well factors mutation genetic drift genetic hitchhiking artificial selection migration ref name griffiths sect ref many generations genomes organisms change significantly resulting evolution process called adaptation selection beneficial mutations cause species evolve forms better able survive environment ref name darwin br earlier related ideas acknowledged ref new species formed process speciation often caused geographical separations prevent populations exchanging genes ref name gavrilets ref comparing homology different species' genomes possible calculate evolutionary


distance may diverged genetic comparisons generally considered accurate method characterizing relatedness species comparison phenotypic characteristics evolutionary distances species used form evolutionary trees trees represent common descent divergence species time although show transfer genetic material unrelated species known horizontal gene transfer common bacteria model organisms common fruit fly ''drosophila melanogaster'' popular model organism genetics research although geneticists originally studied inheritance


wide range organisms researchers began specialize studying genetics particular subset organisms fact significant research already existed given organism would encourage new researchers choose study eventually model organisms became basis genetics research common research topics model organism genetics include study gene regulation involvement genes development cancer organisms chosen part convenience short generation times easy genetic manipulation made organisms popular genetics research tools widely used model


locations genome associated diseases method especially useful multigenic traits clearly defined single gene candidate gene found research often done corresponding homologous genes model organisms addition studying genetic diseases increased availability genotyping methods led field pharmacogenetics study genotype affect drug responses individuals differ inherited tendency develop cancer cancer genetic disease process cancer development body combination events


neighboring cells may escape epithelium ultimately primary tumor escaped cell cross endothelium blood vessel get transported bloodstream colonize new organ forming deadly metastasis although genetic predispositions small fraction cancers major fraction due set new genetic mutations originally appear accumulate one small number cells divide form tumor transmitted progeny somatic mutations frequent mutations


loss function p protein tumor suppressor p pathway gain function mutations ras proteins oncogenes research methods colonies ''e coli'' produced cellular cloning similar methodology often used molecular cloning dna manipulated laboratory restriction enzymes commonly used enzymes cut dna specific sequences producing predictable fragments dna dna fragments visualized use gel electrophoresis separates fragments according length use ligation enzymes allows dna fragments connected binding


ligating fragments dna together different sources researchers create recombinant dna dna often associated genetically modified organisms recombinant dna commonly used context plasmids short circular dna molecules genes process known molecular cloning researchers amplify dna fragments inserting plasmids bacteria culturing plates agar isolate clones bacteria cells cloning also refer various means creating cloned clonal organisms dna also amplified using procedure called polymerase chain reaction pcr


using specific short sequences dna pcr isolate exponentially amplify targeted region dna amplify extremely small amounts dna pcr also often used detect presence specific dna sequences dna sequencing genomics dna sequencing one fundamental technologies developed study genetics allows researchers determine sequence nucleotides dna fragments technique chain termination sequencing developed team led frederick sanger still routinely used sequence dna fragments using technology researchers able study


low cost sequencing sequencing technologies allow production potentially millions sequences concurrently ref name hall ref ref name church ref large amount sequence data available created subfield genomics research uses computational tools search analyze patterns full genomes organisms genomics also considered subfield bioinformatics uses computational approaches analyze large sets biological data common problem fields research manage share data deals human subject personally identifiable information society culture march group


leading biologists urged worldwide ban clinical use methods particularly use crispr zinc finger edit human genome way inherited ref name nyt ref ref name nyt ap ref ref name sci ref ref name nat ref april chinese researchers reported results basic research edit dna non viable human embryos using crispr ref name nyt ref ref name pc ref see also bacterial genome size cryoconservation animal genetic resources eugenics embryology evolution genetic disorder genetic diversity genetic engineering genetic enhancement index genetics articles medical genetics molecular tools gene study mutation neuroepigenetics outline genetics timeline


history genetics plant genetic resources references reading external links


boston 's big dig presented geotechnical challenges urban environment precast concrete retaining wall typical cross section slope used two dimensional analyses '''geotechnical engineering''' also known '''geotechnics''' branch civil engineering concerned engineering behavior earth materials uses principles soil mechanics rock mechanics solution respective engineering problems also relies knowledge geology hydrology geophysics related sciences geotechnical rock engineering subdiscipline geological engineering addition civil engineering geotechnical engineering also applications military mining petroleum coastal

Applied science
Engineering and technology
Civil Engineering
Geotechnical engineering


found ancient egypt ancient mesopotamia fertile crescent well around early settlements mohenjo daro harappa indus valley cities expanded structures erected supported formalized foundations ancient greeks notably constructed pad footings strip raft foundations th century however theoretical basis soil design developed discipline art science relying past experience ref name das ref several foundation related engineering problems leaning tower pisa prompted scientists begin taking scientific based approach examining


earth pressures military ramparts coulomb observed failure distinct slip plane would form behind sliding retaining wall suggested maximum shear stress slip plane design purposes sum soil cohesion math c math friction math sigma math math tan phi math math sigma math normal stress slip plane math phi math friction angle soil combining coulomb 's theory christian otto mohr 's stress state theory became known mohr coulomb theory although recognized precise determination cohesion impossible math c math


fundamental soil property ref name schofield disturbed soil properties geotechnical design schofield andrew n thomas telford ref mohr coulomb theory still used practice today th century henry darcy developed known darcy 's law describing flow fluids porous media joseph boussinesq mathematician physicist developed theories stress distribution elastic solids proved useful estimating stresses depth ground william rankine engineer physicist developed alternative coulomb 's earth pressure theory albert atterberg developed clay consistency indices still used


today soil classification ref name das ref name budhu osborne reynolds recognized shearing causes volumetric dilation dense contraction loose granular materials modern geotechnical engineering said begun publication ''erdbaumechanik'' karl terzaghi mechanical engineer geologist considered many father modern soil mechanics geotechnical engineering terzaghi developed principle effective stress demonstrated shear strength soil controlled effective stress terzaghi also developed framework theories bearing capacity foundations theory prediction


rate settlement clay layers due consolidation ref name das ref name schofield ref name lambe whitman soil mechanics lambe twilliam whitman robert v massachusetts institute technology john wiley sons ref afterwards maurice biot fully developed three dimensional soil consolidation theory extending one dimensional model previously developed terzaghi general hypotheses introducing set basic equations poroelasticity alec skempton work carried extensive review available formulations experimental data literature effective stress valid soil concrete rock order reject expressions


well clarify expression appropriate according several work hypotheses stress strain strength behaviour saturated nonsaturated media rock concrete soil behaviour etc book donald taylor recognized interlocking dilation densely packed particles contributed peak strength soil interrelationships volume change behavior dilation contraction consolidation shearing behavior connected via theory plasticity using critical state soil mechanics roscoe schofield wroth publication yielding soils critical state soil mechanics basis


used geotechnical engineers analyze site conditions design earthworks retaining structures foundations ref name holtzkovacs specific weight unit weight cumulative weight solid particles water air unit volume soil note air phase often assumed weightless porosity ratio volume voids containing air water fluids soil total volume soil porosity mathematically related void ratio ref name nptel void ref math n frac e e math ''e'' void ratio ''n'' porosity void ratio


pores filled water water must squeezed pores allow volumetric compression soil process called consolidation shear strength maximum shear stress applied soil mass without causing shear failure ref name nptel ref atterberg limits liquid limit plastic limit shrinkage limit indices used estimation engineering properties soil classification geotechnical investigation tasks geotechnical engineer comprise investigation subsurface conditions materials determination relevant physical mechanical chemical


properties materials design earthworks retaining structures including dams embankments sanitary landfills deposits hazardous waste tunnels structure foundations monitoring site conditions earthwork foundation construction evaluation stability natural slopes man made soil deposits assessment risks posed site conditions prediction prevention mitigation damage caused natural hazards avalanches mud flows landslides rockslides sinkholes volcanic eruptions ref name terzaghipeckmesri terzaghi k peck rb mesri g ''soil mechanics engineering practice'' rd ed john wiley sons inc ref ref name holtzkovacs holtz r


kovacs w ''an introduction geotechnical engineering'' prentice hall inc ref geotechnical engineers engineering geologists perform geotechnical investigations obtain information physical properties soil rock underlying sometimes adjacent site design earthworks foundations proposed structures repair distress earthworks structures caused subsurface conditions geotechnical investigation include surface exploration subsurface exploration site sometimes geophysical methods used obtain data sites subsurface exploration usually involves situ testing two common examples situ tests standard penetration test


cone penetration test addition site investigation often include subsurface sampling laboratory testing soil samples retrieved digging test pits trenching particularly locating faults slide planes may also used learn soil conditions depth large diameter borings rarely used due safety concerns expense sometimes used allow geologist engineer lowered borehole direct visual manual examination soil rock stratigraphy variety soil samplers exists meet needs different engineering projects


standard penetration test spt uses thick walled split spoon sampler common way collect disturbed samples piston samplers employing thin walled tube commonly used collection less disturbed samples advanced methods sherbrooke block sampler superior even expensive coring frozen ground provides high quality undisturbed samples ground conditions fill sand moraine rock fracture zones ref name coring frozen ground ref atterberg limits tests water content measurements grain size analysis example may performed disturbed samples obtained thick walled soil samplers properties


shear strength stiffness hydraulic conductivity coefficient consolidation may significantly altered sample disturbance measure properties laboratory high quality sampling required common tests measure strength stiffness include triaxial shear unconfined compression test surface exploration include geologic mapping geophysical methods photogrammetry simple engineer walking around observe physical conditions site geologic mapping interpretation geomorphology typically completed consultation geologist engineering geologist geophysical exploration also sometimes used


geophysical techniques used subsurface exploration include measurement seismic waves pressure shear rayleigh waves surface wave methods downhole methods electromagnetic surveys magnetometer resistivity ground penetrating radar infrastructure medium heavy duty percussion drilling winches heavy duty rotary diamond core drill machine light duty geo machine manual winches tripod dynamic cone penetration test machine static cone penetration machine pressure meter test machine field vane shear test machine field cbr california bearing ratio test machine block vibration test machine rapid moisture meter machine situ


width ratio less footings footings often called spread footings spread load structural elements transfer structure loads ground direct areal contact footings isolated footings point column loads strip footings wall another long line loads footings normally constructed reinforced concrete cast directly onto soil typically embedded ground penetrate zone frost movement obtain additional bearing capacity slab variant spread footings entire structure bear


single slab concrete underlying entire area structure slabs must thick enough provide sufficient rigidity spread bearing loads somewhat uniformly minimize differential settlement across foundation cases flexure allowed building constructed tolerate small movements foundation instead small structures like single family houses slab may less nbsp mm thick larger structures foundation slab may several meters thick slab foundations either slab grade foundations embedded foundations typically buildings basements slab grade foundations must designed


allow potential ground movement due changing soil conditions deep pile driving bridge napa california deep foundations used structures heavy loads shallow foundations cannot provide adequate capacity due size structural limitations may also used transfer building loads past weak compressible soil layers shallow foundations rely solely bearing capacity soil beneath deep foundations rely end bearing resistance frictional resistance along length developing required capacity geotechnical engineers use specialized tools cone penetration


test estimate amount skin end bearing resistance available subsurface many types deep foundations including piles drilled shafts caissons piers earth stabilized columns large buildings skyscrapers typically require deep foundations example jin mao tower china uses tubular steel piles nbsp feet driven depth nbsp feet support weight buildings constructed found undergo settlement underpinning piles used stabilize existing building three ways place piles deep foundation


driven drilled installed use auger driven piles extended necessary depths application external energy way nail hammered four typical hammers used drive piles drop hammers diesel hammers hydraulic hammers air hammers drop hammers simply drop heavy weight onto pile drive diesel hammers use single cylinder diesel engine force piles earth similarly hydraulic air hammers supply energy piles hydraulic air


forces energy imparted hammerhead varies type hammer chosen high million foot pounds large scale diesel hammers common hammerhead used practice piles made variety material including steel timber concrete drilled piles created first drilling hole appropriate depth filling concrete drilled piles typically carry load driven piles simply due larger diameter pile auger method pile installation similar drilled pile


installation concrete pumped hole auger removed ref name coduto et al ref lateral earth support structures retaining wall structure holds back earth retaining walls stabilize soil rock downslope movement erosion provide support vertical near vertical grade changes cofferdams bulkheads structures hold back water sometimes also considered retaining walls primary geotechnical concern design installation retaining walls weight retained material creating lateral earth pressure behind wall cause


wall deform fail lateral earth pressure depends height wall density soil strength soil amount allowable movement wall pressure smallest top increases toward bottom manner similar hydraulic pressure tends push wall away backfill groundwater behind wall dissipated drainage system causes additional horizontal hydraulic pressure wall gravity walls gravity walls depend size weight wall mass


resist pressures behind gravity walls often slight setback batter improve wall stability short landscaping walls gravity walls made dry stacked mortarless stone segmental concrete units masonry units commonly used earlier th century taller retaining walls often gravity walls made large masses concrete stone today taller retaining walls increasingly built composite gravity walls geosynthetic steel reinforced backfill soil precast facing gabions stacked steel wire baskets filled rocks crib walls cells built log cabin style precast concrete


timber filled soil free draining gravel soil nailed walls soil reinforced place steel concrete rods ' 'reinforced soil gravity walls'' soil reinforcement placed horizontal layers throughout height wall commonly soil reinforcement ''geogrid'' high strength polymer mesh provides tensile strength hold soil together wall face often precast segmental concrete units tolerate differential movement reinforced soil 's mass along facing becomes gravity wall reinforced mass must built large enough retain pressures soil


form cantilever walls forces basement walls greater conventional walls basement wall free move excavation shoring shoring temporary excavations frequently requires wall design extend laterally beyond wall shoring extends planned base excavation common methods shoring use ' 'sheet piles'' ' 'soldier beams lagging'' sheet piles form driven piling using thin interlocking sheets steel obtain continuous barrier ground driven prior excavation soldier


beams constructed wide flange steel h sections spaced apart driven prior excavation excavation proceeds horizontal timber steel sheeting lagging inserted behind h pile flanges use underground space requires excavation may cause large dangerous displacement soil mass around excavation since space slope excavation limited urban areas cutting done vertically retaining walls made prevent unsafe soil displacements around excavations diaphragm walls type retaining walls stiff generally watertight horizontal movements


diaphragm walls usually prevented lateral supports diaphragm walls expensive walls save time space also safe widely used urban deep excavations ref name bahrami ref cases lateral support provided shoring wall alone insufficient resist planned lateral loads case additional support provided walers tie backs walers structural elements connect across excavation loads soil either side excavation used resist transfer horizontal loads


type sensitivity structures built ground improvement often reduces direct costs saves time slope stabilization simple slope slip section slope stability potential soil covered slopes withstand undergo movement stability determined balance shear stress shear strength previously stable slope may initially affected preparatory factors making slope conditionally unstable triggering factors slope failure climatic events make slope actively unstable leading mass movements mass movements caused increases shear stress loading


lateral pressure transient forces alternatively shear strength may decreased weathering changes pore water pressure organic material several modes failure earth slopes include falls topples slides flows slopes coarse grained soil rocks falls typically occur rapid descent rocks loose slope material slope topples large column soil tilts vertical axis failure typical slope stability analysis considers sliding failures categorized mainly rotational slides translational slides implied name rotational slides fail along


generally curved surface translational slides fail along planar surface slope failing flow would resemble fluid flowing downhill slope stability analysis stability analysis needed design engineered slopes estimating risk slope failure natural designed slopes common assumption slope consists layer soil sitting top rigid base mass base assumed interact via friction interface mass base planar curved


complex geometry goal slope stability analysis determine conditions mass slip relative base lead slope failure interface mass base slope complex geometry slope stability analysis difficult numerical solution methods required typically exact geometry interface known simplified interface geometry assumed finite slopes require three dimensional models analyzed keep problem simple slopes analyzed assuming slopes infinitely wide


therefore represented two dimensional models slope drained undrained undrained condition used calculations produce conservative estimates risk popular stability analysis approach based principles pertaining limit equilibrium concept method analyzes finite infinite slope fail along sliding failure surface equilibrium stresses calculated along failure plane compared soils shear strength determined terzaghi 's shear strength equation stability ultimately decided factor safety equal


ratio shear strength equilibrium stresses along failure surface factor safety greater one generally implies stable slope failure occur assuming slope undisturbed factor safety static conditions commonly used practice geosynthetics collage geosynthetic products geosynthetics type plastic polymer products used geotechnical engineering improve engineering performance reducing costs includes geotextiles geogrids geomembranes geocells geocomposites synthetic nature products makes suitable use ground high


seabed case piers jettys fixed bottom wind turbines maybe floating structure remains roughly fixed relative geotechnical anchor point undersea mooring human engineered floating structures include large number offshore oil gas platforms since floating wind turbines two common types engineered design anchoring floating structures include tension leg catenary loose mooring systems tension leg mooring systems vertical tethers tension providing large restoring moments pitch roll catenary mooring systems provide station keeping offshore structure yet provide little stiffness


paper ralph b peck effort reduce costs construction incurred designing earth structures based unfavorable assumptions words geological conditions soil engineering properties instead design based probable conditions rather unfavorable gaps available information filled observations geotechnical instrumentation measurements example inclinometers piezometers geotechnical site investigation example borehole drilling cpt observations aid assessing behavior structure construction modified accordance findings method


may described learn go ref name peck peck rb advantages limitations observational method applied soil mechanics geotechnique pp ref observational method may described follows exploration sufficient establish general nature pattern properties deposits necessarily detail assessment probable conditions unfavorable conceivable deviations conditions geology plays major role creating design based working hypothesis behavior anticipated probable conditions selection quantities observed construction proceeds calculation anticipated values


method suitable projects whose design cannot altered construction serious blunder applying observational method failing select advance appropriate course action foreseeable deviations disclosed observation assumed design engineer must devise solutions problems could arise least favorable conditions cannot solve hypothetical problems even probability occurrence low must revert design based least favorable conditions ref name peck see also civil engineering


deep foundations institute earthquake engineering earth structure effective stress engineering geology geoprofessions geotechnics hydrogeology international society soil mechanics geotechnical engineering karl von terzaghi land reclamation landfill list publications geotechnical engineering mechanically stabilized earth offshore geotechnical engineering rock mass classifications sediment control seismology soil mechanics soil physics soil science notes references bates jackson glossary geology american geological institute krynine judd principles engineering geology geotechnics mcgraw hill new york div style font size holtz r kovacs w ''an introduction geotechnical engineering'' prentice hall inc bowles j ''foundation analysis design''


naval facilities engineering command ''design manual soil mechanics'' us government printing office https webarchiveorg web http vulcanhammernet geotechnical dm pdf navfac naval facilities engineering command ''design manual foundations earth structures'' us government printing office navfac naval facilities engineering command ''design manual soil dynamics deep stabilization special geotechnical construction'' us government printing office terzaghi k peck rb mesri g ''soil mechanics engineering practice'' rd ed john wiley sons inc santamarina jc klein ka fam soils waves particulate materials behavior characterization process monitoring wiley firuziaan estorff simulation


drawing graph mathematics '''graph theory''' study ''graphs'' mathematical structures used model pairwise relations objects graph context made ' 'vertices'' also called ''nodes'' ''points'' connected ''edges'' also called ''links'' ''lines'' distinction made '''undirected graphs''' edges link two vertices symmetrically '' 'directed graphs''' edges link two vertices asymmetrically graphs one principal objects study discrete mathematics definitions definitions graph theory vary following basic

Formal science
Mathematics
Applied mathematics
Graph theory


ways defining graphs related mathematical structures graph graph three vertices three edges one restricted common sense term '''graph''' ordered pair math g math comprising math v math set '' 'vertices''' also called '''nodes''' '''points''' math e subseteq x mid x v textrm x neq math set '''edges''' also called '''links''' '''lines''' unordered pairs vertices edge associated two distinct vertices avoid ambiguity type object may called precisely


'''undirected simple graph''' edge math x math vertices math x math math math called '''endpoints''' edge edge said '''join''' math x math math math '''incident''' math x math math math vertex may exist graph belong edge '''multiple edges''' allowed definition two edges join two vertices one general sense term allowing multiple edges '''graph''' ordered triple math g phi math comprising math v math set '' 'vertices''' also called '''nodes''' '''points'''


math e math set '''edges''' also called '''links''' '''lines''' math phi e x mid x v textrm x neq math '''incidence function''' mapping every edge unordered pair vertices edge associated two distinct vertices avoid ambiguity type object may called precisely '''undirected multigraph''' '''loop''' edge joins vertex graphs defined two definitions cannot loops loop joining vertex math x math edge


undirected simple graph incident undirected multigraph math x x x math math x mid x v textrm x neq math allow loops definitions must expanded undirected simple graphs definition math e math modified math e subseteq x mid x v math undirected multigraphs definition math phi math modified math phi e x mid x v math avoid ambiguity types objects may


called '''undirected simple graph permitting loops''' '''undirected multigraph permitting loops''' sometimes also '''undirected pseudograph''' respectively math v math math e math usually taken finite many well known results true rather different infinite graphs many arguments fail infinite case moreover math v math often assumed non empty math e math allowed empty set '''order''' graph math v math number vertices '' 'size''' graph math e math number edges '' 'degree''' '''valency''' vertex number


edges incident loop counted twice '' 'degree''' graph maximum degrees vertices undirected simple graph order ''n'' maximum degree vertex maximum size graph edges undirected simple graph permitting loops math g math induce symmetric homogeneous relation vertices math g math called '''adjacency relation''' math g math specifically edge math xy math endpoints math x math math math said '''adjacent''' one another


called ''inverted edge'' math x math ''multiple edges'' allowed definition two edges tail head one general sense term allowing multiple edges '' 'directed graph''' ordered triple math g phi math comprising math v math set ' 'vertices'' also called ''nodes'' ''points'' math e math set ''edges'' also called ' 'directed edges'' ' 'directed links'' ' 'directed lines'' ''arrows'' ''arcs'' math phi e left xy mid x v textrm x neq right math ''incidence function'' mapping every edge


ordered pair vertices edge associated two distinct vertices avoid ambiguity type object may called precisely '' 'directed multigraph''' ''loop'' edge joins vertex directed graphs defined two definitions cannot loops loop joining vertex math x math edge directed simple graph incident directed multigraph math xx math math left x mid x v textrm x neq right math allow loops


definitions must expanded directed simple graphs definition math e math modified math e subseteq left x mid x v right math directed multigraphs definition math phi math modified math phi e left x mid x v right math avoid ambiguity types objects may called precisely '' 'directed simple graph permitting loops''' '' 'directed multigraph permitting loops''' ''quiver'' respectively edges directed simple graph permitting loops math g math homogeneous relation vertices math g math called ''adjacency


relation'' math g math specifically edge math xy math endpoints math x math math math said ''adjacent'' one another denoted math x math math math applications cid ref graphs used model many types relations processes physical biological social information systems many practical problems represented graphs emphasizing application real world systems term ''network'' sometimes defined mean graph attributes eg names associated vertices edges subject expresses understands real world systems network


called network science computer science computer science graphs used represent networks communication data organization computational devices flow computation etc instance link structure website represented directed graph vertices represent web pages directed edges represent links one page another similar approach taken problems social media travel biology computer chip design mapping progression neuro degenerative diseases many fields development algorithms handle graphs therefore major interest computer science


transformation graphs often formalized represented graph rewrite systems complementary graph transformation systems focusing rule based memory manipulation graphs graph databases geared towards transaction safe persistent storing querying graph structured data linguistics graph theoretic methods various forms proven particularly useful linguistics since natural language often lends well discrete structure traditionally syntax compositional semantics follow tree based structures whose expressive power lies principle compositionality modeled hierarchical graph contemporary approaches head driven phrase structure grammar model syntax natural language using


typed feature structures directed acyclic graphs within lexical semantics especially applied computers modeling word meaning easier given word understood terms related words semantic networks therefore important computational linguistics still methods phonology eg optimality theory uses lattice graphs morphology eg finite state morphology using finite state transducers common analysis language graph indeed usefulness area mathematics linguistics borne organizations http wwwtextgraphsorg textgraphs well various 'net' projects wordnet verbnet others


physics chemistry graph theory also used study molecules chemistry physics condensed matter physics three dimensional structure complicated simulated atomic structures studied quantitatively gathering statistics graph theoretic properties related topology atoms also feynman graphs rules calculation summarize quantum field theory form close contact experimental numbers one wants understand chemistry graph makes natural model molecule vertices represent atoms edges bonds approach especially used computer processing molecular structures


ranging chemical editors database searching statistical physics graphs represent local connections interacting parts system well dynamics physical process systems similarly computational neuroscience graphs used represent functional connections brain areas interact give rise various cognitive processes vertices represent different areas brain edges represent connections areas graph theory plays important role electrical modeling electrical networks weights associated resistance wire segments obtain electrical


properties network structures graphs also used represent micro scale channels porous media vertices represent pores edges represent smaller channels connecting pores chemical graph theory uses molecular graph means model molecules graphs networks excellent models study understand phase transitions critical phenomena removal nodes edges leads critical transition network breaks small clusters studied phase transition breakdown studied via percolation theory social sciences moreno sociogram graph


metabolic pathways gene regulatory networks evolutionary trees ecological networks hierarchical clustering gene expression patterns also represented graph structures graph theory also used connectomics nervous systems seen graph nodes neurons edges connections mathematics mathematics graphs useful geometry certain parts topology knot theory algebraic graph theory close links group theory algebraic graph theory applied many areas including dynamic systems complexity topics graph structure


extended assigning weight edge graph graphs weights weighted graphs used represent structures pairwise connections numerical values example graph represents road network weights could represent length road may several weights associated edge including distance previous example travel time monetary cost weighted graphs commonly used program gps 's travel planning search engines compare flight times costs history k nigsberg bridge problem paper written


leonhard euler seven bridges k nigsberg published regarded first paper history graph theory ref name biggs ref paper well one written vandermonde ''knight problem'' carried ''analysis situs'' initiated leibniz euler 's formula relating number edges vertices faces convex polyhedron studied generalized cauchy ref name cauchy ref l'huilier ref name lhuillier ref represents beginning branch mathematics known topology one century euler 's paper bridges k nigsberg listing


introducing concept topology cayley led interest particular analytical forms arising differential calculus study particular class graphs ''trees'' study many implications theoretical chemistry techniques used mainly concern enumeration graphs particular properties enumerative graph theory arose results cayley fundamental results published p lya generalized de bruijn cayley linked results trees contemporary studies chemical composition ref name cayley ref fusion ideas mathematics


chemistry began become part standard terminology graph theory particular term graph introduced sylvester paper published ''nature'' draws analogy quantic invariants co variants algebra molecular diagrams ref name sylvester ref every invariant co variant thus becomes expressible ''graph'' precisely identical kekul diagram chemicograph give rule geometrical multiplication graphs ''ie'' constructing ''graph'' product co variants whose separate graphs given italics original


first textbook graph theory written nes k nig published another book frank harary published considered world definitive textbook subject enabled mathematicians chemists electrical engineers social scientists talk harary donated royalties fund p lya prize one famous stimulating problems graph theory four color problem true map drawn plane may regions colored four colors way


two regions common border different colors problem first posed francis guthrie first written record letter de morgan addressed hamilton year many incorrect proofs proposed including cayley kempe others study generalization problem tait heawood ramsey hadwiger led study colorings graphs embedded surfaces arbitrary genus tait 's reformulation generated new class problems ''factorization problems'' particularly studied petersen k nig works


ramsey colorations specially results obtained tur n origin another branch graph theory ''extremal graph theory'' four color problem remained unsolved century heinrich heesch published method solving problem using computers computer aided proof produced kenneth appel wolfgang haken makes fundamental use notion discharging developed heesch ref name aa ref ref name aa ref proof involved checking properties configurations computer fully accepted time due complexity


simpler proof considering configurations given twenty years later robertson seymour sanders thomas ref name rsst ref autonomous development topology fertilized graph theory back works jordan kuratowski whitney another important factor common development graph theory topology came use techniques modern algebra first example use comes work physicist gustav kirchhoff published kirchhoff 's circuit laws calculating voltage current electric circuits introduction probabilistic methods graph


theory especially study erd r nyi asymptotic probability graph connectivity gave rise yet another branch known ''random graph theory'' fruitful source graph theoretic results representation graph abstraction relationships emerge nature hence cannot coupled certain representation way represented depends degree convenience representation provides certain application common representations visual usually vertices drawn connected edges tabular rows


vertices connected others many edges exact layout practice often difficult decide two drawings represent graph depending problem domain layouts may better suited easier understand others pioneering work w tutte influential subject graph drawing among achievements introduced use linear algebraic methods obtain graph drawings graph drawing also said encompass problems deal crossing number various generalizations


depends graph structure algorithm used manipulating graph theoretically one distinguish list matrix structures concrete applications best structure often combination list structures often preferred sparse graphs smaller memory requirements matrix structures hand provide faster access applications consume huge amounts memory implementations sparse matrix structures efficient modern parallel computer architectures object current investigation list structures include edge list array pairs vertices


adjacency list separately lists neighbors vertex much like edge list vertex list vertices adjacent matrix structures include incidence matrix matrix 's 's whose rows represent vertices whose columns represent edges adjacency matrix rows columns indexed vertices cases indicates two adjacent objects indicates two non adjacent objects degree matrix indicates degree vertices laplacian matrix modified form adjacency matrix


incorporates information degrees vertices useful calculations kirchhoff 's theorem number spanning trees graph distance matrix like adjacency matrix rows columns indexed vertices rather containing cell contains length shortest path two vertices problems enumeration large literature graphical enumeration problem counting graphs meeting specified conditions work found harary palmer


minor containment problem find fixed graph minor given graph minor subcontraction graph graph obtained taking subgraph contracting edges many graph properties hereditary minors means graph property minors example wagner 's theorem states graph planar contains minor neither complete bipartite graph ''k'' sub sub see three cottage problem complete graph ''k'' sub sub similar problem subdivision containment problem


find fixed graph subdivision given graph subdivision homeomorphism graph graph obtained subdividing edges subdivision containment related graph properties planarity example kuratowski 's theorem states graph planar contains subdivision neither complete bipartite graph ''k'' sub sub complete graph ''k'' sub sub another problem subdivision containment kelmans seymour conjecture every vertex connected graph planar contains subdivision vertex complete graph ''k'' sub sub another class problems extent


various species generalizations graphs determined ''point deleted subgraphs'' example reconstruction conjecture graph coloring many problems theorems graph theory various ways coloring graphs typically one interested coloring graph two adjacent vertices color similar restrictions one may also consider coloring edges possibly two coincident edges color variations among famous results conjectures concerning graph coloring following four color theorem strong


perfect graph theorem erd faber lov sz conjecture unsolved total coloring conjecture also called behzad 's conjecture unsolved list coloring conjecture unsolved hadwiger conjecture graph theory unsolved subsumption unification constraint modeling theories concern families directed graphs related partial order applications graphs ordered specificity meaning constrained graphs specific thus contain greater amount information subsumed general operations graphs include evaluating direction subsumption relationship two graphs computing graph unification unification two argument graphs defined


general graph computation thereof consistent ie contains information inputs graph exists efficient unification algorithms known constraint frameworks strictly compositional graph unification sufficient satisfiability combination function well known applications include automatic theorem proving modeling elaboration linguistic structure route problems hamiltonian path problem minimum spanning tree route inspection problem also called chinese postman problem seven bridges k nigsberg shortest path problem steiner tree three cottage problem traveling salesman problem np hard network flow


numerous problems arising especially applications various notions flows networks example max flow min cut theorem visibility problems museum guard problem covering problems covering problems graphs may refer various set cover problems subsets vertices subgraphs dominating set problem special case set cover problem sets closed neighborhoods vertex cover problem special case set cover problem sets cover every edges original set cover problem also called hitting set described


vertex cover hypergraph decomposition problems decomposition defined partitioning edge set graph many vertices necessary accompanying edges part partition wide variety questions often problem decompose graph subgraphs isomorphic fixed graph instance decomposing complete graph hamiltonian cycles problems specify family graphs given graph decomposed instance family cycles decomposing complete graph ''k'' sub ''n'' sub specified trees respectively


classes eg one property graphs imply another finding efficient algorithms decide membership class finding representations members class see also gallery named graphs glossary graph theory list graph theory topics list unsolved problems graph theory publications graph theory related topics algebraic graph theory citation graph conceptual graph data structure disjoint set data structure dual phase evolution entitative graph existential graph graph algebra graph automorphism graph coloring graph database graph data structure graph drawing graph equation graph rewriting graph sandwich problem graph property intersection graph knight 's


tour logical graph loop network theory null graph pebble motion problems percolation perfect graph quantum graph random regular graphs semantic networks spectral graph theory strongly regular graphs symmetric graphs transitive reduction tree data structure algorithms bellman ford algorithm bor vka 's algorithm breadth first search depth first search dijkstra 's algorithm edmonds karp algorithm floyd warshall algorithm ford fulkerson algorithm hopcroft karp algorithm hungarian algorithm kosaraju 's algorithm kruskal 's algorithm nearest neighbour algorithm network simplex algorithm planarity testing algorithms prim 's algorithm push relabel maximum flow algorithm tarjan 's strongly connected components algorithm topological sorting subareas algebraic graph theory geometric graph theory extremal graph theory probabilistic graph theory topological graph


theory related areas mathematics combinatorics group theory knot theory ramsey theory generalizations hypergraph abstract simplicial complex prominent graph theorists alon noga berge claude bollob b la bondy adrian john brightwell graham chudnovsky maria chung fan dirac gabriel andrew erd paul euler leonhard faudree ralph fleischner herbert golumbic martin graham ronald harary frank heawood percy john kotzig anton k nig nes lov sz l szl murty u r ne et il jaroslav r nyi alfr ringel gerhard robertson neil seymour paul sudakov benny szemer di endre thomas robin thomassen carsten tur n p l tutte w whitney hassler notes


references english edition wiley methuen co new york russian moscow spanish mexico roumanian bucharest chinese shanghai second printing first english edition dover new york external links http wwwutmedu departments math graph graph theory tutorial http wwwgfrederickscom main sandbox graphs searchable database small connected graphs https webarchiveorg web http wwwbabelgraphorg linkshtml concise annotated list graph theory resources researchers http wwwkdeorg applications education rocs rocs graph theory ide http wwworgnetcom sociallifeofrouterspdf social life routers non technical paper discussing graphs people computers http graphtheorysoftwarecom graph theory software tools teach learn graph theory http wwwmartinbroadhurstcom graph algorithmshtml list


pages gospel thomas discovered nag hammadi '''gnosticism''' 'having knowledge' collection religious ideas systems coalesced late st century ad among jewish early christian sects various groups emphasised personal spiritual knowledge ''gnosis'' orthodox teachings traditions authority religious institutions viewing material existence flawed evil gnostic cosmogony generally presents distinction supreme hidden god malevolent lesser divinity sometimes associated yahweh old testament responsible creating material universe ref name ep


gnostics considered principal element salvation direct knowledge supreme divinity form mystical esoteric insight many gnostic texts deal concepts sin repentance illusion enlightenment ref name ep ref gnostic writings flourished among certain christian groups mediterranean world second century fathers early church denounced heresy efforts destroy texts proved largely successful resulting survival little writing gnostic theologians ref name ep nonetheless early gnostic teachers valentinus saw beliefs aligned


christianity gnostic christian tradition christ seen divine taken human form order lead humanity back light however gnosticism single standardized system emphasis direct experience allows wide variety teachings including distinct currents valentinianism sethianism persian empire gnostic ideas spread far china via related movement manichaeism mandaeism still alive iraq iran diaspora communities centuries scholarly knowledge gnosticism limited anti heretical writings orthodox christian figures


irenaeus lyons hippolytus rome renewed interest gnosticism discovery egypt 's nag hammadi library collection rare early christian gnostic texts including gospel thomas apocryphon john major question scholarly research qualification gnosticism either interreligious phenomenon independent religion scholars acknowledged influence sources hellenistic judaism zoroastrianism platonism noted possible links buddhism hinduism though evidence direct influence latter sources


inconclusive ref name ep etymology ''gnosis'' refers knowledge based personal experience perception religious context ''gnosis'' mystical esoteric knowledge based direct participation divine gnostic systems sufficient cause salvation knowledge acquaintance divine inward knowing comparable encouraged plotinus neoplatonism differs proto orthodox christian views gnostics oriented toward knowledge understanding nbsp perception learning nbsp particular modality living ref name valantasis ref usual meaning ''gnostikos'' classical greek texts learned intellectual


used plato comparison practical ''praktikos'' intellectual ''gnostikos'' plato 's use learned fairly typical classical texts hellenistic period began also associated greco roman mysteries becoming synonymous greek term ''musterion'' adjective used new testament clement alexandria speaks learned ''gnostikos'' christian complimentary terms use ''gnostikos'' relation heresy originates interpreters irenaeus scholars consider irenaeus sometimes uses ''gnostikos'' simply mean intellectual whereas mention intellectual sect


learned gnostic ref covers various groups valentinus origins origins gnosticism obscure still disputed proto orthodox christian groups called gnostics heresy christianity according modern scholars theology 's origin closely related jewish sectarian milieus early christian sects scholars debate gnosticism 's origins roots neoplatonism buddhism due similarities beliefs ultimately origins currently unknown christianity developed became popular gnosticism proto orthodox christian gnostic christian groups often existing places gnostic belief


widespread within christianity proto orthodox christian communities expelled group second third centuries ad gnosticism became first group declared heretical scholars prefer speak gnosis referring first century ideas later developed gnosticism reserve term gnosticism synthesis ideas coherent movement second century according james robinson gnostic texts clearly pre date christianity pre christian gnosticism hardly attested way settle debate however nag hammadi library contained


gilles quispel scholem detected jewish ''gnosis'' imagery merkavah also found certain gnostic documents quispel sees gnosticism independent jewish development tracing origins alexandrian jews group valentinus also connected many nag hammadi texts make reference judaism cases violent rejection jewish god gershom scholem described gnosticism greatest case metaphysical anti semitism professor steven bayme said gnosticism would better characterized anti judaism recent research origins gnosticism shows strong jewish influence


particularly hekhalot literature ref name kabbalah new perspectives idel moshe ''kabbalah new perspectives'' yale university press https booksgooglecom booksid utwy kz k ic lpg pa p ref within early christianity teachings paul john may starting point gnostic ideas growing emphasis opposition flesh spirit value charisma disqualification jewish law mortal body belonged world inferior worldly powers ''archons'' spirit soul could saved term ''gnostikos'' may acquired deeper significance alexandria central importance birth


gnosticism christian ''ecclesia'' e congregation church jewish christian origin also attracted greek members various strands thought available judaic apocalypticism speculation divine wisdom greek philosophy hellenistic mystery religions regarding angel christology early christians darrell hannah notes ref pseudepigraphical christian text ''ascension isaiah'' identifies jesus angel christology ref shepherd hermas christian literary work considered canonical scripture early church fathers irenaeus jesus identified angel christology parable author mentions


son god virtuous man filled holy pre existent spirit ref name papandrea ref neoplatonic influences gnostic connections neo platonism proposed ugo bianchi organised congress messina origins gnosticism also argued orphic platonic origins gnostics borrowed significant ideas terms platonism using greek philosophical concepts throughout text including concepts hypostasis reality existence ''ousia'' essence substance demiurge creator god sethian gnostics valentinian gnostics seem influenced plato middle platonism neo pythagoreanism academies schools thought


schools attempted effort towards conciliation even affiliation late antique philosophy ref name schenke schenke hans martin phenomenon significance gnostic sethianism rediscovery gnosticism ej brill ref rebuffed neoplatonists including plotinus persian origins influences early research origins gnosticism proposed persian origins influences spreading europe incorporating jewish elements according wilhelm bousset gnosticism form iranian mesopotamian syncretism richard august reitzenstein famously situated origins gnosticism persia carsten colpe b analyzed criticised iranian


finds palestinian samaritan aramaic influence mandaic accept mandaeans shared palestinian history jews buddhist parallels congress median buddhologist edward conze noted phenomenological commonalities mahayana buddhism gnosticism paper ''buddhism gnosis'' following early suggestion put forward isaac jacob schmidt influence buddhism sense either ''gnostikos'' valentinus c nag hammadi texts rd century supported modern scholarship although elaine pagels called possibility characteristics cosmology syrian egyptian traditions postulate remote supreme godhead monad


two principles way inferior ''qualified monism'' second entity may divine semi divine valentinian gnosticism form monism expressed terms previously used dualistic manner moral ritual practice gnostics tended toward asceticism especially sexual dietary practice areas morality gnostics less rigorously ascetic took moderate approach correct behaviour normative early christianity church administered prescribed correct behaviour christians gnosticism internalised motivation important ritualistic behaviour


famously contained apocryphon secret book john describes unknown god similar orthodox apophatic theology different orthodox teachings god creator heaven earth orthodox theologians often attempt define god series explicit positive statements omniscient omnipotent truly benevolent sethian hidden transcendent god contrast defined negative theology immovable invisible intangible ineffable commonly seen hermaphroditic potent symbol containing apocryphon john god


good bestows goodness apophatic statements process divine action used describe effect god pleroma ''pleroma'' greek fullness refers totality god 's powers heavenly pleroma center divine life region light term understood spatially world occupied spiritual beings aeons eternal beings sometimes archons jesus interpreted intermediary aeon sent pleroma whose aid humanity recover lost knowledge


turn around return one epistrophe retracing steps spiritual knowledge contemplation aeon many gnostic systems aeons various emanations superior god monad beginning certain gnostic texts hermaphroditic aeon barbelo ref name apocryphon ref name allogenes ref ref name trimorph ref first emanated various interactions monad occur result emanation successive pairs aeons often male female pairings called ' 'syzygies'' ref name valen syzygy ref numbers pairings varied text text though identify number thirty ref name fragments mead ref aeons totality


materiality positive negative depiction materiality thus resides great deal mythic depictions sophia 's actions occasionally referred hebrew equivalent ''achamoth'' feature ptolemy 's version valentinian gnostic myth jewish gnosticism focus sophia active nbsp ad ''sophia'' emanating without partner resulted production ''demiurge'' greek lit public builder ref name newad demi ref also referred ''yaldabaoth'' variations thereof gnostic texts ref name apocryphon creature concealed outside pleroma ref name apocryphon isolation thinking


physical aspect humanity ref name na demiurge ref demiurge typically creates group co actors named archons preside material realm cases present obstacles soul seeking ascent ref name apocryphon inferiority demiurge 's creation may compared technical inferiority work art painting sculpture etc thing art represents cases takes ascetic tendency view material existence negatively becomes extreme materiality including human body perceived evil constrictive deliberate prison


inhabitants moral judgements demiurge vary group group within broad category gnosticism viewing materiality inherently evil merely flawed good passive constituent matter allows archon late antiquity variants gnosticism used term archon refer several servants demiurge ref name hypostasis according origen 's ''contra celsum'' sect called ophites posited existence seven archons beginning iadabaoth ialdabaoth created six follow iao sabaoth adonaios elaios astaphanos horaios ref name contra celsum ref ialdabaoth head


lion ref name apocryphon ref name mithraic art ref concepts gnostic concepts sarkic earthly hidebound ignorant uninitiated lowest level human thought fleshly instinctive level thinking hylic lowest order three types human unable saved since thinking entirely material incapable understanding gnosis psychic soulful partially initiated matter dwelling spirits pneumatic spiritual fully initiated immaterial souls escaping doom material world via gnosis kenoma visible manifest cosmos lower pleroma charisma gift energy bestowed pneumatics oral teaching


personal encounters logos divine ordering principle cosmos personified christ see also odic force hypostasis literally stands beneath inner reality emanation appearance god known psychics ousia essence god known pneumatics specific individual things jesus gnostic saviour jesus identified gnostics embodiment supreme became incarnate bring ''gn sis'' earth ref name nhlintro ref others adamantly denied supreme came flesh claiming jesus merely human attained enlightenment gnosis


taught disciples among mandaeans jesus considered ''m iha kdaba'' false messiah perverted teachings entrusted john baptist ref name macuch ref still traditions identify mani seth third son adam eve salvific figures development three periods discerned development gnosticism late first century early second century development gnostic ideas contemporaneous writing new testament mid second century early third century high point classical gnostic teachers systems claimed systems represented


limit development conflicts described corinthians may inspired clash wisdom tradition paul 's gospel crucifixion arising mythical story developed descent heavenly creature reveal divine world true home human beings jewish christianity saw messiah christ eternal aspect god 's hidden nature spirit truth revealed throughout sacred history movement spread areas controlled roman empire arian goths persian empire continued develop mediterranean


middle east nd rd centuries decline also set third century due growing aversion nicene church economic cultural deterioration roman empire conversion islam albigensian crusade greatly reduced remaining number gnostics throughout middle ages though mandaean communities still exist iraq iran diaspora communities gnostic pseudo gnostic ideas became influential philosophies various esoteric mystical movements th th centuries europe north america including explicitly


identify revivals even continuations earlier gnostic groups relation early christianity dillon notes gnosticism raises questions development early christianity orthodoxy heresy christian heresiologists notably irenaeus regarded gnosticism christian heresy modern scholarship notes early christianity diverse christian orthodoxy settled thcentury roman empire declined gnosticism lost influence gnostics proto orthodox christians shared terminology initially hard distinguish according walter bauer heresies may well original form christianity many


ideas especially christ heavenly revealer emphasis light versus darkness anti jewish animus johannine material reveals debates redeemer myth johannine letters show different interpretations gospel story johannine images may contributed second century gnostic ideas jesus redeemer descended heaven according deconick gospel john shows transitional system early christianity gnostic beliefs god transcends world according deconick ''john'' may show bifurcation idea jewish god jesus' father


heaven jews' father father devil translations say father devil may developed gnostic idea monad demiurge paul gnosticism tertullian calls paul apostle heretics paul 's writings attractive gnostics interpreted gnostic way jewish christians found stray jewish roots christianity corinthians paul refers church members knowledge ''ton echonta gnosin'' james dunn claims cases paul affirmed views closer gnosticism


proto orthodox christianity according clement alexandria disciples valentinus said valentinus student certain theudas student paul elaine pagels notes paul 's epistles interpreted valentinus gnostic way paul could considered proto gnostic well proto catholic many nag hammadi texts including example ''prayer paul'' coptic ''apocalypse paul'' consider paul great apostle fact claimed received gospel directly revelation god appealed gnostics


claimed ''gnosis'' risen christ naassenes cainites valentinians referred paul 's epistles timothy freke peter gandy expanded upon idea paul gnostic teacher although premise jesus invented early christians based alleged greco roman mystery cult dismissed scholars however revelation different gnostic revelations major movements syrian egyptian gnosticism syrian egyptian gnosticism includes sethianism valentinianism basilideans thomasine traditions serpent gnostics well number minor groups writers hermeticism also western gnostic tradition though


differs respects groups ref name hoeller syrian egyptian school derives much outlook platonist influences depicts creation series emanations primal monadic source finally resulting creation material universe schools tend view evil terms matter markedly inferior goodness lacking spiritual insight goodness rather equal force many movements used texts related christianity identifying specifically christian though quite different orthodox roman catholic forms jesus several


apostles thomas apostle claimed founder thomasine form gnosticism figure many gnostic texts mary magdalene respected gnostic leader considered superior twelve apostles gnostic texts gospel mary john evangelist claimed gnostic gnostic interpreters even st paul literature category known us nag hammadi library sethite barbeloite sethianism one main currents gnosticism nd rd centuries


prototype gnosticism condemned irenaeus sethianism attributed ''gnosis'' seth third son adam eve ''norea'' wife noah also plays role mandeanism manicheanism main text ''apocryphon john'' contain christian elements amalgam two earlier myths earlier texts apocalypse adam show signs pre christian focus seth third son adam eve later sethian texts continue interact platonism sethian texts zostrianos allogenes draw imagery


pre christian tradition possibly syncretic cult incorporated elements christianity platonism grew according temporini vogt haase early sethians may identical related nazarenes sect ophites sectarian group called heretics philo according turner sethianism influenced christianity middle platonism originated second century fusion jewish baptizing group possibly priestly lineage called ''barbeloites'' named barbelo first emanation highest god group biblical exegetes ''sethites'' seed seth


existed middle ages samaritan baptist sects according magris samaritan baptist sects offshoot john baptist one offshoot turn headed dositheus simon magus menander milieu idea emerged world created ignorant angels baptismal ritual removed consequences sin led regeneration natural death caused angels overcome samaritan leaders viewed embodiment god 's power spirit wisdom redeemer revealer 'true knowledge


simonians centered simon magus magician baptised philip rebuked peter acts became early christianity archetypal false teacher ascription justin martyr irenaeus others connection schools time individual acts may legendary stories attached various apocryphal books justin martyr identifies menander antioch simon magus' pupil according hippolytus simonianism earlier form valentinian doctrine basilidians basilideans founded basilides alexandria second century


basilides claimed taught doctrines glaucus disciple st peter could also pupil menander ref name eusebius eusebius caesarea ''ecclesiastical history'' book iv chapter vii ref basilidianism survived end thcentury epiphanius knew basilidians living nile delta however almost exclusively limited egypt though according sulpicius severus seems found entrance spain certain mark memphis st jerome states priscillianists infected valentinianism valentinianism named founder valentinus c


candidate bishop rome started group another chosen valentinianism flourished mid second century school popular spreading northwest africa egypt asia minor syria east valentinus specifically named ''gnostikos'' irenaeus intellectually vibrant tradition elaborate philosophically dense form gnosticism valentinus' students elaborated teachings materials several varieties central myth known valentinian gnosticism may monistic rather dualistic ref br schoedel standard element interpretation


valentinianism similar forms gnosticism recognition fundamentally monistic ref name schoedel ref valentinian myths creation flawed materiality due moral failing part demiurge due fact less perfect superior entities emanated ref name val mon ref valentinians treat physical reality less contempt gnostic groups conceive materiality separate substance divine attributable ''error perception'' becomes symbolized mythopoetically act material creation ref name val mon


followers valentinius attempted systematically decode epistles claiming christians made mistake reading epistles literally rather allegorically valentinians understood conflict ''jews'' ''gentiles'' romans coded reference differences ''psychics'' people partly spiritual yet achieved separation carnality ''pneumatics'' totally spiritual people valentinians argued codes intrinsic gnosticism secrecy important ensuring proper progression true inner understanding according bentley layton classical gnosticism school thomas antedated influenced


thomasine traditions ''thomasine traditions'' refers group texts attributed apostle thomas karen l king notes thomasine gnosticism separate category criticised may stand test scholarly scrutiny marcion marcion church leader sinope present day turkey preached rome around ce expelled started congregation spread throughout mediterranean rejected old testament followed limited christian canon included redacted version luke ten edited letters paul


scholars consider gnosticto first driven opposition nbsp amounts reformation christendom return gospel christ paul nothing accepted beyond shows mistake reckon marcion among gnostics dualist certainly gnostic teachings clearly resemble gnostic teachings preached radical difference god old testament demiurge evil creator material universe highest god


loving spiritual god father jesus sent jesus earth free mankind tyranny jewish law ref name valantasis like gnostics marcion argued jesus essentially divine spirit appearing men shape human form someone true physical body ref name harnack adolf von harnack '' https booksgooglecom books marcionhtmlid al bsqaacaaj marcion gospel alien god '' translated john e steely lyle bierma wipf stock publishers ref marcion held heavenly father father jesus christ utterly alien god


part making world connection ref name harnack hermeticism hermeticism closely related gnosticism orientation positive ref name hoeller stephan hoeller http wwwgnosisorg hermeshtm ''on trail winged god hermes hermeticism throughout ages'' ref gnostic groups serpent gnostics naassenes ophites serpentarians gave prominence snake symbolism snake handling played role ceremonies cerinthus c founder heretical school gnostic elements like gnostic cerinthus depicted christ heavenly spirit separate man jesus


cited demiurge creating material world unlike gnostics cerinthus taught christians observe jewish law demiurge holy lowly taught second coming gnosis secret teaching attributed apostle scholars believe first epistle john written response cerinthus ref name gonz lez gonz lez justo l ''a history christian thought vol i'' abingdon pp ref cainites named since hippolytus rome claims worshiped cain well esau korah sodomites little evidence concerning


nature group hippolytus claims believed indulgence sin key salvation since body evil one must defile immoral activity see libertinism name cainite used name religious movement usual biblical sense people descended cain carpocratians libertine sect following gospel according hebrews school justin combined gnostic elements ancient greek religion borborites libertine gnostic sect said descended nicolaitans persian gnosticism


persian schools appeared western persian province babylonia particular within sassanid province asuristan whose writings originally produced aramaic dialects spoken babylonia time representative believed among oldest gnostic thought forms movements considered religions right emanations christianity judaism manichaeism sogdian manuscript khocho tarim basin manichaeism founded prophet mani mani 's father member jewish christian sect


elcesaites subgroup gnostic ebionites ages mani visionary experiences heavenly twin calling leave father 's sect preach true message christ mani travelled indo greek kingdom sakas modern day afghanistan studied hinduism various extant philosophies returning joined court shapur dedicated work written persian known ''shabuhragan'' original writings written syriac aramaic unique manichaean script manichaeism conceives


prevalent th century still exerted influence emergence paulicians bogomils cathari middle ages ultimately stamped catholic church ref name kurt kurt rudolph ''gnosis nature structure gnosticism'' koehler amelang leipzig ref east rudolph relates manicheanism able bloom religious monopoly position previously held christianity zoroastrianism broken nascent islam early years arab conquest manicheanism found followers persia mostly amongst educated circles flourished central asia


spread iran manicheanism became state religion uyghur empire ref name kurt mandaeism mandaeans prayer baptismmandaeism gnostic monotheistic ethnic religion ref name mandaens ref mandaeans semites speak dialect eastern aramaic known mandaic surviving gnostics antiquity religion practised primarily around lower karun euphrates tigris rivers surround shatt al arab waterway part southern iraq khuzestan province iran mandaeism still practiced small numbers parts southern iraq iranian province


khuzestan thought mandaeans worldwide ref name yaledailynews http wwwyaledailynewscom articles view iraqi minority group needs us attention kai thaler ''yale daily news'' march ref name 'mandaean' said come aramaic ''manda'' meaning knowledge john baptist key figure religion emphasis baptism part core beliefs according nathaniel deutsch mandaean anthropogony echoes rabbinic gnostic accounts mandaeans revere adam abel seth enos noah shem aram especially john baptist significant amounts original mandaean scripture written mandaean aramaic


survive modern era primary source text known ginza rabba portions identified scholars copied early nd rd centuries also qolast canonical book prayer mandaean book john sidra 'yahia according scholars mandaeism originated sometime first three centuries ce either southwestern mesopotamia syro palestinian area however scholars take view mandaeism older dates pre christian times mandaeans assert religion predates judaism christianity islam monotheistic faith mandaeans


believe descend directly shem noah 's son also john baptist 's original disciples ref name drowerharangawaita drower ethel stefana haran gawaita baptism hibil ziwa biblioteca apostolica vatican ref due paraphrases word word translations mandaean originals found ''psalms thomas'' believed pre manichaean presence mandaean religion likely middle ages decline mediterranean world gnosticism lived periphery byzantine empire resurfaced western world paulicians adoptionist group


flourished armenia eastern themes byzantine empire accused orthodox medieval sources gnostic quasi manichaean christian bogomils emerged bulgaria spread throughout europe synthesis armenian paulicianism bulgarian orthodox church reform movement cathars cathari albigenses albigensians also accused enemies traits gnosticism though whether cathari possessed direct historical influence ancient gnosticism disputed critics reliable basic conceptions gnostic cosmology


beck p ref however according islam unlike gnostic sects rejection world performing ''good deeds'' leads heaven according islamic belief strict oneness god room lower deity demiurge according islam ''good'' ''evil'' come one god position especially opposed manichaeans ibn al muqaffa depicted islamic deity demonic entity fights humans boasts victories sitting throne descend would


impossible light darkness created one source since regarded two different eternal principles ref name referenceb tilman nagel ''geschichte der islamischen theologie von mohammed bis zur gegenwart'' ch beck p ref muslim theologists countered accusation example repeating sinner says laid repent would prove good also result evil islam also integrated traces entity given authority lower world early writings iblis regarded sufis owner world humans must avoid


religion traces gnostic ideas found sufi anthropogenic like gnostic conception human beings imprisoned matter sufi traditions acknowledge human soul accomplice material world subject bodily desires similar way archontic spheres envelop pneuma ruh must therefore gain victory lower material bound psyche overcome animal nature human captured animal desires mistakenly claims autonomy independence higher god thus resembling lower deity classical gnostic traditions however since goal


abandon created world free oneself ones lower desires disputed whether still gnostic rather completion message muhammad ref name referenceb seems gnostic ideas influential part early islamic development later lost influence however gnostic light metaphorics idea unity existence still prevailed later islamic thought ref name referencea kabbalah gnostic ideas found jewish variation mystical study kabbalah many core gnostic ideas reappear kabbalah used dramatically reinterpreting


earlier jewish sources according new system kabbalists originated th century provence time also center gnostic cathars scholars middle th century tried assume influence cathar gnostics origins kabbalah assumption proved incorrect generalization substantiated original texts hand scholars scholem postulated originally jewish gnosticism influenced early origins gnosticism ref name scholem jewish gnosticism scholem gershom ''jewish gnosticism merkabah mysticism


talmudic tradition'' ref kabbalah employ terminology labels non jewish gnosticism grounds similar concepts language torah first five books hebrew bible th century zohar splendor foundational text kabbalah written style jewish aramaic midrash clarifying five books torah new kabbalistic system uses completely jewish terms modern times mandaeans ancient gnostic ethnoreligious group survived day found today iraq iran diaspora communities ref name rudolph ref


namesake owes following john baptist thought worldwide ref name yaledailynews ref name rudolph number modern gnostic ecclesiastical bodies set founded since discovery nag hammadi library including ecclesia gnostica apostolic johannite church ecclesia gnostica catholica gnostic church france thomasine church alexandrian gnostic church north american college gnostic bishops ref name taussig ref universal gnosticism samael aun weor number th century thinkers arthur schopenhauer albert pike madame blavatsky studied gnostic thought extensively influenced


even figures like herman melville w b yeats tangentially influenced ref name smith smith richard modern relevance gnosticism nag hammadi library ref jules doinel established gnostic church france altered form passed various direct successors fabre des essarts ''tau syn sius'' joanny bricaud ''tau jean ii'' notably though small still active today early th century thinkers heavily studied influenced gnosticism include carl jung supported gnosticism eric voegelin opposed jorge luis borges included


many short stories aleister crowley figures hermann hesse moderately influenced ren gu non founded gnostic review ''la gnose'' moving perennialist position founding traditionalist school gnostic thelemite organizations ecclesia gnostica catholica ordo templi orientis trace crowley 's thought discovery translation nag hammadi library huge effect gnosticism since world war ii intellectuals heavily influenced gnosticism period include lawrence durrell hans jonas philip k dick


harold bloom albert camus allen ginsberg moderately influenced ref name smith celia green written gnostic christianity relation philosophy ref name green green celia ''advice clever children'' oxford oxford forum xxxv xxxvii ref alfred north whitehead aware existence newly discovered gnostic scrolls accordingly michel weber proposed gnostic interpretation late metaphysics sources heresiologists prior discovery nag hammadi library gnosticism known primarily works heresiologists church fathers opposed movements writings antagonistic


bias towards gnostic teachings incomplete several heresiological writers hippolytus made little effort exactly record nature sects reported transcribe sacred texts reconstructions incomplete gnostic texts attempted modern times research gnosticism coloured orthodox views heresiologists justin martyr c c wrote ''first apology'' addressed roman emperor antoninus pius criticised simon magus menander marcion since simon menander considered 'proto gnostic' irenaeus died c wrote ''against heresies'' c


identifies simon magus flavia neapolis samaria inceptor gnosticism samaria charted apparent spread teachings simon ancient knowers teachings valentinus contemporary gnostic sects hippolytus wrote ten volume ''refutation heresies'' eight unearthed also focuses connection pre socratic therefore pre incantation christ ideas false beliefs early gnostic heretical leaders thirty three groups reported considered gnostic modern scholars including 'the foreigners' 'the seth people' hippolytus presents


individual teachers simon valentinus secundus ptolemy heracleon marcus colorbasus tertullian c carthage wrote ''adversus valentinianos'' 'against valentinians' c well five books around chronicling refuting teachings marcion gnostic texts prior discovery nag hammadi limited number texts available students gnosticism reconstructions attempted records heresiologists necessarily coloured motivation behind source accounts nag hammadi library collection gnostic texts discovered near nag hammadi upper egypt twelve leather bound


lost greek originals proposed though disputed manuscripts date rd th centuries nag hammadi texts demonstrated fluidity early christian scripture early christianity academic studies development prior discovery nag hammadi gnostic movements largely perceived lens early church heresiologists johann lorenz von mosheim proposed gnosticism developed greece mesopotamia spreading west incorporating jewish elements according mosheim jewish thought took gnostic elements used greek philosophy jhorn ernest


gnosticism pre christian phenomenon christian ''gnosis'' one even marginal instance phenomenon according wilhelm bousset gnosticism form iranian mesopotamian syncretism eduard norden also proposed pre christian origins richard august reitzenstein rudolf bultmann also situated origins gnosticism persia hans heinrich schaeder hans leisegang saw gnosticism amalgam eastern thought greek form hans jonas took intermediate approach using comparative approach ''religionsgeschichtliche schule'' existentialist hermeneutics bultmann jonas emphasized


duality god world concluded gnosticism cannot derived platonism contemporary scholarship largely agrees gnosticism jewish judeo christian origins theses notably put forward gershom g scholem gilles quispel study gnosticism early alexandrian christianity received strong impetus discovery coptic nag hammadi library great number translations published works elaine pagels professor religion princeton university especially ''the gnostic gospels'' detailed suppression writings


found nag hammadi early bishops christian church popularized gnosticism mainstream culture also incited strong responses condemnations clergical writers definitions gnosticism according matthew j dillon six trends discerned definitions gnosticism typologies catalogue shared characteristics used classify group objects together traditional approaches viewing gnosticism christian heresy phenomenological approaches notably hans jonas restricting gnosticism identifying groups explicitly called gnostics groups clearly sectarian deconstructing gnosticism abandoning category gnosticism psychology cognitive


science religion approaching gnosticism psychological phenomena typologies messina conference origins gnosis gnosticism proposed designate definition abandoned created religion gnosticism gnosis widespread element ancient religions suggesting homogeneous conception gnosis gnostic religions exist time according dillon texts nag hammadi made clear definition limited better classified movements valentinian mythological similarity sethian similar tropes presence demiurge


dillon notes messian definition also excluded pre christian gnosticism later developments mandaeans manichaeans hans jonas discerned two main currents gnosticism namely syrian egyptian persian includes manicheanism mandaeism among syrian egyptian schools movements spawned typically monist view persian gnosticism possesses dualist tendencies reflecting strong influence beliefs persian zurvanist zoroastrians medieval cathars bogomils carpocratians seem include elements categories however scholars kurt rudolph mark lidzbarski rudolf mac ch ethel drower jorunn


today continue vein harnack reading gnosticism late contaminated version christianity notably darrell block criticises elaine pagels view early christianity wildly diverse phenomenological approaches hans jonas took existential phenomenological approach gnosticism according jonas alienation distinguishing characteristic gnosticism making different contemporary religions jonas compares alienation existentialist notion ''geworfenheit'' martin heidegger 's thrownness thrown hostile world restricting gnosticism late scholars voiced concerns broadness gnosticism meaningful


category bentley layton proposed categorize gnosticism delineating groups marked gnostic ancient texts according layton term mainly applied heresiologists myth described ''apocryphon john'' used mainly sethians ophites according layton texts refer myth called classical gnostic addition alastair logan uses social theory identify gnosticism uses rodney stark william bainbridge 's sociological theory traditional religion sects cults according logan gnostics cult odds society


large deconstructing gnosticism according michael allen williams concept gnosticism distinct religious tradition questionable since gnosis pervasive characteristic many religious traditions antiquity restricted called gnostic systems according williams conceptual foundations category gnosticism rests remains agenda heresiologists early church heresiologists created interpretive definition gnosticism modern scholarship followed example created ''categorical'' definition according williams term needs replacing accurately reflect movements comprises suggests


set groups instance every sect christianity information point believed separate logos created universe god behest likewise believed kind secret knowledge gnosis essential ensuring one salvation likewise dualist view cosmos lower world corrupted meddling divine beings upper world god awaiting chance destroy start thereby helping humanity escape corrupt bodies locations fleeing celestial ones psychological approaches carl jung approached


gnosticism psychological perspective followed gilles quispel according approach gnosticism map human development undivided person centered self develops fragmentary personhood young age according quispel gnosis third force western culture alongside faith reason offers experiential awareness self according ioan culianu gnosis made possible universal operations mind arrived anytime anywhere similar suggestion made edward conze suggested similarities


''praj '' ' 'sophia'' may due actual modalities human mind certain conditions result similar experiences see also esoteric character gospels marcellina gnostic mithras notes subnotes references sources printed sources translated kosack wolfgang ''geschichte der gnosis antike urchristentum und islam'' verlag christoph brunner basel petrement simone ''a separate god origins teachings gnosticsim'' harper row pages pages yamauchi edwin https wwwjstororg stable seq page scan tab contents pre christian gnosticism nag hammadi texts ''church history'' vol pp nbsp web sources ref ref name national book award group web ref


linguistics '''grammar''' natural language set structural constraints speakers' writers' composition clauses phrases words term also refer study constraints field includes domains phonology morphology syntax often complemented phonetics semantics pragmatics currently two different approaches study grammar traditional grammar theoretical grammar fluent speakers language variety ''lect'' effectively internalized constraints vast majority least case one 's native language

Humanities
Languages and literature
Linguistics
Grammar


acquired conscious study instruction hearing speakers much internalization occurs early childhood learning language later life usually involves explicit instruction view grammar understood cognitive information underlying specific instance language production term grammar also describe linguistic behavior groups speakers writers rather individuals differences scales important sense word example term english grammar could refer whole english grammar grammars speakers


language case term encompasses great deal variation smaller scale may refer shared among grammars english speakers subject verb object word order simple declarative sentences smallest scale sense grammar describe conventions one relatively well defined form english standard english region description study analysis rules may also referred grammar reference book describing grammar language called reference


grammar simply grammar see history english grammars fully explicit grammar exhaustively describes grammatical constructions particular speech variety called descriptive grammar kind linguistic description contrasts linguistic prescription attempt actively discourage suppress grammatical constructions codifying promoting others either absolute sense standard variety example prescriptivists maintain sentences english end prepositions prohibition traced john dryden april january whose unexplained objection practice perhaps


led english speakers avoid construction discourage use ref name cb ref yet preposition stranding long history germanic languages like english widespread standard usage outside linguistics term ''grammar'' often used rather different sense may used broadly include conventions spelling punctuation linguists would typically consider part grammar rather part orthography conventions used writing language may also used narrowly refer set prescriptive norms


excluding aspects language 's grammar subject variation debate normative acceptability jeremy butterfield claimed non linguists grammar often generic way referring aspect english people object etymology word ''grammar'' derived greek ''grammatik chn '' means art letters ''gr mma'' letter ''gr phein'' draw write greek root also appears graphics grapheme photograph history first systematic grammar sanskrit originated iron age india yaska th century bc p ini


th th century bc ref name britpanini ref commentators pingala c bc katyayana patanjali nd century bc tolk ppiyam earliest tamil grammar mostly dated th century ad babylonians also made early attempts language description grammar appeared discipline hellenism rd century bc forward authors rhyanus aristarchus samothrace oldest known grammar handbook ''art grammar'' succinct guide speaking writing clearly effectively written ancient greek scholar dionysius thrax bc student aristarchus


century auraicept na n ces arabic grammar emerged abu al aswad al du'ali th century first treatises hebrew grammar appeared high middle ages context mishnah exegesis hebrew bible karaite tradition originated abbasid baghdad ''diqduq'' th century one earliest grammatical commentaries hebrew bible ibn barun th century compares hebrew language arabic islamic grammatical tradition belonging ''trivium'' seven liberal arts grammar taught core discipline throughout middle ages following


influence authors late antiquity priscian treatment vernaculars began gradually high middle ages isolated works first grammatical treatise became influential renaissance baroque periods antonio de nebrija published ''las introduciones latinas contrapuesto el romance al latin'' first spanish grammar ''gram tica de la lengua castellana'' th century italian renaissance ''questione della lingua'' discussion status ideal form italian language initiated dante 's ' 'de vulgari eloquentia'' pietro bembo ''prose della volgar lingua'' venice


franz bopp starting point modern comparative linguistics came theoretical frameworks generative parse tree sentence divided noun phrase subject verb phrase includes object contrast structural functional grammar consider subject object equal constituents frameworks grammar seek give precise scientific theory syntactic rules grammar function developed theoretical linguistics dependency grammar dependency relation lucien tesni link grammar functional grammar structural functional analysis danish functionalism functional discourse grammar role


trees commonly used frameworks depict rules various alternative schemes grammars affix grammar finite lattice backus naur form constraint grammar lambda calculus tree adjoining grammar x bar theory development grammars grammars evolve usage historically advent written representations formal rules language usage tend appear also although rules tend describe writing conventions accurately conventions speech formal grammars codifications usage developed repeated documentation observation time rules established developed prescriptive concept grammatical


say one depending social context formal study grammar important part children 's schooling young age advanced learning though rules taught schools grammar sense linguists use particularly prescriptive intent rather descriptive constructed languages also called ''planned languages'' ''conlangs'' common modern day although still extremely uncommon compared natural languages many designed aid human communication example naturalistic interlingua schematic esperanto highly logic compatible artificial language lojban


languages grammar syntax refers linguistic structure word level example sentences formed though without taking account intonation domain phonology morphology contrast refers structure word level example compound words formed level individual sounds like intonation domain phonology however clear line drawn syntax morphology analytic languages use syntax convey information encoded inflection synthetic languages words word


order significant morphology highly significant purely synthetic language whereas morphology significant syntax highly significant analytic language example chinese afrikaans highly analytic thus meaning context dependent inflections past thus becoming even less synthetic purely analytic time latin highly synthetic uses affixes inflections convey information chinese syntax latin words quite though totally self contained intelligible latin sentence


made elements arranged almost arbitrarily latin complex affixation simple syntax whereas chinese opposite education prescriptive grammar taught primary secondary school term grammar school historically referred school attached cathedral monastery teaches latin grammar future priests monks originally referred school taught students read scan interpret declaim greek latin poets including homer virgil euripides others mistaken related albeit distinct modern british grammar schools standard language


dialect promoted dialects writing education broadly speaking public sphere contrasts vernacular dialects may objects study academic descriptive linguistics rarely taught prescriptively standardized first language taught primary education may subject political controversy may sometimes establish standard defining nationality ethnicity recently efforts begun update grammar instruction primary secondary education main focus prevent use outdated prescriptive rules favor setting norms based earlier descriptive research


change perceptions relative correctness prescribed standard forms comparison non standard dialects preeminence parisian french reigned largely unchallenged throughout history modern french literature standard italian based speech florence rather capital influence early literature likewise standard spanish based speech madrid educated speakers northern areas castile le n see ''gram tica de la lengua castellana'' argentina uruguay spanish standard based local dialects buenos


aires montevideo rioplatense spanish portuguese two official standards respectively brazilian portuguese european portuguese serbian variant serbo croatian likewise divided serbia republika srpska bosnia herzegovina use distinct normative subvarieties differences yat reflexes existence codification distinct montenegrin standard matter controversy treat montenegrin separate standard lect think considered another form serbian norwegian two standards ''bokm l'' ''nynorsk'' choice subject controversy norwegian municipality either


declare one official language remain language neutral nynorsk backed percent municipalities main language used primary schools chosen referendum within local school district normally follows official language municipality standard german emerged standardized chancellery use high german th th centuries almost exclusively written language widely spoken former german dialects nearly extinct standard chinese official status standard spoken form chinese


language people 's republic china prc republic china roc republic singapore pronunciation standard chinese based local accent mandarin chinese luanping chengde hebei province near beijing grammar syntax based modern vernacular written chinese modern standard arabic directly based classical arabic language qur'an hindustani language two standards hindi urdu united states society promotion good grammar designated march national grammar day see also ambiguous grammar constraint based grammar


grammeme harmonic grammar higher order grammar hog linguistic error linguistic typology paragrammatism speech error slip tongue usage language usus notes references american academic press ed william strunk jr et al ''the classics style fundamentals language style american craftsmen'' cleveland american academic press rundle bede ''grammar philosophy'' oxford clarendon press new york oxford university press external links http wwwoxforddictionariescom grammar grammar oxford english dictionary grammar writing linguistics terminology


old geodetic pillar triangulation pillar ostend belgium '''geodesy''' earth science accurately measuring understanding earth 's geometric shape orientation space gravitational field ref name noaa ref field also incorporates studies properties change time equivalent measurements planets known planetary geodesy geodynamical phenomena include crustal motion tides polar motion studied designing global national control networks applying space terrestrial techniques relying datums coordinate systems definition word geodesy comes ancient greek word


shape earth result rotation causes equatorial bulge competition geological processes collision plates volcanism resisted earth 's gravitational field applies solid surface liquid surface dynamic sea surface topography earth 's atmosphere reason study earth 's gravitational field called physical geodesy geoid reference ellipsoid geoid essentially figure earth abstracted topographical features idealized equilibrium surface sea water mean sea level surface absence currents


purely geometrical one mechanical ellipticity earth dynamical flattening symbol ''j'' sub sub determined high precision observation satellite orbit perturbations relationship geometrical flattening indirect relationship depends internal density distribution simplest terms degree central concentration mass geodetic reference system grs nbsp posited nbsp semi major axis flattening system adopted xvii general assembly international union geodesy geophysics iugg essentially basis geodetic positioning global positioning system gps


thus also widespread use outside geodetic community numerous systems countries used create maps charts becoming obsolete countries increasingly move global geocentric reference systems using grs nbsp reference ellipsoid geoid realizable meaning consistently located earth suitable simple measurements physical objects like tide gauge geoid therefore considered real surface reference ellipsoid however many possible instantiations readily realizable therefore abstract surface third primary surface geodetic interest topographic surface


earth realizable surface coordinate systems space locations points three dimensional space conveniently described three cartesian rectangular coordinates ''x'' ''y'' ''z'' since advent satellite positioning coordinate systems typically geocentric ''z'' axis aligned earth 's conventional instantaneous rotation axis prior era satellite geodesy coordinate systems associated geodetic datum attempted geocentric origins differed geocenter hundreds meters due regional deviations direction plumbline vertical regional geodetic data