? Lancaster University, vfridge and aQtive - PDF document

u u u un nd n n d d de er e e rs r r s st s t t ta an a a n n nd di d d i in i ng n n g g g s s s sp pa p p a ac a ce c c e e e We W e el ls l sh s h h M M Ma at a th t h he em e ma m at a ti t ic i c ci ia i an a n n W W e l s h M a t h e m a t i c i a n w wa w w al a a lk l l k k ks s s s i i i in n n n C Cy C C yb y y be b b er e e rs r r sp s s pa p p ac a a ce c c e e e model real space Alan Dix 14 ? Lancaster University, vfridge and aQtive http://www.hiraeth.com/alan un u u u n n nd de d d er e e rs r r st s s ta t t an a a n n nd di d d i i in ng n n g g g c c c cy yb y y b b be er e e rs r r sp s s p pa p a a ac ce c c e e e m m m ma ap a a p p ps s s s model cyberspace my m m m y y yt th t t h h h & & & & m m m ma az a a z z ze es e e s s s ? so s s s ou o o u u ur rc r r ce c c es e e s s s Lober giny Lober giny m ma m m ag a a gi g g ic i i c c c a ghin tyu a ghin tyu mjfhi g ta mjfhi g ta not jkrt not jkrt uyos uyos Lober giny Lober giny a ghin tyu a ghin tyu mjfhi g ta mjfhi g ta not jkrt not jkrt uyos uyos m ma a at th t h he em e ma m a at ti t ic i cs c s s m m a t h e m a t i c s Lober giny Lober giny a ghin tyu a ghin tyu mjfhi g ta mjfhi g ta not jkrtu not jkrtu yos yos Clay c co o og g gn ni n i it ti t io i o on n n c c o g n i t i o n tablet map c co o om m mm mu m un u n ni it i t ty y y c c o m m u n i t y 2200 BC s s s so o ou o u u ur rc r r ce c c es e e s s s c co o on n ns st s tr t r ru u uc ct c te t ed e d d c c o n s t r u c t e d c c co c o o om mp m m p p pu u u ut ta t t at a a t t ti io i i on o o n n n Yorghan Tepe, en e n nv vi v i ir r ro o on nm n me m e en nt n t t e e n v i r o n m e n t Iraq 1

Egyptian Wales garden John Speed 1610 1400 BC garden of a high court official of Amenhotep III at Thebes dr d r ra aw a wi w in i ng n g gs s s d d r a w i n g s cartographic (isomorphic) cartographic (homomorphic) schematic linear episodic labrynth j j j jo o o ou u u ur r r rn ne n n ey e e y y ys s s s always linear Kendal Manchester Airport Newark San Francisco 2

seeing in 3D 2D 2 D D/ / /3 3D 3 D D 2 2 D / 3 D which is closer? Euclid Descartes x, y, z Pythagorus but is it real and is it natural real is easy 2D 2 D D n na n av a vi v ig i ga g at a t ti io i o on n n 2 2 D n a v i g a t i o n which is closer? walking vs. helicopter Poincare property tunnels and flyovers pr p ro r op o pe p e er rt r ti t ie i es e s s o of o f f s sp s p pa ac a ce c e e p p r o p e r t i e s o f s p a c e manipulate in 3D closeness and connectedness see in 2 1 / 2 D fixed orientation/centre flat navigate in 2D infinite objective 3

c cl c c lo l l os o o se s s e e en ne n n es e e ss s s s s s co c c c on o o nn n n ne n n ec e e ct c c t t te e ed e dn d d n n ne es e e ss s s s s s b c metric spaces graph theory a D(a,c) ≤ D(a,b)+D(b,c) topology arcs and points neighbourhoods awareness open and closed sets limits reformulated! Rodden awareness models architecture nimbus, focus, etc. Benford et al. Hi H il i l ll li l ie i er e r r H H i l l i e r s s s sp p p pa ac a a c c ce e e e i is i i s s s t t t th he h h e e e m m m ma ac a a c ch c hi h h i i in ne n n e e e sy s y ym m mm m me et e tr t ry r y y s s y m m e t r y fi f ix i xe x ed e d d c ce c en e n nt t tr re r e e f f i x e d c e n t r e directed f f f fi ix i i xe x x ed e e d d d o or o o r ri r ie i i en e e n n nt ta t t at a a ti t t io i i o o on n n n graphs one-way streets hyperlinks y y ry y r tr r t t et e me e m m mm ym m m y y sy s s s 4

Pietro Vesconte's World Maps, 1321, from Marino Sanudo's Liber secretorum fidelium crusis T-O map of the world Isidore of Seville 560-636 AD http://www.henry%2ddavis.com/MAPS/LMwebpages/LM1.html ma m m m a a ap pp p p p p pa a a a View of the World from m m mu m un u u n nd n d d di i i i 9th Avenue Hereford Cathederal Saul Steinberg 1300 AD 1975 Piaget Donaldson could you see B from A can Ann see Bob Ann A Bob B 5

viewpoints i in n nf fi f in i ni n it i te t e e s sp s pa p a ac c ce e e . .. . .. . . . i i n f i n i t e s p a c e . . . Bali - left/right/east/west Polynesia - what moves fi f in i ni n it i t te e, e , , o or o r r c cy c y yc cl c li l ic i c c f f i n i t e , o r c y c l i c CVE ... The day thou gavest, Lord, is ended, When we've been here ten thousand years, The darkness falls at they behest; Bright shining as the sun, To thee our morning hymns ascended, We've no less days to sing thy praise Thy praise shall sanctify our rest. than when we first begun. As o'er each continent and island The dawn leads on, another day, The voice of prayer is never silent, Nor dies the strain of praise away. The day thou gavest, Lord, is ended, The darkness falls at they behest; To thee our morning hymns ascended, Thy praise shall sanctify our rest. We thank thee that thy church unsleeping, Amazing grace While earth rolls onwards into light, The day thou gavest, Lord, is ended Through all the world her watch is keeping, And rests not now by day or night. John Newton (1725-1807) John Ellerton (1829-93) As o'er each continent and island The dawn leads on, another day, The voice of prayer is never silent, Nor dies the strain of praise away. The sun that bids us rest is waking Our brethren 'neath the western sky, And hour by hour fresh lips are making Thy wondrous doings heard on high. So be it, Lord; thy throne shall never, Like earth's proud empires, pass away, Thy kingdom stands, and grows for ever, Till all they creatures own thy sway. We thank thee that thy church unsleeping, As o'er each continent and island While earth rolls onwards into light, The dawn leads on, another day, Through all the world her watch is keeping, The voice of prayer is never silent, And rests not now by day or night. Nor dies the strain of praise away. The day thou gavest, Lord, is ended, The day thou gavest, Lord, is ended, The darkness falls at they behest; The darkness falls at they behest; To thee our morning hymns ascended, To thee our morning hymns ascended, Thy praise shall sanctify our rest. Thy praise shall sanctify our rest. We thank thee that thy church unsleeping, We thank thee that thy church unsleeping, While earth rolls onwards into light, While earth rolls onwards into light, The day thou gavest, Lord, is ended The day thou gavest, Lord, is ended Through all the world her watch is keeping, Through all the world her watch is keeping, And rests not now by day or night. And rests not now by day or night. John Ellerton (1829-93) John Ellerton (1829-93) As o'er each continent and island As o'er each continent and island The dawn leads on, another day, The dawn leads on, another day, The voice of prayer is never silent, The voice of prayer is never silent, Nor dies the strain of praise away. Nor dies the strain of praise away. The sun that bids us rest is waking The sun that bids us rest is waking Our brethren 'neath the western sky, Our brethren 'neath the western sky, And hour by hour fresh lips are making And hour by hour fresh lips are making Thy wondrous doings heard on high. Thy wondrous doings heard on high. So be it, Lord; thy throne shall never, So be it, Lord; thy throne shall never, Like earth's proud empires, pass away, Like earth's proud empires, pass away, Thy kingdom stands, and grows for ever, Thy kingdom stands, and grows for ever, Till all they creatures own thy sway. Till all they creatures own thy sway. 6

Temple of Bel-Shamharoth, fl f l la at a t t s sp s pa p ac a ce c e e f f l a t s p a c e Discworld b be e en nt n t t s sp s pa p ac a c ce e e b b e n t s p a c e ÒThe floor was a continuous mosaic of eight sided tiles.Ó Terry Pratchett, The colour of magic h h h hy y y yp p p pe e e er rb r r b b bo o o ol li l l ic i i c c c b br b b r r ro ow o o ws w w se s s e e er r r r ( ( (i ( in i i n n nx xi x x ig i i g g gh h h ht t) t t ) ) ) st s ti t ic i ch c hi h in i ng n g g t to t o og ge g e et th t he h e er r r s s t i c h i n g t o g e t h e r data mapped in general relativity hyperbolic space curved space time hyperbolic space differential geometry projected into 2D locally euclidean patches smoothly joined ? cyberspace local vs. global ... sh s h ha a ap pe p es e s s o of o f f s s h a p e s o f co c o om mm m mu m u un ni n i it ty t y y c c o m m u n i t y 7