A Video about the Number 10 - Numberphile
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- Опубліковано 30 вер 2024
- Featuring the friendless number 10 for our 10-year anniversary... James Grime is back where it all began.
More links & stuff in full description below ↓↓↓
James is at The City Ground - see the original 11.11.11 video at:
• 11.11.11 - Numberphile
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Congrats on 10 years! I thought the setting looked familiar and I had to double check the publication date to make sure it wasn't a super old video.
Me too lol
10 years club!
I guess Veritasium had to *verify* the date of uploading for this Numberphile vid. Pun intended.
Hi!
@@ivanv754 Hey. :) I know you were saying "hi" to Veritasium, but I am a nice guy. I hope you are having a great day
And they made the video 10 minutes and 10 seconds long? Truly satisfying 😭😭😭
Yeah
But not on 10/10
@@max3d_0ut it wouldn’t make much sense to do it on 10/10/21 :/
@@max3d_0ut seriously, amd it still would've counted their 10th anniversary
its 10 min's 9 seconds
James hasn't changed in 10 years, he's immortal
James hasn't changed since the 1960's when he starred in dozens of films using his stage name Kenneth Williams.
@@Galenus1234
Yet he claims to have been born in 1980.
@@ragnkja he's fooling no one
I liked him in the Bilbo movies and when he played Doctor Watson.
I think he's a vampire. Has been walking on earth for centuries with different names. I have damning proof but can't talk about it further here due to concerns about my safety.
Can't believe it's been 10 years of numberphile, remembered the early days of numberphile and recognised the place immediately, what a journey this channel has gone through with the iconic brown paper
Unrelated, but a math opinion: Why do we use 10 in our counting system? Yes, I know we have 10 fingers, but not counting our thumbs, each hand has 12 phalanxes (segments). Plus, 12 is highly divisible.
@@thatguyalex2835 Long story short: just cuz it stuck. I agree base-12 would be better, but since pretty much all of modern math is written in base 10, it would be practically impossible to switch, and base-10 happened to be the base we stuck with. we just as well could have gotten stuck with the sumerians base-60, or roman numerals
Anniversary of the channel⭐
@@thatguyalex2835 Because we love 2 and 5
@@ERROR-ei5yv I understand now, and thanks bro/broette. It is kinda the same reason why we still use imperial units in the US, cos it stuck. :) I do hope that we at least switch to metric (which ironically is base-10). Lol...
Wow I can’t believe it’s been 10 years!!! Thank you for all the videos throughout these years!
Yea
Somehow I am the first reply
bprp!
blackpenredpen great to see you! You were a great help in my Calculus 2 class :) -- keep up the great videos sir!
I love your videos too brother!
??
Great, all the perfect numbers are friends with each other. Highschool all over again.
Except for that perfect 10 who everyone assumed had lots of friends but may in fact have none...
In high school, I was always one of the numbers for which it's unknown whether or not they have friends.
false.
I love how James Grime calls back to the numberphile classics... all of them featuring him
*Grime
@@ragnkja my mistake, corrected, thanks
@Wotzinator
It was the common one, adding an “s” at the end of “Grime”.
It's like a montage showing his origin story.
Reminds me of Scott Grimes, the voice of Robin in Teen Titans, Marlton in BO2 Zombies, and Steve from American Dad.
this man hasn't aged a day in the last ten years
He has a painted-by-numbers portrait at home which ages for him.
@@juandesalgado Dorian Grime
@@rarebeeph1783 from "the picture of dorian gray~Oscar Wilde "
He's a true highlander: doesn't age and there can only be one James :-)
@@juandesalgado smart comments enabled :-)
Oh. So Numberphile started on the same day as Skyrim was released? Fascinating 😃
A day that truly changed history
11/11/11.
Which provides some context to the topic of their 1st video...
No, Skyrim released on the same day as Numberphile started... Bethesda tried to surf in the spotlight there!
When is Numberphile releasing a fishing dlc? I'm dying to fish with maths
Now I feel old.
"Let's talk about the number 10."
Proceeds not mention the number 10 for 90% of the video.
So you're saying it was mentioned for *10%* of the video..?
I really do appreciate that both of your comments have exactly 10 likes, the universe is pleased
@@9989126 He first mentions 10 at 9:16, so it was mentioned for 8.9% of the video. Close enough lol
@@shehannanayakkara4162 indians always try to be oversmart and boast thier maths.
@@romekhanna you can just plug it into a calculator lol
The channel that inspired me to take up a major in math.Congrats on the milestone,keep inspiring!
10 years??
I've actually seen every numberphile video and came here from singing banana when James advertised a "new maths based channel" about numbers.
I love all the new content but the videos on numbers also bring back nostalgia
Me too!!
It was a fine treat, indeed!
I think I got here because there were videos I had to watch for math class a couple years ago and the algorithm suggested Numberphile videos to me.
The last ten years have been so much better than they might otherwise have been thanks to Numberphile. Thanks :D
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If I may add, the average abundancy index AI (only referred to as index in this video) is π²/6.
Note how the abundancy index is a multiplicative function if the factors are relatively prime (just like the sigma function). So €(210)=€(10)*€(21)=18/10*32/21=576/210=96/35.
Also we may instead group them not as friends but into abundancy index groups. If we call the abundancy index σ(n)/n=€(n) where each integers fall into a group based on floor(e^€(n)).
Also since π²/6 is irrational and all abundancy index are rational numbers, there cannot exist an integer that has an abundancy index that is equal to the mean of all abundancy indexes π²/6.
huh?
@@batya7 😂
@@batya7 whatever it is it seems to be priced in Euros
OK that's a little startling. The average abundancy index is the same as the sum of the reciprocal squares, π²/6 = 1/1² + 1/2² + 1/3² + ... Coincidence?
Man you made it not fun.
The clip of James saying “awww friends” is now looking rent-free in my mind
A cheeky little "Inbetweeners" reference I think.
@@HermanVonPetri football friend! 👍👍
what is it looking at?
Thumbs up fwiend
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It’s Numberphile’s tenth anniversary, this video is about the number 10, and the length of the video is 10:10 👀
I saw! Its nice
@@zoisitemapping Perfection.
10 years anniversary can‘t be right. He doesn‘t look a day older than then.
ikr
They recorded this video the same day as the 11 video thinking of their 10 year anniversary.
I think you're connect, Manuel
10 years and yet James didn't age a single day.
He's even wearing the same coat!
Plot twist, they filmed it on the same day and didn't release it until ten years later!
Damn. I instantly recognised the film location. Nostalgic!
truly the greatest stadium ever
Happy anniversary, glad to have followed you for about half of it!
This made me feel so old, but it warmed my heart too. 10 may not have friends, but Numberphile has definitely made a lot of friends in these 10 years.
Very nicely put :-)
Okay how does James Grime literally look the same as he was 10 YEARS AGO???!!!
Numberphile is the last place where I expected an Inbetweeners reference
i didnt catch it. what was it?
Friend!
Football friend!
@@debblez 2:50
The length of the video is neat, but can we also get some love for the upload date (11/11) and the fact the first Numberphile video was about 11?
The first video was released on 11/11/11 in fact
It's because it's been ten years to the day since that video (released on 11/11/11).
@Evan Dedels
That’s because it’s also the anniversary of Armistice Day at the end of WW1.
Here's another way to count the index that I found myself but I think someone must have found it before: for each prime factor p raised to the power a, compute (p**(a+1)-1)/((p-1)*p**a) (this expression can also be written as (p**a*p-1)/(p**a*(p-1))) and multiply the results together. It shows that the index of the product of coprime numbers is the product of their indices
what is the limit of this factor as p grows to infinity?
1?
@@NoNameAtAll2 It's 1
Love The Inbetweeners reference. "Oh, friend..."
Do you think that was intentional?
1:45 Small error: you included 5 as a factor in the number 12
The sum was correct though.
Can’t wait until next year when it’s the 11th anniversary on the 11th of the 11th month with an 11:11 minute video coming out at 11:11am
A decade of numberphile videos!
HAPPY BIRTHDAY NUMBERPHILE!
*looks at video length*
I see what you did there, Numberphile, I see what you did there.
*slow clap*
Congratulations, Numberphile! I can’t believe it’s been 10 years! Who knew this channel would be as big as it is all those years ago? Here’s to 10 more!
8:03 "and that's been proven by hand". I first thought that's a mathematician whose surname is "Hand".
Before I clicked the video, I told myself that I'd be sad if it wasn't exactly 10 minutes long. However, I was still pleased with the 10:10.
Constant upload with Dr. James Grime is the best we could ask for this tremendous achievement of passing 10 years
Cannot believe it's been close to this long. Numberphile has certainly had an enormous impact on my interest in mathematics and my intellectual development in general.
Love your stuff
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Congrats! Seriously, I've been watching from the beginning, since I was 12. I recognized the location of this video immediately from your first video on 11. Now I've just finished my bachelor's in math and I'm moving onto a PhD in computer science. Thanks so much for all the videos, Brady!
Are there any friendly numbers that have an index less than 2, ie is there any significance to 10 having an index less than 2 (ie less than a perfect number)?
my thoughts exactly and being less than two give an unique fraction and are there odd numbers that are frendly
Numbers with index less than 2 are called "deficient" numbers. The first few are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21...
The smallest known deficient friendly numbers are 135 and 273, with indices 144/135=16/15 and 297/273=99/91. OEIS only lists known friendly numbers up to 372, so I couldn't find more than that easily. Given that some of the numbers which we don't know if they're friendly are also deficient (like 10), 135 may not actually be the smallest deficient friendly number.
Omg it’s the 10th anniversary of Skyri- I mean numberphile!
The fact that those first videos still have the great quality is worth of an applause👏👏👏👏
Happy birthday Numberphile 🎉🎉🎉🎉
I really want to discuss the number 9. I can't find much discussion on UA-cam. Is there a way of emailing you? Cheers
It would be interesting to see the difference in the equipment used on 11/11/11 and 10/10/21!
Also, is it possible for Dr. G to talk without smiling? 🙂
"is it possible for Dr. G to talk without smiling?"
Why would you ever want to find that out?
I love the 'Hi-tech' writing surface! The sign of a true mathematician: use any and every surface available!
Congratulations on 10 years! It's been a wonderful journey, thank you for sharing with all of us! ♡
What's the smallest known index with a friend and what's the largest known index without a friend?
I'm watching this video which was uploaded 10 minutes ago. So satisfying.
Happy anniversary guys! What an amazing channel making math super fun and exciting!
Wow, a video about the number 10 on Numberphile's 10th anniversary that is 10 minutes and 10 seconds long, and I'm the 10010th viewer. What an honor!
Even similar clothes!
10 years of epic videos from Numberphile!
Thank you for your contributions and keep up the great work.
I randomly came across this channel on youtube as a 12 year old. 8 years later, I am hooked to all things maths, science and computing. I am currently majoring in CS. All because of you guys and other edutainment channels on youtube. Didnt realise its been so long. I hope you guys realise the amount of positive impact you have had on the lives of so many people.
Love from India.
Great material! Enjoyed watching another 'classic' video on Numberphile.
One note:
9:07 Shouldn't there be 'reducible' instead of 'not reducible', when numbers in violet are described?
yes i just wanted to point this out :)
Now I got a question, is there a number with a factor index larger than 3?
JAMES GRIME BACK AGAIN AGAIN! WOOOOOOOOO
One of the things I like about this bit of maths is that it has no dependency on a specific base system to work. It's about the raw numbers (their values) not the numerals (the system used to represent them). 10 truly is special in this case purely on the basis of its factors, and not just because we primarily use a base 10 number system.
Are there any numbers who are like, "with friends like these, who needs enemies?"
no. there is none of these. goodbye
index(9000000100 + 10) = 1.800000002, that's as close a friend for 10 as i have found!
I'm so glad this video is 10 minutes and 10 seconds long
On these ten years of Numberphile, I've only been on this journey for the last four or five years, but I hope see where this channel goes over at least another decade to come as I've very much enjoyed the ride so far!!
As for the last decade of Numberphile, we've seen Matt Parker lose all of his hair, while vampiric James appears not to have aged one bit. The former had a not-so-magic magic square named after him and has published at least one mathematics-themed book -- as quite a few other Numberphile contributors have as well (Simon Singh, Alex Bellos, and I believe Hannah Fry also to name just a few)
I can't believe how nostalgic this made me feel. I.e. especially since i was in my twenties when i found Numberphile.
I am 10's friend, he's an amazing person
This youtube channel shares its anniversary with Skyrim? They occupy two completely different timeframes in my mind, but I suppose it makes sense.
Gosh, same for me! 😂 what a coincidence.
now I'm curious about these indexes
what's the number with the highest known index? does the index trend higher over time, or is it random, or does it stay around an average value? if you keep taking the prime multiples, do they trend towards a particular index?
So nice to have James do this video
10 arbitrarily gets too much attention resulting from the popularity of base 10 with humanity. If we used another base, 10 would be a lot less popular. This notion of 10’s importance is based on misleading arbitrary significance. Thanks for this video, it is nice to see a property for 10 behind not dependent on base 10.
10 in other bases:
10 one’s: 1111111111
Base 2: 1010
Base 3: 101
Base 4: 22
Base 5: 15
Base 6: 14
Base 7: 13
Base 8: 12
Base 9: 11
Base 12: X
Base 16: A
Lol.
The video 10:10 long
Next year
11 years after 11-11-11 recorded at row 11 seat 11
In 11 minutes and 11 seconds?
IN THE SAME DAY OF THE WEEK AS 11 11 11 VIDEO RELEASED??
Videos with James are always a joy to watch! 😃
For one second I thought it was an old unlisted video!
Numberphile was born on Skyrim's release date 🙂
"I used to be an adventurer like you, then I took an arrow in the knee. Now I watch Numberphile videos instead."
10 almost has a friend at 97828, index is only off by 0.00001635523571974495, a Parker Friend perhaps?
Thanks for all the hard work and fantastic video’s these past 10 years!❤️
I also noticed the powers of 2 are all solitary.
Which I suppose makes sense because the index will always be of the form (2x-1)/x for any x that is a power of 2, which would always be non-reducible.
You and Skyrim share the same 10th anniversary!
I'm gonna predict, they also will share their 20th.
Nice to go back to the original Numberphile videos of discussing numbers as topics, and obviously 10 is the only number we should talk about in a 10th anniversary. Here's to a video about the number 20 in the future!
Also on the 10th anniversary of Skyrim! Math and TES, definitely two of my favourite passions ❤️ Thanks so much Numberphile for being an incredible source of knowledge, while always staying fun!
I recognized the stadium instantly :) I was there when the first Numberphile video was uploaded. Doesn't seem that long ago.
Just watched #1 and here are my conclusions:
- Arithmetics are still true
- James didn’t aged
- CD-ROMs are artefacts
9:10 typo on screen, the purple numbers should be labeled "Solitary index but reducible" not "not reducible".
who is part of the 301+ club
I think it’s been long enough now that you can ask who _remembers_ that. The only video left stuck on 301 views now is the Numberphile video explaining it :)
@@ragnkja i know, i was just mocking the people from 2015 when the comments were filled with "WHO IS PART OF THE 301 CLUB LIKE THIS COMMENT"
@@NewtonPL
“Under 301 views” was the exclusive club ;)
During the brunt of the pandemic I watch EVERY numberphile episode. A great 10 years of content 👌
Right now my phone's battery is 10 and it's 10:10 pm here and now I feel like I found a glitch in the matrix
I guess this means Numberphile started on 11/11/11. I never noticed that. Happy birthday!
Incidentally, my favourite colour is green; and I’m solitary, a loner, by nature; so, I would be a solitary number.
Other interesting question: Is every rational number greater than 1 (maybe up to some upper bound) the index of a number?
When I saw the title I immediately thought this must be James Grime. I wish I could predict lottery numbers with half this accuracy.
Video about 10 which is 10 minutes and 10 seconds long, posted at 10th aniversary 10 days ago, can it be better?!
If every positive integer was one of Ramanujan's personal friends, doesn't that prove that 10 in fact does have a friend?
It’s ten days since the channel anniversary, and I’m proud to announce that the next person to click this video makes the view count a multiple of then, and for me, the view count in thousands is a multiple of ten.
* a python code for friendly numbers
import sys
def index_of(num):
sum = 0
for i in range(1, num+1):
if num%i == 0:
sum += i
return sum/num
def friend(num_index):
for i in range(1, sys.maxsize):
if index_of(i) == num_index and i != num:
return i
num = 24
print(friend(index_of(num)))
But how do you prove a solitary number is solitary? There's frequent mention of solitary numbers being "checked by hand", but what does that entail?
"They are friends. Oh friends..." Oh Danish friends!
Happy 10th anniversary!
I can't believe it's been less than 3 years since this anniversary video, or that it was during COVID… It feels like eons ago…
So basically, if you're odd, you have no friends. Psh - knew that one already.
Just interested, what font are you using for displaying text in the (newer) videos? Like at 1:50
faster way to add the factors of a number : if a number, n = a^m * b^n * c^d then the sum of the factors is ( 1 + a + a^2 + a^3 + ...... + a^m ) * ( 1 + b + b^2 + .... + b^n ) * ( 1 + c + .......+ c^d ) = ?
so for 18 =2*3^2
sum of factors of 18 : ( 1 + 2 ) * ( 1 + 3+ 3^2 ) = 3 * 13 = 39
It's great attention to detail that they made the video 10 minutes and 10 seconds long.
I got the video recommendation 10 days after it was released? Coincidence? I think so.
Gandalf eyes Doctor Grimes suspiciously.
"...You haven't aged a day..."
*Grime, it’s just one of him ;)
10 days after the 10th year anniversary of the channel watching a video about the number 10.
On the 10th anniversary of Numberphile, James Grime (that's 10 letters) talks about the number 10 in a video which lasts 10 minutes and 10 seconds.
1:49 Didnt know 5 is a factor of 12
9:05 shouldn't the violet text say: "solitary: index reducible" ?