May 2009 - mathfun@mailman.xmission.com

Re: [math-fun] Erroneous school chart with division by zero
by Dan Asimov 05 May '09

05 May '09

Thanks much, Nick and Kerry. I have now ordered a division chart for my very own, since I always wanted to know how to divide by 0. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] Erroneous school chart with division by zero
by Dan Asimov 05 May '09

05 May '09

Some time ago (years?) I learned of a school division chart, sold by highsmith.com, that included ridiculous values for division by zero. The product was later taken off the market and off the website, but I wonder if anyone knows where I can get a hold of a photo of this chart (the one that appeared for a while on the website). Thanks, --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] Stephen Hawking censored ?
by James Propp 05 May '09

05 May '09

>wvv - first American edition, first printing, with the complete number >row and with the later-suppressed text at page 131; 198 pp., hardcover, >near fine in a near fine dust jacket Didn't Hawking say that his publisher discouraged him from putting equations into the book, claiming that each equation would cut down his readership by 50%? Maybe there was an equation that he originally included and that his editors convinced him to leave out. That might be considered "suppression" by some. Jim Propp

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[math-fun] Enigma machine for sale
by Henry Baker 05 May '09

05 May '09

FYI -- For the mathematician who has everything -- your own Enigma machine: http://www.rauantiques.com/about-us/press/the-discovery-of-a-historical-eni…

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[math-fun] Negative numbers work (sometimes) !
by Henry Baker 05 May '09

05 May '09

FYI -- http://www.economist.com/world/britain/displaystory.cfm?story_id=13528529 Deflation and student loans Payback time? Apr 23rd 2009 Students hope for a bonus as Britain pitches into deflation IN 1960, when Britain last experienced deflation, university students would have been puzzled by the idea of borrowing from the government to pay for their studies. These days, as inflation sinks below zero once moreÂprices fell by 0.4% in the year to March, according to the retail-prices index (RPI), an official measure of broad inflation published on April 21stÂgraduating with hefty debts is the norm. Debtors might normally dread deflation, which increases the real value of their loans. But students now hope that falling prices will provide them with a windfall. Interest on student loans is pegged to inflation, as measured by the RPI, in order to maintain the real value of the debt over its term. The rate is set each year in March, which means that the interest rate prevailing in the academic year beginning in September will, in theory, be -0.4%Âa transfer from state to student. Debtors are giddy at the prospect that taxpayers will be forced to pay off part of their loans for them. The government, which never foresaw such an eventuality, seems unsure. Last month it said a decision would be made if and when inflation went negative; it now says it need not decide until September. Student loans are an unusual case. Dozens of state benefits are pegged to the RPI, but officials have promised that handouts such as jobseekerÂs allowance and housing benefit will at worst be frozen. The state pension, also linked to the RPI, must go up by at least 2.5%, following a promise made by ministers a few years ago when inflation fell and pensioners got shirty. The National Union of Students is adamant that loans taken out before 1998, at least, are eligible for negative interest payments. On more recent loans, it concedes that the government has more room for manoeuvre, thanks to a change to the law which says that interest rates must simply be Âno higher than those which the secretary of state is satisfied are required to maintain the value in real terms of the outstanding amountsÂ. In fact, even the pre-1998 borrowers may face an uphill struggle to get any money back. Unless a Âright of set-offÂ is explicitly included in the contract, interest payment is a one-way street from the borrower to the government, according to Lucy Newcomb, a partner at Addleshaw Goddard, a law firm. ÂFor the government, the worst-case scenario is that no interest is payable,Â she reckons. In the long run, it may be no bad thing for students if they miss out on this particular fillip. The loans are already extremely soft: Nick Barr at the London School of Economics points out that almost a third of the governmentÂs costs are never recovered, because the interest it charges students is less than what it has to pay to borrow the money itself. Many beneficiaries are well-off students who borrow the maximum and pop it in a savings account to earn interest. If they were actually to receive rather than pay interest on their debt, calls to toughen up the system in general would probably get a more receptive hearing.

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[math-fun] 2^65536
by James Propp 05 May '09

05 May '09

Does 2^65536 have a name? Should it? (I say "yes": if 10^10^2 deserves a name, surely 2^2^2^2^2 does!) I'll start things off with the not-very-creative name "boobol". Jim

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Re: [math-fun] 2^65536
by Steve Witham 05 May '09

05 May '09

>From: James Propp <jpropp(a)cs.uml.edu> > >Does 2^65536 have a name? > >Should it? > >(I say "yes": if 10^10^2 deserves a name, surely 2^2^2^2^2 does!) > >I'll start things off with the not-very-creative name "boobol". Alas, according to http://googology.wikia.com/wiki/Boobol which quotes the source "infinity scrapers": http://www.polytope.net/hedrondude/scrapers.htm , The boobol is equal to {10,10,100 (1) 2} in BEAF notation, http://googology.wikia.com/wiki/BEAF before which I quail. Btw, http://googology.wikia.com/wiki/Boobol says to see also goobol gibbol gabbol geebol gibol gobbol gabol boobol bibbol babbol beebol bibol bobbol babol troobol tribbol trabbol quadroobol quadribbol quadrabbol (and probably towers of babol and baobab trees). I like 16^256 = 16^16^2 = 2^2^10 ~= 1.8e308, the um, hexolotl or nibbleplex, which stands just outside the border of the IEEE double. --Steve p.s. Maybe googol should be denegrated in favor of geegel = 10^99 giigil = 2^330 And shouldn't 10^100 be a gOgOOl anyway? Or is googol log OOg backwards?

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Re: [math-fun] 2^65536
by rcs＠xmission.com 05 May '09

05 May '09

Date: Mon, 04 May 2009 12:22:58 -0700 Subject: RE: [math-fun] 2^65536 From: "Payton, Paul" <paul.payton(a)lmco.com> An interesting read: http://en.wikipedia.org/wiki/Tetration [I wrote a column about Ackermann's function, tetration, and generally huge numbers recently for the local San Francisco Mensa chapter.] <Jim Propp's original note about 2^2^2^2^2>

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Re: [math-fun] 2^65536
by Dan Asimov 04 May '09

04 May '09

Boobol sounds like an excellent name. Lessee, 2^65536 = 2^(6553*10 + 6) = 64*(2^10)^6553 = 64*(1024)^6553 > 64*10^(3*6553) = 64 followed by 19659 zeroes. This is big. --Dan << Does 2^65536 have a name? Should it? (I say "yes": if 10^10^2 deserves a name, surely 2^2^2^2^2 does!) I'll start things off with the not-very-creative name "boobol". >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] Xor Multiply
by Steve Witham 03 May '09

03 May '09

>From: rcs(a)xmission.com > >Intel is introducing the PCLMULQDQ instruction, which does a 64x64->128 bit >Xor-Multiplication. On the first Google hit: http://software.intel.com/en-us/articles/carry-less-multiplication-and-its-… the definition has some typos. Fixing but improvising notation: Multiplying a[n-1] thru a[0] by b[n-1] thru b[0] for 0 <= i <= n-1: c[i] = xor( [ a[j] b[i-j] for 0 <= j <= i ] ) for n <= i <= 2n-1: c[i] = xor( [ a[j] b[i-j] for i-n+1 <= j <= n-1 ] ) Note that when i = 2n-1, i-n+1 = n, and there is no j: n <= j <= n-1, but the identity element of xor is 0, so c[2n-1] = 0 I find it a little strange to say that, e.g., "GCM requires the carry-less multiplication of 128-bit operands, producing a 256-bit product." As opposed to a 255-bit product with a zero on top. A picture to confirm the intuition would have helped: a3 a2 a1 a0 PCLMULQUQ b3 b2 b1 b0 ----------------------------- a3b0 a2b0 a1b0 a0b0 a3b1 a2b1 a1b1 a0b1 a3b2 a2b2 a1b2 a0b2 (+) a3b3 a2b3 a1b3 a0b3 -------------------------------------- 0 c6 c5 c4 c3 c2 c1 c0 >Knuth is *emphatically* calling for 8x8bit matrix multiply, both xor and ior. >--rwg There is a kind of associative memory that uses a hash where you rotate the rows instead of shifting, and the sum is a majority (actually half-or-more) operation. --Steve

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