On Stonehenge and its Moving Shadows

O Sto ehe ge a d its Mo i g Shado s

Di it ios S. De d i os

E e itus P ofesso , “ hool of A hite tu e a d U a Desig , U i e sit of

Ka sas, La e e, Ka sas, U“A.

I Reside e at O o d Bea h, Flo ida, U“A.

Co ta t:

f-jf@ea thli k. et

Ma h ,

Sto ehe ge i

. “ou e: B Diego Delso, CC BY-“A . , https:// o o s. iki edia.o g/ /i de .php? u id=

Ta le of Co te ts

A st a t

I t odu tio

Basi P i iples i Shado D a i s

O the A hite tu e of Sto ehe ge

The sa se s’ oute i g itals The T ilitho s e se le

The athe ati al odulus at Sto ehe ge The T ilitho s uasi-ellipti al a

Alig e ts at Sto ehe ge e o d the su e solsti e su ise

The shado s of Sto ehe ge a d thei o e e t i spa e-ti e

The sho t sha p shado s a d Sto ehe ge II ke shado le gth The lo g shado s a d the li ks of the o u e t to its e i o s

So e ge e al thoughts o the e lo g shado s A li tel’s shado

Co lusio s a d suggestio s fo fu the esea h

Notes

Note

.

Ne o ’s o k

Note

. Wh lu a ased o u e ts?

Note

. The B itish He itage sou es

Note

. Mo e o the odulus at Kasta Tu ulus

Refe e es

A k o ledge e ts

Legal Note o Cop ight

A st a t

The pape is set to a al ze the shado s of “to ehe ge Phase II i a - BC . “u h a stud , the pape sho s, allo s o e to de i e plausi le h potheses ega di g the desig spe ifi atio s of the o u e t, i ludi g the height of the t o sets of sa se s i oth sto e e losu es, the dia ete of the oute i le, as ell as the i e T ilitho s e se le fo a d di e sio s. Afte so e ge e al p i iples ega di g the d a i s of shado s a e p ese ted, the pape e a i es i detail the A hite tu e of the o u e t’s t o sto e e losu es. The pape does ot add ess the t o Bluesto e e losu es. It ide tifies the fo of the T ilitho s e se le as a si ple lass, of the sto e e losu es lassifi atio s he e p oposed Ale a de Tho . This suggested si ple lass of e losu es as dete ted the autho to also des i e the A hite tu e of Go ekli Tepe’s st u tu e D La e III.

A athe ati al odulus is ide tified fo the o u e t. It depi ts ke atios a o g the asi o stitue t ele e ts of “to ehe ge II floo pla . The pape pi poi ts the o phalos of the o u e t as ei g the e te of the oute sa se s i le, a d the a e te of the e ti e Phase II st u tu e. Fu the , the pape a al zes the “to ehe ge II shado s a d fi ds that the spatial le gth ise easu e of the o u e t’s odulus is li ked to the le gth of the shado ast-off the oute i g’s sa se s i ludi g thei li tels at oo ti e at e ui o , spe ifi all a le gth of a out si ete s.

The pape , utilizes the o k Ne o alo g ith p e ious o k the autho , as to the i po ta e of a phase t a sitio i the d a i s go e i g the th ee fu tio s des i i g the ast-off sha p “u -i du ed shado s’ le gths o e a ea . This phase t a sitio takes pla e du i g the e al a d autu al e ui o . Whe e, the pape ide tifies the e ui o oo ti e alig e t to ha e ee sig ifi a t also i the desig of “to ehe ge II, esides the do i a t a d ell dis ussed i the lite atu e su ise at su e solsti e alig e t. The sig ifi a e of the i te solsti e su set alig e t is also dis ussed i efe e e to the T ilitho s e se le.

Nu e ous e te sio s of the o k a e suggested, as the a al sis of “to ehe ge II shado s ope s up a e i do i to a al zi g the o u e t, its desig , a d possi l its ultu e elated

I t odu tio

“hado s a e pa t of a asi dualit i o u e ts. That dualit i ludes as a p i al the o igi al st u tu e a d as its dual, the shado it asts off due to eithe su light o oo light. I additio , the ho eog aph of shado s as dis ussed i [ . ] adds o e e t to st u tu es. Thus, it e de s life i to othe ise i a i ate o je ts, th ough thei eithe ast-off o a -o shado s’ otio s. This is pa ti ula l of i po t he d a i s i the o u e ts’ ep ese tatio s eliefs a d othe i o og aph , like pet ogl phs a e i p i ted o to these o u e tal st u tu es.

I a set of p e ious pape s, see efe e es [ . ], [ . ], the autho a al zed the a e i hi h shado s of o u e ts eha e i spa e-ti e, at the i o as ell as a o s ales. Fu the o e, the autho has e a i ed the ole shado s’ spatial a d te po al a o-d a i s ha e pla ed i the e a hite to i desig of Neolithi o u e ts. He has p oposed a d de o st ated this ole i the spe ifi ases of t o Neolithi o u e ts, see the ase of Le G a d Me e i [ . ] a d Go ekli Tepe i [ . ].

The autho , asi all th ough the pape i [ . ], o posed a Ge e al D a i al Theo of “hado s i Neolithi o u e tal A hite tu e. The e, the a o-d a i s of the eha io of shado s e e p oposed a d i itiated, a d the ai te ets of that Ge e al Theo e e dis ussed. These te ets e e stated i su a fo i the I t odu to se tio of the pape i ef. [ . ]. Mo eo e , the i o-d a i s of shado s e e stated a d fo alized i [ . ], he e the Mathe ati s of fuzz shado s e e p ese ted. Fo e it pu poses these su je ts ill ot e epeated he e. The eade is di e ted to these pape s fo details. “o e o e ela o atio of poi ts, fi st aised i oth [ . a d [ . ] ut ot full laid out, ill ho e e e ela o ated he e, ith “to ehe ge Phase II e plo ed as a stud i e pi i al e ifi atio of the Ge e al Theo . He e, hat is outli ed i this pape is a e ie o “to ehe ge’s A hite tu al Desig . Besides the appli atio of the Ge e al Theo of Shado s, a e te sio the autho of Ale a de Tho ’s s he e of sto e e losu es is also e plo ed. This is at the o e of “to ehe ge Phase II, a phase i o st u tio i ol i g the sa se s i le a d the T ilitho s’ uasi-ellipti al st u tu e. The autho i efe e es [ . ] a d [ . ] has e te ded the A. Tho ’s theo of lassifi atio of sto e e losu es fou d i efe e e [ . ]. Taki g off f o the i sightful Tho ’s lassifi atio of the e losu es, the autho has added a te po al di e sio to the , suggesti g that si ple sto e e losu es e e su eeded o e o ple i desig . He e, it as suggested the autho that dati g of o u e ts ould e pegged to thei desig o ple it – a asi e olutio a ule, hi h has E olutio as o e i g a i ease i o ple it p i iple. Mo eo e , i hat as fou d to e the si plest o e of all as a t pe of e losu e dete ted the autho i [ . ] as ei g the o e espo si le fo the desig of Go ekli Tepe’s oldest st u tu e D i La e III, of the e ti e e a ated thus fa Go ekli Tepe o ple . I this pape , the autho esta lishes that this sa e desig is fou d i the T ilitho s uasi-ellipti al shape a d its app o i ate di e sio s, oth i floo pla desig a d also a e e e o e i po ta tl i the size height, idth a d thi k ess of the “to ehe ge t ilitho s a d the Go ekli Tepe pilla s

a d o thostats. The autho has e te ded also the A. Tho lassifi atio s he e suggesti g a si ple , a d thus o e p i iti e, lass of sto e e losu es. It as that si ple s he e that as fou d to e appli a le i the ase of st u tu e D, La e III at Go ekli Tepe. We sho he e that this si ple s he e is also p ese t at the T ilitho s e se le uasi-ellipti al a .

Ce t al otio i this o te t a d poi t of the “to ehe ge Phase II st u tu es is the o phalos

of the o u e t, the a e te of the e ti e st u tu e – hi h is the e te i fa t of the oute sa se s i le. It is th ough that poi t that the ele a t a d u e ous o u e t alig e ts go th ough. A d it is ith the alig e t of oo ti e at e ui o that the ke to the o u e t’s

odulus is to e fou d.

If o e e e a le to esta lish a athe ati al odulus fo “to ehe ge II, i ol i g asi atios a o g the ke ele e ts of the o u e t, a d go e e fu the a d li k these atios to the shado s of a ke o thostat, at a ke lo atio of the o u e t, at a ke hou a d date of the ea , the a pote tiall st o g li kage a e suggested that e isted et ee shado s a d the o u e t’s A hite tu e a d Desig . This is fi l esta lished i this pape ’s th ee se tio s. “pe ifi all , that ke is fou d as shado s a e ast the “outhe ost up ight sa se at oo ti e du i g e ui o . The e, the ke of the desig odulus is fou d.

The pape is o ga ized as follo s: the fi st se tio offe s a set of p i iples of the Ge e al D a i al Theo of “hado s to e applied i this e pi i al stud o “to ehe ge; the se o d se tio add esses the A hite tu e p ope of “to ehe ge Phase II; hile the thi d a d fi al se tio looks at the st u tu e’s shado s a d thei d a i s, a d lo ates the ke shado ’s le gth. Wo k o “to ehe ge has ee e te si e a d f o a sou es a d a gles. The o je ti e he e is ot to eithe su e o dupli ate a of that o k. The fo us of this pape is o the i o ati e a e that shado s e a le o e to look i to “to ehe ge. Befo e e do that, a d de i e a e A hite tu e a d Desig ased app oa h to “to ehe ge II a of shado s, so e sele ted ge e al p i iples f o the d a i theo of shado s suggested the autho ill e iefl listed a d ela o ated to a e te t. As “to ehe ge II is a o ple -d st u tu e, a d the athe ati s of the Ge e al D a i al Theo of “hado s a e stated i te s of a si ple li ea g o o a d its st le, so e si plifi atio s a e e ui ed due to the i e se o ple it a -d st u tu e ith f ee sta di g o oliths a d li tels o top of the e tails i its stud of shado s ast. At a ious aspe ts of o i ato ial p og a i g a d o pute si ulatio s eeded to full add ess the a ious issues i ol ed a d o e tio s possi le a o g all sto es of the o u e t a e hi ted.

Basi P i iples i Shado D a i s

I hat follo s, the asi p i iples to e e plo ed i a al zi g the “to ehe ge shado s’ a o-d a i s i spa e-ti e ill e p ese ted. O the , the a e i hi h “to ehe ge is to e app oa hed he e ill e f a ed. It is oted at the outset that the Ge e al D a i al Theo of “hado s, as fou d i [ . ], is stated i te s of a li ea od, the g o o of a su dial, a d ost i po ta tl its st le the top poi t o the g o o . This g o o ould e a e hi o elisk, pilla , o thostat o olu . I othe o ds, the Ge e al Theo as stated i te s of a li ea

o li d i al o figu atio .

Mo eo e , i [ . ] a fu da e tal e ui ale e the asi s of hi h e e a al zed i [ . ] , as stated: the azi uth- lo k e ui ale e fo li ited spatial ho izo s, i ol i g a pe fe tl flat te ai a d a pe fe tl ho izo tal g ou d, see Figu e . As poi ted out i [ . ] the hou l a gles a e e ual o l fo ases he e the lo k’s flat plai is a e uato ial su dial. Ho e e , at all lo atio s o atte the latitude o the Ea th’s su fa e , the id ight/ oo a d a / p a es a e ide ti al to the /  a d /  azi uths.

O a e ui ale e et ee a lo atio ’s pla e he e azi uth a gles a e sho a d o puted, a d the a ual ale da , i fa t fo a azi uth- ale da - lo k e ui ale e, u h o e is e essa to e said a d d a , ha i g to do ith side eal ti e. It ust e e phasized that this e ui ale e has othi g to do ith the pseudos ie tifi lai that the Neolithi uilde s e plo ed a -da ale da , o a  a d ot a  di isio of a i le i to deg ees. This issue ill ot e e plo ed he e fu the . O the topi of side eal ti e see also Note a d the o k “i o Ne o [ . ]. Mo e o this is also supplied i Note , ega di g the Kasta Tu ulus. He e, a se o d fu da e tal e ui ale e ill e stated: the alig e t-shado e ui ale e. A sto e, o the asis of hi h a lu isola alig e t is o tai ed, is i fa t a a ke of the e ui ale t ast-off shado p odu ed the Moo o the “u o a sta i the Celestial “phe e – e e it possi le to depi t the sta ’s i du ed ast-off shado f o the e hi . I fa t, a state e t a out alig e ts app o i atio s, e o s a d elated li itatio s hides i it a ide ti al state e t a out shado s. A d o e sel , a state e t a out shado s a d thei

o ditio s thus li itatio s o tai s ithi it a e ui ale t state e t a out alig e ts. I ie of the a al sis i [ . ], see Figu e , ega di g fuzzi ess i shado s, it i ediatel follo s that these alig e ts a e ha a te ized suffe i g o spo ti g the sa e ail e t o gift : fuzzi ess. This ought to e kept i i d he sophisti ated alig e ts a e suggested a haeo-ast o o e s as ha i g ee i pla ted i Neolithi o u e ts – alig e ts e ui i g the use of ad a ed su e i g e uip e t lase ased theodolites o te po a a al sts to esta lish.

The Ge e al Theo a e e pa ded, this pape sho s, to si ulate the o e e t of shado s ast off f o a su fa e of a solid, athe tha a e hi . It a tuall i ol es t o solids – o e ei g

the sa se s’ oute i le, hi h a e ie ed as the oute ski of a i le- ased li de ith a hollo i te io ; a d the T ilitho s’ a , i ol i g the oute ski of a uasi-ellipti al li de ith a hollo i te io as ell. The Bluesto es i les ill ot e a al zed he e; thei e ui ale t t eat e t is left to futu e esea h.

A fu the disagg egatio a e iefl outli ed, a d e pe i e tall a al zed, he e the sa se s a d T ilitho s ski s a e su di ided i to se to s, ep ese ti g disti t sto es o sets of sto es – although the shado s of all these i di iduall o side ed sto es to e e pli itl a d i di iduall odeled ould e tail a sig ifi a t o i ato ial a d o putatio al halle ge. The la ge u e sa se s, o sisti g of pilla s a d li tels, plus t ilitho s, o sisti g of te pilla s a d fi e li tels of sto es i ol ed, ge e ate a e la ge u e of o i atio s. Co i ato ial o puti g a d asso iated o pute p og a i g of this s ale e de the a al sis p ohi iti el olu i ous, to a e te t i t a ta le, a d e t to i possi le fo it to e a o odated i a si gle pape . The ag itude of the o i ato ial p o le i ol ed is fu the oosted the de i atio of the R a eas fo ea h sto e; see fo the defi itio of these R egio s the e t se tio , ef. [ . ] a d Figu e elo .

A pa allel p o essi g, supe o pute si ulatio is eeded, to aptu e all possi le otio s a d all possi le i te a tio s a o g all these sto es at diffe e t ti es of the da a d ight o e all da s of a ea . “u h a o pute si ulatio is a o side a le esea h u de taki g, al eit a e p o isi g o e, that pote tiall a a o odate fo al statisti al a al sis. It ust e of ou se assu ed that ot all of these i te a tio s e e i di iduall o puted at the ti e of thei o st u tio , a d that o l a fe e e of i po t. P io a al ses ha e alluded as to hi h sto es a o g the total e e ke i the Neolithi a hite ts’ desig , a d to that ot u h ill e added he e, e ept he o el fi di gs a e to e poi ted out a d so e e sto es to e desig ated as of at least as u h i po t as those al ead ide tified as i po ta t i the e isti g lite atu e o “to ehe ge.

The fo al poi t i this pape is to seek a a s e to the uestio : hat aspe t of the shado d a i s e ou te ed at “to ehe ge is likel to ha e pla ed a sig ifi a t ajo ole i the e desig of “to ehe ge. B that, it is ea t to a s e the follo i g sets of asi “to ehe ge desig uestio s: to hat e te t “to ehe ge shado s dete i ed a h a - ete sa se s i le, ith sa se s pilla s a d li tels of the spe ifi sizes height, idth, le gth e e put i pla e; h e e these + sa se s pla ed e a tl at the lo atio s pla ed; a si ila set of uestio s fo the + sa se s fo i g a fi e-set e se le of t ilitho s. “o e of these uestio s ha e ee add essed e te si el i the lite atu e, a d that ill ot eithe e epeated he e o su e ed, si e this is ’t the o je ti e of this pape . O l o el aspe ts i the a s e s to these fu da e tal uestio s ill e supplied.

Figu e . The sha p le gths of shado s. Dail a d a ual paths of total “u -i du ed ast off shado le gths a e sho i this a o d a i s odel p oposed the autho i efe e e [ . ] A {EA D} is the st le’s t aje to ide tified fu tio  du i g the da of the su e solsti e; a {GA F} is the st le’s t aje to du i g e ui o es, fu tio  ; a d a {CA B} is the st le’s t aje to du i g i te solsti e, fu tio  , at so e lo atio he e the solsti es appea at a a gle ω. As dis ussed i [ . ], a ious su - egio s ithi egio R see pape ’s a ati e fo its defi itio ide tif g ou d ased ale da a d lo k fu tio s fo the e hi a ti g as a g o o of a su dial ith a st le o its e top poi t. I side the shaded a ea, the e hi loses its g ou d ased ale da i di ati g p ope t , etai i g o l its lo k i di ati g apa ilit . Of ou se, if a othe e hi is aised i side the shaded a ea the the al ulus is diffe e t. Co se ue tl , fo a o u e t ith ultiple e hi s, the shaded a ea a ui es spe ial i te est. As e tio ed i the te t, these fu tio s hide i the alig e t fu tio s, due to the

A shado s elated uestio is also this: as the e a ole shado s pla ed i lo ati g the o u e t hi h goes the te “to ehe ge toda he e it is p e isel lo ated, i hat is u e tl ee efe ed to as Wiltshi e at “alis u Plai i u e t da “outhe E gla d see Note fo o e ega di g this e a k . That is, e e the e a o-la ds ape, a o-topog aph a d a o-Geog aph shado - elated o side atio s fo the spatial allo atio of this o u e t at its u e t site. Of ou se, the e e e u e ous othe possi le o side atio s hi h e de this spe ifi site as the ost fa o a le, efe ed to as lo atio al o pa ati e ad a tages i E o o i Geog aph . Agai , this uestio ill e add essed to the e te t that o el i sights a e o tai ed o side i g shado s he the o tai huge le gths, lose to su ise a d su set a d of ou se, oo ise a d oo set .

Fo ea h i di idual “to ehe ge pilla o sta di g sto e the sa se s a d the t ilitho s , the a o spatial a d te po al d a i s of shado s ith sha p edges a e depi ted the autho ’s diag a i Figu e , fou d i efe e e [ . ]. Fo the ide tifi atio of all ele a t poi ts a d li es o this diag a , hi h ide tifies the azi uths of the solsti es a d e ui o es at so e a it a lo atio o a of the Ea th’s latitudes, u de a li ited ho izo a d flat g ou d hi h is pe fe tl ho izo tal, the eade is efe ed to [ . ]. He e, a lose look ill e take o the diag a , a d espe iall o its shaded pa t. It tu s out that it pla s a pi otal ole i the desig of o u e ts,

he e shado s shaped to a e te t thei o pholog .

It should e kept i i d that these shado s’ do ai s a e the p odu t of a li ea e hi , of so e a it a height H, ast off it as a esult of su light a d t a ed du i g a da of the ea , a d o e the app o i ate -da a ual le. The a ious a eas, desig ated u de a li ited ho izo depi ted the i le ide tif i g the azi uth- lo k e ui ale e , p ese t spe ial i te est to the e te t that shado s a d alig e ts a e o e ed.

Of ou se, the total a ea i side the egio R ide tified the poi ts {O,D,F,B,A ,C,G,E,O} is he e ast-off shado s fall o the g ou d f o the e hi i uestio of so e height H at so e latitude he e the solsti es o u at so e a gle ω. “hado s do ot e ist off this egio du i g a ti e of the da , a da of the ea . I effe t, R depi ts the e hi ’s a ket a ea fo shado i te a tio . Be o d this a ea, the e is o effe t eithe f o o to the e hi i uestio . “tated i slightl diffe e t te s, south of the solsti es adii OD a d OE a d o th of the 

fu tio , the p ese e of a H-high e hi , at lo atio O, at so e latitude o the Ea th’s su fa e, has o effe t at the g ou d le el. The e a e u e ous su - egio s i R he e so e ast-off f o the e hi shado effe ts a e seaso al.

The al ulus is diffe e t, if so e othe e hi is aised at so e poi t ithi these su - egio s of R i Figu e . A o g these su - egio s, the shaded a ea i Figu e is of so e e t a i te est. At o ti e of the da a d at o da of the ea , i that su - egio , is the e a g ou d ased ale da fu tio possi le fo the e hi i uestio . Fo the ale da fu tio to e ai tai ed i side the shaded a ea of Figu e , a e hi ust e aised of suffi ie t i i u height, depe de t upo its lo atio ithi that shaded a ea a d the site’s lo atio o the Ea th’s su fa e

its latitude . Thus, i all ases of o u e ts he e ultiple e hi s o thostats, pilla s, olu s, o elisks et . a e i ol ed, this shaded a ea of Figu e a ui es pa ti ula i po ta e. At a lo atio , o th of fu tio  a d south of fu tio  , g ou d ased ale da i di atio s a o l e o tai ed et ee the su e solsti e a d the autu al e ui o , a d the ti e pe iod et ee the sp i g e ui o a d the su e solsti e. A d at a lo atio , o th of fu tio  a d south of fu tio  g ou d ased ale da i di atio s a e o tai ed i the seaso s et ee the autu al e ui o a d the i te solsti e, as ell as du i g the i te solsti e a d the sp i g e ui o . A d agai , the al ulus ha ges if e hi s of app op iate height a e aised ithi these su - egio s. Natu all , the ould e of de easi g apa ilit to a t as

ale da i di ato s the fu the a a the a e f o the shaded a ea of Figu e .

Figu e . This is a figu e sho i g shado s of o je ts f o diffe e t dista es. It as a al zed a d e te si el dis ussed i [ . ]. The photo de o st ates t o fu da e tal p ope ties of shado s, a el thei fuzz atu e a d the effe t dista e has o the . “ou e: the autho a d

Ela o ati g o these p i iples is of so e fu the i te est, as the dis ussio tou hes su je ts of s ale. The height of a e hi o th of the o e at poi t O eed e lo e tha the o igi al e hi at O. A highe e hi fo ale da pu poses is u e essa . Thus, a e hi ust e o side ed ale da - ise su o di ate to the o igi al e hi at poi t O, a d ust e lo e i height tha H. O the othe ha d, the opposite holds fo a e hi south of the o igi al at O. It ust e talle a d thus do i a t o e the o igi al. These a e i t a- o u e t s ale elatio ships, li ki g heights of the o u e t’s a ious o po e ts a d thei sizes as ell as dista es a o g the . We shall see the pla out i the ase of “to ehe ge i late se tio s. A e hi o atte its height to the o th of R, is ot ele a t to the e hi aised at poi t O, as it falls outside its a ket a ea. O the othe ha d, it ust e oted that this e hi ’s a ket a ea is ope a le i -d. It is so that, a e hi to the south of R ould fall i side the g ou d ased ale da use of, at poi t O lo ated, e hi – that is, it falls ithi its a ket a ea, if a d o l if

it is suffi ie tl high at the spe ifi poi t aised. These o ditio s of ou se depe d o the o u e t’s lo atio o the Ea th’s su fa e.

This a al sis pote tiall ties up the latitude of a o u e t to its s ale size . Mo e spe ifi all , if the shado s pal a ole i the desig of a o u e t, the the i itial s ale of so e fi st pla ed fo pilla e hi , o thostat, olu et . i tu dete i es the di e sio s a d s ale of the e ti e o u e t. To a deg ee, this i itial pilla ’s size, o its ele a t su di isio , is the o u e t’s odulus. The su di isio is di e tl elated to the dista e a d size of the othe o po e ts e hi s of the o u e t, a d thei elati e dista e f o the ase e hi . A ief ote is e essa at this poi t to de o st ate the ele a e of the a o e fi di g,

ega di g a othe Neolithi o u e t. I ie of the a o e a al sis, o e a o u de sta d the shape of the st i gs of sto es at Le G a d Me e , at Ca a , dis ussed i efe e e [ . ] a d also i [ . ]. Mo e spe ifi all , the e hi dis ussed o p. , sho i the se ue e of Figu e A . - of [ . ], ould e i st u e tal i ide tif i g the lo atio of at least th ee st i gs of sto es to the No th a d oth East a d West of it, as falli g ithi its a ket a ea at diffe e t ti es of the da o e possi l th ee diffe e t ke ? da s of the ea .

We o lude this se tio of the pape ith a efe e e to the lo g dista e f o a a o-la ds ape, a o-topog aph , o a o-Geog aph , that is a o-spatial i te a tio li ki g the spe ifi site of a o u e t to its oade su ou di g E i o e t. These li kages, if the e ist, o e a out f o the e lo g le gths of the shado s lose to the poi ts B, C, F, G, D, a d E of Figu e . Alo g the a s defi ed these poi ts, a BD a d a CE , a d at the e te ded ho izo as the adius of the i le ith e te at poi t O, a d deli eati g the ho izo , i eases the a ious sk li e featu es fou d at the e d of the ho izo a e tou hed the e lo g shado s ast off the e hi at poi t O. Thus, these poi ts o the ho izo a t as the idges li ki g the o u e t to its la ge-s ale su ou di gs. This is di e tl elated to the alig e t-shado e ui ale dis ussed ea lie i this se tio .

O the A hite tu e of Sto ehe ge

Mu h has ee said a d itte a out the A hite tu e of “to ehe ge, a d this se tio ’s ai is ot to eithe epeat o su e that e te si e lite atu e. The o je ti e he e is to add a e a gle to that od of o k, a off-shot of the autho ’s e te sio of Ale a de Tho ’s theo o the desig of Neolithi sto e e losu es. U de this e a gle, e ill li k the o te ts of this se tio to the pape ’s ai goal, hi h is the stud of the “to ehe ge’s “u i du ed ast-off shado s, thei otio du i g the da a d th oughout the ea , a d the ole these otio s e likel pla ed i the desig of “to ehe ge’s t o ke st u tu es: the sa se s i le, a d the T ilitho s uasi-ellipti al a .

The e a e u e ous sou es he e data a d espe iall the floo a d site pla s o tai i g the A hite tu al detail of “to ehe ge a e fou d, o e ei g the E glish He itage efe e e i [ . ] a d its ited efe e es. The ge e all a epted site pla fo “to ehe ge is that of Figu e . O it, a u e i g of sto es also ge e all a epted is fou d – a u e i g hi h i ol es the sa se s of the oute i le, the uasi-ellipti al a of the T ilitho s, a d the t o Bluesto e i gs. Mo eo e , i the lege d, a eakdo is offe ed a o di g to thei u e t state sto e t pe. A e ui k des iptio , of the asi t o o po e ts the sa se s oute i le a d the T ilitho s’ a of “to ehe ge that e shall add ess i this pape , follo s. This diag a ill e used as a luep i t i the p ese t stud . Co se ue tl , the a u a of the fi di gs iti all hi ge upo the a u a of the floo pla i Figu e .

“to ehe ge Phase II i a – BC , o tai s a i ula s ste of sa se s out of

hi h e e e e ted as o thostats pilla s , suppo ti g a othe sa se s as a i g of li tels. A ope esea h uestio e ists, as to hethe the e ti e i le as e e o pleted, o that it as e e pla ed a d desig ed to e o pleted as des i ed; see this issue ei g dis ussed i the autho ’s pape [ . ]. This uestio is of di e t ele a e he e, fo the follo i g easo : if the oute i g as o pleted at a diffe e t ti e tha the i e a of the T ilitho s as e e ted i the t o e tu ies pe iod, the the i e uasi-ellipti al e losu e ust had ee e e ted fi st

a d the the sa se s i le e e aised. This se ue e e o es of i po t, he the odula st u tu e of the o u e t is to e dis ussed, as it ill e o e o ious f o the a al sis that follo s.

All sa se s o thostats a d li tels had u de go e the uilde s of the o u e t d essi g , i.e., so e fo of p o essi g. This i luded, as it is ell do u e ted i the e isti g lite atu e, a slight e di g of the li tels to follo the o e all i ula st u tu e, a d the slightl up a dl ide i g of the o thostats to o e t fo g ou d pe spe ti e. A hite to i all , oth of these fo s of d essi g e e o st u tio i o atio s at the ti e this Phase of the o u e t as o st u ted. Be di g of li tels is of ou se e ou te ed i the ase of the ea lie Maltese Te ples; ut o e ti g fo g ou d pe spe ti e is a sig ifi a t i o atio that o u ed at “to ehe ge II.

Figu e . “to ehe ge sa se s: the oute a d T ilitho s i gs a d the Bluesto es i les. The floo pla a d its lege d a e due to A to Θoh so ho holds a op ight o it, see [ . ] . The sto es’ u e i g follo s the o e tio al F. Pet ie s ste . Nu e s - depi t the sa se s oute i g o thostats; - the sa se s li tels; - the sta di g T ilitho s; a- a the T ilitho li tels; - the oute Bluesto e i le; a d - the i e Bluesto e i le. The t o Bluesto e i les a e post BC additio s o stituti g Phases III a d IV . The e t al poi t a e te of the o u e t is e a tl he e the oss is at the diag a a o e. Ho e e , as the diag a i Figu e sho s, the e te of the T ilitho s’ uasi-ellipse is ot at that poi t. I the a o e diag a , to e i di ates state of the sto e sta di g o falle a d sto e t pe.

The sa se s’ oute i g itals. These sta di g sto es fo a app o i ate - ete i dia ete i.e., ith a adius of a out . ete s a d a i u fe e e of al ost . ete s pe fe t i le, ith its e te ei g the o phalos of the o u e t, see diag a i Figu e . That i le is d a goi g th ough the e e te of the sta di g sa se s. The a e age sta di g sa se is app o i atel . ete s i height a o e g ou d i total, the easu e a out . ete s i height , . ete s thi k, a d . ete s ide. Thus, the sta di g sa se s fo the ski of a hollo li de ith i e su fa e dia ete of a out . ete s a d a oute ski su fa e of a out . ete s i dia ete . The li tel i g has a thi k ess of a out . ete s ea h li tel is . . , thus the total height of the st u tu e a o e g ou d is lose to fi e ete s. Ho the st u tu e is u e tl e isio ed the o se sus of a heologists is sho i Figu e N i Note see se tio o Notes at the e d of the pape .

With a pe i ete at the ski ’s e te of a out . ete s, a a e age le gth at thei e te of a out . ete s, a d assu i g o pletio of the i le, the sa se s a e spa ed o the a e age at a dista e of a out . ete s. The fa t that the e isti g su i i g in situ dista es a o g the sta di g sa se s is slightl o e tha a ete , adds o e uestio s as to hethe the o u e t as desig ed to e p e isel uilt a d o pleted as des i ed. A ote-pa e thesis is a a ted he e, o atte the spe ulatio ega di g o igi al i te t the a hite t s of “to ehe ge Phase II. The le gth of . ete s is p e isel the odulus fou d the autho to ha e ee used i the Kasta Tu ulus pe i ete all o st u tio , see efe e e [ . ]. I Note , o e ela o atio is p o ided o this issue. The Note a e ds a d e te ds the

o k o this topi fou d i the autho ’s p io pape s o the su je t.

I Figu e , the N-“ a d E-W a es f o the e e te of “to ehe ge a e d a . O the , the u e t azi uths a e esti ated. It is oted that due to shifts i the Ea th’s a is of otatio de li atio , the u e t azi uths a e off f o those at the ti e of “to ehe ge Phase II o st u tio app o i atel  to . A tuall , o o e is e a tl su e hat p e isel is this de iatio , see Note . Mo e o this topi i a it, follo i g the ief outli e of the T ilitho s. Fi all , it is oted that o the su fa e of sa se s # , # a d # a i gs of a e-heads ha e ee fou d. The i po ta e of this ill e fu the dis ussed he the alig e ts of that se tio of “to ehe ge ill e add essed a it late .

We o tu to the T ilitho s’ uasi-ellipti al a . We shall atte pt to e o st u t this pa t of the st u tu e, a d doi g so a i o ati e pe spe ti e o “to ehe ge e e ges.

The T ilitho s e se le. Let us e ie hat is k o a out the T ilitho s a , d a f o the p e ious sou es as ell. The spe ifi uasi-ellipti al o pholog of this a ill e a al zed sho tl , afte the itals of the sto es o tai ed he ei a e p ese ted. The T ilitho s e se le is o ga ized so that the e a e fi e sets of th ee sa se s, pla ed so that ea h t ilitho set o tai s t o sta di g o thostats ith a li tel o top, i.e., ea h set fo s a t iple, hi h is o o l efe ed to as a t ilitho Ρ - Ο . He e, i total, the e a e fiftee sa se s i this uasi-ellipti al a , o ga ized i a s et i patte , alig ed o a a is a d fa i g to a ds the su e solsti e at su ise a d at the a k e d fa i g the i te solsti e at su set.

Figu e . The N-“ a d E-W a es of “to ehe ge, at p ese t azi uths ith the e te of the pla e dete i i g the azi uths at the e e te of the oute i g i le – this ei g the o u e t’s

o phalos. The possi le azi uth of these t o a es at the ti e of Phase II o st u tio is also sho . The N-“ a d E-W a es a e iti al i dis ussi g the la out of the oade site a d floo pla a d i spe ifi sto es # , # , # a d # . “ee fo o e dis ussio o this topi the se tio of the pape o azi uths, as the e e the a d o , a d Note . “ou e: the autho .

The height of the te up ight sto es elo gi g to this e se le is ot u ifo . The tallest t o o thostats a e fou d at the south- este t ilitho set of the uasi-ellipti al T ilitho s e se le; the ould ha e had a height of a out . ete s a o e g ou d ith a total height of a out te ete s , although at p ese t the o l sta di g sa se of this set is a out . ete s i height a o e the g ou d le el. Whe eas the t o pai s of up ight sa se s at the o th-easte ost t iples ha e a height of app o i atel si ete s. The pai of the t iple et ee the t o has a height of a out . ete s. Ho shado s a e li ked to this height diffe e tials ould e of i te est to po de . No a e age thi k ess o le gth easu e is a aila le fo the te up ights.

The athe ati al odulus at Sto ehe ge. O iousl , gi e the asi s of the desig i Phase II, o e o ludes that the o u e t at this stage as uilt o the asis of u e a d the p i e u e s a d , a d of ou se thei ultiples. The u e of sa se s i the oute i g is ; the u e of sa se s i the i e T ilitho s e se le uasi-ellipse is . We he e ust o lude that the egi i g of a odulus is p ese t he e, ased o the p i e u e s a d . The s all a is of the uasi-ellipti al T ilitho s e se le i e ski a out ete s is half the oute i g’s i e ski dia ete of app o i atel ete s. It is oted that the total height of the oute sa se s i le a out fi e ete s is o e si th of the i le’s dia ete . Mo eo e , the total height of the sho test sa se i the uasi-ellipti al a of the T ilitho s e se le si ete s is a out o e fifth of the oute i g’s dia ete as ell. The tallest sa se esti ated to ha e ee a out . ete s a o e g ou d is lose to a out o e fou th its dia ete , a d a out half of the uasi-ellipti al a ’s i o a is. These atios a e e t al i u de sta di g the asis o hi h the o u e t’s Phase II as o st u ted. Ho this odulus as li ked to the ast-off shado s at “to ehe ge, a d he e ho shado s a d thus, alig e ts pla ed i to the e desig of the o u e t is add essed i the e t se tio of the pape , follo i g the p ese tatio of the e fi di gs a out “to ehe ge’s A hite tu e.

The T ilitho s uasi-ellipti al a . I Figu e , The luep i t of the T ilitho s a desig is sho . That desig o sists of t o al ost pe fe t se i i les, sepa ated a dista e of a out . ete s. The diago als AB a d CD of these app o i ate se i i les u pa allel to ea h othe . The se i i les ha e a adius of a out . ete s, easu ed at a out the iddle poi t of the T ilitho s’ sa se s ski . Whe eas the “ou este se i i le is uite o ious, the No th-easte is ’t uite as o ious, thus its dete tio has es aped the a hite to i a al sis of the e se le so fa . Ho e e , the p ese e of the No th-easte se i i le is hi ted the slight i a d e di g of the No the ost sa se s i the T ilitho s e se le, sto es # a d # . I Figu e , the e te of the oute i g of + sa se s up ight o thostats a d thei li tels is also the a e te of the e ti e “to ehe ge Phase II o u e t. This is the o phalos of this se tio of the o u e t at “to ehe ge. Fo desig pu poses, it is fa o e i po ta t tha the spot he e the so alled alta sto e is lo ated – i f o t of sa se s # a , o falle , a d #

Figu e . The ajo alig e ts ith O as the o u e t’s o phalos. The A hite tu e a d Ast o o of “to ehe ge Phase II o tai s the sa se s i le a d the T ilitho s’ uasi-ellipti al o pholog . The T ilitho s’ sto e e losu e o figu atio o sists of t o se i i les ith pa allel dia ete s AB a d CD sepa ated a dista e of a out . ete s. It o tai s the st u tu e’s ai alig e t the su e solsti e su ise as its ajo a is. It is si ila to the sto e e losu e ide tified the autho as the luep i t of Go ekli Tepe st u tu e D, La e III, see [ . ], [ . ]. Both a e si ple e sio s of the Tho ’s sto e e losu e lassifi atio s he e fo Neolithi

Up ight sto e # a d do sto e # oke i to th ee pie es - # a, , se e as the t o pa allel li ks et ee the t o app o i ate se i i les. Of ote is the lo atio of these se i i les’ e te : the o e to the “outh-east, lies at a out the e a e te of the e ti e o u e t as sho i Figu e a d slightl to the “outh- est, off a s all dista e f o the diago al AB . Due to u a oida le app o i atio s i o posi g the asi site pla the B itish He itage, a d o st u tio i pe fe tio s, plus the ti e that has elapsed a d the effe ts of ea a d tea of the o u e t o e the ille ia, the e is o easo to dou t a d easo to a ept that the e te of this se i i le as i te ded to e at the diago al sho i Figu e . Whe eas, the e te of the No th-easte app o i ate se i i le is fou d e a tl o the diago al CD . He e, e dete t i the T ilitho s e se le a fa ilia patte , f o the Tho ’s lassifi atio s he e: t o sepa ated ut li ked se i i les fo i g a uasi-ellipti al st u tu e. This uasi-ellipti al fo has as a i o a is dia ete of the o stitue t i le of a out . ete s, a d a total le gth ajo a is of a out . ete s. Noti e, the total le gth of the ajo ellipti al a is is sho t a s all f a tio of the su . + . = . due to the fa to s al ead e tio ed. Although the T ilitho s e se le is positio ed so that it is s et i al i efe e e to the su e solsti e azi uth li e, it is ’t s et i all lo ated i efe e e to the a e te of the e ti e st u tu e, poi t O i Figu e , the o u e t’s o phalos. Ho e e , the o phalos is at the sa e lo atio as the e te of the -sa se oute i le e ause the de sit of T ilitho e se le sa se s is ’t u ifo alo g the uasi-ellipse.

The oute edge of the T ilitho s sto e e losu e is at a dista e of a out . ete s f o the i e su fa e of the sa se s i le at its i i u app oa h i the No th-east; it is at a out a d o less tha si ete s a a f o the i e su fa e of the sa se s’ oute i g at the othe e d “outh- est . It tu s out that this - ete dista e is a ke le gth fo the e ti e “to ehe ge II desig , as it ill e poi ted out i a it. It is also oted that the so- alled alta sto e la i g i f o t of the “outh este t ilitho set is pa allel to the i te solsti e su ise – su e solsti e su set a is at the  to  azi uth li e see, p. i [ . ] .

The desig has deep oots i sto e e losu e o pholog . Ale a de Tho a d his so A hi ald “. Tho i efe e e [ . ] offe ed a i sightful a d ge e al lassifi atio s he e fo sto e e losu es e ou te ed i the B itish Isles a d B itta . This s he e as e te ded this autho i [ . ] a d [ . ], so that it a ui ed a te po al di e sio , ased o the p i iple of i eased o ple it i the E olutio of Fo . “i pl stated, si ple fo s ust ha e appea ed efo e o e o ple e sio s of a pa ti ula fo a e a out. Fu the o e, e tai ti e pe iods ust elapse i the fo atio of o ple a iatio s of a o igi al si ple fo , the o e o highe deg ee of o ple it e ui i g p opo tio all lo ge ti e pe iods.

Mo eo e , the autho e og ized the p ese e of si ila sto e e losu es falli g u de the Tho ’s lassifi atio s he e i othe Neolithi sites, i ludi g Go ekli Tepe a d Malta. A o di g to this theo eti al, i ol i g te po al d a i s t pe pe spe ti e, it as gauged that La e III, st u tu e D the oldest thus fa e a ated e losu e at Go ekli Tepe as a late Mesolithi to ea l Neolithi st u tu e, a d that Go ekli Tepe as u ied so eti e a ou d the

egi i g of the B o ze Age the app o i ate ti e of Phase II at “to ehe ge , see [ . ]. I additio , t ilitho fo atio s the su je t of i te est i this su se tio a e e ou te ed i the Maltese Haga Qi te ples of the Gga tija Phase o the isla d of Malta, see [ . ].

It is esta lished that the patte a d ot o l , as sto e sizes as ell as e losu e di e sio s a e e si ila too as dis ussed he e fo the T ilitho s e se le at “to ehe ge, is hat the autho des i ed st u tu e D, La e III at Go ekli Tepe to e, see efe e es [ . ] a d its p e u so [ . ]. This fi di g is a ajo o e, si e it di e tl li ks the A hite tu e of Sto ehe ge to that of the Fe tile C es e t. This o e tio i desig has ee i itiall e plo ed i [ . ], he e it as suggested that the o pholog of the T ilitho s e se le as o siste t ith a Bull Cult desig . That C es e t Moo a d ull ho o i atio desig patte has ee i p i ted i the a hite to i s of all st u tu es ea i g the shape of a a o apse , si e ea l Mesolithi . It has ee ide tified i a ultipli it of o te ts, su h as the ea l Natufia Fe tile C es e t A hite tu e, the Maltese A hipelago Neolithi egalithi Te ples of the Gga tija a d Ta ie phases, to the Ri e Bo e passage to s Ne g a ge , do to “to ehe ge.

I the T ilitho s e se le, e fi d a NE-“W ai lo g a is of the uasi-ellipti al a at a azi uth of  the lue li e i Figu e . This li e uts a oss ight i the iddle the dista e et ee sto es # a d # at p ese t, ise ti g the e ti e o u e t. It i te se ts at e a tl

 the AB a d CD i o a es. I Figu e , the  azi uth li e is d a ; it tou hes off the

e southe poi t sa se # . Thus, the i do defi ed the azi uths  a d  is the

su e solsti e su ise i do at “to ehe ge. The fa t that this e e t is still possi le to o se e, offe s st o g suppo t to the p opositio that the azi uth o e e t the p e essio si e the o st u tio date of “to ehe ge Phase II a out . K a has ee i o possi l o

o e tha  to . , possi l less, a o di g to A. Tho i [ . ] .

The eade should keep i i d that o e-deg ee of azi uth is a out the idth of t o “u disks at the ho izo . The eade should also keep i i d that the u e t azi uths ha e o ed lo k ise f o the Neolithi o es. Putti g it slightl diffe e t te s, the Neolithi N-“ a is as slightl to the left of the u e t N-“ a is. Fi all , it is oted that the e te sio of the azi uth fo the su e solsti e su ise, is the i te solsti e a s at su set. Co se ue tl , at the

“outh-este uad a t of Figu e , o e sees the di e tio s a d azi uths of the su set at i te solsti e. It follo s i e e se the paths outli ed fo the su ise a s at su e solsti e the su ise azi uths plus  .

“i ila a i gs to those o sa se s # , # a d # f o the oute i ula e losu e, a dagge a d fou tee a e-heads ha e ee fou d a ed o sto e # of the T ilitho s e se le. Gi e the elati el good o ditio of this sa se elati e to its eigh o i g to the south sa se # , o e a spe ulate that o oth the e ould e a i gs. The i po t he e is the lo atio of sto e # a d pote tiall # i the o te t of the alig e ts i ol ed at “to ehe ge’s i e sa tu – i o i atio ith sto es # , # , a d # .

Alig e ts at Sto ehe ge e o d the su e solsti e su ise. The idsu e solsti e date’s su ise is ot the o l although the ost i po ta t gi e the o u e t’s o e all o pholog of floo a d site pla alig e t a ked the A hite tu e of the t o sa se s’ i gs-e losu es at “to ehe ge. Although it a ha e justifia l att a ted the o e hel i g atte tio of the th

e tu “to ehe ge a al sts, it e tai l as ot the o l o e, although lea l gi e the site pla of the o u e t, see Figu e N , as ell as the spe ifi floo pla of the Phase II sto e e losu es, sho i Figu e it ight ha e ee o e a o g the t o ost i po ta t o es. Wo k i the se o d de ade of the st _{e tu has offe ed e i sights i to the atu e p ope of}

“to ehe ge. “i e the o k Ge ald Ha ki s, C. A. Pete Ne ha , F ed Ho le, Ale a de Tho – a d fo a e te tai i g e ie of this lite atu e see R. Hill [ . ] a d fo a o e e e t a al sis a out sol i g “to ehe ge see [ . ] – u h e o k has take pla e. This e o k, see fo e a ple T. Maede [ . ], [ . ], a d the g oup i [ . ], does ot fo us o the pote tiall e essi e lai s of these ea l a haeo-ast o o e s, ega di g o pli ated lu isola les – les that e ui e oth athe ati al a d ast o o i al sophisti atio lea l e o d these Neolithi a hite ts a d ast o o e s’ apa it fo e o d keepi g. Alo g ith o k this autho [ . ], [ . ], [ . ] et ., this o k is ’t la gel ased o the i ta gi le otio of a alig e t o the e t ao di a app o i atio s e ui ed to a o odate its lai s.

I stead, although of e ual athe ati al a d ast o o i al igo , this e o k fo uses o ta gi le su je ts hi h lea e little dou t as to thei pote tial ole i the o u e t’s desig : thei ast-off shado s a d the shado s’ ho eog aph du i g the da o ight. As this pape asse ts, the e a e of ou se st o g o e tio s et ee shado s a d spe ifi ajo a d o ious alig e ts i p i ted i to the o u e ts’ a hite tu al desig . This e o k does e plo so e ajo featu es f o the ea l a haeo-ast o o lite atu e ho e e , like fo e a ple the Tho ’s lassifi atio s he e of sto e e losu es. Mo e o this su je t of ou se is fou d i the

e t se tio of this pape .

A lose look at the East-West a d the No th-“outh a es allo s fo a deepe app e iatio of the a e t i poi t O a d these t o a es, a d the othe sola - elated alig e ts at “to ehe ge. Although i the u e t lite atu e o “to ehe ge, the alta sto e i f o t of the “outh este t ilitho set is o side ed to e the o phalos of the e ti e o u e t, the i po t of a e te O should ot e u de esti ated. I effe t, the a is of the e ui o es, e eals that the u e t e ui o su ise a s hit sto e # , a d do ot pe et ate the i e sa tu of the T ilitho s e se le fo a o se e sta di g at g ou d ze o, poi t O, “to ehe ge’s a e te . To this e d, up ight # oute su fa e ust had held so e sig ifi a e fo the a hite t s , e gi ee s , ast o o e s , uilde s a d afts e of “to ehe ge II. He e e a e og ize the i po ta e of the a i gs o that pa ti ula sa se , as ell the eigh o i g sto es # a d # . Ho e e , ed li e i Figu e holds so e iti al i fo atio ; goi g th ough the o u e t’s

a e te poi t O , it e eals that a app o i ate -de iatio to the No th a a gle uite lose to the the e ui o azi uth , th ough sto e # a d # , tou hi g the o thostat # , the su ise a s ould pass to the No th of sa se # , pass o thostat # a d pe et ate just off

its “outhe tip the e ti e set of t o sto e e losu es. This alig e t of up ights e likel is ’t a do , a d offe s so e al eit eak suppo t to the a gu e t that the o li uit of the e lipti i that . K ti e i te al a ha e esulted i su h a  a gula ha ge i the e ui o es’ azi uth.

It ust e e phasized that a  ha ge ould e ell a o odated the o u e t’s floo la out, fo it allo s the su e solsti e su ise a s to still pe et ate th ough up ights # a d # a d hit the gap et ee sa se s # a a d # of the T ilitho s e se le a o e the alta sto e, a d ea h the gap et ee the oute i g sa se s # a d # . Up ight sto es # a d # i o i atio ith sto es # a d # ould fo i do s th ough hi h the e al a d autu al e ui o es su ise a d su set a s ould allo fo light to pe et ate the e ti e o u e t. Of ou se, the i po t of e o di g the su e solsti e su ise has ee idel a al zed i the e isti g a haeo-ast o o lite atu e a d ot u h ill e added he e. The i po ta e ho e e of o ito i g the e ui o es is ot so idel dis ussed. But it is a al zed i Note , at the e d of the pape f o a o el pe spe ti e. I ase the up ight sto e # as i the a of the e ui o es’ su ise, the its i te io su fa e ust ha e had a spe ial ea i g to the uilde s of “to ehe ge II, ei g the e epto of the last glea at e ui o .

Fi all , ega di g the ai su e solsti e su ise alig e t, a poi t eed e ade: the

o e it of the T ilitho s e se le i e ei i g the fi st su a s of the da , is also the o a it

of the e se le i epulsi g the i te solsti e last glea . Thus, a dualit i the alig e ts is dete ted, desig ati g diffe e t oles pla ed the up ights at diffe e t ti es of the ea . No , a look i to the i te solsti e alig e ts ill e take . Of ou se, si e the su e solsti e azi uth is at a out  i.e., -  , the i te solsti e ust e at  + , i di ated the g ee li e at that azi uth i Figu e . He e, the i te solsti e su set is at  +  . Fo a o se e at a e te O, the su ise a s at i te solsti e ould e lo ked assu i g all fa to s e tio ed ea lie ei g ope a le he e o thostat # . Ho e e , at p ese t, the fi st i te solsti e a s do pe et ate the o u e t’s i e sa tu , tou hi g the southe tip of up ight sa se # , a d like ise sa se # of the T ilitho s e se le.

The o ti ue th ough the gap et ee the No the ost set of t ilitho s, “outh of sa se # a , a d No th of sa se # ; a d e d up ea hi g the gap et ee oute i g sa se s # a d # – thus totall pe et ati g the t o sto e e losu es. The  a gle sho the t o g ee li es i Figu e , depi t the fou o se uti e i do s allo i g the su of the i te solsti e to o k its a th ough the o u e t, as at these i sta es the o u e t’s t o sto e e losu es e o e t a slu e t. The o ious o lusio is that the floo pla of “to ehe ge Phase II as apa le of a o odati g all si ajo Su - elated alig e ts at the site. Co se ue tl , it has ee de o st ated that “to ehe ge II has ee a fa o e o ple o u e t i its desig a d fu tio s, tha the si ple ope to the su e solsti e su ise o u e t po t a ed thus fa i the lite atu e.

O the shado s of Sto ehe ge a d thei o e e t i spa e-ti e

I hat follo s, so e use is ade of ast o o i al i fo atio a d te s, although the pape is add essed to a ge e al audie e. The athe ati all i li ed eade is di e ted to a lassi al efe e e f o o su je ts o e ed he e, see “i o Ne o [ . ]. Fo o e o the efe e e, see Note . Mu h has ee itte o “to ehe ge’s Ast o o , see fo a ief e ie the autho ’s efe e e i [ . ]. A ke od of o k i this dis ussio is Ale a de Tho ’s iti gs i [ . ], that has i spi ed a e eed of a haeo-ast o o e s ith a spe ial fo us o Neolithi

o u e ts of the B itish Isles a d B itta like fo e a ple, Au e Bu l, see [ . ] .

Figu e .a. Google Ea th ap of “to ehe ge, take o August , . The photo is f o a altitude of a out feet; “to ehe ge’s ele atio is app o i atel feet. Its ap poi te

oo di ates a e:  ’ N,  ’ W. This oo di ate i plies that at su e solsti e oo

O the spe ifi su je t of shado s at “to ehe ge, the eade is di e ted to the o k dis ussed i [ . ]. Of spe ial i po ta e is the o k T. Meade i [ . ], he e the otio of ΡΟ Α Ο is ad a ed as ei g at o k at “to ehe ge a d D o eg, see efe e e i [ . ]. A si ila o ditio , depi ted the ast-off shado s of the t o e t al pilla s o ea h othe , as ide tified also i the ase of Go ekli Tepe’s st u tu es C a d D, a d possi l othe st u tu es ithi the Go ekli Tepe o ple ith e t al pilla s i the , as a al zed the autho i efe e e [ . ] a d [ . ].

I Figu e , a Google Ea th ap s apshot is sho . It as take o August , a o di g to Google Ea th ap e o ds. B usi g the lo k-azi uth e ui ale e, o e a i fe that the shot as take et ee i e a d te o’ lo k i the o i g. The le gths of the shado s ast the diffe e t sto es a e easu ed at so e app o i atio f o the ap . “i e the a tual heights a d idths of the sto es a e k o see the su se tio o the sto es’ itals , o e a esti ate at hat a gle a o e the ho izo the “u as, he the shot as take .

Of i te est i this pape is the a gle ω a o e the ho izo the “u is at, du i g oo ti e at su e a i u , at e ui o es, a d du i g i te i i u solsti e. This a gle ω is of ou se a fu tio of the Ea th’s a ial tilt u e tl esti ated to e lose to  ’ , a d the latitude of “to ehe ge  ’ . At oo ti e du i g e ui o , this a gle is:

ωE =  -  ’ =  ’ ;

at oo ti e du i g su e solsti e, the a gle is:

ω““ =  ’ +  ’ =  ’ ;

a d at oo ti e du i g i te solsti e:

ωW“ =  ’ -  ’ =  ’ .

F o these a gles a d the k o height of the sa se s oute i le, e a esti ate the sha p edges le gth of the ast-off shado f o sa se # a d its li tel , al eit falle at p ese t, the “outhe ost up ight o thostat of the “to ehe ge II oute i g. Gi e the height H i ludi g its li tel a total of a out fi e ete s o e the ou se of a ea , a d at these th ee iti al dates a d at oo ti e, o e a o pute di e tl the sha p le gth L. F o T igo o et , it is k o that, the ta ge t of a gle ω is ta ω=H/L, thus gi e the a o e- e tio ed easu e e ts : at e ui o es, L E= . ete s; at su e solsti e, L SS = . ete s; a d at i te solsti e,

L WS = . ete s. The le gth . ete s is the ke he e: it is al ost e a tl the dista e et ee the T ilitho s’ “outhe ost t ilitho set’s sa se # a d oute i g’s sa se # . This is a st o g i di atio that the o u e t “to ehe ge Phase II as uilt o the asis of the

athe ati al elatio s gi e i the p e ious se tio ’s su -se tio o the athe ati al odulus, a d the a o e fou d dista e L E . These o e tio s full des i e the o u e t’s desig , as the L E le gth dete i ed the asi easu es of the o u e t, the heights of sa se s i the t o e losu es a d dista es a o g the . The otio of this o thostat’s shado th ough the

da , u de su light, o e s the  -fu tio of Figu e , he e A = . ete s. I [ . ] the autho dis ussed the i po ta e of the e ui o  -fu tio , as at this o de a st u tu al ha ge takes pla e o the -d -su fa e, ega di g the fo s of the -d -fu tio s. We o lude that this odal poi t as the iti al “to ehe ge II desig att i ute.

O e a o iousl a this a al sis fo all + up ights i oth e losu es fo the th ee ke ti es of the ea fo oo o a othe ti e of the da u de su light , a d this is left fo futu e esea h a d to a i te ested eade . Mo e ge e al agg egate a al sis o these elati el sho t ith sha p o de s shado s is e t.

The sho t sha p shado s a d Sto ehe ge II ke shado le gth. Fi st, the sho t ast-off shado s of the o u e t ill e a al zed o i so e li ited o i atio s. The a e efe ed to as elati el sho t , si e ast-off shado s lose to oth su ises a d su sets, as sho i Figu e , a o tai sig ifi a tl lo g i le gths sizes. These effe ts ill e add essed i the e t su se tio . I this su se tio , the effe t of sho t i le gth ast off shado s f o the oute i g to the T ilitho s’ e se le, a d f o the T ilitho s’ e se le to the oute i g of sa se s ill e a al zed he so e o i atio s of sto es a e o side ed.

Alo g ith this a al sis, the i te -sto e ast off shado o e tio s ill e e a i ed, as fo e a ple the shado s ast f o the set of up ight sa se s # to # o to the T ilitho s a d oute i g sa se s at su ise du i g the su e solsti e. A se ies of diag a s alo g these li es a e p odu ed to de o st ate the effe t th oughout the da light ti e o ight ti e u de oo light at a pa ti ula set of da s du i g the ea . Co pute si ulatio s a p odu e -d o i g g aphi s to that effe t. Ho e e , the ke poi ts a e ade uatel ade ith so e ke g aphs, although this does ’t p e lude so e additio al fi di gs as a esult of the suggested

o pute si ulatio ased sea h.

O l t o s apshots ill e dis ussed he e. O e is the ase sho i Figu e .a; the othe is the ase of Figu e . .

I Figu e .a, the ase of “to ehe ge II’s ast-off shado s a e sho at the i di ated date, August . The le gth of the shado is a out . ti es the height of the up ight sa se s i ludi g thei li tel . This is the ota ge t of the a gle a o e the ho izo the “u as at the ti e the photo f o Google Ea th ap as o tai ed. I tu , this i plies that the a gle as a out  a d the ti e ust ha e ee et ee : a d a lo al ti e . What is appa e t f o the photo is that the outside i g’s shado s ge tl tou h the T ilitho ’s e se le, du i g thei top’s o e e t to a ds the No th, as the “u is o i g i its appa e t otio to a ds the West. This ge tle tou h is ai tai ed th oughout the otio , as is de o st ated i the follo i g Figu e . , he e the autu al e ui o ast-off shado s a e sho at oo ti e.

Figu e . . E ui o da , oo ti e shado s. “to ehe ge Phase II a d its dual, the shado ast so e of its T ilitho s e se le pilla s a d the li tels of the o pleted, i theo oute i g. The ke dista e of a out si ete s is depi ted; that is he e the shado f o the oute -sa se s i g st u tu e tou hes the oute ski su fa e of the T ilitho s e se le a d the dista e

et ee sto es # a d # is idged. This dista e is the o l a ia le eeded to o pletel spe if the o u e t’s a ious o po e ts easu es a o di g to the athe ati al odulus. “ou e: the autho .

The effe t pf this otio e o es o e e ide t i the sele ted shado s sho i Figu e . . It depi ts the ast-off shado s at oo du i g e ui o . P o i e t i that Figu e is the li tels i g shado o the g ou d. “hado s ast the su i i g up ight sa se s f o the T ilitho e se le a e also sho i this Figu e that sho s the dualit of “to ehe ge II, as dis ussed at the I t odu tio , this ei g a i t i si dualit shado s esto o a o je t u de su light o

oo light . U dou tedl , this dualit did ’t es ape the a hite ts of Neolithi o u e ts. To e e phasized, is a i po ta t fi di g f o the a al sis, i di ated the ast-off shado s at oo du i g the e ui o es i Figu e . as it as also sho i Figu e .a : it is the - ete dista e o e ed the shado s of the “outhe ost poi t of the li tels’ i g tou hi g the “outhe ost sa se of the i e uasi-ellipti al sto e e losu e a of the T ilitho s e se le. That is, the shado ast off f o sto e # o falle upo sto e # .

He e, o e ust also ote the effe ts of ediu i le gth shado s, like those ast off the heal sto e o to the sa se s oute i g at ti e i te als et ee su ise/su set a d oo ti e.

The lo g shado s a d the li ks et ee the o u e t a d its e i o s. No , the possi le effe ts of elati el lo g shado s ill e a al zed, the shado s’ e la ge a o-s ale. The ea o side a le si ila ities to alig e ts, although the a e also uite diffe e t i a espe ts alo g ith the ki d of i fo atio a out the o u e t the o e . At the egi i g of this su -se tio , the elati el sho t seg e t of the lo g ast-off shado s falli g ithi the floo a ea of the “to ehe ge II Phase o u e t ill e looked at a d thei shapes ill e a al zed.

I the set of Figu es .a, . , a d . , the sho t dista e effe t of the pa t of the lo g shado s is e a i ed at su e solsti e, e ui o , a d i te solsti e su ise o espo di gl . That pa t i hi h the li tels pla o ole of the e lo g shado s falls ithi the o u e t’s floo pla , ast-off the still sta di g sa se s at “to ehe ge a e sho i the set of the th ee Figu es. A u e of ke o se atio s a e ade.

As a di e t esult of the Geo et i ol ed, the slits a o g the up ights allo i g su a s to pe et ate the o u e t’s Easte se tio of the oute i g get p og essi el thi e to a ds No th a d “outh. The su a s eithe ea h the T ilitho s E se le Easte se tio of the uasi-ellipse; o go th ough the Easte pa t of the uasi-ellipse a d the tou h eithe the Weste pa t of the uasi-ellipti a , o get to the dia et i all opposi g sa se s o the oute i g. Mo eo e , the thi k ess of the sa se s’ shado s get p og essi el g eate , so that e o d a poi t a poi t that depe ds o the da of the ea u de o side atio the e ti e No the a d “outhe se tio of the o u e t’s floo pla is u de shade.

Figu e .a. The “to ehe ge II floo pla du i g su ise at su e solsti e. The sho t pa t of the e lo g su ise shado s is sho i side the sa se s oute i le. O l the ast-off shado s f o still sta di g sa se s i the oute i g a d the T ilitho s e se le a e d a . The su a s a e pa allel li es. “ou e: the autho .

I Figu e .a, it is sho that the ai alig e t of “to ehe ge II, the su e solsti e su ise, allo s fo light to pe et ate the e ti e floo pla f o th ee spa es et ee the f o tal sa se s of the oute i g: esides the ai a d idest ope i g et ee up ights # a d # , the e a e

t o o e to that ope i g’s eithe side: that et ee # a d # to the No th a d et ee # a d # to the “outh. These th ee slits allo fo a o plete pe et atio of the floo pla . Whe eas the e t t o that et ee # a d # , as ell as that et ee # a d # a e ot t a slu e t, as su a s fall o T ilitho s E se le sa se s. To the No th of # a d “outh of # the floo pla of the o u e t is i shade.

Figu e . . The “to ehe ge II floo pla du i g su ise at e ui o . The spe ifi atio s a e as i Figu e .a. “ou e: the autho .

I Figu e . , the sa e o ditio s a e sho ut fo the su ise at e ui o . “to es # , # , # a d # of the T ilitho s e se le o attai sig ifi a t i po ta e, as the e o e the ai e epto s of the su ise a s i side the o u e t’s i e sa tu . The i po ta e of the e al e ui o has al ead ee add essed i the te t, as it as the i po ta e a d asso iated

a i gs of sto e # .

Figu e . . “to ehe ge II floo pla at su ise du i g the i te solsti e. The spe ifi atio s a e as i Figu e .a. Noti ea le is the t a slu e t atu e of the su ise a s. “ou e: the autho .

So e ge e al thoughts o the e lo g shado s. A u e of e a ks ill e ade he e ega di g the atu e of e lo g shado s, asso iated ith o ditio s e lose to oth su ise a d su set oo ise a d oo set as ell . This t pe of shado s has fuzz o de s, the fuzz atu e of shado s ha i g al ead ee e te si el dis ussed the autho i [ . ]. A ke ule appli a le i shado s is that the fu the a a f o the o je t, the fuzzie the shado gets, i pl i g a lo e i i te sit to e. Thus, e lo g shado s ha e u dis e i le e ds, la gel due to i easi gl fuzz o de s. Mo eo e , the get p og essi el ide as the get lo ge a d fu the a a f o the sou e . “i e the e lo g shado s’ edges a e e o i g p og essi el less sha p, thei e te t e o es i easi gl diffi ult to gauge.

Ho e e , e lo g shado s a e ea s to li k dista t o je ts upst ea su ise o do st ea su set . These o e tio s p o ide a s to asso iate the o u e t’s ele e ts to a ious featu es of the site’s i ediate o dista e e i o e t i ludi g la ds ape, topog aphi al, geog aphi al featu es a d a o alies u ps, ou ds, tells, hills, ou tai peaks et . These asso iatio s tie up the o u e t to its oade lose o dista t su ou di gs. These featu es a ui e additio al i po ta e as g ou d hete oge eit a d a o alies te d to eithe e ha e o dep ess e tai of the o u e ts featu es a d shado s desig . I o i atio , these geog aphi al att i utes a d ho the a e i o po ated i to the site a d floo pla s of a o u e t li k the o u e t to its e i o e t’s lo atio al o pa ati e ad a tages that is to fa to s hi h ake the site suita le fo the pa ti ula o u e t a o di g to the a hite t’s desig a d pla . I tu , this o u e t e ha es the lo atio al o pa ati e ad a tages of the site i a positi e feed a k loop. “hado s a e ta gi le t a es of these lo atio al i te a tio s. Alig e ts a e o e losel o e ted to lo g a ge le gth shado s. “i e alig e ts a e

atu e lo g dista e i te a tio s, e lo g shado s p o ide the ea s to a ifest the i a ta gi le a . This e ui ale e et ee alig e ts a d shado s has ee al ead poi ted out i the I t odu tio to this pape . It ould e useful to he k the effe ts of “to ehe ge II shado s o the su ou di g e i o e t, as ell as the effe ts of the su ou di g e i o e t o “to ehe ge i ie of the a o e ge e al thoughts. This is left to fu the futu e esea h.

A li tel’s shado .

Ho a “u disks ould take to o e o e the li tels height, a d p oje t thei shado s o the g ou d? This uestio is of oth theo eti al a d e pi i al i te est. Whe the sou e of light, as is su ise o su set light, falls elo a li tel’s le el, the the li tel’s shado is p oje ted i the at osphe e ot the g ou d. Although ot di e tl o se a le u less a o je t gets i the a , the athe ati s of shado s des i ed i [ . ] dete i e the e te t a d atu e of that shado as ell.

The o e t of the da , a d the dista e f o the o u e t at hi h the li tels’ shado hits the g ou d dete i es the effe ti e i flue e a ea i spa e-ti e of the li tel a i g o u e t. This e te sio , alo g the otio of a effe ti e i spa e-ti e i flue e a ea

ega di g o u e ts he e li tels a e i ol ed i f ee sta di g sto e e losu es, is pote tiall a i te esti g di e tio to e te d the a al sis p ese ted he e o “to ehe ge a d the Ge e al D a i Theo of “hado s, fi st outli ed i [ . ].

Co lusio s a d suggestio s fo fu the esea h

The ke fi di g of this pape as that “to ehe ge Phase II is a fa o e o ple i Desig st u tu e tha p e iousl thought. Whe eas u h has ee itte ith efe e e to the

so-alled alta sto e , the o phalos of the o u e t is the e te of the oute i g’s i le a d a e te of the e ti e Phase II o u e t ot just of the oute -sa se sto e i le . Phase II of the o u e t as desig ed o the asis of t o ot a si gle ajo alig e ts a d a ke shado , i additio to a athe ati al odulus hi h as i tu ased o atios o e i g the se ue e - - . The t o alig e ts i p i ted o “to ehe ge Phase II e e of ou se the su e solsti e su ise, a issue e te si el a d al ost e lusi el ha i g ee dis ussed i the “to ehe ge e isti g lite atu e. Ho e e , e o d this alig e t t o o e alig e ts a e fou d at “to ehe ge II, a d o e of the pla ed a pi otal ole i its e desig spe ifi atio s. O e is the e te sio of the ai su e solsti e su ise alig e t, a el the i te solsti e su set. The othe is the su ise at e ui o es a d ost i po ta tl , the alig e t du i g oo ti e at eithe e al o autu al e ui o .

The e ui o ’s alig e t is of fu da e tal i po t fo a ke easo : at oo ti e at e ui o , the ast-off shado f o the oute i g tou hes the T ilitho s “outhe ost sa se , thus li ki g the t o sto e e losu es the p i al a d its dual . That dualit is o e tha just s oli : it is he at the p i al the site e ei es the a i u a ou t of da light he the “u is at the a i u a gle a o e the ho izo ; he eas, at the sa e ti e the le gth of the shado the alue of the dual is at a i i u . At that o e t, the le gth of that shado is at a dista e of a out si ete s. That dista e is the pi ot i to the desig of the e ti e o u e t, as ajo aspe ts a d o po e ts of the o u e t o e atios that a e e p essed as ultiples of

u e s , , a d .

The pape a al zed to a e te t the dis ete s apshot d a i s of shado s, espe iall the sho te se tio s of the lo g a d sha p shado s du i g the su e a d i te solsti es as ell as at e ui o . “o e ules go e i g these s apshots a d the otio of these shado s e e outli ed. Mo eo e , the pape dis o e ed that the T ilitho s uasi-ellipti al e se le of sa se s is a si ple ase of those p ese ted Ale a de Tho . This si ple fo falls ithi a set of disti t atego ies, dis ussed i [ . ], he e it as fou d that this sto e e losu e des i es the Go ekli Tepe st u tu e D, La e III sto e e losu e. He e, a othe st o g li k as esta lished i this pape et ee Phase II “to ehe ge a d Fe tile C es e t A hite tu e.

Nu e ous suggestio s ha e ee ade fo fu the esea h. Co pute si ulatio s i -d, i ol i g the shado s’ dail o e e t o e a ea , at the latitude of “to ehe ge, a d u de

diffe e t e i o e tal o ditio s, ould e ha e the do u e tatio of thei effe ts upo the o u e t. Co putatio al o ple it , due to the la ge u e of sto es a d thei elati e positio s i the floo pla , ould e to a e te t ta kled th ough su h o pute si ulatio . Bluesto es a d thei i gs e e ot i luded at this stage i the esea h. O iousl , the pla ed also a ole alo g ith thei shado s i the o ga izatio a d use of spa e at the late date he the e e positio ed as it has ee suggested i the lite atu e. Wo k alo g these li es ight offe o e i sight i to the positio i g of the t o Bluesto e e losu es a d the se ue e i ol ed. Lastl , i te s of e te sio s, of ou se the a gle of the sa se s’ a -o shado s a d thei otio s is a hapte all to itself, i eed of fu the o k. O e eed ot fo get that this is o k i ol i g “u de i ed shado s. O Moo -de i ed shado s, u h is to e still do e, oth a al ti all a d o putatio all .

I o ludi g this fi al e a ks, so ethi g ust e said a out a su je t little add essed he e:

ultu e, s olis a d e e o elated o e tio s fo o u e ts a d thei shado s.

“ olis , e e o , ultu al ole of the o u e t as it ight elate to oth stati a d d a i e sio s of shado s is a a ea suggested as ei g of o side a le i te est fo fu the esea h. “pe ifi all , i ie of the i te p etatio of shado s ithi a ale-fe ale s olis , this t pe of a al sis ight p o ide suggestio s as to the ea i g of the t o sto e e losu es i efe e e to ea h othe . What do the t o sto e e losu es of “to ehe ge Phase II ep ese t? Ma e a ale a d fe ale s ol, he e the T ilitho s e se le sta ds fo the ale a d the sa se s i le fo the fe ale? Could the shado the dual of the o u e t the p i al also e a e ha e e t to this p i o dial ale-fe ale dualit ? No dou t these a e issues to po de , i ie of the o espo di g s olis dete ted at Go ekli Tepe’s t o e t al pilla s p ese t i st u tu es C a d D of La e III. Although s olis a d ultu al aspe ts of this i te o e ti it a o g sto es ha e ot ee pa t of this pape , it does ’t follo that the a e ot as i po ta t.

Notes

Note

: Ne o ’s o k. “i o Ne o ’s lassi al o k, of i te est fa e o d its Ast o o elated ate ial a d itte at the da of the th _{Ce tu , a al zes at g eat}

athe ati al le gths so e asi ast o o i al o epts of use he e ie i g the desig of o u e ts: sola a d side eal a ti e du atio easu ed agai st fi ed sta s a d ot the “u , esulti g i o e o e otatio alo g the Ea th’s a is of otatio o pleted i a ea as a esult of

the Ea th’s a ual o it a ou d the “u , a f a tio less tha the sola , / . da s a d

ti e, ight as e sio Celestial lo gitude a d de li atio Celestial latitude , utatio ha ge i the a gle of the Ea th’s a is of otatio elati e to the Celestial e uato ial pla e due to a fa to s , p e essio of the e ui o es due to the app o i ate K le of the ea th’s a is of otatio , o li uit of the e lipti the Ea th’s a ial tilt , e lipti the appa e t otio of the “u i the Celestial “phe e, due to the Ea th’s o it a ou d the “u , e ui o tial da the slightl lo ge ti e of the da light due to the isi g of the “u ’s top efo e the e te of the “u ’s dis

appea s o e the u o st u ted ho izo a d at osphe i ef a tio a fa to slightl alte i g the isi ilit of the “u du i g su ise a d su set due to the at osphe i o ditio s, a i g a o g a ious geog aphi lo atio s a e so e a o g a othe ke ast o o i al e e ts a d o epts of ele a e he e. The e ui e so e ad a e k o ledge of oth Mathe ati s i ludi g T igo o et a d Cal ulus as ell as Ea th elated Ast o o .

Ho e e , th ee issues that a eadi g of this lassi al efe e e i gs to the fo ef o t, i so fa as the o k he e is o e ed, a e the follo i g: the diffe e e i azi uths et ee the BC a d toda ; a possi le easo h a o g the a lu a les e e of i po t a k the ; a d the oade topi /p o le of app o i atio s. We shall iefl e ie the i tu .

I efe e e to the ha ge i azi uths, o p. i [ . [ o e eads that o e a - ea pe iod – AD Ne o esti ated a ha ge i the positio of the e lipti of less tha ; spe ifi all , he o puted a ha ge f o a out  ’ to a out  ’ o ’. E t apolati g this to a

pe iod of fou a d o e half ille ia BC – AD , a ti e pe iod hi h spa s a out o e

si th of the app o i ate K- ea le of the Ea th’s a is of otatio , p odu es a ha ge of a out

 ’. Ho e e , this is ’t e i fo ati e, as e do ot k o ho u h o the azi uth this ha ge eall ep ese ts keepi g i i d that half of the li al otio i the N-“ a is p oje ted o the azi uth pla e is i the opposite di e tio of the othe half of the otio . No o e has esti ated the ha ge i the e lipti goi g so fa a k, as the o puti g gets ui kl i t a ta le a d o pute si ulatio s a o l suppl g oss app o i atio s. Thus, o e is ot lea o the a tual shift i the N-“ a is f o the ti e of “to ehe ge Phase II to toda . “o e, like A. Tho , p opose that it has ee less tha . With a a i u of a out , its a tual size e ai s u k o . Ho e e , “to ehe ge sto e e losu e sa se s # a d # a e i fo ati e gi e the toda s’ su e solsti e azi uth the e a d a e a offe hi ts e plo ed i the ai te t of the pape .

A se o d ke aspe t of Ne o ’s o k, a d of e t e e i po ta e fo the pu poses of ou dis ussio he e ega di g sola e sus lu a les, is the ote he has o p. i [ . ], ega di g utatio a d p e essio of the e ui o es. Ne o e a ks ithout itatio s that the a ie ts esti ated the le gth of ea s eithe of t o ethods: o e as that easu i g the ti e i te al et ee t o e ui o es; the othe as easu i g the ti e i te al take the “u to o plete a full e olutio i its appa e t otio a o g so e sta s a d the e, e tai Co stellatio s ust ha e ee ke i this ega d . A d he e o es i to the al ulus the i po ta e of the Moo i the esti atio of the ea l le gth. As the “u is ot possi le to t a k i its appa e t e olutio a o g sta s i isi le to thei aked e e he the “u is a o e the

ho izo , the used as a su stitute, the Moo . Ne o e a ks o p. a d ithout a

efe e es At the iddle of a total e lipse of the oo , the latte as k o to e di e tl opposite the su , a d its positio a o g the sta s ould e dete i ed. The dista e of the oo f o the su ould also e easu ed efo e su set, a d f o a sta afte su set.

a pu el e o o i -utilita ia a gle, Neolithi fa e s a d thei elites ould e i te ested i t a ki g do as a u atel as possi le sola les.

O top of that, e u de sta d f o the “o ial “ ie e a gle of A heolog that Neolithi fa e s atta hed e e o ial, as ell as s oli ea i g to the “u a d the Moo ; thus, this is a easo fo t a ki g do lu a les – ti e a ke s fo festi als a d othe elated ultu al a ti it . I additio , as e do toda o e o ati g sig ifi a t so ial e e ts, p o a l so did the a ie ts – the eeded a ale da to keep t a k of e e e i g i po ta t e e ts to the like the e o of the date so e ajo so ial figu e passed a a o as o , o the e e a e of so e sig ifi a t to the so ial e e t the out o e of a aid o attle, fo e a ple .

All the a o e a e easo s to de a d a so ial ale da , i hi h the “u pla ed a ajo ole, as did the Moo – a d hi h o e as o e i po ta t o iousl depe ded o so ial fa to s e o d the i te est of this pape – as did lo all i po ta t e e ts. What this ief set of otes i pl is this: the e ould e o u e ts a d that a i lude also “to ehe ge he e so e alig e ts e e i pla ted, ha i g othi g to do ith ajo lu isola les, pegged to so ial e e ts e si pl a e ot at p ese t a a e. “eeki g i o u e ts si pl o e lusi el lu isola les is

ost likel isleadi g.

Ho e e , e o d all these a eats, the e is a othe easo , suggested i Note , h so e lu a les ight ha e ee of i po t: it as a a to t a k the e i po ta t sp i g e ui o to esti ate the e a t le gth of a ea . I effe t, this a ha e ee the si gle ost i po ta t fa to as to h lu a les e e i po ta t to t a k, si e these les per se do ot i pa t i a di e t a ag i ultu e. A d Ag i ultu e E o o i s, that is a e as fa o e i po ta t to the tha leisu e e edded i so ial e e o ies.

Note : The B itish He itage Sou es. I this Note, e suppl so e o e spe ifi s a out the

o u e t at Wiltshi e’s “to ehe ge i “alis u Plai . The site pla i Figu e N has the i ediatel su ou di g pa t of the o u e t to the sa se s i le a d the T ilitho s e se le e e a i ed he e. The th ee ajo phases of the o u e t a e i di ated. The diag a p o ides the lo atio of so e elated sto es, off the i ediate se tio of the floo pla a al zed i this pape , like the heal a d slaughte sto es – lea l i fo ati e i te s of the e se le’s o ie tatio .

I the last su -se tio s of the last se tio of the pape , the possi ilit as aised a d u h has ee itte alo g these li es i the e isti g lite atu e that the oade site pla ’s shado s also pla ed a ole i the dete i atio of the “to ehe ge II Phase floo pla . This is o siste t ith hat u e ous autho s ha e poi ted out hile add essi g the li ks et ee that Phase of the floo pla a d ot o l the Heal a d “laughte sto es ut also othe featu es of the site pla i te s of alig e t, a d also i te s of shado s, a d so e of that lite atu e is ited i the Figu e N itatio .

I this Note, a e a k ade i the ai te t of the pape ill e fu the ela o ated. The pape e tio ed the o u e t as so- alled at p ese t “to ehe ge at a pla e u e tl alled Wiltshi e at a pla e alled “alis u Plai . It as e tio ed i su h a a e of ou se, e ause these a e u e t te s a d o e latu e ega di g topo s a d o u e ts that u e t so io- ultu al o ditio s e plo i la eli g o u e ts a d sites.

Figu e N . The th ee ajo Phases of the “to ehe ge o ple , ith the a ious o po e ts of the o u e t. The da k se tio is the pa t studied i this pape . Lo atio of a ious sto es asso iated ith the Phase II o u e t o ie tatio heal a d slaughte sto es a e i di ated at the otto diag a . The sto e ot sho he e a d of i po t is the alta sto e, l i g just i f o t of the “outh este t ilitho set, at the e e te he e the slit et ee its t o up ights # a a d # is fou d. “ou e: B itish He itage, https:// . ita i a. o /topi /“to ehe ge

I a pape o Go ekli Tepe, see [ . ], the autho aised the poi t that u e t o e latu e o o u e ts does ot usuall efle t the o e latu e used the ultu e that uilt these o u e ts. “i ila is the ase fo the o u e t at Ne g a ge as ell as all the Ri e Bo e passage to s , Ca a at B itta , a d the Te ples of the Maltese A hipelago, to e tio o l those efe ed to i this pape .

As a esult, a d to a oid u e essa il loadi g a o u e t ith the u e t so io- ultu al aggage, it as suggested fo s ie tifi easo s to use a es fo a heologi al sites d a f o a s ste si ila to those e plo ed ast o o e s i alli g sta s a d gala ies like the Messie o the NGC s ste s, i that ase . Natu all , this s ie tifi s ste of topo s a d o u e ts’ a es ould o-e ist ith a a e a lo al ultu e at a spe ifi poi t i ti e ould hoose to use to all a o u e t o a lo atio , keepi g i i d that these ultu es ha ge o e ti e.

Note . Mo e o the odulus at Kasta Tu ulus. I this Note o e ela o atio is offe ed o

the odula st u tu e of a fa o e e e t o u e t he e a ou d st u tu e as possi l used as a ale da , the late th _{e tu BC A phipolis’ Kasta Tu ulus’ pe i ete all. I efe e e} [ . ] the autho de o st ated that the pe i ete of the tu ulus as li ked to a a ual ale da . Th oughout the ti e pe iod August till O to e , the tu ulus as thought to ha e had a i u fe e e of ete s, a o di g to epeated a d ultiple a ou e e ts oth the a heologi al tea a d the G eek Mi ist of Cultu e a d fo al a hite tu al d a i gs p odu ed a d sho to the pu li – although e e pu lished o p ese ted i a app e ia le detail. I O to e , the a hite t of the a heologi al tea a ou ed that the pe i ete all had a le gth of ete s, ithout a do u e tatio o e pla atio as to h the - ete le gth of the August to O to e ti e pe iod as sudde l i eased to ete s.

I a ase, if the total le gth of the tu ulus’ pe i ete is ete s, the this le gth i plies a atio of . : . gi e the . le gth of the o u e t’s odulus. The u e . is lose to the side eal u e of da s . + – a fi di g hi h ould i pl a u de sta di g of ale da ti e ased ot o sola ea s ut o ti e al ulated ased o the positio of fi ed sta s i the Celestial “phe e. This ould i pl a e u de sta di g f o ou pa t of the ast o o i al k o ledge at the pe iod he the fo atio of the tu ulus at Kasta, i A phipolis took pla e u e tl esti ated to ha e o u ed a ou d the egi i g of the fou th ua te of the th _{e tu BC a d follo i g the death of Ale a de III i Ba lo . Fo o e o} this issue, the eade is di e ted to the u e ous pape s itte o the su je t the autho , see efe e e [ . ].

With this sho t Note, the autho a e ds a d e te ds the ate ial p ese ted i efe e e [ . ] a d all asso iated ith it p io efe e es.

Refe e es

The autho ’s elated o k

[ . ] Di it ios “. De d i os, Θa ua , The Mathe ati s of Mo oliths’ “hado s , a ade ia.edu.

The pape is fou d he e:

https:// .a ade ia.edu/ /The_Mathe ati s_of_Mo oliths_“hado s

[ . ] Di it ios “. De d i os, No e e , I the “hado s of Ca a ’s Le Me e “to es: A Neolithi p oto supe o pute , a ade ia.edu. The pape is fou d he e:

https:// .a ade ia.edu/ /I _the_“hado s_of_Ca a s_Le_Me e _“to es_A_Ne olithi _p oto_supe o pute

[ . ] Di it ios “. De d i os, Ma h , O the Fuzz Natu e of “hado s , a ade ia.edu : https:// .a ade ia.edu/ /ON_THE_FU))Y_NATURE_OF_“HADOW“

[ . ] Di it ios “. De d i os, No e e , Go ekli Tepe: a th _{Mille iu BC} o u e t , a ade ia.edu:

https:// .a ade ia.edu/ /Go ekli_Tepe_a_ _th_ ille iu _BC_ o u e t [ . ] Di it ios “. De d i os, No e e , A Ca a Co je tu e: Neolithi

e pe i e tatio ith P i iti e P thago ea T iples? , a ade ia.edu; the pape is he e: https:// .a ade ia.edu/ /A_Ca a _Co je tu e_Neolithi _e pe i e tatio _ ith _p i iti e_P thago ea _t iples

[ . ] Di it ios “. De d i os, last update “epte e , F o Ne g a ge to “to ehe ge: o u e ts to a Bull Cult a d o igi s of i o atio , a ade ia.edu; the pape is fou d he e: https:// .a ade ia.edu/ /F o _Ne g a ge_to_“to ehe ge_Mo u e ts_to_a_B ull_Cult_a d_O igi s_of_I o atio

[ . ] Di it ios “. De d i os ith Vassilis Pet opoulos , De e e , The Modula “t u tu e of the to / o u e t at Kasta Hill , a ade ia.edu. The pape is fou d he e: https:// .a ade ia.edu/ /The_ odula _st u tu e_of_the_to _at_Kasta_Hill_ _D_De d i os

[ . ] Di it ios “. De d i os, “epte e , Dati g Go ekli Tepe: the e ide e does ’t suppo t a PPNB date ut i stead a u h late o e , i a ade ia.edu. The pape is fou d he e: https:// .a ade ia.edu/ /Dati g_Go ekli_Tepe

[ . ] Di it ios “. De d i os, Fe ua , The Ea th’s O it a ou d the “u , a d the Tu ulus at Kasta , a ade ia.edu. The pape is fou d he e:

https:// .a ade ia.edu/ /The_Ea ths_o it_a ou d_the_“u _a d_the_Tu ulus_ at_Kasta._Update_

[ . ] https://ka sas.a ade ia.edu/Di it iosDe d i os

[ . ] Di it ios “. De d i os, Θa ua , A P i e o Go ekli Tepe , a ade ia.edu. : https:// .a ade ia.edu/ /A_P i e _o _Go ekli_Tepe

Othe sou es

[ . ] B A tho Θoh so - D a Autho AΘ , a o pute o pilatio of data f o a ious su e s., CC BY . , https:// o o s. iki edia.o g/ /i de .php? u id=

[ . ] http:// .e glish-he itage.o g.uk/ isit/pla es/sto ehe ge/histo /

[ . ] “i o Ne o , , A Co pe diu of Sphe i al Ast o o : ith its appli atio s to the dete i atio a d edu tio of positio s of the fi ed sta s, Ma Milla , Ne Yo k. I ele t o i fo the ook is he e:

https:// ooks.google. o / ooks?id=CA DAAAAIAAΘ&p i tse =f o t o e &sou e=g s_ge_su a _ & ad= # =o epage& &f=false

[ . ] Ale a de Tho , , Megalithi Lu a O se atio s, O fo d U i e sit P ess, O fo d. [ . ] Au e Bu l, , The Sto e Ci les of the B itish Isles, Yale U i e sit P ess, Ne Hea e . [ . ] Ale a de Tho , A hi ald “. Tho , , Megalithi Re ai s i B itai a d B itta , Cla e do P ess, O fo d.

[ . ] G. Te e e Meade , , “to ehe ge a d A e u : egalithi shado asti g at the solsti es at su ise , fo th o i g i the Journal of Lithic Studies.

[ . ] A highl spe ialized log is that the a e Do ou look at shado s fou d he e: http:// . egalithi . o.uk/ odules.php?op= odload& a e=Fo u &file= ie topi &topi =

&fo u = &sta t=

It is hosted the site Megalithi Po tal fou d he e: http:// . egalithi . o.uk/i de .php [ . ] G. Te e e Meade , , D o e g “to e Ci le, “W I ela d: desig pla a al zed ith

espe t to su ises a d lithi shado - asti g fo the eight t aditio al ag i ultu al festi al dates – a d fu the alidated photog aph , fo th o i g i the Journal of Lithic Studies.

[ . ] https:// .fa e ook. o /g oups/ /pe ali k/ /

[ . ] Rose a Hill, , “to ehe ge, p ofile Books, Lo do . The ook is also fou d he e: https:// ooks.google. o /

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The autho ishes to a k o ledge the o t i utio s ade to this pape th ough his i te a tio ith e e s of the Megalithi Po tal e site http:// . egalithi . o.uk/i de .php . The autho ishes to tha k the site a age A d Bu ha ; a d also, the e e s of the su -g oup i it Do ou look at the shado s . Withi this g oup, i spe ifi , the autho ishes to e og ize the o t i utio s Da id “ th E e g a , Neil Wise a Fea o , a d Ri ha d Ba tosz O p it . Da id “ th has ee i st u e tal i e ou agi g the autho to pa ti ipate i that g oup, a d fo i t odu i g the autho ’s p io o k to the g oup e e s.

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