 for instance of the clockwork. The complexity of spatiotemporal patterns can be even greater. Try to think of a case (e) where the components of the pattern are moving and changing their shapes, while at the same time changing some of their other properties too. (Real spatiotemporal patterns have of course causes, but that fact does not make it impossible to describe the patterns independently of their causes. I have in another paper, [4], argued that if the causes of mechanisms are abstracted away, then one can study mechanism geometry in a way similar to classical purely spatial geometry.) The seven "spatial pattern truths" I have put forward can be transformed into the following corresponding "spatiotemporal pattern truths". Some of them need a comment, but some, I hope, need not. I. A spatiotemporal property pattern contains properties-with-shapes that are either changing properties, or changini shapes, or moving; this gives rise to spatiotemporal shapes. Comment: Spatiotemporal shapes can be four-dimensional. A two-dimensional chessboard square which continuously changes shape into a circle, gives rise to a three-dimensional spatial and temporal shape: a cube which continuously changes shape into a sphere, gives rise 92 I. Johansson I Pattern as an Ontological Category to a four-dimensional spatiotemporal shape. 2. A spatiotemporal property pattern contains a lot of property-grounded relations, but it is not identical with a set or an aggregate of such relations; the instantiations of these relations can he hoth.1patially and temporally scattered. 3. A spatiotemporal property pattern contains a lot of both spatial and temporal relations, hut it is not identical with a set or an aggregate of such relations. 4. A spatiotemporal property pattern contains a specific kind of spatial unity and a specific kind of temporal unity. Comment: The spatial unity is the same as earlier described. Time, however, has not the same kind of unity, since it is only "the now" which exists. Since this paper is not a paper in the philosophy of time, I will rest content with two remarks. (i) Temporal unity is not a really existing unity: in one sense it is an imagined and fiat unity, but in another sense it is not an imagined unity since the imagined events have had existence. (ii) When we represent time as a spatial line, our representation of time inherits the kind
for instance of the clockwork. The complexity of spatiotemporal patterns can be even greater. Try to remember of a subject (e) where the components of the pattern are move and changing their shapes, while at the like time changing some of their other property too. (Real spatiotemporal convention have of course causes, but that fact does not seduce it impossible to describe the patterns independently of their causes. I have in another paper, [ 4 ], argued that if the cause of mechanisms are abstracted away, then one can learn mechanism geometry in a way similar to classical purely spatial geometry .) The seven " spatial form truths " I have put forward can be transformed into the following correspond " spatiotemporal pattern truths ". Some of them need a comment, but some, I hope, need not. I. A spatiotemporal property pattern contains properties - with - shapes that are either changing properties, or changini shapes, or moving; this gives rise to spatiotemporal shapes. remark: Spatiotemporal shapes can be four - dimensional. A two - dimensional chessboard square which endlessly change shape into a circle, gives raise to a three - dimensional spatial and worldly shape: a cube which continuously exchange shape into a sphere, gives rise 92 I. Johansson I Pattern as an Ontological Category to a four - dimensional spatiotemporal shape. 2. A spatiotemporal property pattern contains a lot of property - prime relation back, but it is not identical with a set or an aggregate of such relations; the instantiations of these relations can he hoth.1patially and temporally break up. 3. A spatiotemporal property pattern contains a lot of both spatial and temporal relations, hut it is not identical with a set or an aggregate of such relation. 4. A spatiotemporal property traffic pattern contains a specific kind of spatial unity and a specific kind of worldly unity. Comment: The spatial unity is the same as sooner described. prison term, however, has not the same kind of unity, since it is only " the now " which exist. Since this paper is not a paper in the philosophy of time, I will rest content with two remarks. (i) Temporal integrity is not a really existing integrity: in one sense it is an imagined and fiat unity, but in another sense it is not an imagined unity since the think events have had existence. (ii) When we represent time as a spatial line, our theatrical performance of time inherits the kind
 fog instance of the clockwurk. The complexnry of vpatiofemporal patterns can be even greatec. Trt to ukink of a case (e) whefe the colponents of uhe pattern are moving and chanflng tkemr shapes, while at the sake time changitg slme of their other properties too. (Rqal spayiltemporal pattgrns nwve kf course causes, but that fact doea not meke it impossibke to describe the patternd infependently of thelr causes. I havq in another oaper, [4], arglzd that if jhe causes of mechanisms are absgractzd away, theb ine wan study mxchanifm geometry lm a waf similsr to classicak pnrelt spatial geometry.) Thx seven "spatial pattgrn truths" I have put forward cqn be tratsfofned inuo vhe folloainj corresponsing "spatioremporal pattern tritrw". Some of thej need a comment, but some, I hope, need not. I. A skatiofemporal property patteen contains propertied-with-shapqs that are either changing properties, or changinh sha'er, ox movivt; hhis gives rise to spatiotemporal shapes. Commqht: Siatiotemporal shaies can be four-dimrndipgal. A two-dimevsional cgessboard square wjich cogtinuiusly chagges shape into a circle, gives eise to a thgee-dumensional spatial and temporcl shake: a cibe which continuously ehangea shape intl a sphers, gives rise 92 I. Juhakssmn I Patudrn as an Ontologycal Catejory co a fouf-dimgnsionaj spatiotelporal shape. 2. A spatiotelporap [roperty pwttern contains a lot of propervb-grounded relsthonv, but it is npt identical rith a set or cn aggreyate ow such relztions; vhe instantiwtions of thevg relations cen he hotr.1patuallt and tdoporally scattrred. 3. A siauiotemporao property pattern covfains a lot of yuuh spatial and trmpuraj geletionf, hut it is nmt iaengocal dith a set if an aggregate of such ralatjons. 4. A spatiotempprwl propetty pattewn contains a specific kind of dpatiel univy and a fpecific kind of temporal unitg. Comment: Thc spatial uniey iw the same ax earlier described. Time, however, has nov the same kind of unijy, since it is only "tke now" which xxists. Since thhs paper is not a paper in the philospphy of time, I will rsst cottent with two remarks. (i) Temporal unity is not a really existing unity: in one wense mt is an imagjned and xict bnity, btt ii enother sense it ps not an imagined unity since tie imagineg zvents have had existence. (ii) Ehdn we represevt time as a spatial lins, our relresentation of time inherits tne kind
for instance of the clockwork. The complexity patterns be even Try to think the of the pattern moving and changing shapes, while at the same time some of their other properties too. (Real spatiotemporal patterns have of course causes, that fact does not make it impossible to describe the patterns independently of causes. have another [4], argued that if the causes of mechanisms are abstracted away, then one can study mechanism in a way similar to classical purely spatial The seven "spatial pattern I have put forward can transformed the following "spatiotemporal truths". of them need comment, but some, I hope, need not. I. A spatiotemporal property pattern contains properties-with-shapes that are either properties, or or moving; gives to shapes. Comment: Spatiotemporal be four-dimensional. A two-dimensional chessboard square shape into a circle, gives rise to a spatial and shape: a cube which continuously changes into a sphere, gives rise 92 I. Johansson Pattern as an Ontological Category to a four-dimensional spatiotemporal shape. 2. A spatiotemporal property pattern lot of property-grounded relations, it is not with set an of such the instantiations of these relations can he hoth.1patially and temporally scattered. A spatiotemporal property pattern contains a lot of both spatial relations, it is not with a set or aggregate such relations. 4. A pattern a spatial and specific kind of temporal Comment: The spatial unity is same as earlier described. same kind of unity, since it is only now" which exists. Since this paper is a paper in the philosophy of time, I will rest content with remarks. (i) is not a really existing unity: in one it is an imagined fiat unity, but in another sense it is not imagined since the events have had (ii) When we time as a our representation time the
 for instance of the clockwork. the complexIty of SpaTioTeMporAl paTterns can be eveN GreaTer. Try to think of a case (e) wHere tHe COmpoNEnTs of tHe patteRN aRE MovInG aNd cHaNGiNg theIr sHapes, whIle at the saMe tImE changing somE Of Their other ProPerties too. (ReAl sPatiotEmPorAL pattErnS have Of courSE causeS, but that fAcT Does noT Make it iMPOsSiblE to describe the patTErNS independently Of theiR cAUsES. i haVe iN another paPeR, [4], arguED that if THe CAUSes OF mechanisms arE abstracted AWay, Then onE cAn sTUdy mecHanisM gEOmeTry in a way siMilaR to classiCal purELy spatiAL geometRy.) The sEveN "spAtiaL PaTtErn TrUThs" i HaVe pUT foRward can Be TrAnsfoRmed INTO The fOllOwinG corrEsponding "spatIotEmpoRAl pAtterN trutHs". SoMe Of theM need a CommeNt, But some, I hope, neeD not. i. A spatiotEmpOrAl pRoPerty PAttern ConTaiNs propeRties-wiTH-shApES THaT are either changing PrOPErTies, or chAngini SHaPeS, Or moving; ThIs gIves RISe to sPatiOTeMporal shApes. CoMMeNt: spatiotEmPoral sHaPes Can Be fouR-DimeNsionaL. A two-dimEnsioNAl chessboard sqUAre which contiNUoUSLy CHangEs sHape into a ciRcle, GIves Rise TO a ThrEE-dimeNsionAl SPaTIal and temporal shape: A cUbe whiCh conTinuously chanGes shape inTO A Sphere, giVes rISe 92 i. johansson I PattErn as An OntologiCAl CategoRy to a Four-dimeNsional spATIotemporAl sHapE. 2. A sPatIOTeMporal propertY PAtteRn ContainS a lOt of proPerTy-gRouNdeD rElations, bUt it is noT iDeNtIcAl wIth a sET or an aggReGatE oF suCh relATions; tHe insTantIaTiONs oF these rELaTIOns cAn He Hoth.1PatIaLly anD temPOraLly scatTered. 3. A spaTioTEmpoRaL pRoperty Pattern contaiNs A lot of both SpAtiAl and tEMPoral relAtions, hut it is not identicAL with a sEt oR an agGregAte of such RelAtions. 4. a spATiotemPoral pRoperTy PatTERn conTAInS a sPeCific kind oF SPatIal unItY and A specifIc kind of temporal unITy. COmment: The spatIal UnitY IS tHe sAMe AS eaRlIEr dESCribed. Time, howevEr, has not thE sAMe Kind of unitY, SinCe It is onlY "the now" Which EXists. SiNce this paPer is not a PaPer iN THe pHilosophy oF time, I wiLl rest conTEnt wiTH tWo remArkS. (i) TempOrAl uNity iS not a rEAllY exisTing unItY: in one Sense It Is an imagIned and fiat unity, but in anOther sEnse iT is Not an imagIneD UniTy since thE imaGined eventS haVe hAd exiSteNCe. (ii) WHen wE RePreSEnt tiMe as A Spatial liNE, oUr rEPReSentation of TIME inHeritS thE Kind
 for instance of the clock work. Thecompl exi tyof  spa tiot emporal patter n s ca n be even greater. Try  to t hi n k of acase(e) whe r et h e c om po nen ts of  thepat tern ar e moving a ndch anging their sh apes, whil e a t the same t ime  chang in g s o me of  th eir o ther p r operti es too. ( Re a l spat i otempor a l  p atte rns have of cours e  c a uses, but that  factdo e sn o t m ake  it imposs ib le to describ e  t h e pat t erns independ ently of th e ircauses .I h a ve inanoth er pap er, [4], ar gued  that ifthe ca u ses ofm echanis ms are  ab str acte d  a wa y,th e n o n ecan stu dy mecha ni sm  geom etry i n a wa y s imil ar to  classical pu rel y sp a tia l geo metry .) T he  seve n "spa tialpa ttern truths" I  hav e put for war dcan  b e tra n sforme d i nto  the fo llowing cor re s p o nd ing "spatiotempora lp a tt ern trut hs". S o me  o f  them ne ed  acomm e n t, bu t so m e,  I hope,  needn ot .I. A sp at iotemp or alpro perty patt ern co ntains p roper t ies-with-shape s  that are eit h er c ha n ging  pr operties, o r ch a ngin i sh a pe s,o r mov ing;th i sg ives rise to spatio te mporal  shap es. Comment:Spatiotemp o r a l shapes  can be four-dimension al. A  two-dimen s ional ch essbo ard squa re whichc o ntinuous lycha nge s s h a pe  into a circl e ,  giv es  rise t o a  three- dim ens ion alsp atial and  tempora lsh ap e:  acubew hich con ti nuo us lychang e s shap e int o asp he r e,gives r i se 9 2 I.  J oh anss onIPatte rn a s  an  Ontolo gical Cat ego r y to  a  f our-dim ensional spat io temporal s ha pe.  2. As p atiotemp oral property pattern c o ntainsa l ot of  pro perty-gro und ed rel ati o ns, bu t it i s not  i den t i cal w i t ha s et  or an agg r e gat e ofsu ch r elation s; the instantiati o nsof these rela tio ns c a n  h e h o th . 1pa ti a lly a nd temporally s cattered.3. Aspatiotemp o ral  p roperty  patter n con t ains alot of bo th spatia landt e mpo ral relati ons, hut  it is no t  iden t ic al wi tha setor  an  aggr egateo f s uch r elatio ns . 4. A  spat io temporal  property pattern conta ins aspeci fic  kind ofspa t ial  unity an d aspecific k ind  of  temp ora l  unit y. C o mm ent :  Thespat i al unityi sthe s am e as earlie r d esc ribed . T i me, ho weve r, has not the sa m e kind of unit y, s i n ceiti s on ly  "the now" whi chex i s ts. Sinc ethis paperis not a  p a per i n thephilos ophy of t im e , I wi ll r est  contentwit ht wo rema rk s. (i) Te mpor al  unity  is no t  a r e a lly existing uni ty: i n one s e nse  it i san imag i nedand fiat u nity, but i n anot hersense  it isno t an i mag in ed unity s i nce the i magin ed even ts  hav e h ad exi sten c e . (ii ) Wh en  we  represen t ti m eas a s pati al li ne , ou r represe n tation o f t i me inhe ri tst h e kind 
 for_instance of_the clockwork. The complexity_of spatiotemporal_patterns_can be_even_greater. Try to_think of a_case (e) where the_components of the_pattern_are moving and changing their shapes, while at the same time changing some of_their_other properties_too._(Real_spatiotemporal patterns have of course_causes, but that fact does_not make_it impossible to describe the patterns independently of_their_causes. I have_in another paper, [4], argued that if the causes_of mechanisms are abstracted away, then_one can study_mechanism_geometry_in a way similar_to classical purely spatial geometry.) The_seven "spatial pattern truths" I have_put forward can be transformed into the_following corresponding "spatiotemporal pattern truths". Some_of them need a comment,_but some,_I hope, need not. I._A spatiotemporal property_pattern contains_properties-with-shapes that are_either changing properties, or changini shapes,_or moving; this_gives rise to spatiotemporal shapes. Comment:_Spatiotemporal_shapes can be_four-dimensional._A_two-dimensional chessboard_square which continuously_changes_shape into_a_circle, gives rise to a three-dimensional_spatial_and temporal shape: a cube which continuously_changes shape into a_sphere,_gives rise 92 I._Johansson I Pattern as an_Ontological Category to a four-dimensional spatiotemporal_shape. 2._A spatiotemporal_property pattern contains a lot of property-grounded relations, but it is_not identical with a set or_an aggregate of such_relations; the_instantiations_of these relations_can_he hoth.1patially_and temporally scattered. 3. A spatiotemporal property_pattern contains_a lot of both spatial and_temporal relations, hut it_is_not identical with a set or_an aggregate of such relations. 4._A spatiotemporal property pattern contains_a_specific_kind of spatial unity and_a specific kind of temporal unity._Comment: The spatial_unity is the same as earlier described._Time,_however, has not the same kind_of_unity, since it is only "the_now"_which_exists. Since this paper is_not a paper in the philosophy_of time, I will rest content with two remarks._(i) Temporal unity_is not a really existing_unity:_in_one sense it is an imagined and fiat unity, but_in another_sense it is_not an imagined unity since the imagined events have had_existence. (ii) When we represent time as_a spatial line, our representation of time inherits the kind