Our Rainbow World

8/17/2019 Our Rainbow World

1/18

OUR

RAI NBOW

WORLD

by

Otto

Rossl er,

Peter

Wei bel

A

rai nbows

ends

stand

i n a pot

of

gol d,

i t

i s

sai d

I ts

l ocati on

i ndeed

poses

probl em

si nce

i t i s

di fferent

for

every

observer

The

rai nbow

actual l y

i s a di storted

vi rtual

i mage of

the

sun

Neverthel ess

i t

l ooks

l i ke a real

obj ect

Coul d i t be

that

si ml ar

di storti ons

appl y

to

other

real

obj ects?

An

O d

uesti on

To

what

extent

depends

obj ecti ve

real i ty

on

the observer?

Si nce

the

i nventi on

of

perspecti ve

i n

the

Renai ssance,

and

the

i nventi on

of

group

theory

(Hel mhol tz-Li e-groups)

i n

the

ni neteenth

century,

we know

that

the

appearance

of the

worl d

depends

on

the

l ocati on

of

the

observer

i n

a

l awul

manner

Computer

program

of the

vi rtual -real i ty

type

accordi ngl y

generate

a

l awul l y

non-i nvari ant

(that

i s,

covari ant)

representati on

out

of an

absol ute

(i nvari ant)

one

that

i s

present

i n the

computer

memory

Even

though

the l awul

di stort i on

of

perspecti vi c

vi si on

i s

tantal i zi ng,

i t

l eaves

our

secure

sense of

an

obj ecti ve

real i ty

exi sti ng

undi sturbed


2/18

The

rai nbow

chal l enges

thi s

securi ty

Vi rtual -real i ty

program contai ni ng

rai nbows

have not

so

far

been devel oped

The transformati on

rul es

are di ff erent than

those

for

other

obj ects

The reason has to do wth the fact

that

rai nbow

i s

rather

speci al

ki nd

of obj ect t i s di storted vi rtual

i mage of

the sun

Thus, i f

the observer i s

travel l i ng, so i s

the rai nbow

f

the

observer

arti f i ci al l y i ncreases the

di stance between the eyes

by the use

of

mrrors whi ch can be

mmcked i n vi rtual -real i ty

si mul ati on by changi ng the

si ze of

the i nternal

representati on

of

the observer), the rai nbow

consi stentl y

keeps

an

i nf i ni te

di stance,

despi te

the

fact

that

i t i s

overl ai d

over

rather

cl oser- by obj ects

Whi l e

no one

doubts

that

pot

of gol d

i s

wai ti ng

at the

foot of

the rai nbow

i t i s

somewhat di f f i cul t

to

si mul ataneousl y

stay

and

watch

and

sneak toward

the

ri ght pl ace

to

catch

the pot

Thus, the

properti es

of certai n obj ects

i n

the present case

thei r l ocati on)

depend on properti es

of

the

observer l i ke

the

l atter s

l ocati on and pupi l shape) i n way

whi ch

goes

beyond

the faml ar

di storti ons

of

3-D Hel mhol tzi an

perspecti ve or 4-D

Mnkowski an proj ecti on

Coul d

i t

be that

the

pri nci pl e

i l l ustrated by the

rai nbow

i s

of

broader

si gni f i cance?


3/18

The

I nterface

between

Observer

and Rest

An

observer

who

i s

part of

the

worl d

cannot

see

that

worl d

from an

obj ecti ve

vantage

poi nt

al gori thm

o

the

f l i ght

simul ators

Newman,

Sproul l ,

1979) shows

how

generate

the

i nti mdated by

the ri ch

sequenti al l y

appl yi ng

perspecti ves, actual l y

needs

thi s

ki nd

of

packagi ng i n

order

to

extract from

i t

the

correct,

i nvari ant

representati on

The

i ntimacy

of

head

near

one s

own i s

l i ke

the l i ghts

and

doorway

of

house

(Rodney, 1991)

The homogeneous

matri x

of vi rtual

real i ty (cf

nontri vi al

task

i t i s

to

ri ght

i nterface

The

observer,

far from

bei ng

and changi ng

structure

of

the

n

pri nci pl e

there

are

many more

parameters to

try out than

those

of

observer l ocati on and si ze

Moti on

of

the observer

comes

to

mnd immedi atel y

Both

vi sual f l ow

phenomena

and

rel ati vi sti c

di storti ons

are

hereby

generated

and can

i ndeed

be

reproduced

simul ati onal l y

(Sutherl and,

1966,

1970) Next,

take

recurrent

moti ons

of

the

observer,

l i ke

shaking

of

the

head

The

effect on

the

i nterface

can be

dramati c,

especi al l y

i f the

shaking

i s

fast

I ndeed,

i rreparabl e damage

can

be

done

to

the

goal

of f i ndi ng

an i nvari ant

representati on

under

such

predi cament

Hstori cal l y,

the

i nterface probl em

was

fi rst

seen by

Boscovi ch (1755)

who asked

what

happens

when

both the observer


4/18

4

and the

surroundi ng

worl d were shri nki ng

concomtantl y, al ong

wth

o

al l

i nvol ved

forces

Obviousl y, the same impressions

woul d

be generated

wthi n the

mnd

The i nterf ace

woul d

remain

unaf fected

Siml arl y,

i

the

shaking

o

the

observer s head

i s

accompanied

by

matchi ng

shaking

o

the rest

o

the

worl d,

nothi ng

i s happeni ng for the

obsever Therefore,

time-dependent

features

o the i nterface

deserve

closer

l ook

The

I nterface Generated

by Browni an Moti on

o f

the Observer

Brownian

moti on

or

because

o

the energy

and

momentum

conservati on

observer who

i s

bui l t

out

thermal

moti on

stands i n an

wth the

rest o

the

worl d

center of

gravi ty

can

never

be moved

the

rest o

the worl d

appear

to

such

an observer?

Thi s

questi on

makes sense to

ask onl y to date

since the

necessary

simul ati on

o many

part i cl es simul ataneousl y

i s

fai rly

recent opti on

(Al der

and

Wainwri ght,

1957)

Archimedean

moti on

i s i nteresti ng

i nvol ved

Any

of part i cl es

that are i n

random

i nteresti ng

dynamcal

rel ati onshi p

Archimedes

f i rst saw that the

j oi nt

How therefore,

does

Every

external

obj ect

wl l

be

found

Brownian

moti on

rel ati ve

moti on

wl l be dependent

mass,

the l arger the

apparent thermal

agi tati on

to be

performng

a

to

the observer

The strength

o

thi s

on the obj ect s mass

The smal l er the

Thi s

i s


5/18

because

the

center

of

gravi ty

of the

observer and the

external

obj ect

are l i nked by a

rel at i ve Browni an

moti on

A very

smal l -

mass obj ect can

therefore

never

be observed

accuratel y by a

thermal l y trembl i ng

observer

The thermal

noi se

of

the observer

wl l always

i nfest the

obj ect

i n

such

way that i t i s

the

l atter

whi ch

appears to be

thermal l y agi tated

by the

temperature

of the

observer, even

i f the obj ect s

actual

moti onal

temperature were zero

The

effect

i s the

same

as i f

the observer was

Brownian

part i cl e

himel f or

hersel f

How

l ooks the

worl d

l i ke

to

a

part i cl e

i n

Brownian

moti on? The

vi rtual -real i ty

paradi gm

can

i n

pri nci pl e be used

to

fi nd an

answer

Quake

r s Worl d

Fi ndi ng the

ri ght tranqui l i ty

of mnd

to try i n

the

ri ght

way

i s not

easy

Numeri cal l y,

the

task

i s

al so very

demandi ng

Wat

i s needed

i s to desi gn

a whole

reversi bl e mcro

worl d i n

computer

The eye

i nsi de (that i s

the

i nternal

macroscopi c

observer)

i s to be

bui l t out

of the

same mcro

consti tutents

as

the

rest

The

speci al thermal

momentumconservi ng

rel at i onshi p

between

that

eye

and

part i cul ar

mcro

obj ect,

val i d i n

the computer

uni verse, can

then

be

l ooked

at by

a

human


6/18

macro observer outsi de

that

worl d

i f he wears the

ri ght

ki nd of

goggl es

t wl l be rewardi ng to impl ement

thi s

task

i n the

year

2010,

say, but even

today

i t

i s

al ready

possibl e to

gl impse some of

the unusual rai nbow

phenomena that

wl l

emanate from thi s

contrapti on

Fal se

Uncertai nty

An i rreduci bl e uncertai nty

i s a

fi rst

impl i cati on The

chaos

i n the

observer transl ates

i nto chaos

outsi de the observer

Apart from

the

uni t

thermal noi se

energy

i nside

the

observer

E , which

i s equal to one

hal f

the

Bol tzmann

constant

times

the

temperature

of the

observer,

we

have

second i ntri nsic constant

T

Thi s

characteri sti c

time

i nterval

i s rel ated to

the

mean

col l i si on

i nterval i nsi de the

observer

After thi s

time

i nterval

has passed, the

mcro dynamcs i nsi de

the

observer

changes course rel ati ve

to the

external

obj ect

A preci se

cal cul ati on

of T

for

cl assi cal bi l l i ard

system

i s

an

open

probl em RBssl er,

1991a The

mean

shaki ng peri od T needs

further cl ari f i cati on

from

a

conceptual

poi nt

of

vi ew

as wel l

I f the observer was

al one i n the

uni verse wth

the obj ect, the

center of

gravi ty

of the observer and

that

of the

obj ect woul d

not

perform

a Browni an moti on

rel ati ve

to each other

However,


7/18

as

soon

as any

thi rd

obj ect (for exampl e,

a

medi ati ng

parti cl e)

i s

coupl ed

to

the

observer,

i t

i s

onl y toward thi s

combi ned

set

that the external

obj ect

remai ns i n a

state

of

constant

moti on

The

mul ti -parti cl e

observer now

i ndeed i n general

reverses

course, every

uni t

time i nterval

T rel ati ve to the

external

obj ect

The

resul ti ng

rel ati ve

di f f usi on between

external

obj ect

and observer

i s governed by

the product

of

E

and

T

di vi ded

by the

obj ect s mass

M

Thi s

resul t

hol ds

true

when

the

external

obj ect

i s di rectl y

(that

i s, wthout a

measuri ng

chai n)

coupl ed

to

the observer

(R6ssl er,

1987)

Unexpectedl y,

the

more

general

case

of i ndi rect

coupl i ng (vi a a measuri ng

chain) i s

sti l l governed

by the

same

l aw si nce the

measuri ng

chai n i s

unabl e to

undo

the

obj ecti vel y exi sti ng

mutual

rel ati onshi p

between

observer

and

obj ect

The

resul ti ng

uncertai nty

mmcs

quantummechani cs

Thi s

i s

because the

presence of

a

di f f usi on

l aw of the same

qual i tati ve

type

as descri bed

above

(an

acti on

l i ke E

times

T

di vi ded

by

the

obj ect s mass)

i s

suf f i ci ent

to

generate

the

Schr6di nger

equati on

(Fenyes,

1952 Nel son,

1966)


8/18

Fal se

Certai

nty

We

sti l l

need to know

what

happens

wh r the observer

forces

mcro obj ect

i nto

certai n

def i ni te

observati onal

state

For

example,

the

measurement si tuati on

may

be

chosen such that the

mcro

obj ect must

reveal i ts

posi ti on i n

yes-or-no

deci si on

The

probl emon

hand

i s

analogous to

the probl em

of

the

formati on

of

an

ei gen state

i n

quantummechani cs

Such

restri cti ng

type

of

measurement can

certai nl y

al so

be

performed

i n

our

si mul ated

worl d

Here

new

phenomenon

ari ses

Whi l e

the previous

f i ndi ng

uncertai nty)

di d not

yet

qual i fy as

rai nbow

phenomenon

i n the

stri ct sense si nce

mere

bl urri ng does

not bri ng i n

new

phenomenol ogical

qual i ty,

i n the present

case

new

qual i ty

emerges

t i s

the qual i ty

of

wel l -def i ned

l ocal i zati on

i n

posi ti on space

or momentumspace,

respecti vel y)

appeari ng for

the observer whi ch

i s at

vari ance

wth the correct

l ocati on

For i f the

observed

l ocati on

of

the

obj ect

were

i denti cal

wth

the correct

l ocati on,

the

rel ati ve

Browni an moti on

of

the

observer

woul d

have

been el imnated

i n effect

even

though

thi s

cannot

happen

Therefore,

the apparent

l ocati on

of the

obj ect,

val i d i n the

i nterface,

i s

di f ferent

from the

obj ecti vel y

appl yi ng

l ocati on


9/18

Thi s

predi cti on can be veri f i ed

i n

the proposed simul ati on

of

the

i nterface

Si nce everythi ng that happens i n

the

simul ati on

i s known expl i ci tl y, i t i s

possi bl e to compare

the content of

the i nterface wth what

real l y

happens to the part i cl e i n

questi on

Thi s

compari son

i s of

course,

a

pri vi l ege

confi ned

to the

external operator

si nce the

i nternal

observer i s

stuck

wth the

i nterface

The

yes-or-no deci si on whi ch

appears on

the

i nterface depends

on

the i nternal dynamcs

of

the observer

as

much as on the

obj ect s

Accordi ng

to

Nel son s

(1966) stochasti c

mechani cs,

that i s

di ffusion

theory,

the probabi l i ty

of a

certai n

deci si on

occurri ng

depends on the square

of

the ampl i tude

of

the

di f fusi on-generated

Schrodi nger equati on

Thi s di ffusi on-

theoreti cal

resul t

can be expected to be conf i rmed

once

the

fi rst simul ati on

of

the i nterface becomes avai l abl e

However,

there i s a

compl i cati on

to be

expected

i n that case

whi ch i s

absent

i n the standard formal i sm

of

stochasti c

mechani cs I n

the l atter, the

occurri ng deci si ons

( ei genstates ) are assumed

to be permanent

Here,

the di stort i on

of

the

obj ecti ve worl d

i s

such

that

the

recorded

state, as

i t

appears i n

the

i nterface,

depends on the

momentary

state of

moti on

of

al l part i cl es i nsi de

the observer

n

other words, the i nterface

i s a

momentary

state

of

affai rs

A l

measurements,

no matter how

l ong

the

measuri ng chai n

i n term

of

space and

time, are

determned

by


10/18

1

the

momentari l y

val i d rel ati onshi p

between

the

i nternal dynamcs

of

the

observer

and the

dynamcs

of

the

rest

of

the

worl d

An

external

super-observer

who watches

the

i nterface

as a

functi on

of

tim

wl l therefore

record

a

superposi ti on

(that

i s

a temporal

i ntegrati on)

over

al l

the

momentari l y

val i d

quantum

decisi ons

The

momentari l y

val i d

of

ei gen

worl ds,

whi l e

mutual l y

di fferent,

al l

fal l

wthi n

the

probabi l i ty

di stri buti on

prescri bed by the

wave functi on

of

stochasti c

mechani cs

momentary

I n

quantum

mechani cs

a

siml ar

probl emi s known

under

the

nam

of

the

measurement probl em

For

example,

i n

the

l anguage

of

Everett s (1957)

rel ati ve

state

formul ati on, the

di fferent

ei gen

worl ds

that appl y

at

every

moment are

sai d

to

be

shi el ded

from

each

other

There exi sts

one versi on

of

Everett s

formal i sm

(due

to

Bel l ,

1981)

i n which

the

di fferent

ei gen worl ds

are assumed

to

exi st, not

simul ataneousl y

as in the

usual

Everett

pi cture

but

sequenti al l y

each

confi ned

to a

very

smal l

tim

wndow

Bel l onl y

wanted

to show

the

mathemati cal

equi val ence

of

thi s

vi ew

wth

the standard,

mul ti pl e-worl ds

i nterpretati on

Both

i nterpretati ons

of

quantum

mechani cs are

usual l y

consi dered

rather

outl andi sh

Here,

the second

i nterpretati on

unexpectedl y

ari ses

agai n

i n a

qui te

di f ferent

context


11/18

Bel l s

i nsi ght that

the observer

woul d not

noti ce

bei ng

i n

a

di fferent

quantum

worl d from

one

moment to the

next

(since

worl ds

by

defi ni ti on

are

complete,

that i s contai n

no trace

of

another

worl d)

i s

appl i cabl e

here as

wel l

I t

fol l ows that

the

i ntegrati on whi ch

an

outsi de

observer

of

the

si mul ated

i nterface

experi ences

i s

an

art i fact

I f

the outsi de

human

observer

were

a part of

the

same i nterface,

bei ng

unabl e

to

escape from

i t

through

the

use

of

an

outsi de memory,

the

phenomenon

of

i ntegrati on

woul d

di sappear and

a

si ngl e

consi stent

ei gen

worl d

woul d appl y

at every

moment,

complete

wth i ts

own

recorded

past and

anti ci pated future

Thus,

the

j ob of

a

demurge

to

noti ce the

impl i cati ons

that hi s own

acti ons

(l aws

and

i ni ti al

condi ti ons)

generate for

the

i nhabi tants

i s

surpri singl y hard

A New

Type

of R

ainbow

The

di storti on of

an obj ecti ve

worl d

as

i t i s

mrrored i n an

i nterface

thus can

go unexpectedl y

far The

noti on

rai nbow

worl d

appl i es to

each di storted

representati on no

matter how

short- l i ved

I n

the one worl d,

for

exampl e,

Schrodi nger s

cat

i s

al i ve and

wel l

whi l e

i n the other,

the

same hel l i sh

contrapti on

(Schrodi nger,

1935) has

chosen the

other course

Moreover,

that

same

branchi ng

may

have

taken

pl ace

some whi l e

ago,

so that the

one

outcome

woul d have

produced

a

cat

that i s


12/18

12

pl ayful

and fri sky

ri ght

nowwhi l e

the

other

entai l s

a

cat that

has

been

subj ected

to

organi c

decomposi ti on

for

qui te

a

whi l e

I t appears very

hard to reconci l e

both

rai nbow

worl ds wth

one

and the

same

exo

real i ty

Equal l y hard

to

accept

i s

the cl aim

that

these

two

di f ferent

i nternal

refracti ons

of

the

same

obj ecti ve

real i ty al ternate

at

a

rapi d pace

i n an

unnoti ceabl e

way

Thi s

rai nbow

movi e

one

time

sl i ce

after the other)

accordi ngl y

contai ns many

consi stent

sub-movies

of whi ch a

di f ferent

one i s

i n

charge

at every

moment

The

counteri ntui ti ve

noti on of

a

rai nbowmovi e

needs

further

scruti ny

One

of

i ts

features,

however,

unexpectedl y

i s

very

cl ose

to

everyday

experi ence

I t

i s

the

fact

that

each moment

has

i ts

own

worl d

ei gen

worl d)

I n

quantum

mechani cs, the

same

1

rel ati onshi p

was

noted by

Deutsch

1986)

Here, the

same

resul t

ari ses

i n

a

compl etel y

trnsparent

context

provided

al l

di ff i cul ti es have

been mastered)

The

i nhabi tants

of a

reversi bl e uni verse

are

strangel y gl ued

to

a

si ngl e

moment i n

time They

cal l i t

thei r

worl d as

i t i s real

now

Whi l e

the

mutual

i ncompati bi l i ty

of the

di f ferent

now

worl ds

l acks

a

representati on

i n the

i nterface

as

menti oned,

the

i nterface

stil l

gi ves

away the fact

that

a

si ngl e

i nstant

i n

time

i s

pri vi l eged over

al l others

because

i t

def i nes

a

worl d


13/18

3

The l atter predi cti on exi stence of a nowworl d

for

i nternal

i nhabi tants

i s

when transpl anted back

to

our

own

worl d,

at

vari ance wth

tradi ti onal sci ence

which

l acks the noti on

of a

pri vi l eged now

The paradi gmof vi rtual real i ty has

made the topi c

of

the

i nterface sci enti f i cal l y

acceptabl e (cf

Ars

el ectroni ca,

1986

Weibel ,

1990)

The momentary posi ti on

of

the camra

di storts

the worl d i n a

way whi ch makes

i t

ful l y

pal pabl e

as

an

i nvari ant new real i ty

Generati ng

such

an i nterface

i s

not easy

and requi res a

l ot

of computer

processi ng

power

Experimenti ng

wth

thi s

i nterf ace i s presentl y

an important technol ogi cal

and

conceptual

chal l enge

How for

example, Looks a

rai nbow i nside

when

i t

i s

reduced by the

verti cal

pupi l

of a

cat rather

than

by

a round

one?

How

about a cat s pupi l

that

i s

many mters

l ong,

ei ther verti cal l y

or

hori zontal l y?

A second

novel

questi on

refers

to

temporal l y

changi ng

real i ti es

i f

the changes occur

i n

both the posi ti on

of

the

eye

and

that of the external obj ect

i n

a

correl ated f ashi on

Such

changes

wl l

obvi ousl y not

show

up

in

the

i nterface

(si nce the

Boscovi ch di f f erence

i s zero Rossl er,

1991b)

Thi rd, there

i s

a

very

special

i nterface,

generated

between

a

mcroscopi cal l y


14/18

4

descri bed

reversibl e

observer

and the

rest

o

the

same

mcroscopi cal l y simul ated

worl d

Phenomena onl y

known

fromthe

counteri ntui ti ve

realm of quantummechani cs suddenly

ari se

as

impl i cati ons

of conceptual l y

compl etel y transparent si tuati on

At the

same

time nowness-bound

rai nbow

worl ds become a

topi c

for

sci enti f i c di scussion

Thus

pl ayi ng wth cameras

can be a rewardi ng

pastime

Dverse phenomena

known

f rom

everyday experi ence

can be

retri eved

At the same

time

a new

type

of suspi ci on regardi ng

our

own worl d ari ses Maybe our own worl d

i s

rai nbow

worl d

too?

Once

such a suspi ci on

has taken hold the logi cal next step

i s to cal l for newdi agnosti c tool s

that

can be

used

i n our own

worl d to demonstrate the exi stence

o

the

new

predi cament and to

expl ore and perhaps mani pul ate i t

Neverthel ess the deci sive

step

i s

getti ng

suspi cious i n the f i rst

pl ace

The present

suspi cion

which

goes

back to

Kant

and Boscovich and before

them

to

Anaximander

has now

found

a

new

medi um

for

i ts

study

To

concl ude

the

concept

of the

rai nbow

has

been

re-examned

from

the vantage poi nt

of

vi rtual -real i ty

simul ati ons

A

rather

unusual type

of vi rtual

real i ty i s needed for such a simul ati on

Eventual l y reversibl e

simul ated

worl ds

wl l be useful to

further

the understandi ng of the human/worl d i nterf ace a


15/18

i s

proposal

w i

at

fi rst si ght

i s

conf i ned

to the

study of

an

i ce

scater

who cannot

get ri d

of

whol e-body angul ar momentum

or of

an

Archimedean

system

of

i nteracti ng

bal l s and spri ngs

l i ke

a

model

drug

molecul e)

The fi rst

detai l ed

report about

the

properti es

of

such a

conservati ve

vi rtual real i ty

wl l come

i n

i n

about

ten

years

time

Presentl y,

onl y

i nformed

guesses

are

possi bl e

I n thi s

way,

a

new

hopeful

suspi ci on

coul d be

arri ved

at

:

The VR

paradi gm

may reveal

more

about

our

own

worl d

than

the

ordi nary

course of

sci ence

has

prepared

us

to bel i eve

For

exampl e,

the wal l s

of

the

pri son of

the now

become

pal pabl e

Further

di storti ons

of the

i nvari ant

exo) real i ty

may

exi st

whi ch

can l i kew se

be

unmasked by the

newHermeti an

paradi gm

of

computer-generated

worl ds

For

J O

R

Otto

RbSSLER

Uni versi ty

of

Ti l bi ngen

Peter

WEIBEL

I nsti tute

for

New

Medi a

Frankfurt-Mai n


16/18

Bi bl i ography

to

ALDER,

B J

WAINWRIGHT, T E

Phase

transi ti ons for

a hard-

sphere

system,

J ournal of Chemcal Physi cs 27

1957,

p

1208

ARS ELECTRONCA

1988,

Phi l osophi es of the New Technology/

Phi l osophi en

der neuen

Technol ogi e

Berl i n

1986

BELL, J

S

Quantum mechani cs

for

cosmol ogi sts , i n

C J

I sham R Penrose, D Sci ama, eds

Oxford,

Carendoi i

Press

1981, p

611-637

BOSCOVICH

R J

De spati o et tempore, ut a nobi s

cognoscuntur On

space and

time, as

they

are

recogni zed by us) ,

J M

Chi l d,

ed

Boscovi ch,

R J

Theory

of

Natural

w

Phi l osophy, Lati n-Engl i sh

Edi ti on

Open

Court,

Chi cago 1922,

p

404-409

Repri nt

of

the

Engl i sh

translati on

:

MT

Press,

Cambri dge,

Mass

1966,

p

203-205 Engl i sh re-translati on i n

R6ssl er

1991b)

Compare

al so : Fischer 1991)

DEUTSCH D

Three connecti ons between

Everett s

i nterpretati on and experiment , i n R

Penrose, C

J

I sham eds

QuantumConcepts i n

Space and Time

Cl arendon

Press,

Oxford

1986,

p

215-225

EVERETT,

H

I I I , Rel ati ve state

formul ati on

of

quantum

mechani cs , Revi ew of Modern Physi cs

29 1957, p

454-462

FENYES, I

A probabi l i ty-theoreti cal foundati on and

i nterpretati on of quantummechani cs i n

German), Zei tschri f t

fur

Physi k

132,

1952, p 81-106


17/18

1 7

FI SCHER,

R. A

neurobi ol ogi cal

re-i nterpretati on and

veri fi cati on

of

Boscovich

covari ance,

postulated i n 1758 ,

Cyberneti ca

34,

1991,

95-101

NELSON, E . Deri vati on of

the

Schrodinger

equati on

from

Newtoni an mechani cs ,

Physics Review 150,

1966,

p

1079-1085

NEWMAN, W M

SPROULL,

R F

Pri nci pl es of

I nteracti ve

Computer Graphi cs

2nd

ed.

McGrawHl l , New

York

1979

RODNEY,

T

.

The

Runaway

Soul

Farrar, Straus

and Groux,

New

York 1991

R6SSLER, O

E

.

Endophysi cs , i n

J

. L

Casti ,

A

Karl qvi st,

eds

. Real

Brains, Arti f i ci al Mnds

North-Hol l and,

New

York

1987, p

25-46

Four

open

probl ems i n

four

dimensi ons ,

i n G Baier,

Klein, eds .

A Chaoti c Herarchy

Worl d

Scienti fi c,

Singapore

1991a, p

365-369

Boscovich

covari ance , i n J

L

Casti ,

A

Karlqvi st,

eds

.

Beyond Bel i ef

: Randomness

Predi cti on

and Expl anati on

i n

Science

CRC

Press, Boca Raton

1991b, p 69-87

P

WEIBEL,

The

two

l evel s

of

real i ty, exo and

endo ,

i n Y

Shi kata, ed. Art

Lab

1st

Symposium

The

Current

Condi ti on

and

the Future of

Dai tal Art Canon,

Tokyo

1991, p

16

SCHRODNGER,

E

.

The

present situati on

i n

quantummechani cs

i n

German),

Naturwssenschaften

23

1935,

p

807-812 ;

823-828

;

844-849

Engl i sh

translati on

:

Proceedings

of the Ameri can

Phi l osophi cal

Society

124, 1980, p

323-338


18/18

1 8

SUTHERLAND

I

E

Computer

i nputs

and

outputs ,

Sci enti f i c

Ameri can

1966,

September i ssue

Computer di spl ays ,

S-i ezti f i c

Ameri can

1970,

J une

i ssue

WEIBEL, P

.

Vi rtual worl ds : The

emperors new

bodi es ,

i n G

Hatti nger,

M Russ el C

Sch6pf,

P

Wei bel ,

eds

Ars

el ectroni cs

1990 vol 2 Veri tas-Verl ag

Li nt, Li nz

1990,

p

9-38

B

OKane, Das

tangi bl e

Bi l d Endoapproa

ch

to

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i n

M Waffender,

ed

.

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Rowohl t, Reinbek

1991,

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(March

8

1992)

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