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Ramanujan Surprises Again (2015)

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Re: Ramanujan Surprises Again (2015)

#41

Post by 8bitsrule »

user2994cb wrote: post #26
nneonneo wrote: post #21

An interesting coincidence: it was recently (2019) discovered that the fastest way to multiply two n-bit integers, in time O(n log n), involves 1729-dimensional Fourier transforms: https://hal.archives-ouvertes.fr/hal-02070778 . It is quite surprising that the asymptotically best way to perform such an elementary operation should be tied to Ramanujan’s famous taxicab number. (Technically, it works for any number of d…

In fact, there seems to be a lot of interesting things about 1729: https://en.wikipedia.org/wiki/1729_(number)

Another fun fact: 1 + 7 + 2 + 9 = 19 ; 19 × 91 = 1729

Re: Ramanujan Surprises Again (2015)

#42

Post by emmelaich »

user2994cb wrote: post #26
nneonneo wrote: post #21

An interesting coincidence: it was recently (2019) discovered that the fastest way to multiply two n-bit integers, in time O(n log n), involves 1729-dimensional Fourier transforms: https://hal.archives-ouvertes.fr/hal-02070778 . It is quite surprising that the asymptotically best way to perform such an elementary operation should be tied to Ramanujan’s famous taxicab number. (Technically, it works for any number of d…

In fact, there seems to be a lot of interesting things about 1729: https://en.wikipedia.org/wiki/1729_(number)

And it belongs to the first pair > 1000 to both have Wikipedia pages!

Re: Ramanujan Surprises Again (2015)

#43

Post by taberiand »

8bitsrule wrote: post #41
user2994cb wrote: post #26

Earlier quoted context omitted.

In fact, there seems to be a lot of interesting things about 1729: https://en.wikipedia.org/wiki/1729_(number)

Another fun fact: 1 + 7 + 2 + 9 = 19 ; 19 × 91 = 1729

This kind of coincidence is just cute, it doesn't imply anything useful mathematically right?

Re: Ramanujan Surprises Again (2015)

#44

Post by rhizome »

unlinked_dll wrote: post #28
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.

Funny to use the word transcendental there, since the Pythagoreans held ratios to be divine but couldn't figure out irrational numbers, like pi. They had trouble squaring that circle.

"Transcendental" also appears in Calculus.

Re: Ramanujan Surprises Again (2015)

#45

Post by dntbnmpls »

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 few more degrees, you get science.

History of science is just as fascinating as history of politics. It's a shame we focus on the latter so much.

Re: Ramanujan Surprises Again (2015)

#46

Post by wenc »

cheerlessbog wrote: post #40
wenc wrote: post #30

Earlier quoted context omitted.

I think most of us are impressed by computational parlor tricks (and indeed raw computational intelligence in general -- being able to process information and compute quickly and accurately), but for me, genius goes beyond that. Genius is about having rare and useful insights that the rest of us are incapable of, and that a computer is unable to easily replicate. For instance, there was this thing on Twitter recently…

It never occurred to me that 7% of 50 is equal to 50% of 7 perhaps because they are equally easy to calculate? Multiply 7 by 5 and fix the decimal point.

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.

Re: Ramanujan Surprises Again (2015)

#47

Post by macewindu »

v64 wrote: post #7

Great read! When you first hear the taxicab number story, your initial impression is to be struck by Ramanujan's innate calculating capability. It's interesting to find out that the real coincidence here is that Hardy rode in a taxicab whose number had happened to show up in Ramanujan's investigations of Fermat's last theorem.

> Ramanujan's innate calculating capability.

Hard work and obsessive work effort on a specific area makes it appear innate.

Re: Ramanujan Surprises Again (2015)

#48

Post by sllabres »

nneonneo wrote: post #21

An interesting coincidence: it was recently (2019) discovered that the fastest way to multiply two n-bit integers, in time O(n log n), involves 1729-dimensional Fourier transforms: https://hal.archives-ouvertes.fr/hal-02070778 . It is quite surprising that the asymptotically best way to perform such an elementary operation should be tied to Ramanujan’s famous taxicab number. (Technically, it works for any number of d…

Interesting but as it seems currently without practical implications for multiplication:

https://en.m.wikipedia.org/wiki/Galactic_algorithm

Re: Ramanujan Surprises Again (2015)

#49

Post by BGthaOG »

taberiand wrote: post #43
8bitsrule wrote: post #41

Earlier quoted context omitted.

Another fun fact: 1 + 7 + 2 + 9 = 19 ; 19 × 91 = 1729

This kind of coincidence is just cute, it doesn't imply anything useful mathematically right?

I would not be surprised if it is found to be useful. My reason for this is the Quran's mathematical composition, founded on the number 19: https://www.masjidtucson.org/quran/miracle/

Re: Ramanujan Surprises Again (2015)

#50

Post by lonelappde »

BGthaOG wrote: post #49
taberiand wrote: post #43

Earlier quoted context omitted.

This kind of coincidence is just cute, it doesn't imply anything useful mathematically right?

I would not be surprised if it is found to be useful. My reason for this is the Quran's mathematical composition, founded on the number 19: https://www.masjidtucson.org/quran/miracle/

That's numerological nonsense like Bible Code.
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