May 2015 - mathfun@mailman.xmission.com

[math-fun] Universe designed to support life?
by Warren D Smith 07 May '15

07 May '15

I'm interested in claims of the kind "the universe's fundamental constants were fine tuned with the goal of supporting intelligent life" and the question of how to assess how valid/crazy such claims are. One can collect various claims of the form "if constant X were changed to become >Y*X, then the universe would become unfriendly." Please list your favorites. I'd like to assemble a collection. But usually when I try to do that I get Y-values of, say, 10. Not 1.01, which would be a lot more impressive. There are certain Christians etc who enjoy collecting such claims, but some of them are misleading (and some are just completely wrong, but I'll ignore those). Two examples: "The neutron/proton mass ratio is about 1.001 and if it were >1.01 or <1 then life would be impossible." Really this is since the electron is 1836 times lighter than the proton, and perhaps one could argue if 1836 were <750 or >3000 the universe would be unfriendly, but that would be a factor-4-wide range, not factor<1.01-wide. "The 'Hoyle state' of carbon: the third-lowest energy state of the carbon-12 nucleus, with an energy of 7.656 MeV above the ground level. According to one calculation, if the state's energy were lower than 7.3 or greater than 7.9 MeV, insufficient carbon would exist to support life; furthermore, to explain the universe's abundance of carbon, the Hoyle state must be further tuned to a value between 7.596 and 7.716 MeV. A similar calculation, focusing on the underlying fundamental constants that give rise to various energy levels, concludes that the strong force must be tuned to a precision of at least 0.5%, and the electromagnetic force to a precision of at least 4%, to prevent either carbon production or oxygen production from dropping significantly." But S.Weinberg responds: The crucial thing that affects the production of carbon in stars is not the 7.65 MeV energy of the radioactive state of carbon above its normal state, but the 0.25 MeV energy of the radioactive state, an unstable composite of a beryllium 8 nucleus and a helium nucleus, above the energy of those nuclei at rest. This energy misses being too high for the production of carbon by a fractional amount of 0.05 MeV/0.25 MeV, or 20 percent, which is not such a close call after all. Weinberg seems to think the only really impressive fine tuning is the Einstein cosmical constant Lambda, which is not zero, but is about 121 orders of magnitude smaller than a naive guess would have been, perhaps due to an amazing almost-cancelation, albeit nobody understands it. It seems to me even a collection of examples with Y=10 each, still seems impressive if you have enough of them. Here is a quote by Martin Rees about this: "Suppose you are in front of a firing squad, and they all miss. You could say, 'Well, if they hadn't all missed, I wouldn't be here to worry about it.' But it is still something surprising, something that can't be easily explained. I think there is something there that needs explaining." Is there? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Sizing permutation graphs (Leo Broukhis)
by Leo Broukhis 07 May '15

07 May '15

On Wed, 6 May 2015 23:38:35 -0400, Warren D Smith <warren.wds(a)gmail.com> wrote: > >> At what point the diameter will be O(sqrt(N)), O(log(N))? Less than >> O(log(N))? > > --Using my argument last post: > None of those things are ever going to happen if your set of primitive > moves, is of > cardinality <=polynomial(N). Indeed, it is easy to see that allowing arbitrary 3-permutations as elementary operations will result in node degree of O(N^3), but the diameter will be O(N/2), as in general no more than 2 elements could be put in their desired places at a time. The diameter will be O(N/3) for O(N^4) node degree, etc. However, "swapbits" gives at least O(2^(N/2)) elementary operations, and that's where things should be more interesting. Decomposing an arbitrary permutation to these elementary operations looks nontrivial. Regards, Leo

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Re: [math-fun] How use UTF-8 (Unicode)
by Hilarie Orman 07 May '15

07 May '15

Oh what a tangled web we weave, When first we practice to receive. The special characters encodings in the digest are only available if you choose to have MIME messages. You can choose whether to get MIME or non-MIME in the digest through your subscription options. https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun Login, scroll down one page, "Get MIME or Plain Text Digests? Your mail reader may or may not support MIME digests. In general MIME digests are preferred, but if you have a problem reading them, select plain text digests." Select the "MIME" button. If you can't login because you don't know your password, use "forgot password" and have it emailed to you. Yes, it's a nuisance, but probably better than sitting the ascii dark. Hilarie

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Re: [math-fun] Sizing permutation graphs
by Leo Broukhis 07 May '15

07 May '15

On Thu, 7 May 2015 00:00:18 -0400, "W. Edwin Clark" <wclark(a)mail.usf.edu> wrote: > This may be of interest: > > Diameter of the Symmetric Group, Polynomial Bounds > <http://people.cs.uchicago.edu/~laci/papers/04soda.diam.pdf> > > And see the references for other papers on this topic. Thanks, I'll attempt to understand it. :) Leo

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Re: [math-fun] How use UTF-8 (Unicode)
by Keith F. Lynch 07 May '15

07 May '15

Bill Mann <wfmann(a)alum.mit.edu> wrote: > Using Thunderbird on Linux, I have no trouble seeing UTF-8 (Unicode) > encoded messages coming via the Math-fun Digest. Are you sure you're getting the *digest* -- multiple messages in one email? If you are, then I am baffled, as in my digest I'm getting literal ASCII question marks. I've looked at the raw bits to make sure: 00111111. There's nothing for Thunderbird or any other software to interpret. Trying to undo this at my end would be like dividing by zero to correct for having multiplied by zero -- the needed information simply isn't there.

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[math-fun] Sizing permutation graphs
by Leo Broukhis 07 May '15

07 May '15

The graph of permutations of N elements with edges corresponding to transpositions has diameter N (obviously, the distance between 2 single-cycle derangements will be N). What happens to the diameter if we add edges corresponding to 1-step rotations (considering both unidirectional, e.g. rotating only to the right, and bidirectional edges)? What if we allow arbitrary rotations? What if we allow combining disjoint same distance transpositions, e.g. 1234567890 <-> 3412765098 For bit vectors, the operation can be described as swapbits(bitvec, mask, distance) { assert (((mask << distance) & mask) == 0); temp = ((bitvec>>distance) ^ value) & mask; return bitvec ^ temp ^ (temp<<distance); } At what point the diameter will be O(sqrt(N)), O(log(N))? Less than O(log(N))? Has this been studied before? Thanks, Leo

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Re: [math-fun] Universe designed to support life?
by Dave Dyer 07 May '15

07 May '15

Whatever the technical merits of fine-tuning arguments, they are arguing a fact that's not in evidence: that without fine tuning life wouldn't exist. Something would exist, and it's simply unknown if that something would support life-like behavior somewhere, sometime, in a very large universe.

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[math-fun] How use UTF-8 (Unicode)
by Bill Mann 06 May '15

06 May '15

Using Thunderbird on Linux, I have no trouble seeing UTF-8 (Unicode) encoded messages coming via the Math-fun Digest. As in this example: A Minsky is a polygon in R². It is completely specified by two real parameters, δ and ε, To enable this option in Thunderbird at least, select your Inbox, then under the Edit tab, choose Folder / General Information, and under Fallback Character Encoding select 'Unicode (UTF-8). Do not check the 'Apply to all' box below. Many email messages include a field saying which encoding was used to encode the message; this encoding can be overridden, but that's usually a mistake. In addition, I have a dedicated Math-fun folder; if you have one too, select it then set its Folder / General Information to 'Unicode (UTF-8)', but DO check the 'Apply to all' box. The Math-fun server does not 'convert to ASCII'; for most ASCII characters the encoding is the same as in UTF-8; for special characters a variable length encoding is used, usually 3 bytes. Under 'View' select 'Unicode'. While composing a message, under 'Options', select 'Unicode'. If you get this right, even earlier, existing messages should start appearing correctly. Virtually all mail readers on all current operating systems have similar features. Possibly you may need to install additional fonts; they are free, and the OS will tell you how to install them. When composing a message, using the special characters depends on your operating system, On my Linux, under the Applications tab, selecting 'Character Map' brings up a huge choice of characters (mostly special), like infinity 'ꝏ'. The Latin section is the most useful for math. Drag and drop these to your documents. -- Bill Mann -- Sudbury, MA -- 978-443-5671 -- cell: 978-460-3287

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[math-fun] quadratic voting -- done by bees? No.
by Warren D Smith 06 May '15

06 May '15

This web page http://rangevoting.org/BogusBeeQV.html refutes massively false THE SPECTATOR piece on this by irresponsible quadratic voting hype artist (Univ. of Chicago Economist, last I saw) E. Glen Weyl.

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[math-fun] quadratic voting
by Warren D Smith 05 May '15

05 May '15

When Weyl's paper came out originally to the accompaniment of great hype in the popular press, I wrote a web page which basically devastated the whole idea and analyzed things way better and more honestly than Weyl's paper. Read it here: http://rangevoting.org/MonetizedRV.html Posner writes "Quadratic voting is the most important idea for law and public policy that has emerged from economics in (at least) the last ten years." This quote is garbage, or at least I hope it is, because if it is not then economics is even more pathetic than I thought. Also, it is deceptive, because it pretends that this idea emerged during the last 10 years. As my web page demonstrates, which N.Tideman pointed out to me, the idea actually had been suggested by Hylland & Zeckhauser in 1980. Just recently, E.Glen Weyl co-authored the following popular press piece: http://www.spectator.co.uk/features/9512322/humans-are-doing-democracy-wron… This piece is to an even greater extent utter garbage, replete with lies-- demonstrated in the following thread at the Center for Election Science forum: https://groups.google.com/forum/#!topic/electionscience/JrC_yTRUW_w I have after these experiences developed an extremely low opinion of both the scientific ability, and the ethics, of the U.Chicago economist E. Glen Weyl. However, I've only examined some of his work related to "quadratic voting," basically because it keeps being shoved into my face. I have not examined any of his work on any other topic.

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