Ramanujan: Knowing The Man Who Knew Infinity
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- Опубликовано: 5 окт 2024
- The first video in a series about Ramanujan. A bit of biography then a look at one of Ramanujan's formulas. This one involves infinite nested radicals.
Here's a more formal look at Ramanujan's nested radical ac.els-cdn.com/...
The proof is quite hard without observation.
(Let me know if the link doesn't work.) [14-10-2020 THE LINK CURRENTLY DOESN'T WORK, I'LL TRY AND FIND A LINK THAT DOES]
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This should be an infinite series.
Yes. This.
azaroma: Vol. 00*-1 is anticlimactic.
;^}
(*my best keyboard approximation of infinity)
Let's see if we can get -1/12
saw you first on Numberphile and didn't know you had your own channel Mr. singingbanana. glad I found it
Hello
Dr.*
@@thesuomi8550 Jr.*
I am very exited to watch this Mr Banana.
+Commandelicious it's dr. banana
Oh snap :D
+Commandelicious I think his interest in the anticlimactic might have also helped choosing this name. As a last name that is.
You didn't say "and if you have been, thanks for watching" so now this feeling of incompleteness I'm having is going to follow me all day.
"... and if you have been, thanks for watching."
...I know, it's not the same...
When he does that, I go watch a different video that does, so it feels complete.
I love two extraordinary people and these two are Srinivas Ramanujan and Nikola Tesla . 🙌
Ramanujan had to give the answer... wow he was head and shoulders above his peers.
I think I'm obsessed with Ramanujan thanks to all these videos.
omg yes! I love Ramanujan!! He's so cool! And so fascinating!!!
Spatial and Temporal intuition are Kantian qualities of mind. Ramanajuan's intuition is of the temporal type. That type of intuition is about the Selection and Order of (mathematical) objects - essentially, creating sets. Spatial intuition is what we commonly measure on IQ tests. In particularly complex problems, temporal intuition precedes spatial, and it is what allows us to associate distant objects with ease, while spatial thinking which follows, deduces (or induces an operator), between each object of the created set.
It's kinda funny to watch this with the automatic captions on, to see how youtube understands the word "Ramanujan". Some interpretation are:
- nomination
- brand new jeans
- religion
- rare in new version
- revolution
(Cool video by the way!)
1:24 I saw what you did there.
yup :)
+great one yap!
+great one 1729
one hell of a parker square
This should get 1729 likes
ramanujan was a genius but he was very unfortunate and he did face a lot of discrimination and racism...
He understood a lot of things we still haven't understood...
This makes me sad cuz i couldn't help him.. I'm too late ..
Wish i could go back in time and help him ..He was a vegetarian and malnourished cuz he didn't get vegetarian food 😳.. i would've cooked him food even though i don't know how to cook..
On a whim, I went to see this film today, partially because of your videos. Turned out that I managed to snag tickets for a q&a session with the director, and the book's author. Maths nerd squeee!
I really wish this movie was playing anywhere near me in America. I saw ads for it in the UK when I was there a few weeks ago, and seeing you and Matt's videos about it I'm really wishing I could see this movie.
"Until [next time], I'll see you next time."
Unless you mean next time is the last time you'll see us, this is a paradox.
+Brian Schiefen he said Until then. Technically he could upload a different video between now and then, and we'd see him "Next Time."
how did i just discover this channel. so fire
I think you were my Stats 2 problem class teaching assistant at York (and maybe for other classes too but I don't quite recall now). :D. It's great to see you on RUclips. Hope everything is well.
Singingbanana: Ramanujan have a side that is as spectacular as his mathematics, will make very good videos, if you want.
From a very early age he started meditation on mathematics and practiced Vaishnav Yoga. Meditating on a subject is an ancient practice by the Vedic Rishis, who went on to discover number theory, arithmetic, geometry (including tiling like Penrose) etc., discovered the big bang, with very high temperature etc. (google Dr. John Hagelin for details). Ramanujan went on to discover 4000 theorems and could solve problems just by viewing them and solved them without proof, giving an insight into his mind ( he claimed that Vishnu's consort Namagiri gave him the knowledge of mathematics. The Brahmans at the temple at Namakkal (near his house, where his mother sang) taught him Vaishnav Yoga. Goddess Namagiri is the goddess of Knowledge.
Please try go a little deeper into the maths instead of trying to explaining it in layman's terms in the other videos of this series.
Can't wait for the series, however the stuff is presented, coz you, Dr.Grime, are awesome.
+Shashank Sistla I'll make you a deal. If what you want agrees with what I've already filmed then I'll do that.
+singingbanana :D Is that a yes?
(oh he replied to my comment, *screams*)
+Eddy Proca A man can dream.
Shashank Sistla lost mind
And if you have been...thanks for watching!!
WHERE WAS THAT!!
Make more on infinity! Man it baffles me!
I also love formulas and equations :D...
... unless they involve infinity
I've been wanting to learn more about his Brahmanic training in Indian Maths. We talk a lot about his lack of "formal training" but we are really saying he wasn't trained in the western college system. My understanding is that he was exposed to a huge body of oral texts and i'm curious how much of the maths we know from him are rooted in that tradition.
+jordan fink He was trained in Vedic astrology by his mother that may be his first initiation into numbers. Ramanujan was a deeply philosophical individual, by that I mean philosophical systems like Advaita rooted in the Upanishads. For the Brahmanic training in Indian maths, you can pick some translated works of Bhaskara, Aryabhata, Brahmagupta.... and other Indian mathematicians. A point to note that many of these people were astronomers. In ancient India the precise calculations of astronomers gave way and were essential for precise astrological predictions...... I'm talking about Vedic astrology with its sacred numerology.... something in which Ramanujan's mother was well versed in.
Just another fact, the Kerala School of mathematics founded by Madhava of Sangamagrama was known to use calculus, maybe not as a rigidly defined branch but they used integral-like methods 200 years before Newton-Leibnitz. You can go through translated texts to know more of the kind of mathematical insight the ancient Indians appreciated, I'd say that it has always had a spiritual connect something the West does not digest easily.
Ramanujan was a Yogi and a devout Brahmin, at least he considered himself one. He often sites that the theorems came to him, he talks about meditative insight and realization of knowledge. For Hindus there is no difference between the Self and the Absolute (or Brahman), all the knowledge that exists without also exists within, it is only a question of discovery. Science looks without, the Yogi looks within. The fact that his spiritual insight let nature give up these golden nuggets of mathematical knowledge was believable to him.
how much of his work was translating vedic math to the western nomenclature? For example, were infinite sums part of the vedas? I've been trying to figure out if the complex plane was known in the texts.
+jordan fink During Ramanujan's time? I don't think so, many non-religious branches and a vast chunk of the Vedas that existed in ancient India are known to have gone extinct and only the ritualistic and philosophical portions have survived... still it is improbable that Ramanujan inherited specific ancient methods of Indian mathematics... talking about oral transmission once upon a time it was considered blasphemous to pen down the Vedas but no one knows how long back that was, even Buddha seems recent in that regard... the only recent Indian school closest to modern mathematics was the Kerala School of Mathematics which disappeared soon after the decline of Vijaynagar empire which had patronized them you might find their translated manuscripts
I heard about ramanujan , he is great.
I want a feature film om Kurt Gödel, and his Incompleteness Theorems of Insanity. Ramanujan is a nice step on the way, though.
1:56 "... This is an example of something called an *infinite nested radical*..."
I think I got a proof. It's trivial to show that x ≤ 3. The problem is to show that x ≥ 3. Defining P(n) = √1+2√1+3√...1+n and Q(n) = √1+2√1+3√...1+(n-1)√1+n(n-2), and writing 3 as √1+2√1+3√...1+(n-1)√1+n(n+2), we can show that P(2n) > Q(n) > 3k^(1/2^(n-1)), where k = (n-2)/(n+2). The last expression can be re-written in terms of the defining limit exp(x) = lim (1+x/N)^N to show that it goes to 3 as n tends to infinity. By the Squeeze Theorem, we have that x = lim P(n) ≥ lim Q(n) ≥ 3.
I'm a little disappointed. "The Man Who Knew Infinity" isn't playing anywhere near me in the US. With the success of "The Imitation Game" and "The Theory of Everything", I would have thought that it would be more prevalent, but I guess not. I might just have to wait until it get's a DVD release and hope I can grab a copy of it.
great work james always a good experience to watch your vids best wishes from India
For those curious, he's Dr. James Grime.
Hey James, I love your nick. It's as nerdy as it should be (very !) :>
ps: 2:35 it's very interesting that the continued fraction(s) of phi also is full of ones (1;1,1,1,1...). I wonder if the continued fractions are linked with continued square roots. I think they are, now that I recall the Babylonian method of calculating the sqrt(x) iteratively.
ps2: wow, this is one of the most ancient YT accounts I've seen!
psFinal: thanks for the link to the paper, it works just fine and looks a really cool read.
Looking at the demonstration, aside from understanding it, the real question is: how could he think of that? The matter here is not the passages from the first point to the last, but how he found that said first point was where he had to start.
Hey James- you're looking good! What's also good is to hear about Ramanujan! Thank you =))
Thank you Dr. Grime.
Yes James Grime video!!!!!!!!!
You really should write a book about something math related. Id buy it immediately.
Excellent.
Very interesting! Look forward towards the rest of the videos
Ramanujan went to college, twice and studied there for a year, and the second year. He failed in mathematics though. Probably he was deeply involved in his work rather than studying for the tests
Leobe Kayombo He didnot fail in Maths, but English.
Yes he failed in all subjects including maths. He gives only final answer without the methods. His answer sheet in Madras musieam.....
Me being a math dummy, please just tell me whether or not Ramanujan would have been the hands down greatest mathematician ever?
Can you please put out a talk on how he actually thought what he thought.
Always nice to see a video from you! :)
When can we expect a next one?
These videos should be in a playlist :)
Only mathematician get 300 likes and 0 dislikes :D Great video btw!
Very exciting, looking forward to it!
what if Ramanujan didn't die??
Welcome back.
But he did not show that the infinite nested radical *converged*. He assumed that the value of the expression was meaningful (finite, in this case) and then proceeded to calculate it.
If you can calculate the limit, then it is convergent.
Why do you think all this was omitted from the movie?
Hopefully we'll look at his Pi formula
A series of videos? A mathematical journey? Could this week GET better? I think not!
NO SPOILER ALERT? I'm literally 5 minutes into the movie!
sir I derive a formula for finding the circumference. of ellipse by my self .can you please help me sir
*Email: sanatanvishwa @ gmail*
Can we have an explanation for why that formula works, or a link to the explanation?
+SmileyMPV OK, I've put a link in the description. The proof isn't obvious without observation.
+singingbanana Thanks :) even if i dont understand, at least i can take a look
1:58 it's called a radical cause it is well wicked
can't wait for the other videos!
Omg so good he look so intelligent. In New York we love her man.
that's a great idea, waiting for your videos.
Love your channel! Thx for sharing!
The window blinds behind you are not level. The left side is slightly higher and shou
lovely. but isn't this a bit simple. could u take up some more difficult results. (or have u already shot everything?)
Sir the movie review and rating of yours plz
And if you have been, thanks for watching!
Hi thanks for this great clip, please I would like to know which of the "the man who knew infinity did you just watch" 2015 or 2016?
Abacus and prime-finding machine in the background... how do you do, James?
Hey, James, is that thing seen in the background the prime number counter featured in an episode of Numberphile?!
It is. I pressed it again before typing this comment. It now reads 226183.
singingbanana: Thanks for confirming that observation of mine, James!
Incidentally, on a lark I found myself wondering about the digit reversal of Ramanujan's famous Taxi Cab Number (9271) and wondered if it were prime. It turns out not to be prime but is the product of two primes: 73 and 127 with the sum of those two primes being exactly 200 --not that that means anything.
Чел я совсем не понимаю английский но у тебя офигенная харизма)
no, it's Rajesh Ramayan Koothrappali
I ❤❤❤❤❤❤❤❤❤Ramanujan
"...We'll take that journey without the use of a taxicab..." LOL
I got that, too.
Ramanujan didn't know Infinity. The problem is, the people "explaining" his Paradox don't know either what Infinity is.
James just rides the wave and doesn't take his time to think about that the Infinite has no numbers. And this is only the small part of the big mistake.
Can you make a video on fermat primes and fermat numbers?
You look and sound like the one on Numberphile? o.O
He is!
+Fat Autist
..........................................
Infinity is not infinity because infinity is not whole all numbers but its a continuous to going to whole all numbers
What's your email. I've got so many infinity paradoxes that I've produced! These were produced while doodling, wandering off, and looking into space during math class here in America. In this world, math is just knowing.
This stuff blows my mind.
I had no clue you had a channel James
Why didn’t you tell me?
I can't wait to see the rest! Love the video's!
Where is this movie? I keep on looking for it. Is it select theaters only?
Interesting stuff. Of course it is formulae not formulas to pedants like me but the story is great.
Thank You!!
How can square roots be in square roots? How do you solve it?
Excellent
Function of a function number series.
Sir ramanujan gave formulas and equations for the study of black holes. And the mathematicians are still not able to understand those formuls. Not a genius!?
Yeah I love ramanujan
What's that device on the desk?
+Jari Komppa youtube search "Warning: Contains Numbers!"
+Jari Komppa it's a thing that shows prime numbers when you press this fancy red button in the middle. Look for a video called "WARNING: Contains Numbers" on Numberphile channel :)
turn on subtitles
your welcome
What's that thing behind you with a button
Love taxi cab “cameo”/easter egg
I love you. *cough* I mean great video.
what is the sum of all prime numbers up to infinite
you look just like the guy from numberphile and his name is James Grime... what are the odds?
Thank.. This is great
Thanks!
Thanks for this !
no brown paper?
Brilliant
I am very proud to say that I belong to his home town
The base of numbering system should be 1729. Only then wrap around is a perfect sequence instead of ten which doesn't. Waste of base ten.