? Lancaster University, vfridge and aQtive - - PDF document

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? 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


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SLIDE 1

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W W W We e e el l l ls s s sh h h h M M M Ma a a at t t th h h he e e em m m ma a a at t t ti i i ic c c ci i i ia a a an n n n w w w wa a a al l l lk k k ks s s s i i i in n n n C C C Cy y y yb b b be e e er r r rs s s sp p p pa a a ac c c ce e e e

Alan Dix

Lancaster University, vfridge and aQtive

http://www.hiraeth.com/alan

?

u u u un n n nd d d de e e er r r rs s s st t t ta a a an n n nd d d di i i in n n ng g g g s s s sp p p pa a a ac c c ce e e e

real space

model

14

model

Lober giny a ghin tyu mjfhi g ta not jkrt uyos Lober giny a ghin tyu mjfhi g ta not jkrt uyos Lober giny a ghin tyu mjfhi g ta not jkrtu yos

cyberspace

?

u u u un n n nd d d de e e er r r rs s s st t t ta a a an n n nd d d di i i in n n ng g g g c c c cy y y yb b b be e e er r r rs s s sp p p pa a a ac c c ce e e e

Lober giny a ghin tyu mjfhi g ta not jkrt uyos Lober giny a ghin tyu mjfhi g ta not jkrt uyos Lober giny a ghin tyu mjfhi g ta not jkrtu yos

s s s so

  • u

u u ur r r rc c c ce e e es s s s m m m ma a a ap p p ps s s s m m m my y y yt t t th h h h & & & & m m m ma a a ag g g gi i i ic c c c m m m ma a a at t t th h h he e e em m m ma a a at t t ti i i ic c c cs s s s m m m ma a a az z z ze e e es s s s s s s so

  • u

u u ur r r rc c c ce e e es s s s c c c co

  • g

g g gn n n ni i i it t t ti i i io

  • n

n n n c c c co

  • m

m m mm m m mu u u un n n ni i i it t t ty y y y c c c co

  • m

m m mp p p pu u u ut t t ta a a at t t ti i i io

  • n

n n n c c c co

  • n

n n ns s s st t t tr r r ru u u uc c c ct t t te e e ed d d d e e e en n n nv v v vi i i ir r r ro

  • n

n n nm m m me e e en n n nt t t t

Clay tablet map

2200 BC

Yorghan Tepe, Iraq

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SLIDE 2

2

Egyptian garden

1400 BC

garden of a high court

  • fficial of

Amenhotep III at Thebes

Wales

John Speed

1610

d d d dr r r ra a a aw w w wi i i in n n ng g g gs s s s

cartographic (isomorphic) cartographic (homomorphic) schematic linear episodic

j j j jo

  • u

u u ur r r rn n n ne e e ey y y ys s s s always linear

Kendal Manchester Airport Newark San Francisco

labrynth

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SLIDE 3

3

2 2 2 2D D D D/ / / /3 3 3 3D D D D

but is it real and is it natural

Euclid Descartes

x, y, z

Pythagorus

seeing in 3D

which is closer?

real is easy

which is closer?

2 2 2 2D D D D n n n na a a av v v vi i i ig g g ga a a at t t ti i i io

  • n

n n n

Poincare property walking vs. helicopter tunnels and flyovers manipulate in 3D see in 2 1/2 D navigate in 2D

p p p pr r r ro

  • p

p p pe e e er r r rt t t ti i i ie e e es s s s

  • f

f f f s s s sp p p pa a a ac c c ce e e e

closeness and connectedness fixed orientation/centre flat infinite

  • bjective
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SLIDE 4

4

c c c cl l l lo

  • s

s s se e e en n n ne e e es s s ss s s s

metric spaces

D(a,c) ≤ D(a,b)+D(b,c) a b c

topology

neighbourhoods

  • pen and closed sets

limits nimbus, focus, etc. Benford et al.

awareness models

c c c co

  • n

n n nn n n ne e e ec c c ct t t te e e ed d d dn n n ne e e es s s ss s s s

graph theory

reformulated! Rodden

awareness

arcs and points

architecture

H H H Hi i i il l l ll l l li i i ie e e er r r r

s s s sp p p pa a a ac c c ce e e e i i i is s s s t t t th h h he e e e m m m ma a a ac c c ch h h hi i i in n n ne e e e

s s s sy y y ym m m mm m m me e e et t t tr r r ry y y y

directed graphs

  • ne-way streets

hyperlinks

s s s sy y y ym m m mm m m me e e et t t tr r r ry y y y

f f f fi i i ix x x xe e e ed d d d c c c ce e e en n n nt t t tr r r re e e e f f f fi i i ix x x xe e e ed d d d

  • r

r r ri i i ie e e en n n nt t t ta a a at t t ti i i io

  • n

n n n

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SLIDE 5

5

T-O map

  • f the world

Isidore of Seville 560-636 AD

Pietro Vesconte's World Maps, 1321,

from Marino Sanudo's Liber secretorum fidelium crusis

http://www.henry%2ddavis.com/MAPS/LMwebpages/LM1.html

m m m ma a a ap p p pp p p pa a a a m m m mu u u un n n nd d d di i i i

Hereford Cathederal

1300 AD

View of the World from 9th Avenue

Saul Steinberg

1975

Piaget

could you see B from A

B A

Donaldson

can Ann see Bob

Bob Ann

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SLIDE 6

6

viewpoints

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

i i i in n n nf f f fi i i in n n ni i i it t t te e e e s s s sp p p pa a a ac c c ce e e e . . . .. . . .. . . . f f f fi i i in n n ni i i it t t te e e e, , , ,

  • r

r r r c c c cy y y yc c c cl l l li i i ic c c c

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.

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)

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 John Ellerton (1829-93)

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.

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 John Ellerton (1829-93)

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.

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 John Ellerton (1829-93)

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.

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SLIDE 7

7

f f f fl l l la a a at t t t s s s sp p p pa a a ac c c ce e e e b b b be e e en n n nt t t t s s s sp p p pa a a ac c c ce e e e

Temple of Bel-Shamharoth, Discworld 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 r r rb b b bo

  • l

l l li i i ic c c c b b b br r r ro

  • w

w w ws s s se e e er r r r ( ( ( (i i i in n n nx x x xi i i ig g g gh h h ht t t t) ) ) )

data mapped in hyperbolic space hyperbolic space projected into 2D

s s s st t t ti i i ic c c ch h h hi i i in n n ng g g g t t t to

  • g

g g ge e e et t t th h h he e e er r r r

? cyberspace general relativity

local vs. global ... curved space time differential geometry locally euclidean patches smoothly joined

s s s sh h h ha a a ap p p pe e e es s s s

  • f

f f f c c c co

  • m

m m mm m m mu u u un n n ni i i it t t ty y y y

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SLIDE 8

8

vfridge

collaboratively building structure in space

c c c cl l l lo

  • s

s s se e e e c c c co

  • l

l l ll l l la a a ab b b bo

  • r

r r ra a a at t t ti i i io

  • n

n n n

p p p pa a a ar r r ra a a al l l ll l l le e e el l l l r r r re e e ea a a al l l li i i it t t ty y y y

coexistent worlds portals and gateways

mabinogion ubiquitous computing

i i i in n n n c c c co

  • n

n n nc c c cl l l lu u u us s s si i i io

  • n

n n n

thereÕs more to space than three dimensions