Murray Gell-Mann: The Quark and the Jaguar

Som thyms ilustrated from elektoral methods.

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( Kapital-i, in 'I, myself', now spels Il as in isle or aisle.
Leter y spels ryd for reed or read and partys for parties.
Leter w spels swn for soon. )



Murray Gell-Mann's popular work ( publish'd by Little, Brown and Co in 1994 ) tels a litl about his personal lIf, mostly his yuth -- tho ther ar a fw jenial anekdots about kolygs. This is just as wel, bekaus as C S Lewis said: He'd never red an auto-biografy yet in wich the erly yers wern't by far the best. Lewis apyrs to hav diskover'd a law of natur, or human natur. Gell-Mann is a student of both.

Gell-Mann's chapter, 'Quarks and al that' ekos '1066 and al that', as if we wud laf-off his most famus diskoverys as ancient history. In fakt, he givs a typikal akount yu mIt ryd in other popular fysiks bwks.

He is much beter on kurent reserch to demystify quantum theory. The paradox of Schrodinger's kat is laid to rest ( tho atempts may be mayd to revIv it ).

Komplex systems.

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Never the les, the fokus has chanj'd, from : wat ar the basik parts of the world? to : how dos every-thing fit together so it works properly? Gell-Mann help'd found the Santa Fe Institute konsern'd with the jeneral propertys of komplex systems and ther emerjent fyturs that mak suksesiv kemikal, biotik and social systems iredusibl houls.

The Quark and the Jaguar sets out to defIn komplexity. Komplexity is in the observer and the observ'd. Observations ar most komplex wen they ar not so aparently random, that no ruls kan be abstrakted by the observer, and wen the observations ar not so regular, that they kan be sum'd-up in a simpl rul.

Konsequently, the skil of observers is most trI'd, as themselvs 'komplex adaptiv systems', wen they hav to distinguish most kerfuly the esential paterns in the data - the sensory 'signals', if yu lIk, from the random nois. ( That is, if yu konsider uon's perseption of the ryl world rather lIk resyving a radio signal, so uon has to fIn twn out the interferens to its mesaj. )

The 'nois' kud be superstitions kaus'd by uon's konditioning to chans asociations betwen events that hav no rational konektion. How-ever, Malinowski's anthropolojy and Jung's sykolojy hav impres'd on us that aparently sily kustoms may hav a ritual valu for the integration of sosiety and of the personality.

No dout much of the para-normal is kredulus. But I dont agry with Gell-Mann's throw-away dismisal of 'sykik detektivs'. The polis ar sientifik investigators ( in a demokrasy ). If they find such pepl yusful at tIms, that is shurly being praktikal rather than dogmatik about things we dont understand.

Any-way, Gell-Mann's trytment of komplexity may be ilustrated by voting methods. Kandidats first past the post in marjinal konstituensys depend larjly on chans faktors to win. 'Ther is no greiter gambl than a British jeneral elektion,' admited uon devoty of the simpl majority system. An oposit fault aplIs in the saif syts, wer results ar tu determin'd. An ajent bousted he kud put up a pint pot of byr in this konstituensy and stil get it elekted.

The random efekts of marjinal konstituensys and the pre-determin'd efekts of saif syts ar both exampls of low 'efektiv komplexity'.

The voters ar kaut betwyn tw extrems and hav difikulty adapting to the system either way. If yu ar in a saif syt, yu no yor vot is unlIkly to mak any diferens. That's wI party politicians tend to favor singl member systems. A saif syt is a lokal monopoly for som party, hws kandidat dos not hav to ern an elektiv proportion of the vot, in kompetition with kandidats of his own party, as wel as of other partys.

In a marjinal konstituensy, yu may hav to vot taktikly for the best chans to mak yor vot kount. The information valu of the X-vot is tu low to rejister mor than a singl preferens, unlIk a rank'd chois.

A kombination of an elektiv proportion and a rank'd chois ( wich exists as a voting system kal'd the singl transferabl vot ) therfor inkryses the efektiv komplexity of a voting system in tw ways. The rank'd chois of a preferens vot reduses al the 'nois' from split vots that interfyrs with and frustrats the popular wil. A proportional kount prevents vots being wasted in prediktabl pIl-ups that mak saif syts.

In short, the voters hav the best chans of adapting the politikal system with transferabl voting.

That's wI the Establishment lyst wants that system, to disestablish its oposition to the world's chanjing nyds. Michels kal'd this evident stait of afairs 'the iron law of oligarky'. But government is supos'd to be the sybernetik prinsipl of the rulers responding to the ( especialy voting ) information fyd-bak of the rul'd. The lyst efektiv government as sybernetik system has minimal fyd-bak methods of voting.

Typikly, thys ar partisan systems that only tel the rulers wat they want to no from the rul'd, naimly that they folow ther party lIns. Indyd, the voters kan do no other, as the lIks of party list systems pre-defIn the terms of the popular vot.

Zipf's law, self-similarity and fraktals.

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I red som-wer that at a konferens, Stephen Hawking had just quoted off the top of his hed an equation about a mIl long, wen Murray Gell-Mann promptly stud up to point out a mis'd term. Yet The Quark And The Jaguar taks an interest in the simplest of arithmetik laws.

They may aplI thru-out the sienses. Zipf's law is uon of many 'skaling laws' or 'power laws' about wich '...we see what is going on but do not yet understand it.' For exampl, yu kan rank 1st, 2nd, 3rd etc the sitys of a kuntry by ther population sIz, wich turns out to be inversly proportional to that rank.

If the first sity has about 10 milion pepl, the sekond sity turns out to hav about haf that number or around 5 milion. The third larjest sity wil hav uon-third the population of the bigest, or som thry and uon-third milion pepl. And so on, down to, say, the hundredth sity at about 100,000 sitizens.

Similar relations hold for ranking kuntrys by ther volum of bisnes in exports, or for ranking firms by ther volum of bisnes in sayls.

Modify'd versions of Zipf's law may produs a formula that is a beter fit of the data, but the point is that ther is an under-lying regularity. Gell-Mann says this is reminisent of self-similarity found in natur. Trys from ther larjest branches to ther smalest twigs, or rivers down to ther smalest tributarys, hav a karakteristik shaip at every skail. The saim is tru to som extent of klouds and mountains and many natural fyturs.

Such fyturs do not hav regular dimensions, uon, tw or thry. But they wer found to hav fraktional dimensions. A skrw'd-up bal of paper is not a proper bal of thry dimensions but is mor than tw dimensions. It may typikly mesur over 2.7 dimensions. LIkwIs, the squigly lIns, say, of rivers on maps, hav a karakteristik fraktional dimension of slItly mor than uon dimension.

Hens, the term 'fraktals', wich relat to 'kaos' theory. In Does God Play Dice? Ian Stewart says: 'The same complexity of structure that lets fractals model the irregular geometry of the natural world is what leads to random behaviour in deterministic dynamics.'

Noing the fraktals of natural fenomena enabls them to be model'd rylistikly as in komputer 'land-skaips'.
Yu kud also simulat a sosiety and an ekonomy, with the help of skaling laws like Zipf's law.

Borda's method

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The Santa Fe Institute inkluds politikal siens in its aray of systems studys. But it is posibl Gell-Mann's kolygs havn't herd of Borda's Method of kounting vots for a singl vakansy. This is aktualy an elektoral version of Zipf's law.

Voters kan order ther chois of kandidats, 1st, 2nd, 3rd, 4th, etc. Thys preferenses ar given du weit in the kount, as a mesur of ther order of importans. If ther wer fIv kandidats, yor first preferens wud get fIv points; yor sekond wud get for points, and so on to yor last preferens geting uon point.
Laplace gav an involv'd prwf of Borda's Method.

In Elections and Electors, JFS Ross pointed out that the mor kandidats standing, the les important the first preferens, yusing Borda's method of weiting the kount with an arithmetik serys.
Ross sujested the preferenses be weited by a jeometrik serys. The first preferens wud kount as uon vot, the sekond as haf a vot, the third preferens as uon-quarter of a vot, the forth as uon-eith of a vot...

A hapy medium, betwen weiting by the arithmetik serys and by the jeometrik serys, wud be to weit preferenses with the harmonik serys. Chois 1 kounts as uon vot; chois 2 kounts as 1/2 a vot; chois 3 kounts as 1/3 of a vot; chois 4 kounts as 1/4 of a vot...

This modify'd version of Borda's Method was uons favor'd by Sir Robin Day. And it is Zipf's law for an elektion, wer-by the kount is inversly proportional to the vot.

Yu kud imajin Zipf's law aplI'd to sitys as an 'elektoral' system of how pepl vot with ther fyt. The larjest sity atrakts twIs as many as the sekond larjest, thry tIms as many as the third larjest, etc. Borda's politikal justis turns out to be a kas of art unkonsiusly imitating natur.

Borda's method was desIn'd to over-kom an objektion to the Sekond Balot, wich dos not weit preferenses to akount for ther order of importans. If thry kandidats kontest uon syt and non wins over haf the vots, the kandidat with lyst vots has to stand down. A sekond balot desIds betwyn the tw remaining kandidats.

But Condorcet pointed out that the eliminated kandidat ( say, a senter kandidat ) mIt hav won mor vots from either a rIt or a left wing kandidat than they wud hav won from ych other. ( By the way, this isnt nesesarily the kais. Extryms may hav mor in komon than moderats. )

Borda's method, in turn, is open to the objektion that the leser weits given to leser preferenses, kount to som extent against a voter's first preferens. That kandidat has a beter chans of wining if the voter refrains from ading further choises.

This problem is over-kom by the transfer of vots, surplus to a quota or proportion of vots nyded to elekt the most prefer'd kandidat, akording to the voters' suksyding preferenses for kandidats, elekted in multi-member konstituensys.
The sIz of the most prefer'd kandidat's surplus vot determins how much weit to asIn to the next preferenses of the most popular kandidat's voters.

Borda's method has to asum wat valu voters asIn to ther preferenses. But with ( the so-kal'd Senatorial ruls of ) transferabl voting, this is a real valu bais'd on the sIz of surplus vots, wich dos not kount against mor prefer'd kandidats alredy elekted.

Benoit Mandelbrot jeneralis'd Zipf's law by ading a konstant, c, to its invers proportion. That is, 1/1, 1/2, 1/3,... bekoms 1/(1+c), 1/(2+c), 1/(3+c),... Let that konstant equal uon, and yu hav the Droop quota, wich givs the elektiv proportion of vots to bekom a representativ in uon, tw, or thry member konstituensys etc.
The Droop quota is yus'd with transferabl voting. Kandidats, wining mor than ther quota, hav ther surplus vots transfer'd to ther voters' next preferenses.

Zipf's law deskribs natural strukturs. Wer-as Borda's method is a similar struktur, konsiusly impos'd by the ruls of an elektoral system.

'Land-slId' majoritys.

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Murray Gell-Mann sIts the work of Per Bak and asociats on how strukturs arIs naturaly without impos'd konstraints.

Koun-lIk hyps of sand had mor grains of sand pIl'd on them. As ther stypen'd sloups bekaim mor unstabl, a kritikal valu was pas'd for avalanches, wich left the sloup bak at the kritikal valu. This sIkl was kal'd self-organis'd kritikality.

The singl transferabl vot is analjus to such 'self-organis'd systems'. The surplus vots transfer'd to next prefer'd kandidats ar akin to the avalanch, a politikal 'land-slId majority', kaus'd by the pIling of extra sand on a mound or koun, abov the valu for a stabl hyp. This kritikal valu kompars to the quota, or proportion of vots nyded to elekt the most prefer'd kandidat ( and in turn the next prefer'd kandidats ).

This voting system is not self-organizing, how-ever, exept in the atenuated sens of automating the kount in a komputer program.

The aktual way that grains of sand tumbl together is extremly komplikated, just as is the way that thousands of voters' preferenses kombin. But ych senario klyrly folows a typikal struktural development. The kontrast is that Per Bak and his kolygs evolv'd formulas from a fenomenum. Wer-as the pionyrs of elektoral siens, from Borda and Condorcet, Andrae and Hare, Clark, Droop and Gregory, onwards evolv'd a fenomenum from formulas.

The former is natural siens, the later is 'moral siens'.

The introduktion to Gell-Mann's The Quark And The Jaguar and the last chapter on a sustainabl world is an admirabl survey that perhaps spyks for many as to the kind of world they wud lIk to work for.

Richard Lung.

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