# Why has the question “Optical methods for number theory?” been closed?

Edit: The MO question has now been reopened, and the two answers here that addressed it have been copied across.

The question Optical methods for number theory? was put on hold. While answers are unlikely to help prove any new theorems, I wonder whether those closing it considered the possible benefit to number theorists (a) explaining their work in a non-specialist (general) context, and (b) collaborating with experimental physicists, who in my experience are often very open to interesting applications of their techniques. Do others agree? Could one or more of the people voting to close explain their reasoning and whether/how the question could be reinstated by editing?

• I am not sure why this is downvoted. Possibly, because "Do you agree?" is in there and somebody thought it is a good idea to answer this question via a downvote. However, this is not the recommended practice on meta.MO. Other than that I consider this question as completely justified (it seems the question was closed without any explanatory comment whatsoever) and attracted some activity that was wositively received. So if it is not a good idea to ask for explantion in such a case I do not know when it ever would be. – user9072 Jun 19 '14 at 9:41
• Thanks Stefan for improving the title. – user25199 Jun 19 '14 at 11:35
• I hope this is not considered as inappropriate, but I was just interested in seeing if people here would appreciate this question. To me personally it seems interesting. – Dilaton Jun 19 '14 at 11:43
• If you're interested in novel ways of implementing computing that use ideas from other disciplines, you may find molecular programming very cool: plus.google.com/u/0/117663015413546257905/posts/3kP9GNKWy5d Personally, I like quantum computing the best as an alternative approach to computing. I'm not sure if MO is the best forum for interdisciplinary topics like these though. On a fun side note, you can even compute with soldier crabs! technologyreview.com/view/427494/… – Yuichiro Fujiwara Jun 19 '14 at 12:39
• @Yuichiro Fujiwara: My favourite is slime mold: youtube.com/watch?v=czk4xgdhdY4 – Emil Jeřábek Jun 19 '14 at 13:45

Actually such devices were at one point in the 20th century the state of the art for doing certain number-theoretical calculations, notably factoring. See http://en.wikipedia.org/wiki/Lehmer_sieve (specifically the 1932 device, pictured in pages 18-20 of http://people.ucalgary.ca/~hwilliam/Sieve_Pictures.pdf).

• This could have been a great answer for the original question had it not been closed. – Gil Kalai Jul 1 '14 at 20:52
• Noam: as the MO question has been reopened, the OP requests that the answers here be made answers there. (I don't have the tools to do that automatically myself.) – Todd Trimble Jul 3 '14 at 12:42

As far as I can tell, the question was founded on the false premise that the linked paper actually described a "physics method for number theory". There doesn't seem to be any number theory less than 2000 years old arising from the idea. The example is a better fit for a question asking for idealized physical models that are good for describing number theoretical concepts in a pedagogical setting. In fact, there are many nice examples of such, e.g., shining a point source of light from the origin of a lattice and seeing which lattice points are illuminated.

Unfortunately, MathOverflow isn't really a forum for the sort of interdisciplinary collaboration that you seem to be suggesting. I think such fora require strong commitment from the participants to overcome the usual barriers of language and practice, and MathOverflow is more of a "spare time" thing.

• Thanks for taking the time to answer. Agreed that the example is not very helpful; it is the question I am mostly drawing attention to. "Forum" is your word, not mine - I am not proposing anything different to the usual question/answer format, just respectfully disagree about whether it might be helpful, even if to just a few. – user25199 Jun 19 '14 at 11:58
• I agree with S. Carnahan, and this was also my reason for voting to close. In addition I was also influenced by the quality of the other questions raised by the same user. Perhaps this second reason is unfair, but it did inform my judgement of how much thought was put into this question. – Lucia Jun 19 '14 at 12:44
• OK, I see that the question would need a complete rewrite, and there is not strong enough support from the OP or community. I still think interdisciplinary questions are in principle valuable for MO, but will take this up some other time. – user25199 Jun 20 '14 at 7:46

I agree with Noam (great pictures, better than I found!). I was excited to post some info but what I had to say (and more) was really all in the answers there albeit as "check out these links" and some cases just in the comments. Now I regret that I didn't.

SO Lehmer first used a device made of bicycle chains and rods and later devices made of gears with holes in them. This 1932 article relates in rather breathless prose that one of the gear mechanisms (combined with theory) proved in a few minutes that

the great unconquered nineteen digit number $3,011,347,479,614,249,131$, known to be a factor of $2^{95} + 1$ and suspected to be prime, is indeed prime.

A few years back (maybe 2000?) there was great excitement over rumors that Adi Shamir had a breakthrough which would speed up (the sieving step of) the number theory sieve. The record factoring of an RSA key was for a 465 bit integer and the breakthrough was rumored to make 512 bit keys "very vulnerable." When the details came out of the punnily named TWINKLE device, it turned out to be an electro optical device using LEDs and filters. There were scoffers but it is agreed to be quite clever. However it has never been built. Enhanced (theoretical) versions might threaten 768 bit keys (for an organization willing in 2000 to invest in 80,000 pentium 2 PCS and 5000 TWINKLE devices for 9 months). 1024 bit keys are probably beyond that and I think that the state of the art in unbuilt (or so they say...) special purpose devices is no longer optical.

If the question is reopened I would export this answer although I'm sure that others could do a better job.

• Aaron: as the MO question has been reopened, the OP requests that the answers here be made answers there. (I don't have the tools to do that automatically myself.) – Todd Trimble Jul 3 '14 at 12:43