Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Ramanujan Surprises Again (2015)

plus.maths.org

Post reply on HN
Print view View original

71–80 of 96 posts

Re: Ramanujan Surprises Again (2015)

#71

Post by saagarjha »

karmakaze wrote: post #24
hnews_account_1 wrote: post #8

Earlier quoted context omitted.

A lot of genius stories are like this. I was also under the illusion that these guys could just do things that fast, but at some point, I read Feynman's biography where he explicitly talks about how he used to solve homework problems or something beforehand and then he used to pretend that he found the solution while solving it if his classmates asked. That threw me for a loop and I started believing shit like no one…

This reminds me of the von Neumann fly puzzle story: https://en.wikipedia.org/wiki/John_von_Neumann#Cognitive_abi...

Of course, once you know how to sum infinite geometric series it's not too hard to come across the answer that way ;)

Re: Ramanujan Surprises Again (2015)

#72

Post by solveit »

JadeNB wrote: post #64
solveit wrote: post #58

Earlier quoted context omitted.

Grothendieck and lack of machinery do not belong in the same sentence. But yes, it is kind of silly.

> Grothendieck and lack of machinery do not belong in the same sentence. They most certainly do! Grothendieck’s work is heavy on definitions , but the essence of his work is that the right definitions obviate (and are seen to be right because they obviate) the need for heavy machinery. See the famous quote, taken from Wikipedia ( https://en.wikiquote.org/wiki/Alexander_Grothendieck#Quotes_... ) because that’s the fir…

I mean, we're arguing semantics at this point, but these definitions we're talking about are things like schemes, which pretty much everybody would call heavy machinery.

Re: Ramanujan Surprises Again (2015)

#73

Post by elSidCampeador »

Psyladine wrote: post #38
hnews_account_1 wrote: post #8

Earlier quoted context omitted.

A lot of genius stories are like this. I was also under the illusion that these guys could just do things that fast, but at some point, I read Feynman's biography where he explicitly talks about how he used to solve homework problems or something beforehand and then he used to pretend that he found the solution while solving it if his classmates asked. That threw me for a loop and I started believing shit like no one…

Feynman was undoubtedly a genius, but he also suffered from a need to be admired. The safecracking episodes at Los Alamos are a perfect example - giving the impression he was an expert safe cracker when his real methodology was guesswork and sometimes subterfuge (birthdays, anniversaries, or even subtlety observing someone inputting their combination).

I get your point, I really do. But if what you call his "real methodology" worked well, why would he use more advanced/safecracker-y techniques?

I'd say the real mistake he made was that he lifted the veil off of how he did things, leading people to say "oh even I could have done that".

Re: Ramanujan Surprises Again (2015)

#74

Post by dr_dshiv »

wsc981 wrote: post #66
dr_dshiv wrote: post #9

Earlier quoted context omitted.

Mathematics are the best expression of the transcendental divine. Pythagoras and Plato had the same perspective.

Not a mathematician, but it was Thomas Paine's view that the hand of the divine can be seen by the study of nature - which I believe was a view shared by Isaac Newton. Thomas Paine wrote on his point of view in "The Age of Reason" [0]: > Each of those churches show certain books, which they call revelation, or the word of God. The Jews say, that their word of God was given by God to Moses, face to face; the Christian…

Thanks for sharing.

Re: Ramanujan Surprises Again (2015)

#75

Post by Sharlin »

JadeNB wrote: post #63
wenc wrote: post #46

Earlier quoted context omitted.

What about 17% of 50? 17*5 isn’t so simple anymore, whereas 50% of 17 is 8.5. To be fair, with most shortcuts, it’s possible to construct difficult cases (17% of 23 is difficult in either order) but where it applies (when one of the pairs is a common percentage), exploiting commutativity can be quite useful. Plus the mental overhead of remembering the rule is extremely minimal.

How can you discover that 50% of 17 is 8.5 if you can’t multiply 17*5? (If the answer is “by halving”, then my response is that halving and then multiplying by 10 is often the easiest way to multiply by 5!)

I’m not sure, but to me at least halving 17 to get 8.5 is an almost completely intuitive process, whereas multiplying 17 by 5 seems to require an extra cognitive step to reduce it to shifting the decimal point and then halving (or vice versa). Never mind the extra step when presented by the problem of taking 17% of 50.

Re: Ramanujan Surprises Again (2015)

#76

Post by psychoslave »

dntbnmpls wrote: post #45
Vinceo wrote: post #4

He credited his work to his family goddess. From wikipedia: "A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess. "An equation for me has no meaning," he once said, "unless it expresses a thought of God.""

Isaac Newton: "All my discoveries have been made in answer to prayer." People forget how religious newton was and he believed his physics was the discovery of god's physical laws. Chemistry comes from mystic alchemy. Astronomy derives from astrology. Just like there is a thin line between genius and madness, the same seems to apply to science and mysticism. Turn the dial a few degrees, you get mysticism. Turn it a fe…

There are no real historical conflict between mysticism and science. Take Russel's essay "Mysticism and logic" for example, Russel having evolved from a more Platonist point of view to a more atheist materialist one over its long lifespan, inventing "neutral monism" on the road.

However there are clear possibility of conflicts between scientific approach and institutional religions. Note that people don't need to be anything close to an atheist to get into trouble when their thoughts are going out of the road promoted by the institutional dogma of the day. Giordano Bruno is one famous case of such a human drama.

Of course religion here is more the mean of political control than anything else, and it can be substituted by other means just as detrimental to independent critical free thought.

Re: Ramanujan Surprises Again (2015)

#77

Post by vidarh »

gameswithgo wrote: post #25
dorchadas wrote: post #11

Earlier quoted context omitted.

What was the quote about Feynman? That he loved to cultivate anecdotes about himself or something similar? Makes a lot of his stories make a lot more sense, too.

i recall him explaining several shortcuts one can use to solve problems in seemingly impossible speeds by drawing on a breadth of experience from similar problems that you have memorized or are easy to compute and interpolating. its still genius but not in the sense of actually being able to do huge calculations in ones head the way a computer would.

Often it's also simply just that people are not used to thinking about more efficient ways of solving a problem.

There's a (quite possibly apocryphal) story about Niels Henrik Abel in primary school, where his teacher supposedly wanted time to do some grading and assigned the students the busywork of adding up all numbers from 1 to 100. Abel supposedly quickly found the well known formula n(n+1)/2 and gave the teacher the answer within minutes, and the teacher supposedly believed he'd somehow "cheated" because he could not imagine any of them could figure it out.

I have no idea if the story is real (I grew up in Norway, so Abel was a popular subject for stories like this) - it was told to me in high school by a maths teacher after giving us the modified task of seeing if we could find any shortcuts to doing the sums, and seeing what we'd come up with. I found the formula quickly, but at that age that's nothing special, especially not when prompted to find an alternative solution.

But the overall idea the teacher was trying to get us to understand was how to pause and think about how to decompose a problem rather than just picking the most obvious alternative, and learning to be "lazy" in the sense of relentlessly looking for an easier way to do things is a large part of what got me into software development..

Re: Ramanujan Surprises Again (2015)

#78

Post by fingerlocks »

vidarh wrote: post #77
gameswithgo wrote: post #25

Earlier quoted context omitted.

i recall him explaining several shortcuts one can use to solve problems in seemingly impossible speeds by drawing on a breadth of experience from similar problems that you have memorized or are easy to compute and interpolating. its still genius but not in the sense of actually being able to do huge calculations in ones head the way a computer would.

Often it's also simply just that people are not used to thinking about more efficient ways of solving a problem. There's a (quite possibly apocryphal) story about Niels Henrik Abel in primary school, where his teacher supposedly wanted time to do some grading and assigned the students the busywork of adding up all numbers from 1 to 100. Abel supposedly quickly found the well known formula n(n+1)/2 and gave the teache…

When I heard this story it was about Gauss.

And I looked it up- Yes, the same possibly apocryphal story is on his Wikipedia page: https://en.m.wikipedia.org/wiki/Carl_Friedrich_Gauss

Re: Ramanujan Surprises Again (2015)

#79

Post by mkl »

wwweston wrote: post #53
pixelpoet wrote: post #33

Earlier quoted context omitted.

I love how the article starts with the most boring facts about 1729: > 1729 is the natural number following 1728 and preceding 1730.

If a fact is the most boring[0], though, certainly that's something notable and therefore interesting about it. Therefore, these are not the most boring facts about 1729. ;) [0] https://en.wikipedia.org/wiki/Interesting_number_paradox

Well, that shows there is no most boring fact, but I think it doesn't preclude a the existence of a set of most boring facts, with none more boring than all the others. Yes, that is an interesting feature of the facts in the set, but does it mean that they are all necessarily more boring than every fact outside the set?

Re: Ramanujan Surprises Again (2015)

#80

Post by vidarh »

fingerlocks wrote: post #78
vidarh wrote: post #77

Earlier quoted context omitted.

Often it's also simply just that people are not used to thinking about more efficient ways of solving a problem. There's a (quite possibly apocryphal) story about Niels Henrik Abel in primary school, where his teacher supposedly wanted time to do some grading and assigned the students the busywork of adding up all numbers from 1 to 100. Abel supposedly quickly found the well known formula n(n+1)/2 and gave the teache…

When I heard this story it was about Gauss. And I looked it up- Yes, the same possibly apocryphal story is on his Wikipedia page: https://en.m.wikipedia.org/wiki/Carl_Friedrich_Gauss

Interesting. Not surprised this is the kind of story people might have adapted rather freely to sound more familiar to a local audience...
Post reply on HN