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[math-fun] Hodge conjecture
by Jon Perry 09 Oct '03

09 Oct '03

While we are on the subject of the $1million questions up for grabs, has anyone seen the lecture at Clay for the Hodge conjecture? The lecturer waffles on about spaces and equivalence and doughnuts for ages, and then right at the end he is asked a question, and says that the Hodge conjecture boils down to something about skew matrices or something else. Does anyone know this - it takes ages to get to on my linear RealPlayer, and I have found no references to it elsewhere. Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] Insomniacs Problem Revisited:
by otto2hoh 08 Oct '03

08 Oct '03

John Conway posted the original insomniacs problem below, which assumes a 12 hour clock with no leading zeros. The following trickier problem also assumes a 12 digit clock. """ Here in washington state I am watching palindromic numbers go by in local time on my on my computers 12-hour clock without leading zeros. I count 281 seconds between two palindromes. How long will it be before I count 281 seconds between two number again? Regards Otto Original Problem: > There's a digital clock at my bedside that shows > hours minutes and seconds, and which I usually look > at the moment I wake up. A few days ago, I happened > to wake up at a palindromic time, and out of interest, > waited until the next palindromic time, and noticed the > interval between them. > > Last night exactly the same thing happened, but the > interval was exactly four times as long as in the previous > case. What did the clock read when I woke up last night? > > John Conway

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[math-fun] Poincare's Conjecture
by Jon Perry 08 Oct '03

08 Oct '03

I think I have proved this, and I am looking for a respectable journal to publish it. Does anyone on this list have any suggestions? I live in the UK and would prefer a UK based journal although this is not a requirement. Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] Re: Cedric Smith - Herbert Wright - 13-coin problem
by Richard Guy 06 Oct '03

06 Oct '03

Sorry to hear of your computer problems. I'm copying this quick reply to `math-fun' and to Rich Schroeppel, who will make sure that you're reinstated on the math-fun list. More later. R.

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[math-fun] 3x+1 problem
by Richard Guy 03 Oct '03

03 Oct '03

I seem to have deleted a recent message which gave the bound to which the 3x+1 problem has been checked (something like 10^17) and an address of a Jeff Lagarias web page which gave info on the problem. Could someone kindlily resend to me? Thanks! R.

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[math-fun] Fwd: RE: Paterson's worms
by Ed Pegg Jr 03 Oct '03

03 Oct '03

This is *very* interesting stuff. I especially like his set of pictures detailing 59 billion steps of evolution. --Ed Pegg Jr Note: forwarded message attached.

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RE: [math-fun] Researchers Create Super-Fast Quantum Computer Sim ulator
by Schroeppel, Richard 03 Oct '03

03 Oct '03

I looked at this a couple of weeks ago, and am leaning to the "mostly harmless" view. I don't have the real paper, just some abstracts. I'm inclined to give the science writer the benefit of the doubt on explaining factoring time. It's so oversimplified it's wrong, but for a target audience that needs an explanation of what factoring is at all, What can you do? Any article with the subexpression O(e^(1.923*cbrt(logN (loglog N)^2))) isn't going to be read by this audience. I did a little web searching for Fujishima, and he seems to have a real research (or teaching?) job at University of Tokyo. I located an abstract of an earlier paper at http://www.securecms.com/iscas2002/Papers/viewpapers.asp?papernum=2130 ISCAS 2002, IEEE International Symposium on Circuits and Systems Sunday, 26 May 2002 - Wednesday, 29 May 2002 Scottsdale Princess Resort, Scottsdale, Arizona ISCAS 2002 Theme: Circuits and Systems for Ubiquitous Computing Paper: 2130; Session: Nanoelectronics I; Location: Ballroom I Time: Wednesday, May 29, 2:00:00 PM - 2:15:00 PM; Presentation: Lecture Topic: Nanoelectronics and Giga-scale Systems: Giga-scale System Design, Memory, etc. Title: An 8-Qubit Quantum-Circuit Processor Authors: Shin-ichi O'uchi, Minoru Fujishima, Koichiro Hoh Abstract: Quantum-circuit processor (QCP) is a parallel processor that executes quantum algorithms at a processing speed comparable to a quantum computer. The QCP emulates the quantum superposition, utilizing massive silicon devices in the fractal hardware-architecture. Its design cost is relaxed due to that recursive structure although a huge amount of devices are required for it. In this paper, 8-qubit QCP was fabricated within a programmable logic device. This is the first realization of the 8-qubit-hardware quantum computing as far as we know. A factoring algorithm is demonstrated by using it in this paper. Mike Stay sent me an abstract of the paper that's raising the fuss. Unfortunately it's a 250K .pdf, but I'll be happy to send copies to people who don't mind that sort of thing. There's a page of text that explains the Quantum Index Processor, and a page of diagrams that try to convey the idea. The abstract is "75-qubit Quantum Computing Emulator" by Minoru Fujishima, Kento Inai, Tetsuro Kitasho, and Koichiro Hoh, mostly from the University of Tokyo. It's from Extended Abstracts of the 2003 International Conference on Solid State Devices and Materials, Tokyo, 2003, pp. 406-407. This paper claims to implement an FPGA simulator for a 75 qbit quantum computer. It seems to fully simulate 11 qbits with 2048 Processing Elements. [This part seems reasonable.] The PEs in turn represent 64 qbit registers with either bit vectors or probability vectors. [This part I don't get.] The paper mainly claims the gadget is useful for developing and testing quantum algorithms. The paper mentions Shor's factoring algorithm, and claims a 10^26 speedup of something or other. It doesn't explicitly say "we've broken factoring". I don't think it represents a factoring breakthrough, but I don't understand it well enough to be sure. A real 75-bit quantum computer could factor numbers of at most around 25 bits, making very generous assumptions about the number of intermediate temporary variables required. Factoring 75 bit numbers is easy with today's ordinary computers. If we make some guesses about scaling: Assume the 11 "full" qbits is 5 + log2(64-qbit register). A 2048-qbit register would be interesting for factoring, and would need 16 "real" qbits for QIP-style emulation. This would need 65536 PEs, with 2048 plain vanilla bits each. This is large for a chip, but would be practical for a program to emulate. This is too good to credit. As Mark Twain wrote in piece about the historical erosion rate of the Mississippi River, "That's the Beauty of Science: Such a wholesale return of Conjecture, from a trifling investment of Fact." Rich rcs(a)cs.arizona.edu

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Re: [math-fun] More on sphere packing
by Dan Hoey 29 Sep '03

29 Sep '03

John Conway <conway(a)math.princeton.edu> wrote: > I didn't read the piece I snipped, but presume that it is supposed > to guarantee to find (in particular) a 25-sphere configuration in 4D if > one exists. I can't really see how it can do that, while still being > approximate. Do you think it can? No, of course not. Why would you presume I attempt such a guarantee, when it is patently impossible? I claim that if there are no (25,4,1+2epsilon) configurations, the algorithm would say so. This is important, because if there are no (25,4,1) configurations, there must be an epsilon for which there are no (25,4,1+2epsilon) configurations. I also claim that every (25,4,1) configuration is represented in the output by an approximation that describes the coordinates of the centers to within epsilon. Each of these can be converted to a (25,4,1-2epsilon) configuration. Dan

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Re: [math-fun] More on sphere packing
by Dan Hoey 29 Sep '03

29 Sep '03

I wrote: > Why would you presume I attempt such a guarantee, > when it is patently impossible? Possibly because about half of what I say has errors in it, including my latest attempt. What I meant to say was summed up correctly by Andy Latto. Dan

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RE: [math-fun] More on sphere packing
by Andy Latto 29 Sep '03

29 Sep '03

> -----Original Message----- > From: John Conway [mailto:conway@Math.Princeton.EDU] > Sent: Monday, September 29, 2003 3:34 PM > To: math-fun > Subject: Re: [math-fun] More on sphere packing > > > On Mon, 29 Sep 2003, Dan Hoey wrote: > I didn't read the piece I snipped, but presume that it is supposed > to guarantee to find (in particular) a 25-sphere > configuration in 4D if > one exists. I can't really see how it can do that, while still being > approximate. Do you think it can? I don't think that one of these epsilon-algorithms could be guaranteed to find a 25-sphere configuration if one exists, because if the algorithm required exact placement, it wouldn't be found, no matter how small epsilon was. But I can imagine an algorithm of this sort with the following property: If a 25-sphere configuration exists, then the algorithm will find 25-sphere configurations for spheres of size 1 - epsilon that all touch a central sphere of size 1, no matter how small epsilon is. Finding such configurations for small epsilon would lend credence to the theory that there is a 25-sphere configuration with spheres of size 1, and examination of the configuration of spheres of size epsilon may help guess the 25-spheres-of-size-1 configuration. Conversely, if there is no 25-sphere configuration, then compactness shows that there is no 25-sphere configuation for spheres of size 1 - epsilon for sufficiently small epsilon, so a program of this sort could provide a proof if epsilon is chosen correctly. Andy Latto andy.latto(a)pobox.com

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