haven't been able to show it.
"There's exactly 32,768 different ways you can do that, Brady. Don't round it up."
This Jewfro mathematician is my favorite on this channel.
2^15 derivation is simple: there are 15 "connection" lines, and each has a possibility of 2 states (friends or not friends). If you want to think of it like a tree diagram, connection 1 has two states, and from each of connection 1's states connection 2 has two states, and so on (2 x 2 x 2....), or 2^15 for short because there are 15 connections.
"You can always find three people, that are [...] your mom and dad."
That would be strange... o.o
I love maths and harry
There's also this result which says there will always be an even number of people that are friens with an odd number of people.
By being friends with two people and the strangers with two, the remaining connection forces the trio of friends or strangers.
I really doubt you will find three people that are my mom and dad :|
Fun fact: Graham's Number, the former largest number ever used in a mathematical proof, actually stems from this fascinating 'order out of chaos' theory, also known as Ramsey theory!
i'm just waiting for one video with this guy in it i'm actually going to enjoy watching.
maybe next time...
5:06 the word that you are looking for is strangers.
Why wasn't the term Ramsey Number mentioned? In the video you showed that R(3,3) = 6. "Paul Erdős asks us to imagine an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5,5) or they will destroy our planet. In that case, he claims, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they ask for R(6,6). In that case, he believes, we should attempt to destroy the aliens."
snappas Yeah, they really missed over the opportunity to introduce the idea of Ramsey theory.
A number of commenters are saying that this is obvious because if less than half the group are friends, more than half will be strangers and vice versa. This is not true because you cannot neatly classify a whole group of people into friends and strangers. You may have two friends who don't know each other, and two people you don't know may be friends.
In a group of eight, for example, you may say that there must be at least one group of four that all know each other or are all strangers to each other. That is not true. Imagine (or rather try graphing it out because it is probably hard to visualize) eight people, numbered one to eight. In this group, two people know each other if they're separated by one or two, otherwise they're strangers. Also, we're using modular arithmetic, so 1 and 8 know each other, and so do 1 and 7. In this group of eight there is no group of four people who all know each other and there is no group of four people who are all strangers. (If you find any, please let me know.)
I hope this helps.
You have 6 light switches. They can either be on or off. At least 3 will be on or at least 3 will be off. Whats the big deal about that?
Collatz conjecture!! 3x+1 problem!!!
It is worth noting that in a group of six there can be a situation were there are no 'triangles' of friends/not friends, but in those cases there is a 'loop' of 4 people which does count for this theorem. In those loops, however, the people across from each other are of a different relation than what makes up the loop. Easy example: take people {1,2,3,4,5,6} with friend connections between 1-2 2-4 4-5 5-1 3-6 and fill the rest with not friends. Here you have a loop of friends in 1-2-4-5 and not friends a couple of ways but 0 triangles of either type.
Not true. {1, 3, 4} forms a triangle of non-friendship.
"A Threesome of Anonymity"
The thumbnail, the moment you realize you haven't seen this numberphile video
3 people that are my mom or my dad? =O Great vid as always Brady and Simon :)
A very minor tweak on the same proof tells that there must be at least two trios (possibly sharing an edge).
Isn't it easier to just say 6(people) / 2(choices) = 3(minimum of one choice). If you just take six and split it in half, you get 3. If you take a smaller group (any 2 or 1), then the opposite group becomes larger than 3. Thus, with 8 people and 2 choices (friends or not), at least 4 people would know each other or not. With 10 people, at least one of the two groups would be made up of 5 or more people.
hang on where did he get the 15 from??
to know the number of possible connections(c) between dots(n) you can use c=(n*(n-1))/2 wich would be p=(6*5)/2=15 you can try is with 3 or 4 or 5 dots on paper and you will see its true. And for every line there are 2 options, a connection or no connection. Thats why he uses 2^15
If you know "Combinatorics", 15 is simply (6 choose 2),
but if you don't, you just have to manually count the possible number of unique "links" between any two people from amongst a group of 6 people.
An efficient way to do that would be counting all the links of one person and then not include that person in any further counting.
e.g
For six people named p1,p2...p6
1) Number of links involving p1, is (6-1) = 5 (he can have a link with any of the six people excluding himself)
2) Number of links involving p2, is (6-2) = 4 (he can have a link with any of the six people excluding himself *and p1*, because then the link p1-p2 would be counted twice)
3) Similarly Number of links involving p3 = (6-3) = 3
...
6) Number of links involving p4 = 6-6 = 0
and so we get the total number of unique links to be 5 + 4 + 3 + 2 + 1 + 0 = 15.
Another clever way would be counting all possible links (not only unique), that would be (6 people) x (5 links for each) = 30
and then dividing this number by 2 because each *unique* link has been counted twice (i.e. once for each person involved in that particular link e.g the link p1-p2 would be counted twice, once for p1 and once for p2) which yields 30/2 = 15.
Count the lines
NotTheRealBassKitten
take one person as a reference point: he is directly connected to the 5 other people
there are six people so 6 different reference points to consider
however for the second reference you have to take away that person's connection to the first reference: so you count 4 connections to other people...
for the third, you take away his connections to the first two references, so you count 3 connections, and so on and so on
you get 5 + 4 + 3 + 2 + 1 = 15 overall connections
If points could connect to themselves the number of connections would be the sum of 1 to n, since they cannot, it is the sum from 1 to n-1. 1+2+3+4+5=15.
The question then leads to why 3? In a group of 6, you always have at least one trio that are all green or all red. Does this hold true for higher group sizes? In a group of 20 people, is it still trio, is it a tensome, is it a different size, etc?
is about ramsey's theorem, R(3,3) is 6 ,r(4,4) is 18(means in a 18 people group ,there will always be a square,"four-some") and thats it , we dont know how many people is needed for pentagon(or "five-some)
🤯 that I randomly watch this video 7 years after it’s been uploaded and I literally know the couple whose photo was used. Lol. Friends and strangers for real.
The first person can has exactly 5 connections with the 5 other people, obviously. The second person has 5 connections as well, but one of those connections is with the first person, which we don't need to count twice, so we get 4. The third person has 5 connections, 2 of which we counted already, and so on. By the time we get to the sixth person, there are no more connections left that we didn't count yet, so the number of connections between 6 people is 5+4+3+2+1=15.
7:44 Did he said 3 people that are your mom and dad? "Three people that are friends with one another, or three people who can't stand each other, or don't know each other, or are your mom and your dad."
They never really talked about any application for this theorem. I get that not every proof is directly applicable to real life, but sometimes these simpler proofs are useful for complex proofs. So what's the potential usefulness of this theorem?
It is the begining of the ramsey theory wich can be then apply to conbinatorics wich is used in computer science,...
An graph theory, wich also is use in computer science.
Also, but i really dont know if its related, there is this problem relating facebook,which wonders: if you can view the profile of the n friend of a friend, how big must be n so you can see all the profile of facebook.
i would have to echo this.....it makes it have a 0% interest factor...they took a interesting concept and just applied a equation....boring....but its a math show, i cant expect philosophy.....
Jaime Cernuda
Isn't that last just a Facebook specific restating of the small world problem? In most contexts where that comes up the mean value of n is 6.
vlademir1 Yeahh basicly, but most of the people had heard about this problem through the facebook problem so thats why i mention it. Ans also because it related to the application of this video.
Look up Ramsey Theory which is a sub-field of Combinatorics, I'm not sure if the Computational Complexity required of an algorithm to solve problems within the field can be applied yet or not? Anyhow, I guess you wouldn't like Pure Mathematics?
"Don't round up Brady" Best damn part of the whole video.
great explanation! thank you!
Can you guys do a video about essential singularities in complex analysis and Picard's Theorem? It's my single favorite Theorem just because of how awesome it is to imagine. Thanks :)
I have to say though, it was a quite complicated explanation. I'm not sure I totally understood it all, but from what I can make out, I'm pretty sure, Bredy is my mother.
1:43 Is that Wednesday?
Well Explained. Thank You
WHY IS N O B O D Y TALKING ABOUT THE L O N G SNOUT IN THE BACKGROUND
W H Y
I feel like I should know this; what's the math to get 2 to the power 15? So the math to get that it's power 15.
Now that I've typed this up ... is it because 5+4+3+2+1=15? Right? (Start with one person who has 5 people that they can be connected to in one of two ways. Move to the second person who has 4 people remaining that can be connected to in one of two ways. Etcetera.)
Thumbs up from me for the Addams Family "friend chart".
If you want to see a generalization of this, look at edge colourings on regular complete graphs.
Ramsey is number one
His eyes are number one
His muscles are number one
RAMSES is number one
What about people who quite facebook entirely? If you have a group of 6 people who quit facebook, is it possible to have less than 3 of those people either be friends or not be friends? Cuz i quit it, and i know a large number of people who have as well.