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1 INTRODUCTION
1.1 Geographyofculture
Geographyofcultureconsiderstheobjectsofnatural
and cultural heritage as elements of geo‐cultural
space (Streletsky, 2005). Culture is understood as a
form of geographic adaptation, in which a person
does not only adapt to the environment, but also
createsit.Thisexplainstheneedtostudytwoareasof
cooperation between human and nature,ʺthe
landscapeincultureʺandʺcultureinthelandscape.ʺ
Subject of the research is the rational content of the
cultureassociatedwiththelife‐support processes. In
contrast to the humanities, applied field and
q
uantitative methods, unlike astro‐archeology and
pa
leoastronomy, objects are seen as elements of the
territorialsystem,ingeneral,studiesarecomplex.
1.2 Themethodologyofresearch
Our interdisciplinary research of ancient heritage
objects is based on the methodology of the natural
sciences, system approach and the doctrine of
geosystemsbyV.B.Sochava.Firstofall,thefollowing
theoreti
cal principles are effective: 1. The concept of
geo‐system structure as its spatial and temporal
organization (according to Isachenko A.G.); 2. The
idea of the constructive role of super‐systems
(accordingtoDyakonovK.N.);3.Theflowsystemas
thebasisofstability(accordingtoArmandoA.D.);4.
The flow of the structure‐funct
ion (according to
ViktorovA.S.);5.Theterritorialnetworks(according
toRodomanB.B.).
ThestudiesofV.I.Paraninonhistoricalgeography
playaspecialroleintheresearchofancientheritage
objects, including his conclusions: 1. names labeling
of elements of territorial systems based on the
orient
ationofthesun;2.mappingmodelsofgeospace
rhythmofnaturalprocesses(suchasthe1850summer
humidification cycle); 3. the role of transport
Cross-disciplinary Researches of Objects of Ancient
Heritage on the Example of Stone Labyrinths and
Petroglyph
A.N.Paranina&R.Paranin
HerzenStatePedagogicalUniversity,St‐Petersburg,Russia
T.N.Khetagurov
NorthernOssetia‐Alania
ABSTRACT:Asanexampleofcross‐disciplinaryresearchesof objectsofancient heritage, labyrinths
–
stone
constructions and petroglyphs are considered. The researches conducted by authors with application of a
gnomonofsolarclockscalendarsopenpurposeofpartsoflabyrinthsasmarkersofageographicalspace‐time.
Resultsoftheanalysisofconditionsofsolarnavigationaregivenindifferentlatitudeswhichisconsideredby
aut
horsasamethodologicalbasisofresearchesinculturegeography.Onthebasisofinstrumentalfunctionof
objectsthecorrectexplanationofthecontradictorysymbolicalinterpretationwhichcollectedinhumanitarian
researches is received. Possibilities of cross ‐disciplinary researches with use of archaeological, historical,
ethnographicdataandthenavigationconceptofinformationalmodeloperationoftheworldareshown.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 4
December 2017
DOI:10.12716/1001.11.04.21
730
communications as flows of matter, energy and
information, forming geocultural space (Paranin,
1990,1998).Thenavigationconceptandthesystemof
methods, developed by the authors, provide for
detection of measured quantitative correspondences
inhierarchicallystructuredsystemofʺculturalobject‐
enclosingspace:informational,geocultural,landscape
and geographical and spatialʺ (Paranina,
2010, 2011,
Paranina
& Paranin, 2015). In this article, as an
example of interdisciplinary research of objects of
ancientheritage,thelabyrinths–stonestructuresand
petroglyphs–areconsidered(Fig.1).
2 OBJECTSANDMETHODS
2.1 Varietyofformsandscientificapproaches
Labyrinths are found on all continents except
Antarctica. Ageofimages reaches
tens ofthousands
of years, as a sign of honor in all cultures – it
correlated with light and shadow, birth and rebirth,
allthestagesofhumanlife(Eliseev,1883,Kern,2007).
Notethatallofthesemeaningscombinetheconcept
ofʺtimeʺ.
The diversity of opinions on
the designation of
labyrinths can be divided into groups: mystical
(fishingandhouseholdmagic),household(fishtraps)
and calendar. The latter differ in the choice of the
astronomical orientation (sun, planets) and
technology (direct projection, direct sight). The
authors, in the course of independent studies
conductedindifferentregionsofRussia,
developeda
calendar model of interpretation, based on the
backsight (in the shade) by labyrinths‐gnomons
(Paranin
&Paranina,2009,Hetagurov,2016).
2.2 Stonelabyrinthsandpetroglyphs
On the territory of Russia authors investigated: the
labyrinths of the White Sea – the Solovetsky
archipelago (Bolshoy Zayatsky island) and
archipelagoKuzova (island Oleshin)and others and
labyrinthsoftheCaucasus.
Northern labyrinths are located mainly on the
coast–capes
andterraces,andrepresentoneortwo
spiralswithadiameterof30m,builtofroughstone
thesizeto30cm.Theimageofstonelabyrinthfroma
human height cannot be read. In the bi‐spiral
labyrinthradialelementsorientedtothehorizonare
located:theentrance
andraysareperpendiculartoit,
radiating from the center. A vertically placed single
stone or stone addition can be placed in the center,
craftedballsandplatescanbeseenaswell.
Caucasian labyrinths are presented, mainly by
drawings, engraved on large slabs, included, as a
rule, in the facades
of medieval buildings – houses
andtemples.Therearedrawingsoflabyrinthsonthe
monuments set on the ancient tombs and on the
roads, on household items, the greatest number of
them is described in Dagestan (Khan‐Magomedov,
2000) The most detailed study was carried out for
Mahcheskiy labyrinth of
Digora Gorge in North
Ossetia‐Alania. Archaeologists and anthropologists
note the autochthony ofthis object andsimilarity of
drawingtosamplesofancientartandthepla nsofthe
northernlabyrinths(Miller.1925,Krupnov,1951).
a
b
c
d
Figure1. Always supply original photographs. Northern
labyrinths.a‐BolshoyZayatskyisland(d=10m);b‐island
Oleshin(d=25m).Mahcheskylabyrinth:c‐inVladikavkaz
Museum; d‐in Digora Gorge (Paranin & Paranina, 2009,
Hetagurov,2016)
731
2.3 Themethodofcalculatingtheheightandthe
installationofthegnomon
The method of calculating the height and the
installationofthegnomon(Paranina,2010),inwhich
the extreme shadows provisions coincide with the
diameters of the inner and outer edges of the
labyrinth, or another rhythmically constructed
structure (including speed), focused on the
geographical meridian, is the solution for the
equationbasedonthetrigonometricidentity(H=tgα
∙A).Bothpartsoftheequationgiveoneresult–the
heightofthegnomon–anddescribetherelationship
oftheangleofincidenceofsunbeam
αandthelength
oftheshadowofA: left–forsummer,right–forthe
winter. Theadjustmentхwas added to the distance
measured from the central addition to the extreme
edgesofthelabyrinth(inthisexample‐1mand5.5
m),allowingtospecifyitsthelocation:
tg48.47(1+х)=tg4.97(5.5+х) (1)
Thesolutionofthisequationmakesitpossibleto
determine all basic dimensions as a result of
calculating the adjustment for the distances x
arbitrarilyselectedtothecenter:
1.13(1+х)=0.09(5.5+х)
1.13
+1.13х=0.5+0.09х
1.13х–0.09х=0.5–1.13
1.04х=–0.63
х=–0.63/1.04
х=–0.61
Adjustmentof the distance to the center isbased
onthedeterminationofthelengthoftheshadowsin
differentseasons(m):
1+х
=1–0.61=0.39
5,5+х=5.5–0.61=4.89
The final solution of the equation (1) gives the
heightofthegnomon(m):
1.13∙0.39=0.09∙4.89
0.44=0.44
2.4 Themethodofcalculatingthecalendarbytheexample
ofMahcheskiylabyrinth
The method
of calculating the calendar by the
exampleof Mahcheskiylabyrinth(Hetagurov, 2016).
Todeterminethepossibilityofusingthelabyrinthas
a calendar it is necessary to find the specific points
and lines. In the center of the labyrinth a recess is
clearly visible – the installation point of gnomon
indicatedonthe diagramD(Fig. 5a).Midday shade
intersectionpointsfromtheverticalpointer(gnomon)
withradiallabyrinthlinesareA,B,C,D,E,F,G.
a
b
Figure5.ElementsofMahcheskiylabyrinth–solarcalendar:
a‐intheplan;b‐intheprofile(Hetagurov,2016).
Weorientthecross(X)onthestonebythecardinal
points so that the points A‐G are located along the
south line South‐North. By the time of crossing the
southshadowofthegnomonOHradiallinesA,B,C,
D, E, F, G of the labyrinth, we
define the
correspondingdateoftheyear.
Figure5Bshowsthesamepositionofthesun:α‐
theheightofthesunabovethehorizonatthesummer
solsticeonJune22,β‐theheightofthesunabovethe
horizonatthewintersolsticeon22December.From
spherical astronomy
we knowthat the heightof the
sunabovethehorizonduringthesolsticesis:
α=90°‐φ+σ (2)
β=90°‐φ‐σ (3)
whereφis latitude of calendar setting point (for
village Mahcheskφ= 42.66 °), andσ= ± 23.44 °‐
declinationoftheSunduringdaysofsolstice.
Since triangles
OHA and OHG and rectangular,
then:
tgα=OH/OA (4)
tgβ=OH/OG (5)
fromwhich:
OA=OH/tgα (6)
OG=OH/tgβ (7)
Accordingtotheformulas(1)and(2)wecalculate:
732
α=90°‐42,66°+23,44°=70,78°
β=90°‐42,66°‐23,44°=23,9°
fromwhich:
tqα=2,88
tgβ=0,44
Having measured length OA = 4.2 cm on the
labyrinth,usingtheformula(6)wedefinethelength
oftheOHindex:
ОН=АО×tgα=4.2×2.88≈12cm.
Based on the properties of a right triangle and
astronomical data, if the
measured length of the
shadowOGisequaltothelengthOGdefinedbythe
formula (7), we can say that the labyrinth could be
usedasasolarcalendarthatdefinesthedays ofthe
solstices.
According to the formula (6) we calculate: OG =
OH/tgβ=12
/0.44=27.27cm,whichisequaltothe
measureditem.
2.5 Acomparisonwithethnographicdata
Acomparisonwithethnographicdatashowsthatthe
intersection of the date of the midday shadow
semicircles corresponds to the folk calendar and
sheep production cycle of Ossetian herdsmen.Thus,
theintersection
ofamiddayshadetolinethehelixat
pointDprovidesday21ofFebruary,whichisthebest
forthestartoflambingsheepandgoatsintheclimatic
conditions of the mountain Ossetia. Lambs born
during these dates by the beginning of the grazing
season(firstdecadeof
May)reachtheagewhenthey
can eat green fodder using pastures in full.
Accordingly,bytheautumnlambsaregrowingwell,
itgivessufficientwoolclip,fullandmeatcarcassand
leftintherace–entersintohibernationmorerobust
and large (Nikolaev, 1973). Lambs born at an
inopportune time, are certainly subject to slaughter
forskins–krimmer.Theoptimalstartdateofmating
sheep and goats – 23 September. This day noon
shadow of the pointer intersects the semicircle at
point C. Usingthis date for mating, lambing canbe
obtained during the most favorable for the
preservation of offspring and maximize production
fromthesheep‐themainoccupationoftheCaucasus
mountaineers since the Neolithic era. Calendar
labyrinth yields and other important dates: the
beginning of shearing (Falvara) and the transition
fromgrazingonstabling(Dzhiorguba).
Differentsegments of thelength of time between
the arcs
of the labyrinth is consistent with the
descriptions of the Ossetian calendar. So, at the
beginning of the XIX century, Julius Klaproth
describedthecalendarofOssetians‐Digors, consisting
of ten months in which there wereʺtwin monthsʺ ‐
ʺMaruja Dua Maiʺ andʺRuh dua maiʺ (two months
Marujaandtwo
monthsRukh)(Kaloev,1967,p.163).
Later, in 1882, V.F. Miller, inʺOssetian etudesʺ
showed calendar of Ossetians‐Digors, where the
duration of the monthʺKomahsanʺ was determined
fromthemiddletotheendofJanuaryandthemonth
ʺGeuargobaʺfollowedbyunnamedperiodcontinued
forabouttwoweeks(Miller,
1882,p.263‐264).Thus,
intheOssetiancalendarmonthswerenot30‐31days
long,but14‐15and59‐60days–multipleofthemoon
phases.CalculationsofcalendardatesforMahcheskiy
labyrinth and their comparison with ethnographic
datashowthatthelabyrinthcouldbeusedasa
solar
calendar up to the XVIII‐XIX centuries (Hetagurov,
2016).
3 DISCUSSIONOFRESULTS
3.1 Labyrinths–solarcalendarsinEasternandSouthern
Europe
Calendar function was proved for Mastischenskiy
labyrinth, found by archaeologists of the Voronezh
State University during the excavation of a Bronze
Age settlement on the high
chalk headland (60 m
abovethe waterlevel in theriver Don) betweenthe
villages Divnogorie and Kostenko. Azimuth
measured from the center of the labyrinth mound,
throughestablishedthereingraniteslabs,corresponds
tothedirectionsofsunrise/sunsetinthedaysofthe
equinoxes and solstices (Chekmenev, 2001). We
calculated the height of the gnomon using the
formula(1)as3.5m(2primariesfathoms)(Paranina,
2012).
CalendaruseofMogorlabyrinthcarvedonrocks
Marina (Galicia, Portugal), has been studied by
mathematicsteacherJoseLuisGalovart,whoproved
thatthecentralpointofthedrawingsattheequinoxes
binds the shadows of the objects, which were set
duringtheseequinoxdays(Historiayarqueología…).
3.2 Structureofsolarcalendars:regionalfeatures
Calculations of solar calendars structure at different
latitudes reveal the regional characteristics of solar
navigation.
Calculationsofmiddayshadelengthforthegnomon,1
mhighshowthat
theoptimumconditionsforcreating
labyrinth calendar is the temperate zone, where the
shadowthroughouttheyearcrossesallarcstwice.In
thecoldzonethepolarnightperiodisnotapplicable,
and inthe hot zone – midday shadow disappears 2
times a year (since the sun is at
its zenith), and the
shadowʺpassesʺsomeparts4times(Paranina,2010).
Bytheratiooftheheightofthegnomon(e.g.,1m)and
the length of its shadow several types of labyrinth
pattern and solar calendars can be distinguished: 1.
Typeʺankhʺ–intheconditionsofapolar
daycentral
part is highlighted as a closed ring structure
(labyrinth of Iceland) 2.ʺlabyrinth‐11ʺ in the polar
latitudes, does not have an arc for midday shade
fixinginthe wintersolstice, as thisshadow ismuch
largerthanthesizeofthelabyrinth;3.atlatitude50‐
60
°shadowsofallmonthsoftheyearareplacedina
circle of arelatively small diameter, a 7‐arcʺclassicʺ
labyrinthisa convenient here;4.atlatitudes 40‐30°
radiusoftheoutercircleistwotimeslargerthanthe
height of thegnomon – a type
of “staff”(≈ 2 m); 5.
Tropical calendar sizes shadows are placed on the
733
gnomon‐a type ofʺrodʺ,ʺscepterʺ (e.g., hexrod of
dervishes)(Paranina,2010.2016).
Theratioofthelengthofamiddayshadeinwinterand
summersolstices(thelongestandtheshortest)ranges
from1x6,4tomorethan1000times(Fig.6A).
Theratio ofthelengths
of shadowsin thewinter and
summersolsticewasproposedbyA.T.Hetagurovasan
indicatorofthecalendarfunctionofculturalheritage
objects,builtonthebasisofbacksighttechnology.A
diagramforthetemperatelatitudes(Fig.6b)maybe
thekeytogeographic,astro‐archaeologicaland local
historyresearch.
-200,00
-150,00
-100,00
-50,00
0,00
50,00
100,00
150,00
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91
a
-1,20
-1,00
-0,80
-0,60
-0,40
-0,20
0,00
0,20
0,40
1 5 9 1317212529333741454953576165697377818589
b
Figure6. The ratio of the lengths of the shadows in the
winter(A)andthesummer(B)solstices:a‐A/B;b‐B/A.
Archaicmeasuresoflengthhavetheratioof1:7 :
foot(about30cm)andstandardstaff(6‐7feet),which
may be measured by the depth under the keel, the
choiceofthewaterway(rememberthewishofʺseven
feet under the keelʺ). Length of seven feet is just
average whip of the shepherd and the rider (the
longest‐8 feet), and the length of his whip ranges
from30‐35cmupto45and70cm(feetandfathoms).
In ancient times, a ratio of the size of objects
indispensable in the steppe landscapes (which
dominatein
theselatitudes),couldbeatemplateand
atoolforcreationofthesolarcalendar,liketablesof
AncientBabylon,inwhich,forthesevenʺclimatesʺof
thenorthernhemisphere,fordifferentseasonsofthe
year human height ratio and the length of their
shadow measured by feet were calculated.
Interestingly,
latitudes,wherethecalendarratioofthe
length of shadows calendar is equal to 1:7, coincide
with the two out of seven abovementioned
boundaries of Ancient Babylon climates, calculated
according to the formula (90º / 7)n: 0º, 12.9º; 25.7º;
38.6º;51.4º;64.3º;77.1º.
Dynamics of landmarks of solar navigation near
the Arctic Circle and the tropics explains the high
level of development of astronomy in antiquity,
noticedforregionslocatedattheselatitudes(Stafeev
& Tomilin, 2006). Different sources indicate on the
preservation of the traditions of orientation on the
SuninEurope.Forexample,thetraditionofinstalling
thegnomonintheyardnearthehouseuntiltheend
of the twentieth century is mentioned in the
ethnographic works of M. Stomma for Poland
(Stomma,
1981). Studies ofthe Pulkovo Observatory
recorded a strong tradition in the steppe regions of
Asia, the Caucasus, the Baltic States and Karelia
(Sundialandcalendarsystemofpeoples…,1985).We
haverecordedmessagesofrespondentsfromKarelia
about vertical installation of a stick on a lined wet
sand (by
fishermen), about stringing of strings on
carved frames of windows, facing south, about the
useofpalm.InLeningradandRyazanregions people
recallthetraditionofmeasuringtheirshadowbyfeet,
in the Ryazan, the use of whip as the gnomon of a
sundialbyshepherdsisalsorecalled.
3.3
Evolutionofthegeographicalspace
Studiesofancientnavigationaltoolstakeintoaccount
the regional and global models developed in
astronomy, physical geography and evolutionary
geography.Itisknownthatthepositionofthepolar
circlesandthetropics,aswellasnaturalandclimatic
conditions of region (especially polar)
affects the
Earthʹsaxistiltchangefrom22.1to24.5º:byreducing
the inclination, border of moderate light zone are
expanding,withanincrease–arenarrowing.Inview
ofthepossiblepositionsofthepolarcircle,wedivide
stone labyrinths of Northern Europe by polar,
circumpolar andtemperate zone
objects. Features of
lightconditionslargelyexplainthedifferencesinthe
structure of objects (figure of objects) (Paranina &
Paranin,2015).
4 CONCLUSIONS
Interdisciplinary studies of ancient heritage sites in
the geography of culture enhance the possibility of
objective understanding of their primary
managementpurpose,asymbolicinterpretationofthe
structure and functions of geo‐cultural space. For
further detailed studies it is necessary to create a
database of objects structure and accommodating
landscape.
Studies conducted by the authors using the
gnomon of asundial‐calendar, open the designation
of labyrinths as markers of geographic space‐time,
and explain the contradictory
diversity of symbolic
interpretations on the basis of the instrumental
functioningsites.
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