5 ms·
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
by nneonneo 7y ago
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 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 dimensions >= 1729, but the proof fails for dimensions less than that. Future work might bring the bound down, or better explain why that bound is necessary.)
- user2994cb 7y agoIn fact, there seems to be a lot of interesting things about 1729: https://en.wikipedia.org/wiki/1729_(number) https://en.wikipedia.org/wiki/1729_(number)
- nexuist 7y agoWell, now I know why my Scheme class in uni was called CSE 1729.
- pixelpoet 7y agoI love how the article starts with the most boring facts about 1729: > 1729 is the natural number following 1728 and preceding 1730.
- russellbeattie 7y agoHeh. I've been reading HN for long enough to never be surprised by the capability of incredibly pedantic people to be incredibly pedantic.
- JoeAltmaier 7y agoWe had to have a home somewhere :) And this is it.
- wwweston 7y agoIf 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 https://en.wikipedia.org/wiki/Interesting_number_paradox
- mkl 7y agoWell, 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?
- 8bitsrule 7y agoAnother fun fact: 1 + 7 + 2 + 9 = 19 ; 19 × 91 = 1729
- taberiand 7y agoThis kind of coincidence is just cute, it doesn't imply anything useful mathematically right?
- BGthaOG 7y agoI 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/ https://www.masjidtucson.org/quran/miracle/
- lonelappde 7y agoThat's numerological nonsense like Bible Code.
- BGthaOG 7y agoIt is not; I invite you to study it before you reject it.
- mangamadaiyan 7y agoThe burden of proof is on the person making the claim. Pray supply something more substantial than a link (to what looks like a religious organisation) in support of your claim.
- BGthaOG 7y agoI agree, hence the link. You are asking me to write out in a comment the information that is presented clearly and accessibly in the link.
- emmelaich 7y agoAnd it belongs to the first pair > 1000 to both have Wikipedia pages!
- pishpash 7y agoIt doesn't appear to be anything fundamental, just a number that makes the proof technique work out. As the authors point out, that dimension is only a condition to get some loose bound working, not a necessary condition generally: It is possible to improve the factor K = 1728 appearing in Corollary 5.5, at the expense of introducing various technical complications into the algorithm. In this section we outline a number of such modifications that together reduce the constant to K = 8 + ϵ, so that the modified algorithm achieves M(n) = O(n log n) for any d ≥ 9 (rather than d ≥ 1729).
- sllabres 7y agoInteresting but as it seems currently without practical implications for multiplication: https://en.m.wikipedia.org/wiki/Galactic_algorithm https://en.m.wikipedia.org/wiki/Galactic_algorithm