[HN Gopher] Ramanujan's lost notebook
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Ramanujan's lost notebook
Author : benbreen
Score : 289 points
Date : 2024-04-15 19:54 UTC (1 days ago)
(HTM) web link (en.wikipedia.org)
(TXT) w3m dump (en.wikipedia.org)
| Der_Einzige wrote:
| I'm an atheist, but when Ramanujan claims to derive all of their
| formulas from god, I ask how we can make it easier for them to
| listen to god, rather than feel the urge to argue against them.
| FieryTransition wrote:
| If you meet him, and he thought discussing god was interesting,
| would you then do it? If he wanted to discuss your faith in
| god, would you do it then?
| cassepipe wrote:
| Discussing is always interesting but I would probably
| interpret it as him not being able to explain his own
| abilities like some people just "see" good chess moves or
| just "know" that there are actually 48 matches on that floor
| mistermann wrote:
| I would wonder what the truth of the matter is, but each to
| their own, the unknown is _not popular /pleasant_.
| methinksstuff wrote:
| If you look the origin of the word genius I think there is a
| good parallel as thinking that your own genius is an external
| spiritual entity whispering you solutions
| vjerancrnjak wrote:
| I feel like his statements on god are very similar to this one:
|
| > Simon P. Norton, an expert on the properties of the monster
| group, is quoted as saying, "I can explain what Monstrous
| Moonshine is in one sentence, it is the voice of God."
|
| https://en.wikipedia.org/wiki/Monster_group#Moonshine
| fuzztester wrote:
| Solid.
|
| Pun intended.
| fuzztester wrote:
| Goddess also, actually.
|
| https://en.m.wikipedia.org/wiki/Srinivasa_Ramanujan
|
| Check section "Personality and spiritual life".
| sumeruchat wrote:
| I feel like this comment and comments by western atheists make
| me think that the west has this idea of judeo-christian god
| that they just bring into any conversation without thinking
| deeply. For ramanujan god is more like an emotion.
| FieryTransition wrote:
| I'll never figured out whether Einstein thought that the god
| as described by Spinoza is a real thing? Since there's so
| many misattributed quotes of him which frames him as talking
| about the judeo-Christian god as most people know by modern
| standards.
|
| Also, there have been other early religions like Gnosticism
| in the west, which also falls into this category. Point is,
| even western religion has way more nuances.
| shagie wrote:
| I would suggest that the answer to that is "yes" in that
| the Spinozan God is... for lack of a better word the
| Universe.
|
| (Kaizo in 1923 https://books.google.com/books?id=vLm4oojTPn
| kC&pg=PA262#v=on... )
|
| > Scientific research can reduce superstition by
| encouraging people to think and view things in terms of
| cause and effect. Certain it is that a conviction, akin to
| religious feeling, of the rationality and intelligibility
| of the world lies behind all scientific work of a higher
| order.
|
| > This firm belief, a belief bound up with a deep feeling,
| in a superior mind that reveals itself in the world of
| experience, represents my conception of God. In common
| parlance this may be described as "pantheistic" (Spinoza).
|
| https://www.gutenberg.org/files/3800/3800-h/3800-h.htm
|
| (Ethics was one of the _hardest_ reads I had back in modern
| philosophy class)
|
| And while it is a gross simplification of Ethics, from
| news://rec.humor.funny ( https://everything2.com/title/Exis
| tence+of+the+System+Admini... ) 1. The
| System Administrator is defined as the most perfect user
| possible. 2. The property of necessary existence
| means that anything which possesses it must necessarily
| exist. 3. If existence is better than non-existence
| (see the ontological proof), then necessary existence is
| better still. 4. Any perfect user must possess the
| property of necessary existence. 5. Therefore the
| System Administrator must necessarily exist.
| However: 6. Being perfect, the System
| Administrator cannot make mistakes, delete the wrong
| account, trash the root directory, mess up a tape load,
| etc. 7. Being perfect, the System Administrator can
| not be capable of goal-directed action, because such action
| would imply that the network is somehow less than perfect
| in its current state. 8. Therefore, the System
| Administrator is really more of a force of nature within
| the system. 9. Arguably, then the System
| Administrator *is* the system itself. Counter-
| argument: 1. None, since the System
| Administrator has been defined to the point where it is a
| totally useless concept, there's no point in arguing.
| At least this resolves one of the major issues: the
| Spinozist argument proves that *if* the System
| Administrator does exist, it cannot be intelligent.
|
| ---
|
| The God of Spinoza and Einstein is the magnificence of the
| universe as it reveals itself to us. The universe is real
| as is its majesty.
| TomK32 wrote:
| Re 6. Listing so many mistakes the System Administrator
| surely never does is Blasphemy!
| monktastic1 wrote:
| I was with you right up until the word "emotion." Although
| "Hinduism" is vast and covers quite a few disparate beliefs
| and philosophies, none of them (to my knowledge) even
| approximately equate God with an emotion. Even bliss (ananda)
| is only one aspect.
|
| I don't claim to know the particular religion of his village
| and/or lineage, but I understand his God to be something
| closer to the Consciousness that (supposedly) gives rise to
| all of reality.
| fuzztester wrote:
| >Although "Hinduism" is vast and covers quite a few
| disparate beliefs and philosophies, none of them (to my
| knowledge) even approximately equate God with an emotion.
|
| Bhakti does.
|
| https://en.m.wikipedia.org/wiki/Bhakti
|
| >covers quite a few
|
| Tons.
|
| >Hinduism
|
| There is no such thing.
|
| The term is a Western invention, by complacent sneering so-
| called scholars about India.
| monktastic1 wrote:
| You are confusing using emotion to reach God with emotion
| _being_ God.
|
| And of course there is "such a thing." You even described
| what it refers to, a definition which is sufficient for
| the purposes of this thread.
| fuzztester wrote:
| There you go with your weasel words again.
|
| Hey academic philosopher, God is everything, and there is
| nothing else, so God can be emotion and emotion can be
| God :) :) :)
|
| Don't you know about Brahman?
|
| There is nothing else ;)
|
| https://en.m.wikipedia.org/wiki/Brahman
|
| QED.
| hprotagonist wrote:
| > For ramanujan god is more like an emotion.
|
| for most jewish, christian, and muslim mystics and some
| theologians, as well.
|
| the 'new atheist' conception of what "all christians" think
| about when they think about god is, well, not very
| representative.
| sumeruchat wrote:
| True. I was just commenting on the lack of depth in some
| modern discussions in the west
| rdtsc wrote:
| > I feel like this comment and comments by western atheists
| make me think that the west has this idea of judeo-christian
| god that they just bring into any conversation without
| thinking deeply. For ramanujan god is more like an emotion.
|
| From https://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Person
| alit...
|
| > While asleep, I had an unusual experience. There was a red
| screen formed by flowing blood, as it were. I was observing
| it. Suddenly a hand began to write on the screen. I became
| all attention. That hand wrote a number of elliptic
| integrals. They stuck to my mind. As soon as I woke up, I
| committed them to writing.
|
| That doesn't seem like an emotion at all. It's a very visual,
| concrete image. It's closer to the "western atheists" view of
| god that just an abstract feeling of some sort you were
| describing, wouldn't you agree?
| sumeruchat wrote:
| Its a bit of a psychedelic experience. If someone was on
| LSD and seeing stuff i would compare it an emotional
| experience. Of course it goes deeper but just explaining
| the reasoning behind the word emotion
| subsubzero wrote:
| I had a similar experience while in college, although not
| as dramatic! While studying CS I was working on problems
| every night late into the night. I came a across a issue I
| could not figure out, and went to sleep frustrated. That
| night I had a dream where a very specific solution was told
| to me(a voice with text) and it was in a way I had never
| thought of. I tried it out the next day when I woke up and
| it worked. It always freaked me out as I don't know how
| that solution was given to me, my assumption is maybe the
| subconscious is more powerful than we thought in terms of
| reasoning.
| devnull3 wrote:
| Atheism is an accepted school of thought in Hinduism [1]
|
| Indian philosophy is diverse and vast. See the comparison of
| these philosophies [2]
|
| [1] https://en.wikipedia.org/wiki/Charvaka
|
| [2] https://en.wikipedia.org/wiki/Indian_philosophy#Compariso
| n_o...
| sumeruchat wrote:
| Sure is. Doesnt invalidate my argument that western atheism
| lacks depth
| keiferski wrote:
| "Western atheism" doesn't lack depth, it's more that the
| people actively arguing with others that call themselves
| atheists tend to lack knowledge of their own position.
| Dawkins, Hitchens, etc. are notoriously uninformed on the
| topic of religion.
| skruger wrote:
| [reference needed]
| keiferski wrote:
| https://old.reddit.com/r/askphilosophy/search?q=dawkins&r
| est...
|
| https://en.wikipedia.org/wiki/New_Atheism#Criticisms
|
| No one in the philosophy world takes the works of the New
| Atheists seriously. They are pop-culture writers, not
| serious philosophers (other than Daniel Dennett.)
|
| If you want a serious thinker's thoughts on atheism, you
| are better off picking up a book by Nietzsche, Charles
| Taylor, David Bentley Hart, the Oxford Handbook of
| Atheism, or any other number of thinkers, or browsing the
| articles here: https://plato.stanford.edu/search/searcher
| .py?query=atheism
| spaceman_2020 wrote:
| Yeah, Hinduism has enough room for non-believers too. I'm not
| religious at all, so when someone asks me if I'm keeping a
| fast for such and such occasion, or celebrating some
| festival, I simply tell them that I don't believe in these
| things and I'm usually left alone.
|
| Although this aspect of Hinduism seems to be changing and
| becoming a bit more hardline
| DiggyJohnson wrote:
| Why would you have to believe in these things as "real" to
| still keep a fast? Why would you not answer a simple "no"
| instead of the answer you give?
| blueprint wrote:
| Then you need to understand it from a theoretical perspective
| first. Firstly, when people use the word "god" they honestly
| ought to define what they refer to by using that word, and what
| the abilities of that god are supposed to be.
|
| If we're in a physical universe with energy, then it's been
| explained that a creator-like god can be argued to have
| 'created' the principle of existence, itself, on which all
| other things then evolved with energy. So then, what is that
| principle, stated concretely? Modern physics has already found
| out almost everything about it.
|
| What is left of an entity if it becomes capable (at least
| beyond some meaningful threshold) of functionally discarding /
| disobeying the influence of untruth?
|
| Is someone (in properly controlled circumstances) going to be
| more or less perceptive of 'what is' when they are more
| truthful?
| kloch wrote:
| I have a personal theory about human intuition.
|
| It feels like answers come "from outer space" or "from God" but
| it's really just a highly optimized and efficient part of the
| brain for a very specific function. For that narrow function
| your brain has an effective IQ of something like 2000. As our
| brains have a much lower average IQ, we don't have the context
| to understand how we found the answer so we experience it and
| describe it as intuition.
|
| If our entire brain operated at an IQ of 2000, we wouldn't
| experience it as intuition or a flash of genius, we would just
| say "I figured it out".
|
| What I have read about Ramanujan sounds like he had some form
| of high functioning savant syndrome.
| https://en.wikipedia.org/wiki/Savant_syndrome
| harperlee wrote:
| https://en.wikipedia.org/wiki/The_Origin_of_Consciousness_in.
| ..
| citizenpaul wrote:
| Its been a while since I read about it but there is some
| theorizing on the split halves of the brain and the corpus
| callosum that connects the two halves.
|
| One theory is that the connection between the two halves is a
| recent evolution and that people used to and some still do
| perceive the other half of their brain as a separate entity
| that communicates with them. Possibly being due to the corpus
| callosum not being the same in everyone. The greater theory
| being that this is basically the root of all religion.
| paulpauper wrote:
| Not expecting too many comments here. These formulas are
| complicated and it took a single person in the later 20th century
| to re-derive a good chunk of them.
| ykonstant wrote:
| If you are talking about Bruce Berndt, Bruce did not rederive
| Ramanujan's results alone; he has a big network of
| collaborators and students who have worked with him, and of
| course many independent researchers have derived some of his
| formulas. His books contain all the relevant attributions and
| history (I talked with him extensively and got some of his
| classes when I was a phd student in UIUC).
| paulpauper wrote:
| yes that is him. Same for Peter Borwein
| hi41 wrote:
| In the spirit of openness which is the hallmark of FOSS such as
| GNU/Linux, would this book be scanned and published for all to
| see? That would be great. Like FOSS, math too belongs to the
| world. I heard someone say that the university has not published
| many of his works. That would be sad. If published someone like
| Terrence Tao could write formal proofs for them like he and his
| team did some improvements for the work by Yitang Zhang.
| bigbillheck wrote:
| > If published someone like Terrence Tao could write formal
| proofs for them like he and his team did some improvements for
| the work by Yitang Zhang.
|
| From the second paragraph:
|
| > George Andrews and Bruce C. Berndt (2005, 2009, 2012, 2013,
| 2018) have published several books in which they give proofs
| for Ramanujan's formulas included in the notebook
| svat wrote:
| The notebook (like Ramanujan's three previously known
| notebooks) has already been published, in 5 volumes by Bruce
| Berndt and George Andrews, with extensive annotation (e.g. just
| flipping at random, in the third volume Chapter 6 is called
| "Theorems about the Partition Function on Pages 189 and 182",
| and occupies 24 pages, and indeed contains formal proofs etc).
| A raw scan of the notebook(s) is even available online:
| http://ramanujan.sirinudi.org
| Analemma_ wrote:
| Unfortunately the actual notebook links on that site appear
| broken
| LegionMammal978 wrote:
| The page number selector appears to link to working PDFs.
| svat wrote:
| Just enter a page number; it works fine. Or if you wish,
| here are the direct links:
|
| http://ramanujan.sirinudi.org/Volumes/01/01.pdf
|
| http://ramanujan.sirinudi.org/Volumes/02/02.pdf
|
| http://ramanujan.sirinudi.org/Volumes/03/03.pdf
|
| http://ramanujan.sirinudi.org/Volumes/04/04.pdf
|
| Ramanujan's total known/preserved output today is 37
| published papers and these four notebooks; all of it is
| available on the site. The notebooks have been transcribed
| and published in several volumes with explanation (as
| mentioned above); those are the only thing not included on
| this site (and arguably, not "by" Ramanujan).
| dhosek wrote:
| This sounds exactly like the thing I've kind of wanted--a
| compilation/overview of Ramanujan's work, ideally with
| commentary. I'll have to take a closer look at this. What
| I'd really like is something akin to Yves Hellegouarch's
| _Invitation to the Mathematics of Fermat-Wiles_ which
| seems to be not only out of print, but rather rare now
| (it's listed on Amazon at over 400 bucks although that
| could be algorithmic madness among the sellers).
| svat wrote:
| I think Bruce Berndt's _Number Theory in the Spirit of
| Ramanujan_ (2006) may be along the lines of what you 're
| looking for, and also possibly G. H. Hardy's _Ramanujan:
| Twelve Lectures on subjects Suggested by His Life and
| Work_ (originally 1940, but republished 1991 /1999 by AMS
| with further commentary by Berndt). I'm not qualified to
| say for sure, as they get too hard for me pretty fast. :)
| [Some of Ramanujan's easier papers I was able to read
| (very slowly) for quite a few pages though, such as the
| one on highly composite numbers.]
| eesmith wrote:
| FWIW,
| https://archive.org/details/invitationtomath0000hell .
| dhosek wrote:
| That is quite possibly the most disappointing URL in the
| history of URLs. Invitation to Math Hell, indeed.
| dartharva wrote:
| His penmanship is quite aesthetic
| rob74 wrote:
| Yeah, when I read "more than one hundred pages written
| [...] in Ramanujan's distinctive handwriting" in the
| Wikipedia article, I was thinking "almost indecipherable
| scrawl", but this borders on calligraphy...
| mavhc wrote:
| All those links 404 for me
| cobbaut wrote:
| They are http ... some browsers may default to not
| loading them.
| mavhc wrote:
| Thanks, I'd set my browser to always switch to https
| lynx23 wrote:
| FOSS != piracy
|
| And, frankly, I find it pretty upsetting that you seem to
| negate that equation.
| falcor84 wrote:
| Sorry for nitpicking, but just trying to clarify what seems
| like a double negative - do you mean "to affirm that
| equation", i.e. that the author claims they _are_ equal?
| lynx23 wrote:
| I guess you're right, negating an inequality is likely the
| same as affirming an equality? I am not a native speaker.
| Galaxity wrote:
| Is that not the same logically in every language?
| delta_p_delta_x wrote:
| I think the parent commenter was using the word 'equation'
| in its colloquial sense to refer to any mathematical
| expression or statement, despite their statement containing
| a 'not equals to' symbol, rather than actually _equating_
| them (which would have an equals sign).
| bigbillheck wrote:
| He's been dead for 104 years, where's the piracy?
| interpjinx wrote:
| I expect future AI models to be like Ramanujan. Has tremendous
| intuition but can't accurately explain it's reasoning for
| arriving at a solution.
| shwaj wrote:
| Perhaps this will be true, for the types of insights that also
| require tremendous intuition for people to see. One difference
| is that it will be possible to examine the full state of the AI
| which lead to the insight, and perhaps learn from it.
|
| (edit: rewrote to flow a bit better)
| troq13 wrote:
| It seems like a misconception that Ramanujan could not explain
| his reasoning.
|
| He did not write it down on his notebooks (and before going to
| England he mostly lacked the language of formal proofs to do
| it), but for the most part the equations are arranged in a
| logical order, and when meeting with Hardy he had no trouble
| explaining where each equation came from (though a lot of his
| reasoning was too unrigorous for Hardy's liking).
| ldjkfkdsjnv wrote:
| I almost feel like there is a random ramanujan posting generator.
| Every day it runs on a cron job, and with some probably something
| about him is posted. Much like the dunning krueger effect. Some
| topics arise with such consistent regularity. Almost makes you
| wonder what the reasoning is
| gnatman wrote:
| Because he's a fascinating and mysterious character on top of
| being the most brilliant mathematician since Euler.
| mycologos wrote:
| One quarter thought out software project, mild overthinking
| conspiracy theory, and a non sequitur misspelled reference to
| Dunning-Kruger. This is like a parody of a Hacker News comment
| gus_massa wrote:
| From
| https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...
| it looks likethere are like 5 or 6 post per year.
| __lbracket__ wrote:
| can we please stop spending more ink on this hack?
| pingohits wrote:
| What's hacky about Ramanujan?
| __lbracket__ wrote:
| So we dont know anything about his math/theorem generation
| process. By his own admission he saw visions of math/theorem
| god, which is a BS claim since god doesn't exist. So "god
| whispered theorems in my sleep" is just a proxy for "I coped
| it from someone". Many of his so called theorems are false
| (by Hardy's own admission). Lot of progress in math depends
| on the "process", not just the end result. But he shares
| nothing about the process.
| lupusreal wrote:
| > _By his own admission he saw visions of math /theorem
| god, which is a BS claim since god doesn't exist_
|
| Shit reasoning like this from atheists like you is why I
| cringe to admit I'm an atheist when people ask me about my
| religious beliefs. It is entirely conceivable that he saw
| visions of math, produced by his own subconscious, and
| attributed these visions to a god. It would not be terribly
| dissimilar from any artist who attributes their creative
| visions to a muse. Do you accuse any such artist of
| plagiarism too?
| __lbracket__ wrote:
| He didnt have formal training in math. So where did his
| subconscious "learn" the advanced stuff in his visions?
| vaidhy wrote:
| Lacking formal training does not equate cannot understand
| something. As far as copying something goes, there should
| have been an equivalent mathematician nearby from whom he
| can copy, right? Who is it?
|
| As an atheist myself, I do not believe in god and I do
| not believe Ramanujam got it from god. However, it does
| not change the fact Ramanujan thought he got it from god
| because he could not necessarily explain how he made
| those intuitive leaps.
| troq13 wrote:
| "we don't know anything about his math generation process"
| My man just look at the notebooks. He did not use formal
| proofs but he was very organized and most of his equations
| had quite a logical buildup from equations that he wrote
| before. And even the ones that came out of nowhere are
| obviously worthy discoveries.
| DiggyJohnson wrote:
| You seem so sure of yourself. How did you end up like that?
|
| > ... is just proxy for "I coped it from someone".
|
| How can you be so confident in this claim?
| __lbracket__ wrote:
| Lets just say that I feel "he copied" is more plausible
| than "theorem god whispered to me in my sleep"
| DiggyJohnson wrote:
| I see that. But you're making it sound like you know that
| for sure. Do you see that there's a middle ground? I.e.
| "I had a dream where it seemed that God was describing to
| me these new theorems"?
| snendroid-ai wrote:
| explain yourself
| gwern wrote:
| > However, Wilson died in 1935 and Watson seems to have lost
| interest in the project in the late 1930s.[3] After Watson's
| death in 1965, J. M. Whittaker examined Watson's papers (which
| were in disarray, due to be incinerated in a few days) and found
| Ramanujan's notebook
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(page generated 2024-04-16 23:02 UTC)