June 2016 - mathfun@mailman.xmission.com

Re: [math-fun] Very cool new stone vault structure using 100% compression
by Henry Baker 11 Jun '16

11 Jun '16

May I pass "Martin's Marbles" pix on to Philippe at block(a)arch.ethz.ch ? Do you have a reference to the eponymous "Martin" ? At 07:30 PM 6/9/2016, Bill Gosper wrote: >I'm surprised they didn't use Martin's Marbles technology >gosper.org/dodex.gif >gosper.org/martinsmarbles.png >which is indifferent to the sign of g. --rwg >On 2016-06-08 16:02, Henry Baker wrote: >> (Watch the 4.5 minute vimeo video using the link below to see the >> structure being built.) >> >> Look ma, no mortar! >> >> Dr. Philippe Block (no kidding!!) is from MIT. >> >> http://www.wired.com/2016/06/compression-keeps-24-tons-stone-collapsing/ >> >> https://player.vimeo.com/video/167868985

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[math-fun] Draft of my June 2016 blog post
by James Propp 10 Jun '16

10 Jun '16

Hi, funsters. I started writing a new draft titled "Sri Ramanujan and the Secrets of Lakshmi" and would love to get people's feedback. I plan on publishing it on June 17 (though I'll continue to be able to make changes to it even after I publish it on my blog). Please leave your feedback here: https://mathenchant.wordpress.com?p=770&shareadraft=5759cd2567b5c Keep in mind that all feedback is by default anonymous; I won't be able to reply to your comments (if, say, you have questions), or acknowledge your contribution, unless you tell me who you are. Title: Sri Ramanujan and the Secrets of Lakshmi Beginning: [caption id="attachment_773" align="alignleft" width="268"] Srinivasa Ramanujan[/caption] What can you say about a thirty-two-year-old mathematician who died? That he loved numbers and equations. That he had a mysteriously intimate understanding of infinite sums, infinite products, and infinite co... Read more: https://mathenchant.wordpress.com?p=770&shareadraft=5759cd2567b5c Thanks, Jim Propp

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[math-fun] Very cool new stone vault structure using 100% compression
by Bill Gosper 09 Jun '16

09 Jun '16

I'm surprised they didn't use Martin's Marbles technology gosper.org/dodex.gif gosper.org/martinsmarbles.png which is indifferent to the sign of g. --rwg On 2016-06-08 16:02, Henry Baker wrote: > (Watch the 4.5 minute vimeo video using the link below to see the > structure being built.) > > Look ma, no mortar! > > Dr. Philippe Block (no kidding!!) is from MIT. > > http://www.wired.com/2016/06/compression-keeps-24-tons-stone-collapsing/ > > https://player.vimeo.com/video/167868985 >

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[math-fun] another hidden number problem
by rcs＠xmission.com 09 Jun '16

09 Jun '16

Here's another hidden number problem to play with. I have a secret number (positive integer) N. N is not a multiple of 10. I tell you the sum of the digits, and perhaps an upper bound. You give me a multiplier M1. I tell you the digit sum of M1*N. You give me M2, I tell you the digit sum of M2*N. Etc. Eventually, you guess the number. Puzzles: Can you determine a unique N? Is there a better strategy than just using 2,3,4,... for Mi? For ten-digit N, a program can run through all the possibilities consistent with the current state-of-play. But What if N is twenty or thirty digits? Is there some non-enumerative algorithm that's more efficient for finding N? Extra credit: N^Mi instead of Mi*N. I've had some ideas about this puzzle, but nothing I'd call a solution. Rich

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Re: [math-fun] Diamonds for dopes
by Keith F. Lynch 09 Jun '16

09 Jun '16

Mike Stay <metaweta(a)gmail.com> wrote: > Actually, you just need to have a neutron tunnel from one nucleus to > the other across the barrier. True, but the adjacent carbon atoms are so distant from each other on a nuclear scale that what you're describing is a C13 decaying by emitting a neutron, and that neutron eventually being captured by a C12 nucleus. If C13 (or C12) decays by that or any other means with a half-life of less than about 10^21 years, I'm sure someone would have noticed by now. Several isotopes of much less common elements are known to have half-lives of 10^21 up to more than 10^24 years. Henry Baker <hbaker1(a)pipeline.com> wrote: > If we're going to store the entirety of human history & culture > in a diamond lattice, it makes sense to ensure that the info won't > degrade for a while, at least! I agree. That's why I think diamonds make more sense than other crystals. Diamonds are more durable. They're also no more expensive, given that carbon is ubiquitous and any such crystal would have to be assembled by molecular nanotechnology in any case. So the rarity of natural diamonds is irrelevant. They're also lighter, atom for atom, than most other crystals. And less toxic. And prettier. > BTW, suppose that some civilization has *already* encoded its > information in diamond & sent it Fed Ex (via meteorite drone) to > Earth. Why are we wasting time with SETI instead of reading every > diamond we find? Reading every diamond we find might be worthwhile once we get molecular nanotechnology. We're *already* in the era of big data. They may already be doing automated scans of images from nearly all cameras viewing the public, for images of wanted criminals. In a few years they may test all trash for fingerprints and DNA traces, and all sewage for DNA traces, for the same purpose. > Also, BTW, it looks like DNA data storage may be a lot closer to > hand than C12/C13 diamond storage. Is there a way to somehow > crystallize & stabilize DNA at room temp (or higher) for stable > data storage over thousands of years? I don't know. DNA is notoriously fragile. And bacteria eat it. > Alternatively, is there an error-correcting information coding > scheme for DNA that "heals" itself automatically against > evolutionary pressures so that we could store the DNA info > in real biologic organisms -- e.g., bristlecone pines ? I doubt it, given that DNA was naturally selected to be capable of mutation. (If there was ever a race of organisms using a more stable genetic substrate, it was outcompeted by DNA-based organisms, as the latter were more capable of adapting to their ever-changing environment.) > Perhaps some of this "noncoding DNA" is *already* a message from > the past -- e.g., intelligent dinosaurs that were destroyed 65Mya. There are any number of ways to plant a message that could survive on Earth for millions, or even billions, of years. But if the goal is also for it to be *noticed*, well, see my April Fool's Day post of last year.

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[math-fun] unusual things
by Simon Plouffe 09 Jun '16

09 Jun '16

Hello math-funsters, there is an interesting site here, http://www.futilitycloset.com/?new=true a representation of 1/7 in decimal on an ellipse. the other pages are interesting as well, quite amusing, in the same vein , http://www.laboiteverte.fr/ that one is original, very original, I counted at least 100000 original images and pages. http://www.laboiteverte.fr/?s=math like this 'etch-a-sketch' on a sphere : http://www.laboiteverte.fr/le-doodle-dome-de-tyco-lardoise-magique-spheriqu… and with Pi digits here ??: http://www.laboiteverte.fr/le-doodle-dome-de-tyco-lardoise-magique-spheriqu… This is what I call original. one drawback : the whole site is in french, not the images. Have fun. Cheers. Simon Plouffe

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Re: [math-fun] Digit product proof
by Keith F. Lynch 08 Jun '16

08 Jun '16

> I've pushed a little further. I've confirmed that David Wilson's > greedy algorithm works for all numbers less than B^9 for bases 2 > through 8, and for bases 10, 11, 12, and 16. For instance I've > confirmed that it works in base 10 for all numbers less than a > billion. (By "numbers" I mean the numbers whose digits are to be > multiplied, not necessarily the products thereof). I've pushed it further again. I've confirmed that it works for all numbers less than B^12 in the above-mentioned bases. For instance for all numbers less than a trillion in base 10. > It fails quite rapidly for all other bases through at least base 85. And I've pushed that through base 1000. Interestingly, the first failure in each base always has three digits, and, except in base 9, it's the *same* pair of three digits numbers for two or more consecutive bases. (Well, not the same *numbers*, but the same patterns of digits.) And for bases 18 and above, the number of repeats appears to always be even. For instance 55I (greedy) 2FF (actual) for bases 22,23,24, and 25, an even number of consecutive bases. Why should it always either fail rapidly or (apparently) not at all? What's special about 2,3,4,5,6,7,8,10,11,12,16? (Not in OEIS.)

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[math-fun] Very cool new stone vault structure using 100% compression
by Henry Baker 08 Jun '16

08 Jun '16

(Watch the 4.5 minute vimeo video using the link below to see the structure being built.) Look ma, no mortar! Dr. Philippe Block (no kidding!!) is from MIT. http://www.wired.com/2016/06/compression-keeps-24-tons-stone-collapsing/ https://player.vimeo.com/video/167868985

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Re: [math-fun] Diamonds for dopes
by Keith F. Lynch 07 Jun '16

07 Jun '16

Veit Elser <ve10(a)cornell.edu> wrote: > Not sure what?s driving this discussion, or the fascination with > carbon isotopes, ... Perhaps it's slightly off-topic here, but I for one find it fascinating because it could hold all the world's knowledge (books, journals, movies, TV shows, newspapers, web pages, databases, letters, emails, security videos, genomes, paintings, etc.) in a crystal smaller than an ant, a crystal that should last for at least billions of years even with no special storage precautions. The longevity of the world's information is currently a major concern, everything from nitrate-based movie films from the early 20th century to computer tapes and diskettes from the late 20th century. Not to mention much older stuff. Henry Baker <hbaker1(a)pipeline.com> wrote: > Although I don't know enough quantum physics to do the calculation, > my gut still tells me that the probability of exchanging an adjacent > C12 for a C13 nucleus is non-negligible. My gut tells me otherwise. :-) How do you think it would happen? Thermally? Without disrupting the extremely rigid lattice? Each carbon atom is at the center of a regular tetrahedron, with a covalent bond at each vertex. In general, the Arrehenius equation predicts reaction times of much more than trillions of years when applied at absolute temperatures that are small fractions of the temperatures at which the reaction proceeds at a reasonable rate. Quantum tunneling? The distance between the centers of adjacent atoms in a diamond is 1.54E-10 meters. That's 57,000 times the 2.7E-15 meter radius of a carbon nucleus. And for it to happen, two nuclei would have to simultaneously tunnel into each other's positions. It could happen, but for diamond to spontaneously turn into graphite is far more likely -- and has never been observed, even though most natural diamonds are billions of years old. None of this has anything to do with *electron* delocalization, but there's little of that too. Pure diamond is an excellent electrical insulator, with a breakdown voltage of more than a million volts per millimeter. (It's a good conductor of heat, but that's due to phonons, not electrons.) > So I would guess that the probability of an adjacent C12<->C13 > exchange would be dramatically improved with 100x atmospheric > pressure, and floating on top of molten tungsten at 6500-7000 > degrees F. I agree. Of course the lattice would cease to exist first. > So the real question is: what is the falloff in exchange > probability as we lower the temperature from 3500F to 100F ? Apply the Arrhenius equation to find out.

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Re: [math-fun] Diamonds for dopes
by Keith F. Lynch 07 Jun '16

07 Jun '16

Henry Baker <hbaker1(a)pipeline.com> wrote: > Re Charles Stross & C12/C13 isotope lattices: Cool! > Did Charles Stross have any ideas about how to read out these data? Here are his original posts on the subject: Newsgroups: rec.arts.sf.composition From: Charlie Stross <charlie(a)antipope.org> Subject: Re: The Cafe on the Common Date: Thu, 17 Jul 2003 18:04:58 +0100 Stoned koala bears drooled eucalyptus spittle in awe as <oak(a)uniserve.com> declared: > (So is 'does not involve floppy disks in any way, shape, or form', these > days. The good ones are old and the new ones you can get are junk.) This has *always* been true. That is: there's a double-digit percentage defect rate on floppies. Reliable ones get reused indefinitely, defective ones get binned with a "the new ones you can get are junk" comment attached. Floppy disks -- better than saving to compact cassette, in much the same way that being subjected to the pilliwinks is 'better' than going to the gallows. I can't wait for diamond-phase storage to show up. (A zero is a carbon-12 nucleus, a one is a carbon-13 nucleus, you use nanotech assemblers to read/write the stuff, it stores 10^22 bits per gram with serious redundancy and error correction and has a half life measured in gigayears. Plus, you can wear it as jewellery.) -- Charlie Newsgroups: rec.arts.sf.composition From: Charlie Stross <charlie(a)antipope.org> Subject: Re: The Cafe on the Common Organization: foobar quux Date: Thu, 17 Jul 2003 19:14:48 +0100 Stoned koala bears drooled eucalyptus spittle in awe as <mra(a)pobox.com> declared: > It's a stone bitch to read, tho. I'll grant you it *is* an archival medium, and Drexler-complete to boot (to the extent of requiring a mature nanotechnology base with general purpose assemblers to make it really practical). On the other hand, what's not to like about the idea of being able to carry the sum total of human recorded media (film, audio, video, text ...) around on a ring? Or a couple of thousand serialised and recorded human personalities, if you buy Moravec's estimate of the computational complexity of the human brain. -- Charlie > Re adjacent C12/C13 swapping: in a quantum universe, never > say "never". > The probability & half-life of such swapping should be calculable. The atoms are locked into a rigid lattice. It's enormously more likely that the lattice will break down than that atoms will swap in an intact lattice. So it's the half-life of the lattice that you should calculate. > Perhaps it's 1000 years. Perhaps it's 1000 billion years. I can't immediately find the answer online, but given how chemical and evaporative processes tend to scale with temperature, I'd bet money that it's enormously longer than 1000 billion years at room temperature. I really think cosmic rays will destroy it first. Or neutrinos (!) if you shield it from cosmic rays by placing it in the center of a large non-radioactive asteroid. Except that in the time it would take for neutrinos to do their damage, the background neutrino flux would probably drop off greatly due to the cosmological expansion of the universe. The same effect would also cool it to close to absolute zero. So might diamonds really be forever? No. Quantum tunneling will get them in the end if nothing else does, though that may take closer to a googolplex years than to a mere googol years. It's also possible that C12 and/or C13 is slightly radioactive. I don't think a half-life of much more than 10^24 years would have been noticed yet. Fred Lunnon <fred.lunnon(a)gmail.com> wrote: > Rather more than "all of Earth's carbon" I imagine, if literally > "literally", since the recording process itself would be recorded; That obviously depends on the resolution of the video recording. A resolution of one millimeter would more than suffice to determine who was doing what to whom. That's about 5.1E+20 pixels for the surface of the Earth. At 100 frames per second that's 1.6E+40 pixels for ten billion years of recording. At 30 bits per pixel, that's 4.8E+41 bits total, about 8E+17 moles of bits. One mole of bits requires 12.5 grams of carbon, so 6.4E+13 kilograms of carbon. Sources quoted in Wikipedia give crustal abundances of carbon from 200 to 1800 ppm. The mass of the Earth's crust is at least 2.4E22 kg, so at least 4.8E+18 kilograms of carbon. Only about one percent of that is C13, so 4.8E+16 of C13 plus another 4.8E+16 of C12 for your library. So the amount of carbon suffices to store 1500 copies of our video. And that's not taking into account video compression or the fact that the amount of C12 and C13 doesn't have to be equal. (What the most efficient data encoding is when one-bits cost more than zero-bits is a topic for another day.) Someone please double-check my arithmetic. Thanks. On the other hand, the Stross novella in question, "Palimpsest," depicts an Earth and sun which are re-engineered to last trillions of years, not mere billions. And not just one timeline is recorded, but a vast number of different ones, caused by time-traveler intervention. So maybe they'd better use compression and other techniques to maximize the use of that carbon. Of course they can also bring in more carbon from extraterrestrial sources, or from below Earth's crust.

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