Will your name become extinct? - Numberphile 

I can confirm that the Lemon name has not died out.

How about we add a " -1 " which kills the brother next to you. That ought to spice things up.

As an only son of an only son this video triggered my existential dread.

* rolls a zero for the first generation. game ends *

“17’s a number” Indeed.

"13 sons, all boys." What a Genius, I would have never guessed!

2 James Grime videos in one day? I'm in heaven.

Vsauce: will we run out of names? Numberphilie: will your name be extinct? I feel lost. What should I do

I'm surprised the Dr. Grime didn't fully explain the intuition behind his equation. That is the essence of the problem, and much more interesting than the graphical solution to the problem. He should start with x is the probability that a line goes extinct starting with one individual. There is a 1/6 chance it ends right away, 1/3 chance there is one son and that son's line will go extinct with the same probability x, 1/3 chance there are two sons each with probability x of their line going extinct so probability of both going extinct is x^2, and 1/6 chance of 3 sons, each with probability x of their line going extinct so probability of all three going extinct is x^3. Therefore x=1/6+x/3+x^2/3+x^3/6. The equation seemed to come out of nowhere here.

The entire video I was thinking about the scenario he called the one exception. So I’m glad he said it!

I did something kind of like this once not too long ago when I was doing some personal research for a campaign of a roleplaying game that I was running. I wanted to have details of all of the families in some of the towns I had created for the game. I had a couple dozen family names for each town, and I worked up some rules for intermarrying and having kids (resolved by rolling dice). I noticed that eventually most of the family names went "extinct." It was not because they did not have any children, but none of their children were male (and in these fictional towns only males carried on the family name). So it didn't matter that every couple had children, what mattered was whether the children were male or female. I didn't even have to go through that many generations to have a large percentage of the names wiped out, maybe four or five. (And, no, I never did use the research or the fictional towns, the campaign fell through, people were too busy. I continued to do the math for a few weeks anyway, just because it was interesting, but eventually I had to give it up... the record keeping of thousands of individuals and their offspring was too tedious.)

"Sir-Lee Temple" hahahahahaha nice

"A family of thirteen sons, all boys" - well, there's a coincidence!

RIP Sir Lemon and his noble family. His family name will be remembered.

This applies to every name except Nguyen, the last name that will never die.

Dr. Grimes explains complicated stuff more elegantly than just about anybody. Double his salary!

I've heard the Lemons' family reunions are quite the party.

2 videos with James! Love it.

The family of 13 boys is from my hometown. That’s pretty cool. They did a write up on the family around 2004. All of the brothers served in the military, several in WW2. Never expected to hear Sullivan, Illinois in a Numberphile video!

You aren't guaranteed to go extinct, but the probability of extinction approaches 100% (and equals 100% after infinitely many generations). But even if its probability is 0%, it is still possible to have more kids every generation. That still exists in the sample space, unless every number on the die is 0.

Wow, I just finished watching the unlisted version and you uploaded it now.

I had a dream about a variant solution to this problem, and came to the conclusion that you have 100% chance of your name going extinct as long as there is a "0" outcome available on the roll. There is always the probability that you will have all zeroes, but never the probability that a new name is created, so the list is deteriorating. It's similar to the wondering ant on a rubber band being stretched.

Another video with James? I'm digging it!

If you never grow in average, and you always have chances to lose, you will eventually lose all.

Ohhh, I just realized -- this is the gambler's ruin!

Oh well. From the title I thought this was actually going to be about your *name*. Which you might well share with a hundred thousand people rather than just your immediate family, and yet even so it might, and indeed likely will, go extinct. Unless it's Smith, Li, or Nguyen. I believe the fancy name for that is "the Galton-Watson process". Wasn't there a Numberphile video on that a couple years ago? I can't seem to be able to find it.

This video does a nice job of briefly explaining some very deep mathematics. Awesome!

12:26 such a lovely noise!

Imagine my surprise at seeing this video fresh in my feed having watched it 2 hours ago.

In Puerto Rico (and I believe in many Latin countries) kids receive two last names-mom’s first last name and dad’s first last name, hyphen in between. My kids have a name from me AND from hubby. Kind of changes the game.

was not expecting that expression at 7:09 😂😂 made my night

Sir Lemon? That's Earl Lemon-Grab! UNACCEPTABLE!!!!

Waiting for the Numberphile podcast with James Grime

This is great. Interesting topic and very elegant solution.

This video is simplified calculus of infinite series. Just took my exam and didn’t expect to think of this again.

This was very unclear to me. Why multiply the probability by x^1, x^2 etc.? What does that mean?

James's smile of certain extinction made my day.

Sir Lemon at the top of the family tree ... I see what you did there

"a family of 13 sons, all boys" really? All the sons are boys... man, i was confused before you pointed that out.

i've just studied Applied Statistics at college recently, and it was really nice seeing something i learned in this video (the expectancy of a variable according to the probabilities of the outcomes it can be). This is a random comment but it was just nice seeing something i learned actually used in real life haha

1:06 "...thirteen sons, all boys." what other sort of son is there?

What kind of maniac does not close an open parenthesis of an equation in a public video available on the internet...

Another video with James- this is better than Endgame!

Me: *cheats on exam Me: *fails Me: 2:21

Dang it Numberphile, I'd just watched your last video and was about ready to get back to work and now this...

I'm gonna roll that die to decide how many kids I'll have…

I was thinking on the first one how lucky he was that he didn't have to awkwardly draw the lines because of how close he made the dots, then the second set lost all hope.

Was about to write a smart comment about the dice with only ones on it and how it will never go extinct but he saw that one coming

I used the same dice to determine how many kids to have.

No comments before today? Was this video unlisted by mistake?

5:36 This is bringing me back to my biology test today(di-hybrid Punnit square)...

Please James, next time actually roll the die, not just only drip it. My inner nerd was slowly dying during the first segment of this video.

The dice with all sides of one gives the average roll of 1, but it also gives the formula g(x) = x^2. It crosses the x=y line at both 0,0 and 1,1.

13:45 I was thinking about that one THE WHOLE TIME

How can I send a request for a video? Is that even possible? I think I have a subject that might be interesting :)

Gotta love that galton-watson process

make a video on family trees and acyclic graphs

Why the two back-to-back videos about the maths of birth? Is Grime expecting?

3:42 that time lapse's audio is really scary

It's not only last names that die out. There's an amazing video out there charting and graphing the decline and fall of 'Bob's in competitive sports. In this case it's more a memetic decline than direct children.

For those interested, you can find out more by searching for “Galton-Watson Branching Processes”.

Cant you get extremely lucky and just roll 1s Infinitly many times even though your probability of doing it is extremely low

2 videos in one day?

THX Doc.

I thought you guys had run out of “butcher’s“ brown paper ;-)

Ive finally found what probability generating functions are used for

I just watched two or three minutes of the sofa moving problem because I hit the next button on this video without realizing it. I thought it was a flashback, and was wondering why it ran so long DX

'13 sons, all boys' What the?

While watching this whole video i was so excited that I found an exception to his rule, until the very end of the video where he said exactly what I was thinking. :(

How did the Victorians calculate the probabilities? How did they decide on the values for their dice?

Reminescent of a Leslie's Model and Leslie Matrix. I imediately remembered that it depends on one special value (this case average) for the Matrix that either drives the population to extincion or lets it survive.

Great video!

I played the dice game, and trust me, it is time consuming. Thank you Numberphile, for wasting my time preciously.

Woah we just had this in school, so this is the first video where i actually know what he will do

Two videos today and they're both related! They're also related to being related!

So in Spain we all have two family names. One from the father and from the mother...

A beaitoful lesson, everything in life is ruled by the mathematics ❤️.

I thought, well certainly I could continue to roll numbers, even if the average is 1 or below. But then I remember the infinite forest episode, and think about how it's impossible to get a perfect integer by rolls, because eventually, you'll stray off of 0. So the fact that the chance

During the entire video I was thinking the all 1s dice has average 1😅

(I am bad at Maths) Would it be correct to say you *always* have a chance of extinction (or will definitely go extinct sooner or later) so long as you have a chance to have 0 on at least one side of the die ?

Branching process yay!!!

8:07 As soon as I heard co-efficients I got flashbacks to my A levels and I could feel where this was going

At what level would a name need to be at to ensure dominance? Meaning how long would it take for every last name to become the same?

but how do i generate a probability distribution of a given family in the first place? do i generate it statistically based on the knowledge of my heretofore family tree, and if so -- how? also if so, what if my knowledge of the number of it's branches is incomplete for some of it's leaves, and what if i only know it back until a particular leaf and not all the way back to its root?

One question about the G(x) formula , how do we know to connect the x^3, x^2 , x to which number, how can we form a formula with probability like that, did the order of number / coefficient matter ?

OH NO. That's the probability of penultimate extinction! I really really hope he says those words in that order.

Generating functions of dice are fun. Maybe Numberphile could do a video on Sicherman dice. The Wikipedia proof using cyclotomic polynomials is dear to my heart (I wrote it).

This from the Department Of Redundancy Department (@ 1:00): "...a family of thirteen sons -- all boys"! ;^}

Ah, yes the noble Lemon family. Their parties are something to behold!

I won't say, that you calculated the average. You calculated the expected value It's just my addition to this great video. :)

Just learnt this from Stochastic Processes

Does this equation apply to Genghis Khan's descendants?

3 surnames in my family lines died out Bell, Fletcher & Chidley.

So...... how long is it going to be before Sharpie are official sponsors of the channel?

I thought you were going to talk about first names going extinct. Are there any maths on that subject?

That man can explain maths on a way that is a joy to learn maths! Só great that he makes new numberphiles again!!

so nobody's gonna mention Sir Lee Temple?

How do you get the prob. distribution, though?

Why does he always remembers me to Sheldon cooper

before he talked about the last case, all i can think was am I the last one from my family?