Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.
ฝัง
- เผยแพร่เมื่อ 27 ก.ย. 2024
- The Mathologer sets out to make sense of 1+2+3+ ... = -1/12 and some of those other notorious, crazy-looking infinite sum identities. The starting point for this video is the famous letter that led to the discovery of self-taught mathematical genius Srinivasa Ramanujan in 1913 (Ramanujan is the subject of the movie "The man who knew infinity" that just started showing in cinemas.) Find out about how these identities come up in Ramanujan's work, the role of "just do it" in math, the rules for adding infinite sums on Earth and other worlds, and what all this has to do with the mathematical super star the Riemann Zeta function.
You can download the jpeg of Ramanujan's letter to Hardy that I put together for this video here: www.qedcat.com/...
(quite large)
You can access a scanned copy of Ramanujan's notebook here: www.imsc.res.in...
or check this out
books.google.c...
If you want to watch some other videos that deal with these strange identities I recommend the following:
• Why -1/12 is a gold nu... (a Numberphile video featuring the mathematician Edward Frenkel who is also talking about the connection between the Riemann Zeta function and Ramanujan's crazy identity.)
• Ramanujan Summation (James Grime's video (singingbanana & Numberphile) which aims at making sense of the formula at the heart of Ramanujan summation which I only flash briefly in the last part of the video.)
• What does it feel like... (a very nice 3Blue1Brown video that makes sense of the identity 1+2+4+8+ ... = -1 in a way that is totally different from the one I am talking about in this video.)
This week’s video is in response to a large number of you and my students at university asking me for my take on the whole 1+2+3+... =-1/12 business. Initially, the plan was to come up with one of my usual 15 minute long videos. However, after several unsuccessful attempts at not exceeding the magic Mathologer time limit, I realised that any “short” video like this would just be a clone of one of those wrong/misleading accounts of this topic that TH-cam is full of. So, rather than just give up completely on this project I decided to do what you should never do if you actually want people to watch your videos, namely simply go for it and not look at the clock. The result - a video that is an insane 35 minutes long in which I say all the things that I think need to be said and can be said only using elementary math to (just barely) do this amazing topic justice.
Thank you very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.
Enjoy!
P.S.: If you know calculus and want to read up on all this some more, beyond what is readily available via the relevant Wiki pages and other internet resources, I recommend you read the last chapter of the book by Konrad Knopp, Theory and applications of infinite series, Dover books, 1990 (actually if you know German, read the extended version of this chapter in the original 1924 edition of the book). People usually recommend Hardy's book, Divergent series, but I'd say only look at this after you've looked at Knopp's book which I find a lot more accessible. The Hardy who wrote this book is the Hardy who I mention at the beginning of the video! Having said that, Hardy's book does have quite a bit of detail on how Ramanujan summation applies to the Zeta function; see chapters 13.10. and 13.17.
Imagine this;
A guy comes up to you and offers you $1 on day 1, $2 on day 2, $3 on day 3... all the way to $n on day n and he keeps doing this for the rest of eternity. You might think that he's giving you free money but a mathematician will quickly realize that he is trying to con you and steal a twelfth of a dollar.
But now you know.
+Tahmid Islam (Tanveer) Fine of $0.09Mathematician: That guy lost 2/3 of a cent because of this
+Tahmid Islam (Tanveer) That's just what Federal Reserve and other central banks do.
I know I'm 9 months late, but I wanted to let you know this is the best comment I've ever seen on youtube.
Tah mid Tanveer, But why only 1/12 and why not any other figure
Tahmid Tanveer nice comment
before i started watchibg mathologer i hate math and have bad grades
after i found this channel, i love math, and still bad grades
luv dis channel
hahahaha XDXD
LOL!
Lul
Adriann Coello ñhk )0
Nike Air
emejing
Every time I make a mistake on a maths paper, I'm going to hear that sound and be scolded and scared out of my skin by Ganesha descending from the ceiling.
Jumpscare
This comment made me jump out of my bed laughing😂😂. Truly insane😂😂
List of jumpscares:
4:02
9:28
11:53
22:50
30:12
31:57
34:14
PickyMcCritical 😂😂😂😂
PickyMcCritical You ignorant knob!!
PickyMcCritical terrifying
Lol
Thanks muck. This helped me prep.
It is like the software running the universe got overwhelmed and gave error - 1/12 Integer Overflow
Binayak Thakur I was thinking along similar lines when he had all powers of 2 summed up to -1
Actually probably the Universe spat out "Cannot compute! Error: 1/137 "
-1/12, my favourite integer
It's real number not integer
it is not error it is a smarter idea of an indian and i am proud to be an indian
A simple stack overflow bug. God will patch it in the next update.
Skylark Phoenix 😂😂😂😂
There is no bug under his rule my friend
'stack overflow'. EVERY PROGRAMMERS LOVE!!!!
Rohit Upadhyay but i see bugs everyday
@@wliaputs 🤣🤣
thanks to Ganesha I will never forget infinity can't be subtracted from itself.
Why u can't subtract infinity from infinity ? Becoz u can't think up to infinity? Or u can't make sense about infinity ? Or u want to just follow others' work?
@Sam please elaborate a little bit😀
@@gulshansharma2131 u can't subtract infinity from infinity , but u can subtract 2 numbers tending to infinity and get 0
@@rishisingh1035 we’re not talking about limits here ok?
@@beastgamer4932 then u cannot subtract infinity from infinity
man who knew infinity
now i understand why the title of his biography makes sense
Remember: Ganesha knows when you stop paying attention...
😂😂
Someone had to address the Elephant in the room 👍
@@danielharris9403 😂😂😂
No, it does not. Just stop lying.
@@IbrahimKhan-gv6cw we have a religious fanatic here
On a scale of 1 to -1/12, how would you rate this convergent series?
Kevbotomy infinity
XD
0
i
@@teamplayer2helper Lol amazing pun
When he pauses for Hardy and then said "He is not dummy either", lol
i havent watched the video yet, but thankyou for 3 reasons, 1. ramanujan 2. infinite sum of natural numbers 3. 30 minutes
+heyits- alex Well, if you like Ramanujan, I'll probably do at least two more videos this year featuring his math :)
+Mathologer yassss
+Appleguysfriend A video on Galois theory would be nice (probably a 60 minute one though :)
+Mathologer yes
+Mathologer yes
4:02 that scared the hell out of me lol
Same here xd
Ganesh is the remover of obstacles and the lord of knowledge and light-- so yeah, makes sense he would scare the literal hell out of you! lol
@@himanv the sound was scary
And he never answers the question posed.. what's the point of even showing it?
I'm watching at 3am 😂 and i almost died
who else was baffled by how breath-taking gorgeous that handwriting was?? jeez.
Happy Ganesh Chaturthi :)
Love and respect form India
@danny supersell Bruh
If this guy had been by math teacher is high school, I’d probably be a mathematician by now. Amazing what a good, passionate teacher can do for you.
😂 yeah a mathematician who's trying hard to find contradictions to proof that originally do not have any contradiction
he has been my teacher
I feel the same
@@jacksummer4041 isn't that what good mathematicians do
@@angelc9818 I've read someone commenting the same. Which school was it?
Oh my freaking goodness, I jumped right out of my seat with my headphones in at 4:00.
:)
Kai Widman
7
me too 😅
I jumped twice, second time at 9:29
great video but this fuckin elephant freaked me out
The elephant god of jump scares (aka. purple heart attack)
+marksmod Ganesh?
+McRaylie He means that every time that it appears the sound is VERY ANNOYING. I was using headphones when I was watching this video and it is a very unpleasant sound that makes you jump because it is unexpected and awkward.
+marksmod Ganesh is secretly trying to murder all the mathematicians.
hahahahaha all this comments have made me laugh so hard!!! hahahaha and yeah! freaking Ganesh! my heart almost stops >_
Be kind
Those interjections by Ganesha are terrifying
Jay shri Ganesh
"You are encapsulated by evil energies. Pray to Bhagwan Narsimha. Stay calm. Respect fellow people. Don't get into alcoholism.*
The loud noise of the elephant thing coming up scares the crap outta me every time xD
+André Reis Yes, me too.
+André Reis That's Ganesh (Hindu God) XD
Elephant thing is more accurate
lmao
+André Reis I may not agree with you, but I will defend to the death your right to make an ass of yourself
Srinavaasa Ramanujan said every equation was a prayer for him. Ever since I learned about him in my Calculus 2 class 30 years ago, he has been my Mathematics role model. He approximated the value of 1/Pi to a few decimal places using infinite series.
Srinavaasa Ramanujan gave our world his gift of genius and departed peacefully from this material world. It feels sad to loose men of great minds like him.
Although he was not a trained Mathematician, he was able to enlighten our world of Mathematics with his genius of Mathematical deductions and profound insights. I am impressed at how he caught the attention of Professor GH Hardy of Cambridge University by his(Ramanujan) letter of theorems on infinite series that diverge( 1+2+3+ ... = -1/12.
I think Ramanujan was quite aware of what his sum meant. He mentions it's the "center of balance" of the series. You can get the -1/12 value using the Euler-Maclaurin formula with an expansion around 1/n -> 0. This is a pretty novel way to interpret the value of the zeta function.
Anyway, about this confusing people in calculus, I think people learn much more math by analyzing where the -1/12 comes from than when they dismiss the formula.
well said
The problem is that people do not understand how limits work, often
Functions like F(x)= Sin(x)/x has a limit equal to 1 at x-->0, but the function itself does not exit at 0.
So you can pin a value to F(0), but this does not mean the function at that point actually exists.
Kind of a divide by zero accident
@@Entropy3ko people conveniently skip the word "approach" when studying limits and then complain when shit blows up
Interestingly, this video is the zeta function output of all the videos on TH-cam being added together.
rofl, I agree
Clever beaver.
Wicked
As in the case of quantum mechanics, I understand very little, but it’s enough to appreciate the beauty of it all. Amazing stuff.
One Word for Ramanujan, "Genius of Genuis", He is a idol of motivation for math students, #Respect
that is three words
@@robsonishere9062 lmao
This week’s video is in response to a large number of you and my students at university asking me for my take on the whole 1+2+3+... =-1/12 business. Initially, the plan was to come up with one of my usual 15 minute long videos. However, after several unsuccessful attempts at not exceeding the magic Mathologer time limit, I realised that any “short” video like this would just be a clone of one of those wrong/misleading accounts of this topic that TH-cam is full of. So, rather than just give up completely on this project I decided to do what you should never do if you actually want people to watch your videos, namely simply go for it and not look at the clock. The result - a video that is an insane 35 minutes long in which I say all the things that I think need to be said and can be said only using elementary math to (just barely) do this amazing topic justice.
I just finished watching this because I'm a time traveller. Great video!
Jesus, that Indian God works as almost a screamer
+Hououin Kyouma lol. me too. and nice name
+Matti Kauppinen Fill me in on the secret of time travelling sometime. Would make for a great video I am sure :)
great video ! the cesaro methode is cool :) But can we.. take the average of the average of the average... and so on to the infinite ?
Ramanujan was genuinely a masterpiece
Next time when you get wrong in ur maths question, remember to tell your teacher about maths in another world, your answer is definitely right in atleast one planet in the universe
If universe is infinite then your answer is right on the infinite amount of planets
1 = 2 is right in our planet.
Assume 1= 2
1/0=2/0
1×0=2×0
0=0
LHS and RHS are equal
Hence proved.
Infact any number is equal to any number.
@@shimpiyaa Adding one more proof
d/dx (X ^2) = d/dx(x) + d/dx(x) +d/dx(x) ... x times ....+d/dx(x)
2X= 1+1+...X times +1
2X=X
Dividing X both the sides
2=1
the teacher would be like : then go on dat planet
@@hamiltonianpathondodecahed5236 correct 😅😂😂😂😂
He does this to show off his t-shirt collection
There are easier ways to show off ones t-shirt collection :)
😂😂😂
😂😂😂
Lol
He is laughed at this comment because all his shirts are awesome and related to the videos usually lol
If given access to a time machine, my first stop would be to visit Hardy when he firsts open and reads that letter from Ramanujan. I can't even imagine what the next few hours and days of his life must have been like. He probably thought he was losing his mind.
Dustin Rodriguez nope he actually read it, showed it colleagues and set everything into motion Ramanujan got financial support and transport to England. Harvey was baffled someone with no formal training could deduce all that. but the content of the letter at best slightly surprised him. the shocker for Hardy was Ramanujans talent
I would have made certain Ramanujan's health would be okay. Then we could have enjoyed his brilliance so much more and witness more math miracles.
@Tangent of circle. Thanks for giving me the idea. 😉
I'll teach him a few things in exchange of being my mathematician.
Dustin Rodriguez: if given access to a time machine, your first stop would be the explosion when you turned it on. That’s what happens when a backward-going time machine occupies the same space-time as a forward-going one.
Certainly
Therefore, 1 > 1+2+3+4+5+...
You jerk! lol
and that's why 0 isn't a natural number :)
That's only using the Cesaro convergent, which deals with averages rather than sums. Such could make sense in the regular mathematical system of an alien planet, but we decided our system would be different. That doesn't stop mathematicians from find answers outside of our mathematical system though.
Unless I misunderstood, the Cesaro convergent only deals with the averages which are still positive, it's the analytic continuation of the Riemann function that gives the sum a negative value.
I find the use of word "alien" quite confusing. Isn't it just some sort of fun experiments with maths? Or do they describe actual physical realities in some way, that addition→finding converging point of average of partial sums would actually be useful in simplifying physical equations in certain cases? Please do tell me more. I would be really grateful.
The elephant god jumpscared me for many times...
his name is lord ganesha well dont say like he is bad i and many more than a billion people around the world worship him
+Firicious Gaming- Clash Royale and More i dont think everyone in india is a hindu
around 80 % are
***** well i said around the world just google it
Stimulus and response
*WARNING*: Ganesha will scare the shit out of you.
+Ramiro de Souza Every time.
+Ramiro de Souza yes he did -_-
This is much better than an intense film. That Elephant jump scares.. 😂
Hindu God Ganesh.
I never knew Ramanujan was SUCH A GENIUS !
Thanx to mathologer.
He actually could do much much more than this!
But don't read this comment any further or you will regret it.
Remember, I warned you. Stop reading this comment.
Really.
Ramanujan was such savage genius that he even caught in London Tbc instead of Covid.
@@u.v.s.5583 Exactly, the man who knew infinity catches TBC in the heart of the nation that looted and pillaged more than half the world and was still grappling with TBC!! So much for being a pomp regime. Such a shame!!
He actually wrote many formulas and assumptions in last year of his life. Researches are still going on. Many of his formulas are still used to find the black hole😲😲
Ramanujen once wrote just for fun
that the sum of the numbers from one
was not aleph naught
as we might have all thought
but one twelfth times negative one
This is the best math poem I have ever read. (Haven't read many, but I had a laugh.)
aleph null isnt the sum of all the natural number aleph null is the total number of natural number
@@gaymerjerry In cardinal arithmetic, the sum of all natural numbers is indeed aleph null. In ordinal arithmetic, it's omega, which is equal to aleph null in the most common formulation of set theory.
@@petrie911 i dont think you know what cardinal and ordinal means if you said that
cardinality literally mean sizeof or absolute value while ordinal means ordered lists
you can have -omega but -aleph null is nonsense
aleph null is the amount of counting numbers there are while omega is ordering them then adding another one at the end of the list (as adding another one at the beginning of the list still cant really make omega as ordinal infinity is communitive)
@@petrie911 and also its not called cardinal arithmetic "Cardinal numbers" are a generalization of the natural numbers to describe sets of infinite size in set theory thats it if you ever put on any math test that all natural numbers add to a cardinal number you will get 0 points because the act of adding number is ordinal numbers
if you were saying you can combine 2 sets to get a larger set you can do that to prove 2 * aleph null = aleph null
you have the set of {0,2,4,6,8,10,12,14,16,....} and {1,3,5,7,9,11,13,15,...} now according to standard axioms if a set is infinite but can still be made into an ordered list its size is aleph null set one is clearly listed where each term matched to 2x and set to each term matches to 2x+1 and the fact i could put a ... to imply more number further proves its an ordered list so combine these 2 sets of size aleph null creates {0,1,2,3,4,5,6.....} which is the natural numbers which is the set that aleph null is based on but can also map each term to x
so combining these 2 sets we show 2 * aleph null = 0
For anyone who wants to know what is the number shown in his shirt (from 16:53 to 26:09), its the expansion of *pi* in base 3 = 10.01021101222201.........
+Hari Prasad thanks XD
He showed that one in his video about hating pi (not pie) already.
That's base 4
stefstefstef6789 it should be base three, ...
Thank you. Got confused by that number
It's hard enough learning this, just imagine how hard it was to solve in the first place
the sound that plays when ganesh appears to say something keeps startling me
+slouch Yes, OP. Pls remove the horrible ding sound.
+slouch But it should! You should be scared when doing such an insanely wrong step in the Great Ganita*. The Elephant God is there to remind you of that.
(*Ganita = Sanskrit word for Mathematics)
roar falcon well that's not true
the mathematics of ancient india and hindu mythology is actually related to is science , it's just that theories aren't been explained and we are still unable to understand coz it's too fuckin advance for us . the verse of an ancient book contains the distance to sun which was later later found out by scientist .
Pranav Zarekar you are saying dumb shit here.
I get a shock each time the elephant god appears! You should have toned it down a bit
+MemberHomei One does not simply tone down a goddamn Elephant God :P
+Bon Bon Hahaha :P
+Bon Bon What about a bugbear? :D
StrategicGamesEtc What about him? The mead tasted good ;J
Bhaswar Roy Ki?
Jai shree Ganesha Cutest God 🙏😇
The God of Wisdom .
Jay shri Ganesh
@@KhvLeD yea what’s wrong with that? I’m an atheist but even I don’t think anything is wrong with believing in multiple gods lmao.
@Store Patternator 😂 lol we don't belive in man made religion like Islamism, Christianity ..
@Store Patternator nothing...just carry on with our respective lives 😂
I did the maths and came up with 42.
😐
EpicGuyRandom you don't get it.
+Dean Thorton no i do 😂 but that is the answer to everything ...
EpicGuyRandom lol, so silly
I did it and came up with 69.6969696969696969696969...
I'm a PhD student in Theoretical Physics and I found this video really helpful and entertaining, thank you so much! :)
Ramanujan was no doubt a god-send, whose mind formed in such a beautiful way that these came to him out of nowhere. It is spiritual, it came to him by itself, as if Universe conspired to make him aware of these nuances of maths in the Universe.
Mathematician Love poetry:
How do I love Thee
let me count the ways
-1/12 ways
It is actually nice to see a video that so elegantly shows the beauty of math, and in such a simple and fun way too, thank you very much
True knowledge comes from humblest of origin.....
Not necessarily.
@@rosaliacastro1551 necessarily
@@KodamatiUdayaPrabhuKiran not necessarily.
@@jovian304
I guess your name says you are dumb and arrogant
@@KodamatiUdayaPrabhuKiran Well I know meaning of ur name is sunshine. There's nothing wrong in having name as "sunshine". Just don't judge others.
I got scared every time Ganesha appeared with that scary sound.
abe mc ahir itna mat dar teri maa pujti hai unhe
Now I'm at home in the curfew I have never thought I would watch a math video and enjoy it like I have just done.
thank you, this is the most complete video about this subject that has been killing my mind for 2 years...
Thanks for an excellent presentation. A related area that I am reading about now is Borel-Laplace summation and transseries. It is amazing that Ramanujan uses grade school arithmetic to perform the difficult task to extend the Riemman zeta function in the complex plane to z= -1. Another approach for the early part of the video: f(x)=1/(1+x) = 1-x+x^2-x^3+..., take the derivative df(x)/dx= -1/(1+x)^2 = -1+2x-3x+4x..., and set x=1 so result is 1/4=1-2+3-4+...
I've just earned the mathologer seal of approval and I'm proud of it!
+denjam Cool, I really wonder how many people watching this video can say this of themselves :)
Complex analysis is funky.
The man was a genius (Ramanujan)
NILAVA DEBNATH genius
nope
@@iampol9957 Anybody that thinks that cows, particularly, are sacred has serious problems
@@TheChzoronzon and people that bring trees into their homes arent, weird people everywhere my guy. We all bleed red at the end of the day
@@shweatypalms4423 Yeah, hippies are the worst...Cartman for president! No, wait
Man, I was really following the video understanding everything, being convinced at the end of this I'd understand the Riemann Zeta function only for you to hit me with that 32:27 lmao
I think it is similar with defining sin(-30°). We cant see an angle like -30° in triangle, but we use it because it is useful and continuous. I think 1+2+3... is similar with my example. We think it diverges, but if we define sum of series in other way, it is -1/12 and it is continous and useful.
Ramanujan as one of the greatest mathematicians of all time.
The sheer genius of Ramanujan in number theory always fascinated. The great man often ignored proofs for many of the derivations. It’s like this; a genius looks at a problem, the path looks obvious, so he skips the steps, reaches the solution, but the mathematicians are still pondering on the left conjectures.(like the professor above) So yes Ramanujan also did interesting mathematics in the field of infinite summation
Amazing!!! Our sum is negative! It looks like god plays with numbers in a bizarre way. This shocking result is not known to many non-mathematicians. Number-theorists call it “One of the most remarkable formulae in science”. This summation is a secret of mathematics kept away from layman. Further, it is interesting to know ‘S’=-1/12 has been used to derive the equations in “string theory”, quantum field theory and in some complex analytics.
So now you know sum of positives can be negative. We knew much less during schooling about summation of numbers. The result teaches how universe can be more complicated than we think and how we need to keep an open mind to learn more.
And everything is correct in the real world. But some people will never get it like the professor here
Must read-- “The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?” by Mark Dodds link.medium.com/bK8txtm760
Professional mathematicians certainly make mistakes and fool themselves, but this was never the case here. Neither Hardy, nor Littlewood, nor Ramanjuan ever thought that they “proved” that the natural numbers add up to a negative magnitude.
As a student only in pre-calc, i genuinely look forward to working with numbers such as these someday.
On a side note i watched the whole video and everything made perfect sense, thanks for making it so clear.
+whatby101 Mathematics is a very interesting field and its amazing that people can be so intrigued by it no matter their education!
I struggled to love maths for awhile now but I like to think I see the inherent beauty in it now.
Before he announced it but showed us the complex realm, I was freaking out because it dawned on me that he was about to mention the Riemann-Zeta function which in itself I tried to understand awhile back and walked away agreeing to disagree with the maths..hah
+Password1andUsername That's not really an option for me. Even if I myself am capable of just skipping calculus, I am only in high school. Ap Calc is the highest level class they offer. I will take that junior year, then the following year I plan to take 3 different science classes and take a class on statistics.
Sadly in any public school, there are not enough mathematically gifted students for there to be an even higher level course. At best I can take a summer class at a college either this or next year.
This happened to me as well I took AP calc this past year as a junior, and I am not without a math class. To fix this problem I made a deal with a college nearby, and now I am able to take further math classes there. I don't know if that is a possibility for you, but it was the only way for me, for my school only offers two AP classes that I haven't yet taken. Hope you are able to take more maths instead of having a gap year.
I have an option for you. Hang out with us on math.stackexchange.com We have tons of smart people, and we're always willing to explain super weird topics (plus we can help with calc if you need.)
Ganesha appearing with the horror sound is basicaly a jumpscare
I like your videos! Several times I've had a technical comment that you specifically addressed at some point later in your video. I'm reviewing topics that I already know. Your explanations are pretty good! I also appreciate that your animations are simple and enough.
Mathematics are similar to these granular tests we do at engineering university. Out of a boring standard soil, you’ll always all sorts of gems at every filtering layer…
From the natural numbers to Ramnujan summations, through fractions, irrational numbers and the complex domain, a wonderful world of discovery!
4:23 blew my mind, the way that man' mind must of worked. How he approched math, crazy. Talk about thinking outside the box.
Of course, green aliens have three fingers, that's why they use base 3 ;)
+pierineri Exactly :)
is this true ?
...
There are several articles on the web explaining this trick. Scientific American (for example) noted the intellectual dishonesty of redefining terms without telling the reader. But the best (and funniest!) explanation is at Physics Buzz blog. it clearly shows that "-1/12" is an area obtained by graphing the integration of x(1+x) / 2. (This is the formula alluded to by SR)
Raising x to a power (in the formula) gives various answers but what's interesting is that x to the 13th gives...-1/12 - the same as x to the 1. LOL
LoL I tried praying Lord Ganesha and I found myself more concentrated with some inner voice. Will love to do maths with Lord Ganesha in future :::))) My extraordinary wisdom source.
It's amazing how complex analysis pops in...Really cool video. I enjoyed the visualizations, but the elephant God was a bit scary..
+ΣΚΡΟΥΤΖ ΜΑΚ ΝΤΑΚ He came out of nowhere, I am going to have nightmares for weeks
+Ace shinigami lolxd
I guess it's more the sudden noise that accompanies him
The Ganesha entry sound FX is dramatic and scary. I kept spilling my beer every time it chimed.
+Selenium Glow Hehe, so my friend the elephant did succeed in getting peoples' attention :) But seriously, just a bit of an oversight during editing the video to not also limit the peaks of this entry sound just like the rest of the audio.
This video took me on an interesting tour: up the insane-o-meter to the fourth degree, down to the first again, and at the same time up to the fourth level of maths enlightenment. Thank you Burkard & Ganesha
Ramanujan was God Gifted
All I know as a programmer, is that if you keep adding up positives and get a negative result, you probably had an overflow. We can fix that by putting more bits into our sum accumulator. Unfortunately, if we're adding up an infinite amount of positives, there aren't enough resources in the universe to make the variable big enough to hold the result, hence it will always overflow. It's all clear now! yay me! ;-)
You could just define 1 + 2 + 3 + 4... as -1/12, just like how pi and e are usually defined in programs instead of calculated.
Alessandro Ghignola Grats you broke the code!
But I don't think overflow applies here, ramanujam is just performing simple arithmetic operations on the whole infinite series, not adding it integer by integer as a program would.
I m.studying computer science engineering but all i get to learn at my college is total shit help me..i want to learn cse
Alessandro Ghignola it’s not just negative, it’s also a fraction. So you’d never get a fraction from adding integers. Even with overflows. This has nothing to do with overflows.
Enjoy your channel. I'm sorry to point out that your elephant sound byte scares me.
You should go over his theory on how to calculate the number of primes within a given integer, this is what really impressed Hardy.
Numbers and math are human inventions and are not absolute in any sense of the word. Mathematicians and magicians have a lot in common. Circular reasoning and deflection can explain almost any non-conforming result. Once you have to begin "manipulations" to force an answer it becomes problematic. Much of Ramanugan's work was approximately correct in the same way the 22/7 is approximately Pi. In many cases math works, in many it doesn't and is broken. My issue has always been the series of bandages can become so prevalent the original patient is no longer recognizable. Humans have the unique ability and flaw to somehow believe they can discover the truth in all things. Truth is an illusive and dangerous creature - just like math. Truth is what man wants it to be, not always what it is. As always a great presentation. Thanks for sharing.
christ sake the elephant keeps giving me a heart attack everytime he appears
+dance1211 Well, it's a long video, so I thought I better have a wakeup call every once in a while :)
+Mathologer
Please, no more. I'm afraid of it popping up. :(
I felt a cold shiver through my body into my feet when it first came up.
+Mathologer It's actually taking me a lot longer to finish the video because I have to take a break to calm myself down every time the elephant shows up, and it's kind of hard to focus because I'm too scared of when the next one will pop up...
It's also surprisingly hilarious in a twisted way XD !
+dance1211 agree. @Mathologer: the elephant "boom" noise is way too loud. Thanks for the video though, awesome content as usual.
4:02, I never thought I would ever be jump scared on a math video
this is awesome i did not mind the length one bit because it was all relevant and interesting and developed very well
+Kyle Serrecchia That's great, quite a common response which means that I'll probably do more videos like this in the future :)
2:43 the most telling and interesting of this entire segment👀! Insight into Ramanujan himself (see graphology) ✍
those elephants that pop up scare the crap out of me!
I say it's funny
onresonance Why? Seems an odd reaction to me
Our Indian culture. 😂😂😂
Perhaps this is the best presentation I ever have seen on Math or Science. Awesome!!
Those loud bangs when a footnote appears are terrifying when you wear headphones.
Ganesh scared the crap out of me at 4:02
Virtuoso80 lmao
Yeah, totally not thought through.
Thanks for this video - there aren't many other videos about explaining analytic continuation or what these divergent sums really mean, and you "summed" it all up really succinctly. Another very interesting place that these sums pop up are in real life - calculations in string theory and of the casamir effect seem to suggest that certain values are actually equal to divergent series like 1^3+2^3+3^3+..., and interestingly enough experiments to determine these values seem to agree with the value of the series when defined by the function's analytic continuation at that point. Spooky!
+Hwd405 Actually this is something else I'd really like to do, explain how exactly the Casimir effect can be calculated using 1^3+2^3+3^3+... . The usual "just do it" physics explanations are nice but in the end just don't do it for me :)
Congratulations!! Your attempt at this is indeed very successful. Many many thanks for this explanation both here and other planets!! We know our maths is just an approximation as we are not perfect. If we get enlightened, we will see things very clearly. This is the inspiration to lead the kindly light.
S. Ramanujan did this without any college degree without any internet under extreme poverty under Britisher.
Well these things were coming to him, what comes to me is mosquitos
😭😭😭
+Mathologer 1+2+3+... = -1/12 is not a normal summation, so therefore different symbol must be used instead of '+'. Mathematics is about rigor and this ambiguity must be rectified.
110% Agreed... all this conjecture on Infinity paradoxes are not "summations" of these sequences but "assumptions" made about them... yes they never "end" but they do have a beginning... "substituting & shifting" these different infinity sequences will give rise to these imaginary values bc yes they may all end in a paradox of Infinity but they all start with different values... these are "summations" of what can be observed in the beginning but by NO Means is this a "Summation" bc the sequences never end!
+Henry Clarite its like saying that infinity begins somewhere but has no end, right? . How can
it begin somewhere? If you look at it from the other side it begins
nowhere and ends somewhere, that makes no sense.
Infinite has no beginning and no end
+Jimmy Diaz Infinity in the context of infinite series means an endless series. The series goes on ad infinitum. But it certainly has a beginning as there is one term which is not preceded by any. And that is
the first term.
+Jimmy Diaz It's almost as if the ∞ for infinity explains infinity..the no beginning and no end paradox is like a mobius strip that has 'two sides' but 1 surface (something else that is a closed loop with no beginning and no end)
Thank you for this, you just showed me that math can be more beautiful than I ever thought.
He showed this in other videos. This isn't the first one
Props to anybody who can understand this type of math , as for myself, I have no idea what’s going on but I watched the whole video,
Absolutely mind boggling
After you thoroughly explained it. I have come to the conclusion that my hatred of math is fully justified.
Thank you for making these really high quality mathematical videos
The real beauty of math is when you reach a dead end when trying to find a proof, you can often solve it by applying a seemingly unrelated field.
the elephant god gives me heart attack
+oldcowbb I was watching youtube before sleep here, and then that goddamn elephant kept showing up with perfect unexpected timing.
Needless to say, I'm gonna be tired tomorrow... :(
+oldcowbb Looks like you won't forget this video then. I'd say mission accomplished :)
I saw the Ramanujan sum mentioned in a talk on quantum field theory.
Goal of Man is to make sense where there is not sense ...Well done !!!
I think you should give a image of NAMAGIRI the Hindu goddess on whom "Ramanujam" ( actual name not Ramanujan) had faith.
@Adarsh Jha it is.. She is a feminazzi.. Who just wants credits for no reason..
Correct
He had faith over all Hindu Gods
In Hinduism you can worship any god but that doesnot mean people who worship Devi dont have faith in Ganesha
Ganesha is known as obstacle remover
Right? Its so poor research, he actually credits Goddress Namagiri for revelations. How easy would that have been to quote.
Ramanujan had Vedic mathematics education, Many Gurukul students still get ancient Indian Vedic mathematics education and they can do wonders, Aryabhatta, Brahmgupta etc have studied the Vedic mathematics, It works on a completely different level, even Prof. CK Raju has researched on this topic!
"This is insane yes, but remember that this guy is a genius."
My teacher says the following: since the result is negative it's a contribution and it's infinitely large
-1/12 is closely related to string theory. Strings are basic elements of particles like electrons , protons and neutrons
Haha.
The first sentence is true, unlike the second.
The level 4 requires a minimum knowkedge of anaylitic functions and its very nice properties. The video is very interesting. Many thanks.
I get so focused on the math he's doing and then all of a sudden a jumpscare pops up and I have mini heart attack