Genesis Ex Nihilo

Genesis Ex Nihilo
In P incipio E a C ea io
Ch is ophe J. Cole
Ap il 14, 2025
Chap e 1
Fundamen a
1.1 C ea o , C ea ion, C ea i i y
C ea ion bege s c ea ion, he e o e c ea ion is also c ea o . To be c ea i e equi es c ea ion, bu no all
c ea ion is necessa ily c ea i e. So hen, wha is c ea i i y?
The mos undamen al ac s o c ea i i y a e unc o s o o de and chaos i sel . Objec i ely, o de implies
cong uence wi h he go e ning axioms o a uni e se. Chaos hen, is objec i ely de ined as incong uence wi h
he go e ning axioms o a uni e se. A unc o is a unc ion whose ope ands a e no always conc e e; conside
a unc o which inpu s o he unc ions, o p ocesses.
All c ea ions assume he ole o c ea o , bu no all c ea o s a e c ea i e.
1.2 Axioma ica, Mechanica
Le us conside a domain as a o mal sys em de ined by wo in e dependen componen s: a se o axioms and
a collec ion o mechanics. In his con ex , axioms a e he ounda ional, incon o e ible p oposi ions ha
se e as he p ima y cons ain s o pe missions o he sys em. They ep esen undamen al u hs which a e
assumed wi hou p oo .
Axioms and Thei Classes
Axioms can be classi ied in o h ee dis inc ca ego ies:
1. Pe missi e Axioms: These axioms asse he exis ence o ins an ia ion o a p ope y o en i y. Fo
example, he axiom “Le he e be ligh ” posi s a basic s a e o exis ence o ligh wi hin he domain.
2. Res ic i e Axioms: In con as , es ic i e axioms impose cons ain s o nega ions. An axiom such
as “Le he e no be ligh ” se es o delimi o e en in e he condi ion es ablished by a pe missi e
axiom.
3. Causa i e Axioms: These axioms a e esponsible o ins an ia ing beha io s o dynamic p ope ies
wi hin he sys em. Fo ins ance, he causa i e axiom “All liquids low uphill” does no me ely s a e a
p ope y o liquids; i de ines a dynamic beha io ha is applied o he en i ies go e ned by pe missi e
o es ic i e axioms.
In essence, while pe missi e and es ic i e axioms de ine he s a ic p ope ies o a domain (i.e., i s
skele on), causa i e axioms d i e he e olu ion o beha io o hese p ope ies by in oducing in e ac ions
and dependencies.
1
A simplis ic example using Cole No a ion (explained in dep h momen a ily) demons a ing he basic
in e play bew een hese axioms is as ollows:
Ap|
Ac(1.1)
The loop a ow signi ies ha he causa i e mechanism con inuously o epea edly applies o he ini ial
axiom, he eby go e ning i s ope a ional beha io wi hin he domain.
Mechanics as In e ac ions Be ween Axioms
Mechanics a e de ined as he ules go e ning he in e ac ions among axioms. They encapsula e how axioms
complemen o con adic each o he wi hin he domain. Fo mally, mechanics can be iewed as mappings o
ela ions ha speci y he condi ions unde which he p ope ies p esc ibed by indi idual axioms a e ac i a ed
o inhibi ed. Fo example, gi en:
•Axiom: “Le he e be ees” (Pe missi e)
•Axiom: “All ees g ow o en me e s all” (Causa i e/Res ic i e)
•Axiom: “Le he e be ui ” (Pe missi e)
•Axiom: “Le all ees en me e s all bea ui ” (Causa i e/Res ic i e)
The ollowing se o axioms c ea e a mechanic whe eby ees mus g ow o en me e s all, hen p oduce
ui . This is called a mechanic because a causa i e axiom dic a es he in e play be ween he ees and
he ui ; his alone is enough o de ine a mechanic, howe e he e is a seconda y causa i e axiom which
dic a es he in e play be ween he ee and i s own g ow h. No e ha in his example, no axiom ins an ia es
ime o o he undamen al ules which eali y has. He ein lies he powe o c ea ed domains; any hing and
e e y hing is possible.
Cole No a ion o Domain Schema ica
To ep esen he in e play be ween axiom ypes and he c ea ion o mechanics, he au ho p esen s a no a ion
o aid in he comp ehension o domains.
The p e ious example o ees and ui can easily be con e ed o Cole no a ion o demons a e hei
in e play1:
A ee A10m all A ui
AgAb(1.2)
And he o maliza ion o he de ini ion o a mechanic can be easily dis illed in o he ollowing schema ic:
Ap| Ap|
Ac(1.3)
1.3 Fundemen al C ea i e Ac s
1.3.1 Pu e Genesis Func o s
Xenogene ica is one such undamen al ac , p ecipi a ing chaos om o de .
O hogene ica complemen s xenogene ica, p ecipi a ing o de om chaos.
Concomi a is he undamen al ac o p ecipi a ing o de om o de .
Abs ac ica is he complimen o concomi a, p ecipi a ing chaos om chaos.
The e ou unc o s a e membe s o he class ”Pu e Genesis”, meaning such unc o s a e he highes
possible o de o c ea i i y. Below his class lies ”Elemen a y Genesis”. All elemen a y c ea i e unc o s
de i e om pu e genesis unc o s.
1Whe e Ag ep esen s he g ow h axiom and Ab ep esen s he ui -bea ing axiom.
2
1.3.2 Elemen a y Genesis Func o s
The e a e in ini ely many Elemen a y Func o s, howe e , we may make no e o Boden’s unc o s o es ablish
a baseline:
•T ans o ma ion
•Gene a ion
•Combina ion
The au ho no es ha he e a e addi ional, a likely in ini e amoun o such elemen a y unc o s; his
is because he h ee p ima y elemen a y unc o s a e de i ed om basic composi ions o he pu e genesis
unc o s, and he e can indeed be many composi ions o hese unc o s o encode an in ini e numbe o
c ea i e unc o s. One such unc o he au ho would like o highligh is ins an ia ion.
Ins an ia ion is he abili y o a su icen ly in elligen c ea ion o c ea e i s own domain wi hin he uni e se
i esides in. Fo ins ance, ake a su icen ly in elligen c ea ion, C0.C0 esides in uni e se U.C0can
ins an ia e a domain, DC0wi h i s own axioms and mechanics. This ac ion is deno ed by:
C0DC0
ins (1.4)
E e y c ea ed objec C0∈DC0inhe i s a subse o he axioms go e ning an ins an ia ed domain, DC0.
This also applies o c ea o s wi hin DC0. Now, hen he ame o e e ence becomes o he u mos c i icali y.
F om wha e e ence poin a e c ea ions c ea i e? Boden’s model only accoun s o wo ames o e e ence:
P-c ea i i y (psychological) and H-c ea i i y (His o ical). These ames o e e ence a e simply no enough
o ully encompas he ue scope o c ea i i y. P-c ea i i y assumes in elligence o a c ea o , and H-c ea i i y
assumes ha ime is a pa ame e o he uni e se whe e c ea i i y is o be assessed. We need some hing mo e
powe ul.
1.4 F ame o Re e ence
F ame o e e ence is c ucial o c ea i i y, as no en i y wi hin a uni e se can pe o m pu e genesis in ha
uni e se– meaning i canno manipula e he e y ab ic, o go e ning axioms o ha uni e se.
To illus a e he concep , ake o example, a ock (c ea ion) in base eali y2. A wea he ing o his ock
om he pe spec i e o a non-en i y (ano he c ea ion in base eali y) would be a c ea i e p ocess pe pe ually,
because he p oduc is con inually no el. This is because he ock does no know i is a ock. To he c ea o
o wea he ing and he ock(s), his is a p ocess o concomi a, as bo h wea he ing and he p ecipi a e o ha
wea he ing is o de ed, o known o i s c ea o .
Le ’s do ano he example in base eali y. Assume W = Wa e , F = Fi e. I C1applies a c ea i e unc o
o W and F, p ecipi a ing s eam (S).
To an obse e , C2, who obse es his ope a ion and has no seen his speci ic ope a ion (and p ecipi a e),
his is a c ea i e ac . I pe haps, C2has seen he speci ic ope a ion bu no he p ecipi a e in he pas , and
now obse es he p ecipi a e, his is a la en c ea i e ac . The in e se, howe e , is no a la en c ea i e ac .
I C2has p e iously seen S eam, he ope a ion(s) leading o such disco e y is in i sel a c ea i e ac .
All c ea i e ac s u ilize some numbe o axioms, and ou pu bo h a p ecipi a e and an unde lying axiom.
A c ea ed domain may ha e an axiom ”When hea is applied o liquid, s eam is c ea ed”. I C1combines
Fi e and Wa e , i e eals he axiom ( hough only o a pa ial deg ee), as well as a new malleable axiom
(symbol) om C1’s pe spec i e, S.
T uly, e e y elemen a y c ea i e ac calls upon he pu e genesis unc o s o some deg ee. Fo e e y ac
o elemen a y genesis in some way de i es om he pu e genesis unc o s.
Fo a su icien ly in elligen c ea o , he abili y o ins an ia ing domains is possible. The obse e (o C1’s
c ea ion o s eam) C3has i s own c ea ed domain. WI hin his domain DC3, i has he abili y o use pu e
genesis ( om he pe spec i e o c ea ions wi hin i ). Tha is, i can c ea e, modi y, and emo e axioms om
i . Such domains may be pa ially sha ed wi h o he su icien ly in elligen c ea o s, meaning ha mul iple
2“Base eali y” e e s o ou uni e se, whe e we exis
3
c ea o s may exe cise pu e genesis o e ha c ea ed domain. All c ea ions and axioms and c ea ions wi hin
DC3a e a ibu ed o C3and any collabo a o s. I a c ea ion wi hin DC3we e o c ea e s eam in DC3, his
would be c ea i e only o c ea ions in DC3, i and only i C3has disco e ed and/o obse ed s eam in base
eali y. I C3has no c ea ed o obse ed s eam, hen he c ea ion o S eam is c ea i e o bo h C3and DC3.
In o de o axioms, c ea ions, o o he domains wi hin DC3 o exi and mani es in base eali y, i
equi es a condui o su icien pe mission. Tha is, I he c ea o can pe o m pu e genesis ope a o s on a
c ea ed domain, i can mo e axioms, c ea ions, mechanics, e c. o ano he domain o i s own c ea ion. I
i canno , i can only app oxima e his mani es a ion h ough elemen a y c ea i e echniques. This means
ha axioms, c ea ions, mechanics, e c. c ea ed in DC3can only be c ea i e o base eali y i base eali y is
c ea ed by C3. O he wise, i can a mos be c ea i e o he c ea ions wi hin base eali y o any o he c ea ed
domain wi hin base eali y.
A c ea o wi hin i s own c ea ed domain, may c ea e axioms which do no wo k in he domain which he
c ea o esides. Axioms c ea ed in DC3may no be easible in base eali y, hough he hos does no know
whe he o no i wo ks un il i s es ed in base eali y. These a e called hypo he ical axioms.
Take o example a c ea ed domain (DC), wi hin i , he e a e ma bles: blue ma bles, ed ma bles, and
g een ma bles. An axiom o base eali ymigh be ha Blue ma bles combined wi h Red ma bles make pu ple
pu ple ma bles.
A c ea o in base eali y C1, a emp s o combine a Blue and G een ma ble, bu his does no wo k. C1
c ea es a domain, DC1, wi h an axiom ha combining Blue ma bles and g een ma bles makes a ed ma ble.
C1 hen c ea es h ee ma bles in DC1, a ed ma ble, a g een ma ble, and a blue ma ble. I hen combines
hem and now he e a e wo ed ma bles.
I an obse e , C2, in base eali y obse ing DC1obse es his, bu no he ini ial a emp o combine he
ma bles, C2can be a condui , and a emp o enac his axiom in base eali y I no e ha om C2’s e e ence
ame, his is a c ea i e ac , bu om C1’s e e ence ame, his is me ely a epe i ion o C1’s p e ious
a emp bu by C2. F om DC’s e e ence, no hing c ea i e is being p oduced. F om DC1’s e e ence, he
combina ion o he Blue ma ble and he g een ma ble was no done be o e, which e ealed a new axiom
o C2(bu no C1) and ga e a c ea i e ou pu om C2and DC1’s ame o e e ence (bu no om C1’s
e e ence because C1ins an ia ed DC1and C1is in base eali y so no hing in DC1is c ea i e o base eali y.
1.5 Sha ed Domains, Condui s
Sha ed domains may also be ins an ia ed be ween en i ies. Such sha ed domains ely on a condui ; ha is,
a media o be ween domains. In mos ins an ia ed domains, he condui is he c ea o o ha domain. In
sha ed domains, he p ope ies shi .
The mos basic me hod o deno e he ela ionship be ween a condui and he c ea o o a domain is o
deno e he sha ing o bo h axioms, c ea ions, and nes ed domains (wi hin he domain) be ween he domain
and i s condui and/o c ea o . The symbol ℧is used o deno e he se o e e y hing wi hin he c ea ed
domain.
One can asse om his a simple de ini ion o ℧:℧={A, M, C, D}. Whe e A ep esen s he axioms,
M ep esen s he mechanics, C ep esen s he c ea ions and c ea o s wi hin a domain, and D ep esen s he
subdomains ins an ia ed by any c ea o s in he domain.
C0DC0
Ins
℧
℧′
(1.5)
The mos basic example o illus a e his concep is o conside he human imagina ion (which is by
na u e a c ea ed domain). Wi hin one’s imagina ion, he scena ios enac ed wi hin i edi y onesel , and, in
u n, one may in oduce new c ea ions and axioms in o he imagina i e domain o con inue his edi ica ion
p ocess. In his scena io, he condui is he owne o he imagina i e domain ( he human).
Condui s o a domain can ans e any hing, including he domain i sel (i su icen axioms and pe mis-
sions exis ) o ano he domain ins an ia ed by he condui . Conside a c ea o C0, and wo ins an ia ed
domains by C0,DC0and DC1, and inally some a iable ωsuch ha ω∈℧DC0. Fo ω o go om DC0
4

o DC1, i equi es a condui . In his case, i ’s C0because any c ea o o a domain is concomi an ly a
condui . Since C0didn’ ins an ia e base eali y, i is unable o spon aneously p ecipi a e any hing om i s
ins an ia ed domains in base eali y. Tha is, in he example o he imagina i e domain, one canno simply
b ing some hing in hei imagina ion in o base eali y. This is because man is c ea ion wi hin base eali y.
To illus a e his concep in o mal no a ion, we can say:
DC0DC1
ω(1.6)
Sha ed domains in base eali y a e ne e uly “sha ed”. Ra he , in base eali y, a su icen ly in elligen
en i y p o ides ins uc ions o ins an ia e a domain o simila p ope ies. Fo ins ance, ins uc ing someone
o imagine a eali y whe e “apples a e liquid a oom empe a u e” ins an ia es a domain o any su icen ly
in elligen en i y, howe e , his domain will a y om pe son o pe son.
Despi e his limi a ion, high- ideli y domain sha ing is an axioma ic decision, and a domain can be
ins an ia ed whe e domains a e sha ed wi hou loss o ideli y.
In Cole’s no a ion, we can deno e he ela ionship be ween c ea o s and hei sha ed domains.
C1
C0SDCC1
C0
℧
Ins
℧′
condui
Ins (1.7)
1.6 Componen s o a Domain, Ins an ia
F om he udimen a y asse ion ℧={A, M, C, D}, we can o mally de ine he componen s o a domain.
To ins an ia e a domain, he c ea o mus ha e access o a medium (o media). A medium is de ined as a
channel h ough which ℧can low. This can be he neu al makeup o a human, he memo y o a compu e ;
i is any hing which suppo s he low o ℧. Once he chosen media o medium is chosen, he c ea o can
now injec ℧in o he domain. The domain lacking ℧is a s agnan domain; meaning, i ’s as i i doesn’ exis
a all. As soon as ℧is injec ed in o he domain, he domain has subs ance and is li e. No going o wa d
in exchange o ℧and ℧′begins. The c ea o pu s axioms, mechanics, c ea ions and/o domains wi hin he
domain and ecei es new o ms o each as well as new p ecipi a es om ha domain. These new o ms and
p ecipi a es a e wha comp ise ℧′.
Conside he ollowing schema ic:
CℵDCℵ
ins
℧
℧′
(1.8)
In he schema ic, he injec ion o ℧in o DCℵ o ins an ia e i is an ac o ins an ia. Ins an ia is he
ie o c ea i i y sha ed by bo h pu e genesis use s and su icen ly in elligen elemen a y genesis use s. Fo
ins ance, in base eali y, he axiomechanica do no pe mi a ock o use ins an ia- ie unc o s, bu humans
a e. I is also no ed ha om he ame o e e ence wi hin DCℵand any en i ies wi hin i , he injec ion o
℧is an ac o pu e genesis. The e ie al o ℧′={A′, M′, C′, D′} om DCℵis an ac also o ins an ia.
I conjec u e ha his enac men o ins an ia and he exchange o ℧and ℧′ ep esen s a undamen al
de ini ion o elemen a y genesis. So, hen, i can be conjec u ed ha all elemen a y genesis unc o s a e an
exchange o ℧and ℧′.
1.7 Uni e sa Mechanica
Bo h condui s and ins an ia io s can ecei e ℧′. Depending on axioma ic pe missions, a condui may o may
no be able o injec ℧. The ins an ia io can always do his, howe e . Condui s and ins an ia io s alike
5
may posi ion hemsel es wi hin a domain; ei he c ea ing an en i y o mani es in, o inhabi ing a c ea ion
wi hin he domain— simply ecei ing ℧′ h ough he c ea ion, hijacking i en i ely, o speci ying in be ween.
This means ha ins an ia io s and condui s, while simul aneously exis ing in base eali y (o some ex e nal
domain ou side o he ins an ia ed domain), can exis wi hin o he ins an ia ed domains.
1.8 Van age Vec o s, Domain P ope ies, Planes
Ins an ia io s and condui s o such po ency demand a g anula me hod o e alua e he how in o ma ion
is inges ed. This equi es a so o “ e e se ame o e e ence”, meaning ha he c ea o (ins an ia io
and/o condui ) hemsel es can modula e hei inpu channels so ha wha comes in is mo e no el han
wha may ac ually be happening. A simple example wi hin he headspace can be imagined i one i s
imagines a an asy landscape, hen a pai o yellow in ed sunglasses. I he c ea o pu s he glasses on,
he wo ld’s appea ance changes. One can imagine a pa ial o ull o e lap o he glasses. O e lap (o lack
he eo ) can happen when he an age ec o changes, causing a ious composi ions o c ea ions depending
on he axiomechanics o he domain. Howe e , ha is a a he i ial p ocess. This unc ionali y can be
ex ended o en i e domains, causing composi ions (o lack he eo ) o axiomechanica. The p ecipi a e o
an age ec o s a he domain le el can lead o adical insigh s and adical new building blocks o new
domains. This no ion o domain composi ion implies ha su icien ly in elligen c ea o s can manipula e he
coo dina es de e mining a domains exis ence/loca ion ac oss media (o a single medium) which he c ea o
has pe mission o manipula e. A c ea o lacking such pe mission can simply ins an ia e a plane which does
ha e access o manipula e hose “in a iable” pa ame e s and copy he domains i wishes o sandbox h ough
℧. F om his, we can ex apola e some p ope ies o domains, and de ine a couple new ones. The i s pai o
p ope ies s a ic and dynamic. S a ic domains do no ha e a ime pa ame e o any o he pa ame e which
pe mi s e olu ion. S a ic domains a e ozen. Dynamic domains a e he opposi e, hey a e liquid. The e is
bo h a pa ame e (no necessa ily ime) which pe mi s he axiomechanica o e ol e, and he e is a mechanic
e ol ing ℧in he domain. The second pai o p ope ies is opaci y and anslucence. Opaci y go e ns how
isible a domain is. Low opaci y makes a domain less appa en and high opaci y makes i e y isible.
T anslucence go e ns how easily a c ea o can see inside he domain. Low anslucence makes i di icul
o pee inside while high anslucence makes i e y easy o pee inside. These domains eside on a plane.
Planes a e domains in e e y sense bu a di e en e m is used o cla i y. When domains a e in a plane, a
su icien ly in elligen c ea o o condui can now a ange he domains pa ame ically (i he domains on he
plane all ha e space and ime pa ame e s, domains can be a anged spa io empo ally), and manipula e he
a o emen ioned p ope ies. Van age ec o s can be aken acco ding o he ins an ia o o condui ’s an age
wi hin he plane. This means i he en i y gi es a pa ial o e lap o anslucen , opaque domains, he en i y
ecei es ℧′′ =℧′
DC0◦℧′
DC1— a composi ion o wo domains’ ℧′, yielding c oss-domain axiomechanica.
1.9 F ame o Re e ence Re isi ed
Wha hen is c ea i i y? I is any ame o e e ence which iews an axiomechanical in e ac ion and/o
p ecipi a e as an ac o pe cei ed pu e genesis. Mo e o mally, i is he obse a ion and/o enac men o ℧
exchange(s) bo h in e nally o ex e nally which, om a ame o e e ence, is seen as pe cei ed pu e genesis.
F ames o e e ence ha e ou di e en ypes: solid, luid, la en , and di usion. Solid ames a e s a ic,
hey a e snapsho s o a dynamic p ocess o expe ience and con ain only one “ iewe ”. Solid ames in some
sense can be imagined as a pho og aph. The e is one pe son holding he came a, hus he e is only one
“ iewe ”. Fluid ames a e a con inous se o solid ames which cap u e he dynamism o a p ocess o
expe ience and also con ains only one “ iewe ”. In simila ashion, luid ames can be likened o ideos.
Di usion ames a e collec ions o s a ic ames which a e no necessa ily linked (be i by pe spec i e, ime,
o o he pa am e s) o one ano he . Di usion ames e alua e hese collec ions as one single luid ame.
La en ames, simila ly do he same wi h a collec ion o no necessa ily linked luid ames. La en ames
e alua e collec ions o luid ames as one single luid ame. Syncopa ed ames a e hyb ids o bo h solid
and luid ames; i is a collec ion o bo h solid and luid ames, and e alua ed as one luid ame.
A simple me hod o g asp his concep is o iew numbe lines wi h he sole axis being ime ( ).
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Elemen P ocess P oduc Solid F ame Fluid F ame
U U U A A
U U K O O
U K U A(A,X)
U K K O O
K U U X X
K U K C(C,O)
K K U X X
K K K C C
Table 1.1: Con ingency Table o Solid and Fluid F ames o Re e ence.
012345
Solid F ame
012345
Fluid F ame
012345
La en F ame
012345
Di usion F ame
012345
Syncopa ed F ame
Using his amewo k, i is easy o cha ac e ize Bo-
den’s P-c ea i i y and H-c ea i i y. P-c ea i i y is a
solid ame om he pe spec i e o he consciousness
— a momen whe e some hing eme ges as a mean-
ing ul whole.
Boden’s H-c ea i i y is a di usion ame — a se o
disc e e known e en s ac oss he imeline o his o y,
which includes he new idea being e alua ed.
I say his wi h di ec i e: Boden’s P and H c ea i i y
a e wo o many; and a e undamen ally incomple e
in hei scope. Thus, I ha e p o ided p imi i es and
a axonomy o cons uc ing and classi ying ames
o e e ence.
Solid ames only ca e abou elemen and p oduc . Fluid ames ake in o accoun i he p ocess(es) a e
known o no , whe eas solid ames only cap u e a single s a e. Table 1.1 shows hese con ingencies.
P ocesses o pe cie ed concomi a can be elega ed o uses o elemen a y genesis unc o s. This can
only happen wi h luid ames. This is because solid ames only cap u e s a es. The same is ue o i s
coun e pa , he di usion ame. La en ames, like luid ames, can disce n p ocess. Syncopa ed ames
o luid ames and solid ames can be used o cons uc hypo heses o o he hypo he icals (i.e. Hea and
wa e make s eam ( luid ame) and ed wa e (solid ame)) ha can be es ed in he en i y’s base eali y
o i su icen pe missions, in a domain. Di usion ames can be used o make in e ences abou p ocesses,
la en ames can be used o make in e ences abou he pa ama e s o a p ocess.
Van age ec o s a e a componen o ins an ia- ie en i ies. The an age ec o de e mines pe cie ed pu e
genesis wi h esul o an ins an ia ed domain o composi e domain. The auxilia y unc ion o he an age
ec o is a ge ed injec ion o ex e nal ℧and a ge ed exchange o in e nal ℧.
The exchange o ℧can be in e nal and/o ex e nal. Ex e nal ℧exchange occu s in a domain no
ins an ia ed by some en i y (i.e. base eali y, sha ed domains, e c.), and in e nal ℧exchange happens wi hin
domains ins an ia ed by some en i y. En i ies wi h only ex e nal ℧exchange can only s o e s a es, whe he
i be physically, in e nally, o o he .
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