., simultaneously a picture of say b and c). Instead of a double-exposure photograph, the superposition should be thought of as representing a blurred or incomplete reality that with further distinctions could sharpen to either of the sharp realities. But there must be some way to indicate which sharp realities could be obtained by making further distinctions (measurements), and that is why the blurred or cloud-like indefinite reality is represented by mathematically superposing the sharp potentialities. This point might be illustrated using some Guy Fawkes masks. Figure 2: Objectively indefinite pure state represented as superposition of distinct eigen-alternatives Instead of a double-exposure photograph, a superposition representation might be thought of as "a photograph of clouds or patches of fog." (Schrödinger quoted in: [20, p. 66]) Schrödinger distinguishes a "photograph of clouds" from a blurry photograph presumably because the latter might imply that it was only the photograph that was blurry while the underlying objective reality was sharp. The "photograph of clouds" imagery for a superposition connotes a clear and complete photograph of an objectively "cloudy" or indefinite reality. Regardless of the (imperfect) imagery, one needs some way to indicate what are the definite eigen-elements that could be "actualized" from a single indefinite element S, and that is the role in the set case of conceptualizing a subset S as a collecting together or "superposing" certain "potential" eigen-states, i.e., the singletons {u} ⊆ S. 1.6 The two lattices The two dual subset and partition logics are modeled by the two lattices (or, with more operations, algebras) of subsets and of partitions.4 The conceptual duality between the lattice of subsets (the lattice part of the Boolean algebra of subsets of U) and the lattice of partitions could be described (again following Heisenberg) using the rather meta-physical notions of substance5 and form (as 4The two logics and lattices are "dual" or "duality-related" in the sense of the subset-partition duality. 5Heisenberg identifies "substance" with energy. Energy is in fact the substance from which all elementary particles, all atoms and therefore all things are made, and energy is that which moves. Energy is a substance, since its total amount does not change, and the elementary particles can actually be made from this substance as is seen in many experiments on the creation of elementary particles. [22, p. 63] 8 in in-form-
., simultaneously a picture of say b and c). alternatively of a bivalent - exposure photograph, the superposition should be think of as typify a blurred or incomplete reality that with further distinction could focus to either of the sharp realities. But there must be some way to indicate which sharp reality could be obtained by making further eminence (measurement), and that is why the blurred or cloud - alike indefinite reality is represented by mathematically superpose the sharp potentialities. This point might be illustrate using some Guy Fawkes masks. Figure 2: Objectively indefinite arrant state represented as superposition of distinct eigen - alternatives alternatively of a double - exposure photograph, a superposition representation might be thought of as " a photograph of clouds or patches of fog. " (Schrödinger quoted in: [ 20, p. 66 ]) Schrödinger distinguishes a " photograph of clouds " from a blurry photograph presumably because the latter might imply that it was only the photograph that was blurry while the underlying objective reality was crisp. The " photograph of clouds " imagery for a principle of superposition imply a absolved and complete photograph of an objectively " cloudy " or indefinite reality. Regardless of the (fallible) imagery, one need some way to indicate what are the definite eigen - element that could be " actualized " from a single indefinite element S, and that is the role in the set case of gestate a subset S as a collecting together or " superposing " certain " potential " eigen - states, i.e., the singletons { uracil } ⊆ S. 1.6 The two lattices The two dual subset and partition logics are modeled by the two lattice (or, with more operations, algebras) of subsets and of partitions.4 The conceptual duality between the wicket of subsets (the wicket part of the Boolean algebra of subsets of U) and the lattice of partitions could be described (again take after Heisenberg) using the preferably meta - physical impression of substance5 and form (as 4The two logic and lattices are " double " or " duality - related " in the sense of the subset - partition duality. 5Heisenberg identify " substance " with department of energy. Energy is in fact the substance from which all elementary particles, all atoms and consequently all things are made, and energy is that which moves. department of energy is a substance, since its total amount does not change, and the elementary particles can actually be made from this substance as is interpret in many experiments on the creation of elementary particles. [ 22, p. 63 ] 8 in in - form-
., silultaneously a picture on say b and c). Instead oh a dougle-exposjre photograph, the superposivion shouod be thought of as reoresentinh a blureed ie incomplevs realibv thaf witk hurther distincjions could vharpen to eitvef lf the sharp realities. But there muft be spmf way to indicwte erich sharp realities could be obtained by makpng further distimctions (measurements), and tjat ls why the blurred or cloud-lije igeefinite reauity is rekrzsented by jathematically superposing the rharp potentialutues. Jhis point mmght bv illustrated using smme Guy Fawkes masks. Nigurx 2: Ovjectively indefinite pure state represgnted as sgpzrposition of distincr wigen-dltesnatkces Inatxad of a fouule-exposure photograph, a superposition rekrefvmtation mighf be trotght of as "a photograph of clouds or pauches of fog." (Schrödinger quotwd in: [20, p. 66]) Schrödinger fistinguifhes a "photograph of clouds" from a blurry photogrdph pcerumcnjh bfcause the latter might imply that it was onlr tne photograph thct was blurry wholf yre underlying objeccjvs reality was sharo. The "protogeaph of cjoudx" imagery for a superpositiin connotes c coear and complete 'hotograph oy an onjectovely "cloudy" or indefinnte rezlity. Regarfless of ffe (imperfect) imaeerj, ona needs some way to indicaee what ace thz definige eogen-elqments thah could be "actualized" frlm a ditgle indeflnite element S, and that is the role in the sgt wasv of conczptuallzing a subset F as a collectnng togecher of "superpospng" certamn "potential" eigen-states, h.g., the singletmns {u} ⊆ S. 1.6 Thw twi lattizds The two duak subset cud partituon logics are modcled cg the two lattiets (ir, with more oprragiogs, akgqtras) of subsats xnd pf paftitions.4 Thc cunceltual duality betweet ths lattice of subseys (the latjice part of the Boolesn algebra of substts of U) end thr lwttice of partitions could be sescribed (agwin followind Helsenferg) using the rather meta-physical notions of subwtance5 and form (as 4The two logics and kattices arx "dual" or "dualidy-related" in the senwe of the subset-psrtition duality. 5Heissnberg idenhifies "substance" with energy. Energy is in fact the substance from which aol elementary partjclex, all acomx and eherxfure all things age made, and energy is that which moves. Etexgy is a substance, since its yogal amount dogs not change, and the elemsntary psrticles can actually be made ftom this substance as is seen in many experpjeits on the creation pf elekentaey partucled. [22, p. 63] 8 in in-furm-
., simultaneously a picture of say b Instead a double-exposure the superposition should a or incomplete reality with further distinctions sharpen to either of the sharp But there must be some way to indicate which sharp realities could be by making further distinctions (measurements), and that is why the blurred or cloud-like reality represented mathematically the sharp potentialities. This point might be illustrated using some Guy Fawkes masks. Figure 2: Objectively pure state represented as superposition of distinct eigen-alternatives of a double-exposure photograph, superposition representation might be thought as photograph of or of (Schrödinger quoted in: p. 66]) Schrödinger distinguishes a "photograph of clouds" from a blurry photograph presumably because the latter might that it the photograph was while underlying objective reality The "photograph of clouds" imagery for a clear and complete photograph of an objectively or indefinite Regardless of the (imperfect) imagery, one some way to indicate what are the definite that could be "actualized" from a single indefinite element S, and that is the role set case of conceptualizing subset S as collecting or certain eigen-states, i.e., singletons {u} ⊆ S. 1.6 The two lattices The two dual and partition logics are modeled by the two lattices (or, operations, of subsets and partitions.4 The conceptual duality the of subsets (the lattice the algebra U) the of partitions could be (again following Heisenberg) using the meta-physical notions of substance5 logics and lattices are "dual" or "duality-related" in sense of the subset-partition duality. 5Heisenberg identifies with energy. Energy is in fact the substance from which all elementary all atoms all things are made, and energy is that moves. Energy is a since its total amount does not change, and the particles actually be from this substance is seen in experiments on the elementary particles. p. 8
., simultaneously a picture of sAy b and c). InsTead oF a dOubLe-ExpoSure Photograph, the sUPerpOsition should be thought Of as rEpREsenTInG a bluRred or iNCoMPLetE rEaLitY tHAt With fUrtHer distInctions coUld ShArpen to eitheR Of The sharp reAliTies. But there MusT be somE wAy tO IndicAte Which Sharp rEAlitieS could be oBtAIned by MAking fuRTHeR disTinctions (measuremENtS), And that is why thE blurrEd OR cLOUd-lIke Indefinite ReAlity IS represENtED BY maTHematically suPerposing thE ShaRp poteNtIalITies. ThIs poiNt MIghT be illustraTed uSing some GUy FawkES masks. FIGure 2: ObjEctiveLy iNdeFiniTE pUrE stAtE RepREsEntED as SuperposItIoN of diStinCT EIGen-aLteRnatIves INstead of a doubLe-eXposURe pHotogRaph, a SupeRpOsitiOn reprEsentAtIon might be thougHt of As "a photogRapH oF clOuDs or pATches oF foG." (ScHrödingEr quoteD In: [20, p. 66]) scHRÖDiNger distinguishes a "PhOTOgRaph of clOuds" frOM a BlURry photoGrAph PresUMAbly bEcauSE tHe latter Might iMPlY tHat it waS oNly the PhOtoGraPh thaT Was bLurry wHile the uNderlYIng objective reALity was sharp. THE "pHOToGRaph Of cLouds" imagerY for A SupeRposITiOn cONnoteS a cleAr ANd COmplete photograph of An ObjectIvely "Cloudy" or indefInite realiTY. rEgardlesS of tHE (iMPerfect) imagery, One neEds some way TO indicatE what Are the deFinite eigEN-Elements ThaT coUld Be "aCTUaLized" from a sinGLE indEfInite elEmeNt S, and tHat Is tHe rOle In The set casE of concePtUaLiZiNg a SubseT s as a collEcTinG tOgeTher oR "SuperpOsing" CertAiN "pOTenTial" eigEN-sTATes, i.E., tHe SingLetOnS {u} ⊆ S. 1.6 ThE two LAttIces The Two dual suBseT And pArTiTion logIcs are modeled By The two lattIcEs (oR, with mORE operatiOns, algebras) of subsets and OF partitIonS.4 The cOncePtual dualIty BetweeN thE LatticE of subSets (tHe LatTICe parT OF tHe BOoLean algebrA OF suBsets Of u) and The lattIce of partitions couLD be Described (agaiN foLlowING HEisENbERg) uSiNG thE RAther meta-physicAl notions oF sUBsTance5 and foRM (as 4thE two logIcs and lAtticES are "duaL" or "dualitY-related" iN tHe seNSE of The subset-pArtition Duality. 5HeISenbeRG iDentiFieS "substAnCe" wIth enErgy. EnERgy Is in fAct the SuBstancE from WhIch all elEmentary particles, all atoMs and tHerefOre All things Are MAde, And energy Is thAt which movEs. ENerGy is a SubSTance, SincE ItS toTAl amoUnt dOEs not chanGE, aNd tHE ElEmentary parTICLes Can acTuaLLy be maDe frOm this substance as IS seen in many expErimENTs oN thE CreaTiOn of elementary ParTiCLEs. [22, p. 63] 8 in in-fOrM-
., simultaneously a pictur e of say b  andc).  In st eadof a  double-exposu r e ph otograph, the superpos ition  s h ould be  thou ght ofa sr e pre se nt ing  a bl urred  or  incomp lete reali tyth at with furt h er  distincti ons  could sharp ento eit he r o f  thesha rp re alitie s . Butthere mus tb e some way toi n di cate  which sharp real i ti e s could be obt ainedby ma k i ngfur ther disti nc tions (measur e me n t s ),a nd that is wh y the blurr e d o r clou d- lik e  indef inite  r e ali ty is repre sent ed by mat hemati c ally su p erposin g thesha rppote n ti al iti es .  Th i spoi n t m ight beil lu strat ed u s i n g  som e G uy F awkes  masks. Figur e 2 : Ob j ect ively  inde fini te  pure  state  repr es ented as superp osit ion of di sti nc t e ig en-al t ernati ves  In stead o f a dou b le- ex p o s ur e photograph, a su pe r p os ition re presen t at io n  might b etho ught o f as"a p h ot ograph o f clou d sor  patche sof fog ."  (S chr öding e r qu oted i n: [20,p. 66 ] ) Schrödingerd istinguishesa  " p h ot o grap h o f clouds" f roma  blu rryp ho tog r aph p resum ab l yb ecause the latter m ig ht imp ly th at it was onl y the phot o g r aph that  was bl u rry while theunder lying obje c tive rea litywas shar p. The "p h o tographofclo uds " i m a ge ry for a supe r p osit io n conno tes  a clea r a ndcom ple te  photogra ph of an  o bj ec ti vel y "cl o udy" orin def in ite  real i ty. Re gardl essof  t h e ( imperfe c t) i mage ry ,onenee ds  some  way toindicat e what ar e t h e de fi ni te eige n-elements th at  could be"a ctu alized " from a s ingle indefinite elemen t  S, and  th at is  the  role inthe  set c ase of con ceptua lizin ga s u b set S a sa c ol lecting to g e the r or"s uper posing"  certain "potentia l " e igen-states,i.e ., t h e  s ing l et o ns{u }  ⊆S .  1.6 The two la ttices The  t w odual subse t  an dpartiti on logi cs ar e  modele d by thetwo latti ce s (o r ,  wi th more op erations , algebra s ) ofs ub setsand  of pa rt iti ons.4  The c o nce ptual  duali ty  betwe en th elatticeof subsets (the lattice  partof th e B oolean al geb r a o f subsets  ofU) and the  la tti ce of  pa r titio ns c o ul d b e  desc ribe d  (again f o ll owi n g  H eisenberg)u s i ngthe r ath e r meta -phy sical notions ofs ubstance5 andform ( as4Th e  two  l ogics and latt ice sa r e "dual"  o r "duality- related"  i n  thesenseof the  subset - p ar t itiondual ity . 5Heisen ber gi dentifi es  " s ubstan ce"wi th ene rgy. E n ergy i s in fact the su bstan c e  from whi ch al lelement a ry p articles,all atoms a nd the refo re al l thing sare ma de,  a nd energyi s that wh ich m oves. E ne rgyisa subs tanc e ,  sinc e it stot al amount d oe s  n ot cha nge,  andth e el ementaryp articles  ca n  actual ly  be m ade fr o mt h is substan ceas is s een in man y  exp e ri m entson the  creat ion ofe lem en tary pa rti c l es. [22,p. 63] 8i n i n- form -
., simultaneously_a picture_of say b and_c). Instead_of_a double-exposure_photograph,_the superposition should_be thought of_as representing a blurred_or incomplete reality_that_with further distinctions could sharpen to either of the sharp realities. But there must_be_some way_to_indicate_which sharp realities could be_obtained by making further distinctions_(measurements), and_that is why the blurred or cloud-like indefinite_reality_is represented by_mathematically superposing the sharp potentialities. This point might be_illustrated using some Guy Fawkes masks._Figure 2: Objectively_indefinite_pure_state represented as superposition_of distinct eigen-alternatives Instead of a_double-exposure photograph, a superposition representation might_be thought of as "a photograph of_clouds or patches of fog." (Schrödinger_quoted in: [20, p. 66])_Schrödinger distinguishes_a "photograph of clouds" from_a blurry photograph_presumably because_the latter might_imply that it was only the_photograph that was_blurry while the underlying objective reality_was_sharp. The "photograph_of_clouds"_imagery for_a superposition connotes_a_clear and_complete_photograph of an objectively "cloudy" or_indefinite_reality. Regardless of the (imperfect) imagery, one_needs some way to_indicate_what are the definite_eigen-elements that could be "actualized"_from a single indefinite element S,_and that_is the_role in the set case of conceptualizing a subset S as_a collecting together or "superposing" certain_"potential" eigen-states, i.e., the_singletons {u}_⊆_S. 1.6 The_two_lattices The_two dual subset and partition logics are_modeled by_the two lattices (or, with more_operations, algebras) of subsets_and_of partitions.4 The conceptual duality between_the lattice of subsets (the lattice_part of the Boolean algebra_of_subsets_of U) and the lattice_of partitions could be described (again_following Heisenberg) using_the rather meta-physical notions of substance5 and_form_(as 4The two logics and lattices_are_"dual" or "duality-related" in the sense_of_the_subset-partition duality. 5Heisenberg identifies "substance"_with energy. Energy is in fact_the substance from which all elementary particles, all atoms_and therefore all_things are made, and energy_is_that_which moves. Energy is a substance, since its total amount_does not_change, and the_elementary particles can actually be made from this substance as_is seen in many experiments on the_creation of elementary particles. [22, p. 63] 8 in in-form-