Welsh Mathematician walks in Cyberspace

1. Welsh Mathematician walks in Cyberspace Alan Dix Lancaster University, vfridge and aQtive http://www.hiraeth.com/alan

2. model ? 14 understanding space real space

3. model ? Lober giny aghin tyu mjfhi gta not jkrt uyos Lober giny aghin tyu mjfhi gta not jkrt uyos Lober giny a ghin tyu mjfhi gta not jkrt uyos Lober giny a ghin tyu mjfhi gta not jkrt uyos Lober giny a ghin tyu mjfhi gta not jkrtu yos Lober giny a ghin tyu mjfhi gta not jkrtu yos understanding cyberspace cyberspace

4. maps myth &magic mazes mathematics sources

5. cognition community constructedenvironment computation sources

6. Clay tablet map 2200 BC Yorghan Tepe,Iraq

7. Egyptian garden 1400 BC garden of a high court official of Amenhotep III at Thebes

8. Wales John Speed1610

10. drawings cartographic (isomorphic) cartographic (homomorphic) schematic linear episodic

11. journeys always linear Kendal Manchester Airport Newark San Francisco

12. labrynth

13. Euclid Descartes x, y, z Pythagorus 2D/3D but is it realand is it natural

14. seeing in 3D which is closer?

15. real is easy which is closer?

16. 2D navigation walking vs. helicopter Poincare property tunnels and flyovers

17. manipulate in 3D see in 21/2 D navigate in 2D

18. properties of space closeness and connectedness fixed orientation/centre flat infinite objective

19. b c a topology neighbourhoodsopen and closed sets limits awareness models nimbus, focus, etc. Benford et al. closeness metric spaces D(a,c)  D(a,b)+D(b,c)

20. awareness reformulated! Rodden connectedness graph theory arcs and points architecture

21. Hillier space is the machine

23. symmetry directedgraphs one-way streets hyperlinks symmetry

24. fixed centre fixed orientation

25. T-O mapof the world Isidore of Seville 560-636 AD

26. Pietro Vesconte's World Maps, 1321,from Marino Sanudo's Liber secretorum fidelium crusis http://www.henry%2ddavis.com/MAPS/LMwebpages/LM1.html

27. mappa mundi HerefordCathederal 1300 AD

28. View of the World from 9th Avenue Saul Steinberg 1975

29. Piaget could you see B from A A B

30. Donaldson can Ann see Bob Ann Bob

31. viewpoints Bali - left/right/east/west Polynesia - what moves CVE ...

32. infinite space ... finite, or cyclic

33. When we've been here ten thousand years, Bright shining as the sun, We've no less days to sing thy praise than when we first begun. Amazing grace John Newton (1725-1807)

34. 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. 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, While earth rolls onwards into light, Through all the world her watch is keeping, And rests not now by day or night. 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. The day thou gavest, Lord, is ended John Ellerton (1829-93)

35. We thank thee that thy church unsleeping, While earth rolls onwards into light, Through all the world her watch is keeping, And rests not now by day or night. 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, While earth rolls onwards into light, Through all the world her watch is keeping, And rests not now by day or night. 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. The day thou gavest, Lord, is ended John Ellerton (1829-93)

36. 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, While earth rolls onwards into light, Through all the world her watch is keeping, And rests not now by day or night. 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. The day thou gavest, Lord, is ended John Ellerton (1829-93)

37. flat space bent space

38. Temple of Bel-Shamharoth, Discworld “The floor was a continuous mosaic of eight sided tiles.” Terry Pratchett, The colour of magic

39. hyperbolic browser (inxight) data mapped in hyperbolic space hyperbolic spaceprojected into 2D

40. stiching together general relativity curved space time differential geometry locally euclidean patches smoothly joined ? cyberspace local vs. global ...

41. shapes of community

43. vfridge collaboratively building structure in space

44. close collaboration

45. parallel reality portals and gateways coexistent worlds mabinogionubiquitous computing

46. in conclusion there’s more to space than three dimensions