September 2013 - mathfun@mailman.xmission.com

Re: [math-fun] notation query
by Adam P. Goucher 23 Sep '13

23 Sep '13

Apparently it's a common but not completely standardised notation for the two-point compactification of the real line: http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html Sincerely, Adam P. Goucher http://cp4space.wordpress.com > ----- Original Message ----- > From: James Cloos > Sent: 09/22/13 07:09 PM > To: math-fun(a)mailman.xmission.com > Subject: [math-fun] notation query > > I read a paper today which used a notation I do not remember seeing > before; I'm curious whether it is common. > > The paper discussed the union of the reals with a pair of points at > infinity by using an overbar over the set R. It didn't explain the > notation, but it was clear from the context. > > For those with utf-8 support: > > ℝ̅ ≡ ℝ ⋃ { −∞, +∞ } > > or in TeX: > > \bar{\mathbb{R}} \def \mathbb{R} \bigcup \{ -\inf, +\inf \} > > or maybe \overling{\mathbb{R}}. > > Is that common? > > Thanks. > > -JimC > -- > James Cloos <cloos(a)jhcloos.com> OpenPGP: 1024D/ED7DAEA6 > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] The Simpson's, is a mathematically sophisticated television show ...
by Stuart Anderson 23 Sep '13

23 Sep '13

... if you freeze frame it and look hard enough http://www.theguardian.com/tv-and-radio/2013/sep/22/the-simpsons-secret-for…

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[math-fun] notation query
by James Cloos 22 Sep '13

22 Sep '13

I read a paper today which used a notation I do not remember seeing before; I'm curious whether it is common. The paper discussed the union of the reals with a pair of points at infinity by using an overbar over the set R. It didn't explain the notation, but it was clear from the context. For those with utf-8 support: ℝ̅ ≡ ℝ ⋃ { −∞, +∞ } or in TeX: \bar{\mathbb{R}} \def \mathbb{R} \bigcup \{ -\inf, +\inf \} or maybe \overling{\mathbb{R}}. Is that common? Thanks. -JimC -- James Cloos <cloos(a)jhcloos.com> OpenPGP: 1024D/ED7DAEA6

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Re: [math-fun] near regular dodecahedron with integer vertices
by Adam P. Goucher 22 Sep '13

22 Sep '13

Nice idea! Much more optimal (in terms of the size of the integers compared with accuracy of the angles) is to take all sign changes and even permutations of: (x,z,0) and (y,y,y) where x, y, z are three consecutive Fibonacci numbers. For instance, this dodecahedron is slightly more regular than yours, and much smaller: {{1597, 1597, 1597}, {-1597, -1597, -1597}, {1597, 1597, -1597}, {-1597, -1597, 1597}, {1597, -1597, 1597}, {-1597, 1597, -1597}, {-1597, 1597, 1597}, {1597, -1597, -1597}, {987, 2584, 0}, {-987, -2584, 0}, {2584, 0, 987}, {-2584, 0, -987}, {0, 987, 2584}, {0, -987, -2584}, {987, -2584, 0}, {-987, 2584, 0}, {-2584, 0, 987}, {2584, 0, -987}, {0, 987, -2584}, {0, -987, 2584}} I wonder whether this series gives the best rational approximations to the dodecahedron? Sincerely, Adam P. Goucher http://cp4space.wordpress.com > ----- Original Message ----- > From: James Buddenhagen > Sent: 09/09/13 06:06 PM > To: math-fun > Subject: Re: [math-fun] near regular dodecahedron with integer vertices > > On Mon, Sep 9, 2013 at 11:19 AM, Mike Stay <metaweta(a)gmail.com> wrote: > > Is it a pyritohedron? > > Yes. It is one of an infinite family given by 1 rational parameter. > This one uses parameter value 1597/987 a continued fraction convergent > to the golden ratio. Many curious forms including non-convex and > self-intersecting arise for other parameter values, and not > surprisingly, we can approximate regular ones as closely as desired. > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] NIST Re-evaluating Cryptography Guidance
by Henry Baker 21 Sep '13

21 Sep '13

FYI -- Due to the interest in random numbers & elliptic curves on this list, I thought you might be interested in this announcement, which is roughly analogous to withdrawing a published paper from a journal. http://www.govinfosecurity.com/did-nsa-influence-taint-security-standards-a… Did NSA Influence Taint IT Security Standards? NIST Re-evaluating Cryptography Guidance By Eric Chabrow, September 17, 2013. Follow Eric @GovInfoSecurity The National Institute of Standards and Technology, in a very rare move, is re-evaluating a set of its special publications because of concerns expressed by the cryptography community that the National Security Agency might have corrupted the guidance. NIST, in a supplemental bulletin issued last week, strongly recommends that a key part of the guidance being re-evaluated "no longer be used." http://csrc.nist.gov/publications/nistbul/itlbul2013_09_supplemental.pdf The guidance under review specifies mechanisms for the generation of random bits using deterministic methods (an algorithm which, given a particular input, will always produce the same output), which are based on either hash functions, block cipher algorithms or number theoretic problems, which in turn are based on elliptic curves. The NIST bulletin says the method based on number theoretic problems should no longer be used. Cryptographers raised renewed concerns over the published guidance, Special Publication 800-90A, which specifies techniques for the generation of random bits by applications using cryptography, after revelations that the NSA circumvented much of the encryption that shields Internet communications (see Report: NSA Circumvented Encryption). "Recognizing community concern regarding some specific standards, we reopened the public comment period for Special Publication 800-90A and draft Special Publications 800-90B and 800-90C to give the public a second opportunity to view and comment on the standards," says a NIST statement, which did not mention the suspension of the guidance based on number theoretic problems. "If vulnerabilities are found in these or any other NIST standards, we will work with the cryptographic community to address them as quickly as possible." Beyond Revision NIST often revises its guidance as technologies and processes change, but it's highly unusual - though not unheard of - for the Commerce Department unit to re-evaluate a special publication a year after it's issued because of other reasons, such as experts questioning the reliability of the guide. SP 800-90A was finalized in January 2012. By re-opening the guidance for further comments, NIST effectively makes the document a draft, and not a finalized guide. A NIST spokeswoman stopped short of saying NIST had withdrawn the publication. The other two guides, SP 800-90B and 800-90C, have only appeared as drafts and were never finalized. Stakeholders have until Nov. 6 to comment on all three drafts. Asked if other NIST cryptography and encryption guidance would be reviewed for possible inappropriate NSA influence, Donna Dodson, NIST's Computer Security Division chief, says the institute plans to continue its current approach with a "re-invigorated sense of purpose." Dotson, who also serves as NIST's deputy chief cybersecurity adviser, says NIST and NSA officials will meet to discuss the agency's motivation behind its recommendations on the guidance. But she didn't provide additional details about those sessions, including who would participate in them and when they would occur. "We'll systematically work on continuously reviewing standards, especially those where new technologies have changed the risk landscape," Dodson says. "We'll continue to work with the worldwide cryptography community to produce strong standards in an open and transparent way that have strong mathematical underpinnings." The NSA declined to comment on the developments. Reputation at Stake Seth David Schoen, a senior staff technologist and encryption specialist at the Electronic Frontier Foundation, a technology civil rights organization, expects NIST will re-open other guidance, calling it "a perfectly natural step." NIST's reputation is at stake, Schoen says. "It's very damaging, both for NIST's reputation - creating a risk that implementers will actively avoid NIST standards - and for the actual safety of end-users and organizations who rely on cryptography to protect themselves every day," he says. "It also undermines the sense of collegiality and trust that prevail within standards-development organizations and the research community, communities that historically have been able to proceed as if contributors' technical contributions were made in good faith." Federal law requires NIST to collaborate with the NSA in developing its IT security guidance, a practice NIST champions because some of the brightest cryptographic minds work for the Defense Department agency. Dodson says NIST works with NSA and other federal agencies, such as the Department of Homeland Security, in a number of ways in developing its IT security standards. "These interactions include face-to-face meetings and/or discussions at NIST workshops or other events," she says. "We give talks or attend conferences and workshops hosted by other organizations where NSA staff may also be in attendance. NIST cryptography experts also participate with NSA and other agencies on U.S. and international committees sponsored by non-profit standards development organizations." But some in the cryptography community say the NSA may have used these types of interactions to exploit NIST's guidance for its own advantage. 'Inferior' Approach Phil Zimmermann, the cryptographer who created in 1991 the data encryption program known as Pretty Good Privacy, or PGP, is among those experts who suspect the NSA used its sway to get NIST to create SP 800-90 set of guidance. Zimmermann characterizes number theoretic problems as inferior to other approaches, and suggests those weaknesses could allow NSA to exploit them. "The natural instincts of a good crypto-engineer is to use block ciphers and hash functions as a basis to generate random bit streams," he says. "Nobody who has any common sense in crypto-design would use a number theoretic algorithm to do it. It's just too damn slow, for one thing. And, to do it using a public-key algorithm where somebody who knows the private key for it, which isn't part of the algorithm to predict its output, is just reckless and stupid and should never have been put into the NIST document. [For] everybody who looked at it, it didn't pass the sniff test." Concerns over NSA's influence over NIST's cryptography standard aren't new. An article written by Bruce Schneier, the highly regarded cryptographer and author, raised questions about it in 2007. "It's in the standard only because it's been championed by the NSA," Schneier wrote. "The math is complicated, but the general point is that the random numbers it produces have a small bias. The problem isn't large enough to make the algorithm unusable ... but it's cause for concern. Cryptographers are a conservative bunch: We don't like to use algorithms that have even a whiff of a problem." Follow Eric Chabrow on Twitter: @GovInfoSecurity

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[math-fun] Asimov maxvol regular simplex in n-cube problem
by Warren D Smith 20 Sep '13

20 Sep '13

in dimensions n=4k+3, (and n=1) the answer is the regular simplex arising from n rows of mXm Hadamard matrix, where m=n+1. V(n)=m^(m/2) / n! where m=n+1. Assuming usual conjecture said matrices keep existing. In other (mod 4) dimensions, the problem will be more difficult. If you go down up to 3 dimensions to get 3 mod 4, use Hadamard to inscribe regular simplex in cube-face (of the reduced dimension) then build back up, then you will not lose out too horribly (although this will not be optimal). -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] A Jewel at the Heart of Quantum Physics
by Warren D Smith 20 Sep '13

20 Sep '13

> From: Ray Tayek <rtayek(a)ca.rr.com> > Subject: [math-fun] A Jewel at the Heart of Quantum Physics > https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-qu… > > > Physicists have discovered a jewel-like geometric object that > dramatically simplifies calculations of particle interactions and > challenges the notion that space and time are fundamental components > of reality. --the underlying huge (about 140 pages) paper this came from appears to be http://arxiv.org/abs/1212.5605 it is difficult for me to tell quickly whether this paper is worthless, or worth a lot. They only did their stuff in unphysical fake quantum field theories in lower-than-actual dimensions. Can it be made to work for field theories anybody actually cares about? Are their underlying profundities really profound and useful? Can they quantify their quality by using computational complexity? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Nima Arkani-Hamed complaint transmission
by Henry Baker 19 Sep '13

19 Sep '13

Perhaps I don't know enough physics, but I find Nima's lectures a lot more comprehensible than those of most physicists. I'm not aware of any of this generation of physicists who have Feynmann's gift of both accuracy & clarity of exposition. That having been said, I haven't yet had a chance to look at this particular video of Nima's, but I'm looking forward to it. At 12:36 PM 9/19/2013, Warren D Smith wrote: >somebody on the net was complaining that math is hard because you need >to prove theorems, physics is hard because your theories have to >work, but Nima Arkani-Hamed does neither theorems nor physics that >works, so his life is easy. (He got a $3M prize for an example.)

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[math-fun] Nima Arkani-Hamed complaint transmission
by Warren D Smith 19 Sep '13

19 Sep '13

somebody on the net was complaining that math is hard because you need to prove theorems, physics is hard because your theories have to work, but Nima Arkani-Hamed does neither theorems nor physics that works, so his life is easy. (He got a $3M prize for an example.)

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[math-fun] Probability that all molecules of a gas are in one half of the container
by Warren D Smith 19 Sep '13

19 Sep '13

>rcs at xmission.com rcs at xmission.com Then make it a linear programming problem: Assign non-negative weights Wi to vectors Vi, with sum Wi = 1. Put W = sum WiVi. Then require the dot products W.Vi >=0. The dot products are linear in the weights, so it's a conventional linear programming problem. If it's feasible, you have a solution W. We need to prove that if there's a solution, there's one in the convex hull of the Vi. This seems plausible, but I don't see an immediate proof. --seems to me, rcs here (after removing crud) has a perfectly good reformulation of the problem: there is an empty hemiball if and only if the linear program x . V[i] < 0 for each i=1,2,3...,N has a solution-vector x. There is no need to have a solution "within the convex hull of the V[i]" nor to make weighted combinations of the V[i]. The solution to the gas problem thus also tells us the probability that an LP of this form has a solution (when the V[i] random on sphere). -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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