April 2014 - mathfun@mailman.xmission.com

[math-fun] In search for Ron Mayer
by Joerg Arndt 24 Apr '14

24 Apr '14

For many years I tried to find out how to contact Ron Mayer, he apparently had the emails address mayer(a)acuson.com (long invalid). As some of the readers on this list are a few semesters older than me, I dare to ask: does anyone have a clue who he is (how to contact him)? Background: Ron wrote some _very_ fine code for the fast Hartley transform, which I (years ago) polished quite a bit. I'd like to say "thanks" to him, and I bugs me I can't. Best, jj

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[math-fun] "reliable" quantum bits
by Warren D Smith 24 Apr '14

24 Apr '14

Superconducting quantum circuits at the surface code threshold for fault tolerance http://www.nature.com/nature/journal/v508/n7497/full/nature13171.html R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland & John M. Martinis Nature 508(24 April 2014) 500-503 Published online 23 April 2014 They claim to have 5 qubits and do operations on them with "99.92% fidelity." This level of reliability is claimed to be a new record and for the first time surpass threshold necessary to allow "quantum error correction" to function. Although just barely. In practice I don't think it'll work unless they could get a couple more nines.

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Re: [math-fun] hitorical mytery
by Henry Baker 23 Apr '14

23 Apr '14

I love the cynicism of politicians using "decimalization" to rationalize inflation. Perhaps we can do it again to remove the penny, the nickel and the dime, and replace them with the "bit" (the "Shannon" ?) (1/2 of a quarter). At 03:42 PM 4/23/2014, Mike Stay wrote: >http://tywkiwdbi.blogspot.com/2012/11/thirty-nine-ninetieths-of-dollar.html > >On Wed, Apr 23, 2014 at 4:23 PM, Dan Asimov <dasimov(a)earthlink.net> wrote: >> Total off-the-wall guess: In old financial conventions, some of which persist to this day, a year is reckoned as 360 days (which I guess simplified the arithmetic), and so one quarter of a year is 90 days. >> >> --Dan >> >> On Apr 23, 2014, at 3:13 PM, Bill Gosper <billgosper(a)gmail.com> wrote: >> >>> R. Weyhrauch notes that >>> http://digital.library.pitt.edu/cgi-bin/t/text/pageviewer-idx?c=darltext;cc… >>> (a document older than the dollarsign) >>> prescribes a bunch of tariffs in 90ths instead of %. I thought I had a mathematical >>> motivation, but was wrong. NeilB thought of a historical, rather than mathematical >>> explanation, but it seems decreasingly plausible. >>> >>> Can someone at least provide a good guess? >-- >Mike Stay - metaweta(a)gmail.com >http://www.cs.auckland.ac.nz/~mike >http://reperiendi.wordpress.com

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[math-fun] hiſtorical myſtery
by Bill Gosper 23 Apr '14

23 Apr '14

R. Weyhrauch notes that http://digital.library.pitt.edu/cgi-bin/t/text/pageviewer-idx?c=darltext;cc… (a document older than the dollarsign) prescribes a bunch of tariffs in 90ths instead of %. I thought I had a mathematical motivation, but was wrong. NeilB thought of a historical, rather than mathematical explanation, but it seems decreasingly plausible. Can someone at least provide a good guess? --rwg

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[math-fun] The NRA computes pi ??
by Henry Baker 22 Apr '14

22 Apr '14

FYI -- http://arxiv.org/abs/1404.1499

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[math-fun] intel and bad instruction sets history/philosophy
by Warren D Smith 21 Apr '14

21 Apr '14

Re swap, there should be a <--> b built into language. It's a matter of syntax. Also it should be a hardware instruction too. Jorg Arndt by saying templates can fix this, is missing my point. My point is: syntax matters. SWAP(a,b) is simply poor syntax for such a common operation. Common stuff, should be short. Principle of the Huffman code. This well known principle was one that ADA, otherwise quite a good language, ignored tremendously. And that single decision alone by the ADA designers, goes a long way toward explaining why ADA achieved far less success than it should have. (And they can say all they want about how syntax does not matter, but their massive failure is just staring us all in the face.) Another huge error made by ADA was making garbage collection optional. As a result, few put it into their compilers. As a result, Joe Programmer could not use garbage collection unless his program was nonportable. As a result, the whole idea completely kamikazed. Re C deficiencies, another huge one is no array bounds checking. It should be provided as part of the language -- for example, A[n] would be bounds checked by default, but one could turn it off by, say A[[n]] or explicitly declaring A to be unchecked int A[77]; or some such. Or even a compiler overrule flag to turn off/on all boundschecking. A tremendous number of bugs have been caused by this one incredibly simple and easy to fix C language design error, plus this is probably the top reason underlying security flaws in everything today. And re add-with-carry, not allowing multiprecision arithmetic, as a result you cannot write good cryptography in C alone. You need assembler. Virtually everything Joe User does today, involves crypto. So it's insane. And yes, add-with-carry does require some thought to see how to put it into an HLL, but the best choice was NOT "completely surrendering." >The proper approach is (of course!) to write programs that write programs. --The proper approach is to make the language have enough power that I do not have to in many common cases. I'm not opposed to your idea per se. >The designers of C didn't think of every possible use 30 years in the future. They should really be ashamed. --I think you were being sarcastic, but I completely agree with this. The bottom line is: they designed something without the future in mind and now we are paying for it. Huge. Security flaws that would not be there if C had included array bound check, are costing literally billions. This would have far far overpaid for the whole C development effort. And if C had included various machine language stuff like in MMIX, then people would have used it, which means CPU designers would have put it in hardware. Instead since it was "not used" CPU designers were not going to supply it. Which meant it was silly to put in an HLL. Vicious circle. >And, by the way, there is a threshold in programming language criticism where "Write your own or cork it!" applies. --ah. The trouble is, writing your own is (a) hard, and (b) virtually certain to be a wasted effort. Which is exactly the problem. Just look at all the wasted language ideas that are out there in languages essentially nobody uses. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Knight's suit of armour gets lick of paint ...
by Fred Lunnon 20 Apr '14

20 Apr '14

Taking a fresh look at that infernal knight's move distance formula, I had to admit that version 6 of my Lemma 4 proof was confusingly cryptic about folding neighbours of the target point back into the first octant; and anyway this tortuous (and arguably dubious) manoeuvre may be avoided altogether, by weakening the constraints on Lemma 3. Warren D Smith <warren.wds(a)gmail.com>, Fri, Apr 11, 2014 at 11:28 PM --- << As I remarked to Lunnon in email, I still do not accept that he has proved the N-distance formula. Despite him seeming to think he has. >> Whether I have identified the issue raised above (with customary daisy-cutter precision) remains unclear. Regardless, relevant amendments, correction of gruesome typos, a modicum of signposting, flag-waving, grand-standing (er, maybe time to take a break) and further tidying are provided for the benefit anyone who might still be following, by version 7 at https://www.dropbox.com/s/nzmzjswtctju23f/knights_path.txt If only this would stabilise for a while it might even manage to get properly typeset. Also my plots of symmetric 4-valent graphs derived from a 6x6 toric board were inadvertantly trashed; subtly enhanced replacements are at https://www.dropbox.com/s/8b0stotr8343mq2/semi_6x6.pdf https://www.dropbox.com/s/gyispnh717ayz86/semi0_6x6.pdf I have in mind an animation showing one graph morphing symmetrically into the other; but cannot presently visualise a suitable permutation. Resort to the computer seems tedious overkill ... Fred Lunnon

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Re: [math-fun] Surface puzzle
by Adam P. Goucher 20 Apr '14

20 Apr '14

Spoiler alert: a solution is included beneath the quoted text. > ----- Original Message ----- > From: Dan Asimov > Sent: 04/20/14 11:11 PM > To: math-fun > Subject: [math-fun] Surface puzzle > > Puzzle: > > Start with a vertically flattish spheroidal surface, and make one Y-shaped cut in the top surface and an identical Y-shaped cut in the bottom surface. Each leg of each Y, after being cut, gives rise to two edges that we'll call "neighbors". > > Now identify each of the 12 edges created this way with one other of these 12 edges, as follows: Given an edge on top, identify it with the neighbor of its corresponding edge on the bottom. > > The resulting depiction of a surface in 3-space can be thought of as crossing itself along three segments sharing a common endpoint, making a Y in space: > > > * > * * > > | > * | * > | > / \ > * / \ * > / \ > > * * > > * * > * > > > > > QUESTION: Identify which topological surface this depicts among all the compact connected surfaces without boundary.* > > --Dan > _____________________________________ n > * Which are the sphere S^2, the connected sum of n tori # T^2 for any n >= 1, > k=1, > n > and the connected sum of n projective planes # P^2 for any n >= 1. > k=1 > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun It's evident that if you walk through a cut and over the sphere, you end up changing your chirality; consequently, the surface is non- orientable so is a connected sum of n projective planes. Now we wish to determine the value of n. When you make the cut followed by the identification, you don't alter the number of faces or edges (in a hypothetical triangulation), but you end up with four fewer vertices and thus have an Euler characteristic of -2. Hence, I claim this is the connected sum of 4 cross-caps. Sincerely, Adam P. Goucher

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Re: [math-fun] new language - anyone?
by Ray Tayek 20 Apr '14

20 Apr '14

At 10:29 AM 4/20/2014, you wrote: >Do you want to work on defining a new computer language? >Send me email. yes. thanks --- co-chair http://ocjug.org/

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[math-fun] intel and bad instruction sets history/philosophy
by Warren D Smith 20 Apr '14

20 Apr '14

> When reading Knuth a long time ago, I never cared much for his MIX code; I just skipped over it. Why should I waste my time trying to understand some assembly code for a non-existent computer? --I was kind of annoyed by MIX too. One of the reasons C language was originally successful, was it tried to make a high-level language which also enjoyed the benefits of,and unashamedly tried to connect to, assembler. (As opposed to pretending assembler did not exist.) So Knuth would have been better off using C than MIX in many ways. However, C fell short of its design goal plus now with C++ has become horrible mess. But anyway, apparently with MMIX, Knuth is trying to be a bit of a prosyletizer for what instruction sets ought to have, rather than just trying to approximate what they are. Also a bit of a bizarre move for a textbook, but I hope it'll influence people a bit to overcome the energy barrier. >I used to like elegant instruction sets: the PDP-10 and the Motorola 68000. National Semiconductor came out with a yet better instruction set in their 32000 microprocessor. We seriously thought about using the 32000 in our medical lasers at Coherent, but when we talked to the National Semiconductor rep, they had totally inferior in-circuit emulators and such development hardware. We went with the 68000. > As hardware technology advanced, we had prefetching, simultaneous instruction execution, pipelining, and so on. The nail in the coffin for me (or should it be the stake through the heart?) was when I was told by someone I trusted that modern compilers can produce faster executing code than all but the most expert hand coding of assembly. At that point, I changed over completely, and now I just couldn't care less about instruction sets. --umm. Well, it depends: do you want performance? If you do, then you should care about instruction sets and architecture. But here is the thing: 90% of computer customers have never heard of the POPCOUNT instruction, much less want to use it and know they want to. So as a business matter, intel does not care about making good instruction sets. What a heck of a lot of computer buyers DO care about, is: can I run some piece of software for shooting monsters with great graphics, or watching porno movies, that was originally written in assembler for performance? And I want that software right now, I do not want to wait a few years for somebody to re-code it. So the fact that, if better instruction sets & architectures are provided, then in 5 years we'll get better performing software, is not a matter of business importance. As a total guess I'd think we could get 2X speedup and/or electrical power reduction with better architectures, but businesswise they do not care because that speedup is for FUTURE software, not today's software. Almost nobody buys a computer because of hoped-for future software. >Warren, what is this better architecture that Intel ran up a flagpole? What should we search for to look it up? --itanium. And by the way, looking into this, it seems ARM and itanium have made some business progress, BUT the way they did so was by going into entirely new markets, like servers and cell phones. In those markets, the software was not already there. So the buyers really *DID* care about "future software" as opposed to "old software." So they really did care about performance. So that allowed these new better architectures to gain some business success. > Why did Apple switch from the 68000 to the x86? Steve Jobs may have been an asshole, but he was a smart one. > Yes, backward compatibility is very important. Nobody wants to be endlessly rewriting their code; we want to move on to newer and better things, not rehashing the old. > What makes a computer language "better"; that seems to be a matter of personal opinion. I did my 68000 coding at Coherent Medical in C, and I liked the language. Later, Coherent switched over to Windows based controllers and C++, but by then I had moved from software engineering to optics and laser engineering. I never learned C++, but I can appreciate its usefulness. I'm still fond of Fortran. I tend to detest new languages, and the only one I've embraced is Python. Once at a computer show, I asked a Forth guy what's so good about Forth. He told me astronomers like it, but otherwise go read about it. When I asked a real astronomer, he said "Nah, we don't use Forth." Then there was Smalltalk; it was supposed to solve all the problems of the universe. I said that when it takes off, there will be plenty of books to read about it; I'm still waiting. --quite. But if you look at some of the languages, they have nice ideas. And I have ideas of my own too for what should be in languages. But all that usually is not going anywhere due to the same energy barrier as Esperanto, only with some new bad-incentives added to (like: fear that the language will go away and you'll be left twisting in the wind). > So, why are we not speaking Esperanto? Maybe because its only use is to converse with fellow fanatics. --it is because, even though it is a better language, and humanity would be better off if we all spoke it -- we'd outperform old-style humanity by a lot -- the average Joe does not find it to his individual benefit to learn Esperanto right now. It only works if nearly everybody does it. If 1 person does it, it's the opposite of useful. It's a barrier to human progress caused by the difference between individual and society-wide incentives. And similar remarks could be made about, e.g. switching to better energy sources... switching to better voting systems... This is a fundamental common problem-structure that comes up in many guises.

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