November 2013 - mathfun@mailman.xmission.com

Re: [math-fun] how many decimal places exist in the mass of an electron (& other such things)?
by Dave Dyer 24 Nov '13

24 Nov '13

Concepts such as "the rest mass of an electron" are human abstractions which are meaningless to nature. Electrons are not billiard balls and cannot rest.

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Re: [math-fun] how many decimal places exist in the mass of an electron (& other such things)?
by Henry Baker 24 Nov '13

24 Nov '13

There's a bit of a problem in gathering together a million-electron blob: they repel one another like crazy. In fact, the amount of energy require to confine them is significant in the m=E/c^2 sense. It might be easier to estimate the mass of an electron & an anti-electron by colliding them together & measuring the energy. At 01:46 PM 11/23/2013, Warren D Smith wrote: >If you try to measure the mass m of an electron, some experimental error DELTAm, >and the energy-time uncertainty principle combined with the finite lifetime >of the universe (at least so far...) causes a limit on the accuracy of m. > >So one could argue, the mass of the electron is inherently unknowable >and undefined to more than a certain number of decimal places. > >Except, somebody could measure the mass of a million-electron blob to try to dodge >that limitation. > >So anyhow... what are the inherent limits on how many decimal places >can exist in such quantities (any further would have no meaning) and >if so, estimate them. >-- >Warren D. Smith >http://RangeVoting.org <-- add your endorsement (by clicking >"endorse" as 1st step)

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Re: [math-fun] Goldbach conjecture update
by Adam P. Goucher 24 Nov '13

24 Nov '13

Yes, I can get arbitrarily large values of your N (and therefore infinitely many) by choosing increasingly sparse admissible k0-tuples. Specifically, if you give me m, then I find a k0-tuple such that no two elements are within m of each other. Then run through the proof and apply the infinite pigeonhole principle, and you end up with some N > m with the property of infinitely many prime pairs with distance N. Sincerely, Adam P. Goucher > ----- Original Message ----- > From: Dan Asimov > Sent: 11/24/13 08:54 PM > To: math-fun > Subject: Re: [math-fun] Goldbach conjecture update > > Just wondering if anyone knows: Do all of these results, from the original Zhang constant down to Maynard's 600, imply only that there exists *at least one* number N no more than the constant such that there are infinitely many primes separated by exactly N ??? > > Or is there some reasoning within the proofs of these theorems that would imply more than one such N ??? > > --Dan > > > On 2013-11-20, at 6:46 AM, Fred Lunnon wrote: > > > Since this topic has subsided from public view, a priesthood incorporating > > James Maynard, Andrew Granville, Terry Tao, has been assiduousy shaving > > Zhang's original 70 million, and refining and simplifying the proof to > > the point > > where a normal mathematically-inclined human (if such an entity exists) might > > possibly be able to follow it with the assistance of a powerful computer and a > > sabbatical year or two --- by which time it would no doubt have undergone > > further drastic improvement. > > > > The current result asserts that there are infinitely many > > consecutive prime pairs with difference h for some h <= 600 . The result generalises to > > finite arithmetic progressions of m consecutive primes with span h , for which instead > > h <= exp(8m + 5) . > > > > For those with time to spare and robust self-esteem, there is > > (considerably) more detail available at > > http://terrytao.wordpress.com/2013/11/19/polymath8b-bounded-intervals-with-… > > > > Fred Lunnon > > > _______________________________________________ > 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] Goldbach conjecture update
by Fred Lunnon 24 Nov '13

24 Nov '13

Since this topic has subsided from public view, a priesthood incorporating James Maynard, Andrew Granville, Terry Tao, has been assiduousy shaving Zhang's original 70 million, and refining and simplifying the proof to the point where a normal mathematically-inclined human (if such an entity exists) might possibly be able to follow it with the assistance of a powerful computer and a sabbatical year or two --- by which time it would no doubt have undergone further drastic improvement. The current result asserts that there are infinitely many consecutive prime pairs with difference h for some h <= 600 . The result generalises to finite arithmetic progressions of m consecutive primes with span h , for which instead h <= exp(8m + 5) . For those with time to spare and robust self-esteem, there is (considerably) more detail available at http://terrytao.wordpress.com/2013/11/19/polymath8b-bounded-intervals-with-… Fred Lunnon

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Re: [math-fun] how many decimal places exist in the mass of an electron (& other such things)?
by Warren D Smith 23 Nov '13

23 Nov '13

ok, to reply to the commenters 1. particle physicists are experts on error analysis. --well, methinks they overrate themselves, but anyhow, this does not answer my original question which pertains to the FUNDAMENTAL limitations on knowability of electron mass. Not the limits of measurements so far, which are almost irrelevant. See, you might say, the electron mass is a real number, defined to infinite #decimals. Due to human inadequacies, we do not know them all, but they exist. But instead you might say, NO, the electron mass really is not, and cannot ever be, defined to more than 50 decimal places. (Or something.) 2. What means 5667565+-11 in the physics literature? --yes, normally this denotes "+-1 standard error" meaning RMS deviation. If other meaning is intended, the author should say so. 3. Million electrons... they repel... try measuring energy of electron/positron annihilation? --yes, electrons do repel and that would be an issue. The annihilation plan will encounter a limit from the momentum uncertainty of starting ingredients, which due to Heisenberg & the finite size of the observable universe sets a fundamental limit on the accuracy of this measurement. However, by measuring not 1, but 1000000 events, then you can decrease the error by factor 1000. Hence my point is, this "fundamental limit" aint necessarily so. Which leads to the question, again, what is the fundamental limit, or maybe there is none? On 11/23/13, math-fun-request(a)mailman.xmission.com <math-fun-request(a)mailman.xmission.com> wrote: > Send math-fun mailing list submissions to > math-fun(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > or, via email, send a message with subject or body 'help' to > math-fun-request(a)mailman.xmission.com > > You can reach the person managing the list at > math-fun-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of math-fun digest..." > > > Today's Topics: > > 1. Re: Newman = -1/Oldman (Bill Gosper) > 2. Fwd: [LifeCA] Geminoid replicator (rcs(a)xmission.com) > 3. how many decimal places exist in the mass of an electron (& > other such things)? (Warren D Smith) > 4. Re: "Happy Valentinukkah?s Day!" (Mike Speciner) > 5. Re: how many decimal places exist in the mass of an electron > (& other such things)? (Henry Baker) > 6. Re: how many decimal places exist in the mass of an electron > (& other such things)? (Rowan Hamilton) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sat, 23 Nov 2013 11:54:21 -0800 > From: Bill Gosper <billgosper(a)gmail.com> > To: math-fun(a)mailman.xmission.com > Subject: Re: [math-fun] Newman = -1/Oldman > Message-ID: > <CAA-4O0EsQAE9Y4o9eTXrHpo45dRSWpSU+=bJaNfNwVmKNntmYg(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > On Thu, Nov 21, 2013 at 5:01 AM, Bill Gosper <billgosper(a)gmail.com> wrote: > >> >> rwg>Maybe later today NeilB and I can find a way to speed this up, or >> maybe >> discover that it's all a bad dream. >> ------ >> Sure enough, Neil quickly realized that Adam's page >> http://cp4space.wordpress.com/2013/10/24/enumerating-the-rationals/ >> contains logarithmic-time recipes for both the forward map >> pos2newman(index) -> rational and newman2pos(rational)->index. >> Using these, the scrozzlement of the 11 term of coth 1 = 1 3 5 7 9 11 ... >> occurs at oldman step 16712177, which could be found >> by log search, if nothing else, even if Neil never writes, >> e.g., newmanposinterval that works on things like Coth[1], since >> we can work with finite CFs and generalize afterward: >> >> Recall >> >> In[68]:= newmanstep[n_] := 1/(2*Floor[n] + 1 - n) >> >> In[74]:= tim[newman2pos[FromContinuedFraction[{1, 3, 5, 7, 9, 11, 2}]]] >> >> 0.000284 (seconds) >> >> Out[74]= 206191919601 >> >> The terminal 2 could be any rational > 1. Using our log search value, >> minus a couple: >> In[75]:= tim[Divide @@ pos2newman[% - 16712179]] >> >> 0.000157 seconds >> >> Out[75]= 577/602 >> >> Here's the magic moment, stepping forward (opposite of oldman): >> In[85]:= ColumnForm[ContinuedFraction /@ NestList[newmanstep, %75, 4]] >> >> {0, 1, 23, 12, 2} >> {24, 12, 2} >> {0, 24, 1, 11, 2} >> {1, 23, 1, 11, 2} >> {0, 1, 1, 22, 1, 11, 2} >> >> We can now simulate the effect of 206191919601-16712178 >> newman steps on Coth[1]: >> >> In[79]:= {Numerator[#], Denominator[#]} &@ >> Convergents[{1, 3, 5, 7, 9, 11, 2}][[-2 ;; -1]] >> >> Out[79]= {{15331, 32042}, {11676, 24403}} >> >> In[80]:= {Numerator[#], Denominator[#]} &@ >> Convergents[{24, 12, 2}][[-2 ;; -1]] >> >> Out[80]= {{289, 602}, {12, 25}} >> >> In[81]:= %.Inverse[%%].{{Coth[1]}, {1}} >> >> Out[81]= {{-30876 + 23515 Coth[1]}, {-1229 + 936 Coth[1]}} >> >> In[82]:= ContinuedFraction[Divide @@ %, 6] >> >> Out[82]= {{24, 12, 13, 15, 17, 19}} >> >> I.e., we've back up past the 11. Step once forward. >> >> In[83]:= Simplify[newmanstep[(Divide @@ %%)[[1]]]] >> >> Out[83]= (-1229 + 936 Coth[1])/(-29345 + 22349 Coth[1]) >> >> In[84]:= ContinuedFraction[%, 6] >> >> Out[84]= {0, 24, 1, 11, 13, 15} >> >> Now it should be easy to chronicle the scrozzlements of ... 7, 9, 13,15, >> etc. >> --rwg >> [...] >> > Not completely easy--the overshot predicate can give false negatives. Here > are the > scrozzlings of the first few terms of coth(1) = {1,3,5,7,9,...} : > Out[275]= {1, {0, 4, 5, 69}} > {241, {0, 8, 1, 7, 69}} > {497, {0, 16, 9, 69}} > {16712177, {0, 24, 1, 11, 69}} > {33489393, {0, 36, 13, 69}} > {281406290723313, {0, 48, 1, 15, 69}} > {562881267433969, {0, 64, 17, 69}} > {1208907373433436732588529, {0, 80, 1, 19, 69}} > {2417833193048065907294705, {0, 100, 21, 69}} > {1329226728136733477867453629484433905, {0, 120, 1, 23, 69}} > {2658454723921649350771260689764778481, {0, 144, 25, 69}} > > which means that after oldman step 1, {1,3,5,7,9,...} becomes {0,4,5,69} > and after > step 241, {0,8,1,7,9,11,...} and after step 497, {0,16,9,11,13,...}. > Running each > 1 more step (-1 newmans): > > In[276]:= % /. {n_, cf_} :> {n + 1, cfzewm[cf, -1]} > > Out[276]= {2, {4, 1, 4, 69}} > {242, {8, 8, 69}} > {498, {16, 1, 8, 69}} > {16712178, {24, 12, 69}} > {33489394, {36, 1, 12, 69}} > {281406290723314, {48, 16, 69}} > {562881267433970, {64, 1, 16, 69}} > {1208907373433436732588530, {80, 20, 69}} > {2417833193048065907294706, {100, 1, 20, 69}} > {1329226728136733477867453629484433906, {120, 24, 69}} > {2658454723921649350771260689764778482, {144, 1, 24, 69}} > > we see the penultimate term alternately upscrozzled after a long run > or downscrozzled after a (relatively short) doubling. > > Instead of trying to guess the general sequence function(s) here, I > switched to the simpler > In[317]:= ContinuedFractionK[1, k, {k, \[Infinity]}] > > Out[317]= BesselI[1, 2]/BesselI[0, 2] > > i.e., {1,2,3,4,5,...} > > Out[306]= {0, {1, 2, 69}} > {1, {0, 3, 3, 69}} > {25, {0, 5, 1, 4, 69}} > {57, {0, 10, 5, 69}} > {15417, {0, 14, 1, 6, 69}} > {31801, {0, 21, 7, 69}} > {132152377, {0, 27, 1, 8, 69}} > {266370105, {0, 36, 9, 69}} > {17523732937785, {0, 44, 1, 10, 69}} > {35115918982201, {0, 55, 11, 69}} > {36857494466319121465, {0, 65, 1, 12, 69}} > {73750982613738224697, {0, 78, 13, 69}} > {1237637881581459231343672377, {0, 90, 1, 14, 69}} > {2475577920866839506242796601, {0, 105, 15, 69}} > {664573435548828553977895141880396857, {0, 119, 1, 16, 69}} > {1329187433441286490429798672020569145, {0, 136, 17, 69}} > {5708903659867095197427783744328276684889422905, {0, 152, 1, 18, 69}} > {11417894430690934721660927622126257230420409401, {0, 171, 19, 69}} > {784634723779399736220988131476081826687296432438576708665, {0, 189, 1, 20, > 69}} > {1569272440702734831700461809377040128700090862996581022777, {0, 210, 21, > 69}} > {1725434941194652898093349545431774267571649300435431096073764288363577, > {0, 230, 1, 22, 69}} > > In[307]:= % /. {n_, cf_} :> {n + 1, cfzewm[cf, -1]} > > Out[307]= {1, {0, 3, 69}} > {2, {3, 1, 2, 69}} > {26, {5, 5, 69}} > {58, {10, 1, 4, 69}} > {15418, {14, 7, 69}} > {31802, {21, 1, 6, 69}} > {132152378, {27, 9, 69}} > {266370106, {36, 1, 8, 69}} > {17523732937786, {44, 11, 69}} > {35115918982202, {55, 1, 10, 69}} > {36857494466319121466, {65, 13, 69}} > {73750982613738224698, {78, 1, 12, 69}} > {1237637881581459231343672378, {90, 15, 69}} > {2475577920866839506242796602, {105, 1, 14, 69}} > {664573435548828553977895141880396858, {119, 17, 69}} > {1329187433441286490429798672020569146, {136, 1, 16, 69}} > {5708903659867095197427783744328276684889422906, {152, 19, 69}} > {11417894430690934721660927622126257230420409402, {171, 1, 18, 69}} > {784634723779399736220988131476081826687296432438576708666, {189, 21, 69}} > {1569272440702734831700461809377040128700090862996581022778, {210, 1, 20, > 69}} > {1725434941194652898093349545431774267571649300435431096073764288363578, > {230, 23, 69}} > > Here the long steps are at > {1, 26, 15418, 132152378, 17523732937786, 36857494466319121466, ...} > > which has the empirical formula > 2^(3*n + 2*n^2) - Sum[2^(k*(-1 + 2*k))*(-1 + 4^k), {k, 0, n}], n=0,1,2,... > I'll yell if Koutschan's q-thing can do the sum. > --rwg > > > ------------------------------ > > Message: 2 > Date: Sat, 23 Nov 2013 14:43:32 -0700 > From: rcs(a)xmission.com > To: math-fun(a)mailman.xmission.com > Cc: rcs(a)xmission.com > Subject: [math-fun] Fwd: [LifeCA] Geminoid replicator > Message-ID: <20131123144332.n1lvq95na8gss04w(a)webmail.xmission.com> > Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; > format="flowed" > > Dave Green has put together a replicator for Conway Life. > He has several versions. The smallest, fastest, has a > bounding box of 3.7M^2, and takes 89M ticks to make a copy. > If I'm reading his description correctly, the population of ON > cells is 150K, most of which is information-carrying gliders. > > Rich > > ----- Forwarded message from david.m.greene(a)gmail.com ----- > Date: Sat, 23 Nov 2013 14:15:34 -0600 > From: Dave Greene <david.m.greene(a)gmail.com> > Reply-To: LifeCA(a)yahoogroups.com > Subject: [LifeCA] Geminoid replicator > To: LifeCA <LifeCA(a)yahoogroups.com> > > The phase-shifted linear replicator is finally done -- several > versions, actually, all using the same single-arm universal > constructor and the same basic recipe. See > > http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&p=9908#p9901 > > The smallest pattern file is only 27K compressed, but the uncompressed > macrocell file is almost 100K so I won't try quoting it here. There > are links in the forum posting. > > Keep the cheer, > > > Dave Greene > > > ------------------------------------ > > Yahoo Groups Links > > <*> To visit your group on the web, go to: > http://groups.yahoo.com/group/LifeCA/ > > <*> Your email settings: > Individual Email | Traditional > > <*> To change settings online go to: > http://groups.yahoo.com/group/LifeCA/join > (Yahoo! ID required) > > <*> To change settings via email: > LifeCA-digest(a)yahoogroups.com > LifeCA-fullfeatured(a)yahoogroups.com > > <*> To unsubscribe from this group, send an email to: > LifeCA-unsubscribe(a)yahoogroups.com > > <*> Your use of Yahoo Groups is subject to: > http://info.yahoo.com/legal/us/yahoo/utos/terms/ > > > > ----- End forwarded message ----- > > > > > ------------------------------ > > Message: 3 > Date: Sat, 23 Nov 2013 16:46:16 -0500 > From: Warren D Smith <warren.wds(a)gmail.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: [math-fun] how many decimal places exist in the mass of an > electron (& other such things)? > Message-ID: > <CAAJP7Y2HDV3+MVsoE3qX1zwp01gqsfrE9xznryhQsLqNJw-W3g(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > If you try to measure the mass m of an electron, some experimental error > DELTAm, > and the energy-time uncertainty principle combined with the finite lifetime > of the universe (at least so far...) causes a limit on the accuracy of m. > > So one could argue, the mass of the electron is inherently unknowable > and undefined to more than a certain number of decimal places. > > Except, somebody could measure the mass of a million-electron blob to > try to dodge > that limitation. > > So anyhow... what are the inherent limits on how many decimal places > can exist in such quantities (any further would have no meaning) and > if so, estimate them. > > > > -- > Warren D. Smith > http://RangeVoting.org <-- add your endorsement (by clicking > "endorse" as 1st step) > > > > ------------------------------ > > Message: 4 > Date: Sat, 23 Nov 2013 16:54:31 -0500 > From: Mike Speciner <ms(a)alum.mit.edu> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] "Happy Valentinukkah?s Day!" > Message-ID: <52912417.9010300(a)alum.mit.edu> > Content-Type: text/plain; charset=windows-1252; format=flowed > > At some point, the Gregorian calendar would add or subtract a February > 29th out of the standard scheme in order to keep the calendar in sync > with the seasons. It's a bit more interesting to contemplate what change > should be made to the Jewish calendar in order to keep the seasons in > sync. Two months have leap days and there is a leap month, so there are > lots of possibilities, but not all combinations are allowed in any given > year due to restrictions on the day of week. > > I suppose another possibility is to just adjust the orbit of the earth, > although one of the calendars would still have to be adjusted since > their average year lengths are different. > > --ms > > On 22-Nov-13 23:32, Henry Baker wrote: >> Cute discussion about the collisions of various calendars over the next >> 10's of thousands of years; >> >> http://www.slate.com/articles/life/explainer/2013/11/thanksgivukkah_when_wi… >> >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> > > > > > ------------------------------ > > Message: 5 > Date: Sat, 23 Nov 2013 16:05:19 -0800 > From: Henry Baker <hbaker1(a)pipeline.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] how many decimal places exist in the mass of > an electron (& other such things)? > Message-ID: <E1VkNDB-0004Gj-3Z(a)elasmtp-scoter.atl.sa.earthlink.net> > Content-Type: text/plain; charset="us-ascii" > > There's a bit of a problem in gathering together a million-electron blob: > they > repel one another like crazy. In fact, the amount of energy require to > confine > them is significant in the m=E/c^2 sense. > > It might be easier to estimate the mass of an electron & an anti-electron > by > colliding them together & measuring the energy. > > At 01:46 PM 11/23/2013, Warren D Smith wrote: >>If you try to measure the mass m of an electron, some experimental error >> DELTAm, >>and the energy-time uncertainty principle combined with the finite >> lifetime >>of the universe (at least so far...) causes a limit on the accuracy of m. >> >>So one could argue, the mass of the electron is inherently unknowable >>and undefined to more than a certain number of decimal places. >> >>Except, somebody could measure the mass of a million-electron blob to try >> to dodge >>that limitation. >> >>So anyhow... what are the inherent limits on how many decimal places >>can exist in such quantities (any further would have no meaning) and >>if so, estimate them. >>-- >>Warren D. Smith >>http://RangeVoting.org <-- add your endorsement (by clicking >>"endorse" as 1st step) > > > > > ------------------------------ > > Message: 6 > Date: Sat, 23 Nov 2013 19:57:45 -0800 > From: Rowan Hamilton <rowanham(a)gmail.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] how many decimal places exist in the mass of > an electron (& other such things)? > Message-ID: > <CAM7qsEGM1HcQv_Zv=_dzPsoiM0ifb7rScnsju89ghfRL9O1f3A(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > Physicists spend a great deal of time and effort on understanding the > errors in any physical measurement. A particle physics PhD involves about 2 > years of classes, 2 years of slave labor, 1 year of measurement and then 3 > years of error analysis. This is no joke. Since particle physics is an > inherently statistical field, particle physicists are experts at error > analysis. > > http://pdg.lbl.gov/2013/listings/rpp2013-list-electron.pdf > > > On Sat, Nov 23, 2013 at 4:05 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> There's a bit of a problem in gathering together a million-electron blob: >> they >> repel one another like crazy. In fact, the amount of energy require to >> confine >> them is significant in the m=E/c^2 sense. >> >> It might be easier to estimate the mass of an electron & an anti-electron >> by >> colliding them together & measuring the energy. >> >> At 01:46 PM 11/23/2013, Warren D Smith wrote: >> >If you try to measure the mass m of an electron, some experimental error >> DELTAm, >> >and the energy-time uncertainty principle combined with the finite >> lifetime >> >of the universe (at least so far...) causes a limit on the accuracy of >> > m. >> > >> >So one could argue, the mass of the electron is inherently unknowable >> >and undefined to more than a certain number of decimal places. >> > >> >Except, somebody could measure the mass of a million-electron blob to >> > try >> to dodge >> >that limitation. >> > >> >So anyhow... what are the inherent limits on how many decimal places >> >can exist in such quantities (any further would have no meaning) and >> >if so, estimate them. >> >-- >> >Warren D. Smith >> >http://RangeVoting.org <-- add your endorsement (by clicking >> >"endorse" as 1st step) >> >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> > > > ------------------------------ > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > End of math-fun Digest, Vol 129, Issue 29 > ***************************************** > -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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"Happy Valentinukkahs Day!"
by Henry Baker 23 Nov '13

23 Nov '13

Cute discussion about the collisions of various calendars over the next 10's of thousands of years; http://www.slate.com/articles/life/explainer/2013/11/thanksgivukkah_when_wi…

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[math-fun] how many decimal places exist in the mass of an electron (& other such things)?
by Warren D Smith 23 Nov '13

23 Nov '13

If you try to measure the mass m of an electron, some experimental error DELTAm, and the energy-time uncertainty principle combined with the finite lifetime of the universe (at least so far...) causes a limit on the accuracy of m. So one could argue, the mass of the electron is inherently unknowable and undefined to more than a certain number of decimal places. Except, somebody could measure the mass of a million-electron blob to try to dodge that limitation. So anyhow... what are the inherent limits on how many decimal places can exist in such quantities (any further would have no meaning) and if so, estimate them. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Fwd: [LifeCA] Geminoid replicator
by rcs＠xmission.com 23 Nov '13

23 Nov '13

Dave Green has put together a replicator for Conway Life. He has several versions. The smallest, fastest, has a bounding box of 3.7M^2, and takes 89M ticks to make a copy. If I'm reading his description correctly, the population of ON cells is 150K, most of which is information-carrying gliders. Rich ----- Forwarded message from david.m.greene(a)gmail.com ----- Date: Sat, 23 Nov 2013 14:15:34 -0600 From: Dave Greene <david.m.greene(a)gmail.com> Reply-To: LifeCA(a)yahoogroups.com Subject: [LifeCA] Geminoid replicator To: LifeCA <LifeCA(a)yahoogroups.com> The phase-shifted linear replicator is finally done -- several versions, actually, all using the same single-arm universal constructor and the same basic recipe. See http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&p=9908#p9901 The smallest pattern file is only 27K compressed, but the uncompressed macrocell file is almost 100K so I won't try quoting it here. There are links in the forum posting. Keep the cheer, Dave Greene ------------------------------------ Yahoo Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/LifeCA/ <*> Your email settings: Individual Email | Traditional <*> To change settings online go to: http://groups.yahoo.com/group/LifeCA/join (Yahoo! ID required) <*> To change settings via email: LifeCA-digest(a)yahoogroups.com LifeCA-fullfeatured(a)yahoogroups.com <*> To unsubscribe from this group, send an email to: LifeCA-unsubscribe(a)yahoogroups.com <*> Your use of Yahoo Groups is subject to: http://info.yahoo.com/legal/us/yahoo/utos/terms/ ----- End forwarded message -----

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[math-fun] MMA free on Raspberry Pi
by Tom Duff 22 Nov '13

22 Nov '13

Just saw this, which I don't think has been mentioned here before: The Wolfram Language and Mathematica on Raspberry Pi, for free http://www.raspberrypi.org/archives/5282 -- Tom Duff. Could you guys be any cooler?

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[math-fun] dual palindromes
by Warren D Smith 22 Nov '13

22 Nov '13

The Latto-Asimov finiteness argument leaves me unimpressed. Essentially same argument instead predicts infinitude: The number of N-digit binary numbers that are palindromic is 2^(floor(N/2)-1+parity(N)) which is bounded between two positive constants times sqrt(2^N). Assuming base-2 and base-3 palindromitude are "independent" then the expected number of N-bit numbers that work in both radices is bounded between two positive constants. Now summing over N, we find the total number of dual palindromes is infinite and the predicted number below B is of order logB. In fact under the probabilistic independence assumption I can prove an infinity exist with probability=1.

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