Constancy and contrast IIIA

Acta Psychologica 25 (1966) 222-292; @ North-Holland Pubhbhing Co., Amstmtim * Not to be mprodme3by photoprintor microfilmwithout*written

CONSTANCY AND CONTRAST IIIA * H, K. W. MOEI:,

coN’rEms

OF PAFCr IlIa

6. TABLESOF DEVIAZIONS . . . . . . . . . . . . . . . . . . . . s . .p. 222 222 6.1. Objectively determined deviations ............... 224 6.2. Subjectively determinei deviations ...............

7.

....................... sPECIALEX.PEKSMEN’K§

7.1. General remarks ....................... 7.2. The standard case. ..................... 7.3. specialcase&. ........................ 8. AMBI<4uiw07: THEOBJECTIVE STIMULUS............... 8.1. Br@tness deviations ..................... 8.2. Contrast deviations ...................... 8.3. Objective brightness value and the objet’ e stimulus 8.4. The mirror model ......................

......

234 234 246 257 2

Part III of the paper completes the synthesis in the description of ‘constancy” and ‘contrast’: in any experiment they are complementary parts in the perception of the objectively determined whole. From a description of the process of perception a personal constant is defined as the individual value of the relative distance from objective? reality: four diffe modes of perce#on itself are distinguished. The objective and subjective descriptions of phenomenal reality are shown to converge at one point, viz., the concept of identity; the corresponding metrios a hyperbolic and elliptic respectively. ‘The usual ‘lens model’, relating to causal trams of events, does not fit in with the present description; a ‘mirror model’, pointing to a final cau jn pe?;twqtier a, Ie dekleloped instead. 6.

TALUS OF DEVIATIONS

6.1. Objectively Determked Deviations

From the average resrllts of the evaluations of the backgrounds (table 7) the relative deviations have been calculated by means of [29]. -+ Parts 1, IJ: Acta Psych., 1964, 22, 272-320; 1965, 24, 99-166. 222

~O~STAN~~

AND CONTRAST lIIA

223

’ thus found are given in table 17, their values being lly with respect to the standard value (tan 6’ = 0).

yI block); left: shaded; ri t: fully lighted j

/ .OOOj -.495

b-g

) --.878 / --G

ns of the illumin tions have been calculated from he ~v~l~~ationsin table 8, by means of [33], [35] he values of ea, e’ an tan ‘xi’ are given in table 18. TABLE18

Relative deviations of illuminations @:-- 1 :1.48 I : 3.74 1 : 13.0

i ’ ,

e’==l.OOO 0.396 0.114

i

) 1

tan&i’=.000 .433 .796

Fir,ally, in table 19 the values of tan bi’ and tan 8’ are compared

with the standard values calculated from geometric series [71] of two and of three steps. TAW.E 19

~~rn~~~$~n with standard arrangements

As already mentioned in section 5.7 (fig. 19) the present arrangement deviates wkely from the standard type II, but it might be cLjmpared with standa:*d type III (some elements missing). One value of tan 0~1’is missing, since a non-translucent screen has not been used. The omission of a second grey sha.de of the backgrounds appears to be compensated by the two values .88 and .49 which arise from poles g-b and w-g not lying on one and the same line of contrast c (figs. 10 and 11).

224

H. K. W. MOED

6.2. Srcbjectivelylktermiped Deviations

From the readings WDand WI.,in tables 10-12 the relative deviations of the cards have been calculated for all the adaptations to subjective equality. The deviations tan y’ thus found are given in tables their values being arranged in rows after the common valu cards, and in columns under the va!ues tan oci’and tan /I’ of conditions. The three columns in ~he middle of each table do not differentiate objecti-.-cty,since they have the same value of tan #Y(===. from left to rig&6 these columns correspond to experiments with two black, tv. o ;ley, and two white backgrounds respectively, as in tables 10-12. The order of the outer columns deviates from that in tables 1042, their values of tan #3’being ranged symmetrically with respect to the standard value, as in table 17. In table 23 the mean values of tan y’ are given, calculated for each column separately, and, moreover, for the three middle columns taken together, TABLE 2x) Relative deviations, no shading

.oo

.oo

.oo

.oo

/ .96

.88

.49

.OO

.OO

.oo

-.49

-.88

-.96

12.9 . . .

)

22.5 . . .

. /

. . . .

.45 .51 .49 .56 .55 .58 .55

.36 .4*5 .46 A4 A6 .46 .4§ .45

.29

“11 .03 -.01 .Ol -.Ol -.05 -.03 -.O6

.12 .19 .ll .I1 .I1 .09 .05 .OS

-Al -.32 -.31 -.32 -30 -.35 -.31 -.25

-.33 -.30 -.36 -A0 -.35 -.35 -.23 -.19

-.48 -.49 -.46 -.50 -A6 -.50 -.47 -.46

.59

.48

.28

-AM

.OS

-.34

-*IS

~$6

. . . .

.61

. . . .

A0

* . . .

.26 .18 .18 -22 .26 .28 .28

.OO .OO .Ol .O2 .02 .06 .Ol

.(13 .Ol .02 ,02 .Ol .02 .Ol

- 34 -.33 -.3O -.27 -.24 -.2O -,13

-.14 -.12 -.13 -.a9 -.07 -.OS -.ll

-.4S -A0 -,38 ~32

o . . .

.59 .57 .55 .54 .55

.37 .29 .34 .28 JO .28 .23

321.3 . . . .

.51

.26

.25

.06 .08 .08 .06 .08 *lo .ll .06 .lO .O4 .06 AM .07 A4 .OS *IS .u7 .06 .02 AH

97.4 . . . .

.03

AM?

.03

.Ol

j

tan (9’

32.1 37.6 48.5 57.8 70.4 81.5

. . . . /

. . . * a . .

.

. . . * . . * .

116.8 133.3 156.0 180.0 205.3 236.8 274.4

. 5. . . . . . . . . .

.oo

, .oo ---

.oo

tan c41

__--~

44

.35 .39 .34 .30 -28 .29 -27

360.0 . . . -/ P-e

--

-

WD

!

l--l

--

s-w

tan r’

.oo

-

225 TABLE 21

Relative devotions, sli ----

I._

”

.21 .2l .I3 .12

.3

$9.8 90.4 83.5 97.4 116.8 133.3

.

A5

I

*.

.,

.

.

*

f

.

.

s

‘

.

.

.

. . . . .

. . . . .

* . . * .

* a *

.68 . 7

.

. . . .

. . . .

* . . .

31

.l

-.96

.13

-.12

-.31

-.69

.22

-.2O

-.30

-.63

.27 .23 .68 ,18 .16 .15 .lO .lO AI4 .06 .OO

-.21 -.20 -.26 -.33 -.29 -.32 -.42 -.42 -A0

-.42 -.43 -.33 -.31 -.23 -.21 -.18 -.17 ~16

-.63 -.65 -.60 -.59 -.57 -54 -.51 -.45

-.38

-.16

. . . .

.51 .49 .46 -46 . .43 .42 A0 .36

.09

.70

‘51 .49 .a .48 .49 A7 .45 .36 .30

.I9 .I8 .I7 .I5 .19 .15 .13

.I1 .t2 .10 .Ol -. -. -.02 -.02

.

.29

.34

.16

.04

.67

.25

.32

.14

.w

-.06

A8 .83 ‘80 .80

.24 .24 .25 .27

.33 A0 .43 .47

.15 .15 .12 .13

.03 .04 .04 .I2

-.03 -.03 .oo .oO

.

. 1 .?i

.08

c___l--__D___~_g__^-~.______^________

e-m-

-.88

.t0

156.0 . . . .

2os.3 236.8 274.4 321.3

-49 I

____

Bo .Oo .OO -

conclusions given in this chapter can be rea from the graphs S. 7-9 or from tables 20-23. Their generality has not been limited by the fact that in the experiments concerned the experimenter himself acted as subject-this has little or no effect on the results, as has been found in an experiment performed for verifying purposes with another person acting as experimenter. With another n&j& wide differences may occur in the results; even on repetition of an experiment by one and the same subject tinder much the same conditions, the result will never be exactly the same (section 4.4). The

H. K. W. MOED

226

TABLE

22

Relative deviations,

tan (xi

I

tan 8”

.8O

.80

-G

-80

.88

.49

.67 70

.58 .61 55

heavy shading

.80

-,96

.oo

.09 .19 .27 .26

40 .ll .26

-.62 -.52 --I., ‘1 -.413

-.65 -.70 -.67 -.66

.Oo

-.30

-.62

57.8 . . . .

.78

.7O

.67

70.4 . . . .

.81

.71

.68

81.5 . . . .

-82

.73

97.4 . . . .

.83 .84 .85 .85 .?2

116.8.... 133.3 - - . . 156.0 . . . 180.0...

I

205.3 . . . I ’

.81 .88 .‘12

236.8 . . . .

.37

274.4 . u . .

.8G

321.5 . . . .

.90 ,711

360.0.

---Wil

!

.14 .31 .29

.25

-42

.3l .26 .21 .2l

.64

.42

.19

.27

.75 .75 .?4 .72 .53 .72 .54 .74 .58 .78 .58 .59 .67

.66 .6B .6\

-42 .48 .50

.13 .OO .08

A4

.53

-54

.63

_---

.oo

.24

-.I7

-.2”,

-A0

.18

-.21

-.57

-.I8

-.53

.32 .32 .22

-.I5 -.12 .OO -.I8 -.39 -.38

.-.06 .uO .oo

-.48 -.43 -.37

.OS

.25

-. 321

.Oo

-.31

.54

. 1’;) .

.20

-.3@

“04

-53

.55

.20

.20

-.2;

*OS

*SO

.56

.21,

.17

.I0

.50

.55

.23

.12

.14

A9

.54

.27 .32 .27

.OO

.21 -27

. . . I

----

.w -p--

-.&I

.66

. . . . ,

.

-I;;;;

.71

. . . .

.80

.Oo

.75

. . . .

.80

.OO

48.8 . . . .

. . . .

-

.Oo .36 A0 .56 A7 .49 A4 .45

12.9 22.5 32.1 37.6

.80

- --- -___

.- .-_-__-

_.--___

tan *I)’

The conclusions found, however, are of such a general nature as to leave much stop : to the individual pet-formance of the experiment; in fact they concern the universal bounds of this individual freedom. At the outset of the experiments the experimental room was divided arbitrarily into two parts, one part (thil; arran,gement) being carefully evaluated, the other part receiving no atterrtion at all in the description. The p,articularitie:s of the room that are not accounted Ior in the de-

227 TABLE23

values of relative deviations

.a7 f

.08

1

! --. * 9P

‘28 I&=.04 9 & .04

I / .@I --.Ol _---.~-. __\____~__

20

.-

MQ t= .06 f .02 M& = .Ol .06 f .03 A&f .05 m = .04 -&-.04

.43 k .04 -.30 * .O8 I j I .29 / .37 ‘09 .07 j m = .lO f .06 I E_~--.-L _,.~.-I _.m_____ll___L_ MI, = .48 -f .05 / .68 & .OQ Ii 59 & .06 f .15 Mg .19 f .08 I -=-.I3 -22 -.15 MW==.2! -& .06 I .41 .37 I .28 .22 gm = .29 f .13

Puesof tan y’* conjugate sets; (M =t M9/2;

values of tan y’, black, grey and whi:e backgrormcds; nd mean of tctn r’, identical backgrounds.

scription, however, may have a disturbing e et; in the standard case this could be detecterl directly (section 4.8). Thus, whenever a comparison : that standard has to be made, the actual standard which has not described exactly is to be distinguished from the ideal case which cannot be realized in perception. ~h~nom~n~lly, the above bipartition of he room is entirely fictitiousthe only bouudar~lin~ havin phenomenal reality is that which deterform of the object “2; in the field of vision the object forms a hole with its entire environment (sections 5.12 and 5.13). eneral, any conclusion referring to the test-arrangement (whkh arrangement fills only part of the field of visionj in fact refers to a modal of substitution where the objective values of the arrangement apply to the whole field. Here, in the description, a part has been substituted for the whole, but actually there will be a deviation from the ideal model owing to the finite dimensions of the arrangement. 68 As observed by Hugenholtz (28; p. 148), in perception the field of vision is not limited in such a way as to show an outer boundary-line.

H. K.

228

W. MOBD

From the above ib.follows that two kinds of conclusions will arise: those which apply to what its really experienced and those applyin to what is really described, the latter serving as an ideal model with which thie former are to be compared. 85 7.2. Thle Standard Case n the standard case the backgrounds of the two oiej their illuminations, are identical; thus, the values of both relative deviations, tan 8’ and tan a{, are zero (conditions C&eSO).In the circular diagrams (e.g. fig. 26) this case is represented by the centre-point, the origin 0. To the standard case 0 the fallowing conclu3sion (I) applies: I. If two objects: with identical backgrounds and identical illuminations, are subjectively the same, they will have approximately the same objective value. This can be written :

Itan r’o,oI
WI

where 1 tan y’o,o1 is tYherelativt: deviation of the reflection factors of the objects compared in the cE.se a’ == p’ = 0, and the sign of y’ is ignored. The averages of these deviations can l.~ found from the three middle columns in table 20; their valuxcsare given in table 24.

Average deviations of the objects in

the)

standard case

Two black backgrounds . . . . . . Two grey backgrounds . . . . . . Two white backgrounds . . . . . . OwraU

averages

. . ,

. L . . . .

The overaIl average OF 5 % in table 24 can be compared directly with the average value of 0.65 % found from the evaluations of the a JIn lthe no&&ion clQ distiction vah~cs are place4 within brackets.

has been maintained: in the formulae the ideal

229 r aS in b~tk cases the deviations were determined or [31] respectively). The comparison cy rca~~~edin the evaluations is necessary to have any si nificance at all.

show that the points of su ttcred towards tne two sides of the oints lie on one side of that line, his ~symrn~tr~~is measured by the grand mean of les 23 and 24). ows from table -_ 0.06 and =+-0.19. which values indicate stimul ~rsequivalence 54; the latter value is never exceeded,

1981

tan y’0.0<

1 tan

F~O 1

parison of the mean value of all deviations, MM, with the above shows that stimulus equivalence ilere produces a values 0. adequate m el of description than stimulus equality. rds the standard decrded upon, the deviations tan ~‘o,ocannot be anticipated from anything in the description of the conditions; so the given level of description, not ‘legitimate’ and as such handled in a statistical way. They are ignored in the calculation of the deviations which arise from an intentional change of conditions; this equivalence to zero con be written: 1991

tan

y’o,0

-

(tan

y’0,d

with the ideal value (tan y’0,0)= 0. Thu zero value can only be anticipated in the ideal case of perfectly identical conditions throughout the whole experimental room, where the two semi-fields would show perfect symmetry with respect to their common boundary-line. The identical conditions themselves would be w The value 0.19 follows for the deviation 1 tan ur) 1 of the non-corrected sthulus line in the case of no shading, by means of [20] and [Ml.

H.

230

K. W.

MOED

indicated in the objective diagram (fig. 29) by the centre point, determined by the ideal vialue (Ah) = 0.

[!tOl] ‘7.3. Special Cases

Two special cases arise if one of the two ob_jectiveconditions devi from the standard case of conditions C&aSC): 1. the Co- s experiments, in which (x’ # 0; they are performed by shading one of the semi-fields, the backngrounds bein 2. the CoSOexperiments, in which @’+ 0; the two identical backgrounds are replaced by two d&ring ones, the illuminations bein Instead of the approximate equality of the objective values in the standard z.se (conclusion I), the objects will then have more or less differin values when they are perceiT!ed as s8uhjectivelythe same. In the diagrams the PSE de\ Jate more or less from the straight line denoting object equality. The two cases mentioned are the ordinary experiments oip constancy and on contrast; they are represented in the objective diagram (e.g. fig. 27) by points on the lines CM and B respectively. In scheme I (section 2.1) they are indicated by A and B; to the experiments A and B the following conclusion (II) applies: II.

A I

If two objects, with identical backgrounds a -id non-identical illuminations, a:*e subjectively the same, in general they will have differing objective values; the objective difference between the objects, compared with the objective difference between their respective illummations, goes in the opposite direction ; the relative magnitude of the folrmer diflerence will be smaller than that of the latter.

If two objects, with idlzntical illuminations and non-identical backgrounds, are subjectively the same, in general they will h.ave diRering objective values; the objective difference between the objects, compared with the objective alfference between their respective backgrounds, the SCllYte direction; the relative magnitude of the former difference will be smaller than that of the latter.

CONSTANCY

AND

the object of the higher reflection is ptaced in the semifield hav&g the weaker alienation ; the r~~a~~~ decagon from object ~de~t~t~will smaller than the relative d~~ts~f~ iflprrni~~ti~~identit~.5”lg6 sointhi

CONTRAST

MA

231

So in this case the object of the higher white-value is placed on the background having the higher whitevalue; the relative deviation Corn object rdentity will be smaller than the relative deviation from backgroundidentity.55~56

compared with Jaensch’s law: ‘Gesetze des ‘ransformationserscheinungen, ken den Terminus ‘“C~mfeld”ersetzt durch aurn” ’ (‘Parallelgesetz’; 11, p. 272). ‘Transformationserscheinungen’ concern ; so it should be possible that the above asses into conclusion IIA by an interchange of the

does not prove to be the case: if the terms and ~~ll~rninati~~~s~are interchanged, there will still be left, namely that berwcen the words in italics, “opposite’ besides the analogy found by Jaensch an inversion occurs, e of signs in the description of the results of the experiments. It is, however, possible to obtain perfectly corresponding conclusions IlrA and IIB by bullding up this inversion beforehand in the description of the objective conditions. This, in fact, has already been done in the notation of the standar case: instead of the symbo!s Co-to, where the line t in fig. 13 is characteristic of the illuminations, the notation Co- se has been used, thF: stimulus line s being substituted for the line t, the angle FXchanging sign (fig. 14, formula [40]). This artifice does not of course eliminate the fundamental inversion, but it does result in a unifor ity in formr;lation, which, especially *when applied raphical representation of the results, facilitates the survey.

Conclusion II is then simplified as foilows (see fig. 10):

sB The relative deviation from identity is half the relative difference; the general formula [94] shows this factor 4 explicitly. a8 The general formulation of conclusion II allows a second interpretation, in which the absorption factor, the shading, and the black-value are the variables in calculating the relative deviations. This would apply to part of the results of the present experiments, but is left out of the discussion here.

H. K. W. hK%D

232

In a diagr,Lm of an experimerit on constancy with identical backgrounds the PSE’s lie between the pole marking zero constancy and the I’ne denoting obrect equality. So in this case the PSE’s lie between ehe lines s and o.

i ~ 1

In a diagram of on Contras1 with illuminations the between the pole contrast and the object equality.

an experiment identical PSE’s lie rn 1;

So in this case the PSE’s

lie

the lines c and o.

In the formulation given of conclusion IIl3 (and I&B) the inva~ance

principle concerning the backgrounds, mentioned in szction 5.6, has in een introduced as an objective model of description. All she poles C on one and the same line c (fig. 10) are considered to be equivalent in so far as only the relative deviations, tan fl, are used, the individual points C on a line c not being distinguished in the description (no more than tne points on a line t in fig. 13). According to the given interpretation of concllusion 11, ,where the reflection factors (or the corrected white-values) and the illuminations are to be used in calt:ulating the relative deviations, conclusion II can be written:

[102&B)

twGo

<

(tanygj

tar_ “VI ‘+!L
1

’

(tanY&B’)

~4th the ideal values

tLe subscripts of y’ refF;rring to the measures LX’and 8’ of the o’bjectiv conditions. Ial accordance with conclusion 111and for:mula [41), the ideal value in \103A] may be written: [lW

(tan &,)

= tan 0~‘.

The three angles, aa’, #?‘, and y’, are measured with respect to the line of object equality; in the tables the counterclockwise rotation is signed positive. --‘i’ is meant to be a warning that an inversion is implicit @m@y 67 The &script the ia~erse proportionality [37J in case A).

r limit of the deviations has been given; 1991and [lW], the effect of the deviation nt under a transformation of the easured ; any continuous used, provided Cat the tity) be preserved. For 30 the values tan y’ and tan p’, at the head with the idr:a; values, tan OLD’ tirely in accordance s never reached; as in the standard case ere, the ideal lower COLVW this can be anticipated only if the standard conditions are small, the legitimate effects blurred by the scattering of the PSE’s already found in the standard .Q15; in the :;tandard ix negative values, s being negligible. QWS that these casts are accounted for by [993,

(table 21, middle column), averaging I_ ,035

the ideal limits are also marked (:%Ifigs. 7-4 only the non-corrected stimulus lines arc indicsited). .3Qb shows that the asymmetry of the bars B and B*, representing of the three experiments on contrast, also occurs in the bar 0. The same is found from the figures in table 23: the mean value of tan y’ in the stand’ard case (grn = .O4I&I-04) equals c (AM& ,03) of t. e three nean values (M+ = .O% ~8 and - AN) in the cases B,B*, The three experiments on contrast are shown separately in fig. 31. Summarizing the above it follows that in the results of the experiments no departure from conclusion II can be found that might not already appear in the standard case; the same applies to the symmetry of the conjugate sets B and B*, which symmetry entails the equivalence : HO]

tan yO,p; -

- tai n yO,+.

W. K. W. MOED

234

I

I 1

t

56

4c

Fig. 30a. (upper figure). Ranges of experiments on constancy. C) standard case, AI slight shadin AZ heavy mading; tan y’ relative deviation of objects; inscribed fi

three experitnents on contrast. B, B* conjugate exwriments.

Fig. 31. Ranges of experiments on contrast. 8.

8.1.

AMFIIG~JIT~’0F THE OBJECTIVI: STIMULUS

BrighJness Deviations

Formally, in conclusion III the divergence from the Jaensch parallel principle has been eliminated; only the subscript in “Ill,’ points to the hidden inversion (which is implicit in the reference value determined by ihe zero pole s in the diagi*am). 1~ rl:ality, of course, the experimentally stated inversion can never be eliminat.ed. Yet, in an&her transformation of conclusion II the inversion seems to have dis,nppear ed completely, and so a contradiction seems to arise. To introduce this crucial case, it may be observed that in experiments on constancy, with identical backgrounds, tht!2objective brightnesses of the semi-fields are in proportion to their respective illuminatrons; in experiments on contrast, the identical illuminations produce brightnesses

CONSTANCY

AND

CQ1”
235

ion to the white-values of the backgrounds. Thus, ven of conclusion II, the values of the semi-fields y the brightness values, without affectirig the be written in the form :

l

In an experiment on contrast tlze ubject of hig/zer white-value lies in the brighter semi-field; the relative difference of the objects will be smaller than that uf their environments.58959

ere the term ’ ter’ refers to objective brightnesscs; the inversion will then not cted by the substitution of the values of the semifields. However, the latter is true only if corrected brightness values are used which are determined b? the corrected values of the illuminations, This implies that in the two semi-fields differing units of brightness must be used, their ratio beinp el (===the ratio of the unit values of the illuminations, see section 5.5). In case A the brightnews of the identical rounds are then in proportion to t corrected values of the ations, and in case B the identical illuminations produce brightnesses which are in proportion to the corrected whit+values of the a constant unit of (physical) brigt,tness, not only would the above proporbe afFected, but, moreover, an inversion might be introduced in the deof the background{ might be inversed, tion of case B: here a small diffe ram et -:: E~o/&,o I = the non-corrected owing 50 tha eff&ctof the gradient of Ii illuminatian ratio in th 2 zti,lr without shading), and ER being in proportion to the tress, it follows &at the brightness difference and the difference of the in opposite directions if

[28] and (34) this condition can be written: WI

1 tan

a0 ( > tan p’ > 0,

8s A second interpretation, lib, arises if the black-values of the objects and the ‘darkncsses’ of the semi~fieP;dsare considered (‘objective darkness’ = diminution of objective brightness). s@ What is perceived as the environment of the object may actually lie in a different plane (e.g. in experiments where the ‘hole method’ is used).

H. K. W. MOED

236

where tan /Y determines the contrast line c (fig. lo), End I tan OLO1 corresponds to the non-corrected stiuIus line s in the case without shading. Thus, by using the physical brightnesses an inversioat is introduced in the description 8, in an experiment on contrast, the zero pole C lies htween the line o of object equality and the line s of stimulus equality.

The purposed transformation of conclus;on II arises “f in IIW the objective brightnesses are also used for measuri objects (instead of the white-values). It can be of the object-values never affects case B, whereas it introduces ahi inversion in case A, which neutralizes the original inversion contained in conclusion II. In case B the argument given for the backgrounds also holds for the ob_jects: the corrected. objective brightness-values are in direct porportion to the corrected white-values--consequently no inversion INillhere be introduced by the change of the object-values. argument it follows, from II, that in case B the relative brightness difference of that objects will be smaller than that of their respective environments. Here again, if a con&t:& unit of physical brightness were used, an inversion might occur, namely in the case of

WI

RLIRD < el c: m/m.

TJsing [B], [31], and [34] this can be written: tan 0 >

YlO91

1tan

ix01 > tan y’,

where tan y’ corresponds to a oint of subjective equality. Thus, by using the physic 11 brightnesses an inversron is introduced in the description if, in an experiment WI contrast, tbt: zero pole C and the PSE lie on opposits sides of the non-corrected stimul ‘,s line. The difference of the backgrounds does n>t change its sign in the description, but the (smaller) difference of the objects does; since the two differences then go in opposite directions, conclusion IIB would be invalidated.*0

In case A the ratio of the objective brightnesses of the objects equals e’*rn/rL, where e’ is the corrected ihu4!~iinationratio. From IIW it can be seen that in the A-experiments the value of rn/rr, is greater than unity, since ~1,refers to the object in the brignter semi-field; the substitution -

6o This result will be seen at unce if it is borne in mind that the line s, indicating stimulus equality, determines the zero value of brightness dilference; brightness diltferencehcorresponding to points on opposite sides of that line have unlike signsthey go ELIopposite directions.

NCY AND

237

CONTRAST EiIA

bj~~t-valves then entails an invr rsion if the value of the brightness ratio iq smaller than unity. The atter condition can be written

n M’ to the corrected stimulus n Cl111 is satisfied by t

results of the present experiments; or, more directly, from the values les 2 I and 22). Even the four negative iment with slight shading, do not here: the value of PI$=Lis then smaller than unity, &uated. Thus, in all the A-experiments htness ratio of the objects is smaller than unity, the value of the just as the value e’ of the illumination ratio; the relative brightness difference of the objects and the relative difference of their illuminations then go in the same direction -the inversion originally contained in conclusion IIA has disappeared. In order to visuali;_ the above, fig. 32 show the relationship between the variables in the experiments with shadin ---_- E’ +-_----_-___- I3

(a) no compensation

s_-p__

E &&-_-_--_-_

4

B

(b) partial compensation

E’

r-==--w

(c) complete compensation

Fig. 32. Compensation of the difference in illumination.

rithmic difference log ED’/EL’ = log e’ in illumination, +r logarithmic difference log ra/r~ = log x of the o;r?ects, + rithmic brightness difference log BD/BL of the objects. fThe brightness ratio e’sra/rx, gives the logarithmic brightness diaerence log e’ -+ log ~D/Q,; the first term has a negative value (e’ c l), the second term is positive (~D/I’L> l), and thus, in the figure, the corresponding directed line segments go in opposite directions. ig. 31a shows the limiting case in which the objects compared are

238

H. K. W.

MQED

identical (log r&r, = 0); their brightness ratio 6quals the illumination ratio. Fig. 31~ shows the other limiting case, where thn difference of the illuminstioos is fully ‘compensated’ by the difference of the objects (log r&L == -- log e’). The brightness difference of t e objects is then zero, i.e. stimulus equivalence occurs. In ordiniuy cases (fig. 31b) the difference of the ill~~~~ti~n$ is partly comp6nsated (0 c log ID/& < - log e’) ; part of it remains uncompens~tted and gives the brightness difference of the objects. Of course, this re=naining part goes in the same direction as the whole; moreover, it will be smaller than the whole. By [46], an3 the analogous formula for the brightnesses, it then follows that the relative bri deviation of the objects goes in the same direction as the relative deviation of the illuminations; moreover, the former deviation will be smaller than the latter. The same relationships apply to the relative brightness deviation of the objects and that of their environments, since the brightnesses of the identical backgrounds are in proportion to their illuminations. 51*.\ms;tting the above it follows that by introducin the objective brigl,tnesst:s for measuring the diff6r6nCeSof the objects as well as those of their environments, an inversion arises in the description of the A-experiments, which neutralizes the original inversion contained in conclusion II. The outcome can be written : In e:xperiments on constancy and in experiments on contrast the object of higher brightness lies in the brighter semi-field; the relativ6 brightness deviation of the objects is smaller than that of their environments. The next point would be to oJm?are the above statement with the original conclusion E, in order to make the disappearance of the inversion clearer. It will then be seeg, that this inversion is hidden in the method of measurrment of the object differences in the experiments. In conclusion II the deviation from object identity is measured with respect to the line o in the diagram of r-values, line o producing the zero value in this measurement; the deviation increases as the angle y’ increases. However, when the brightnesses are considered, line s gives the zero value, the brightness difference corresponding to a point on that line

~~QNS~AN~Y

AND

CONTRAST

IJIA

239

ce ths: PSE lies between lines s and Q (conclusion Iii), relative devit~jtX.n Iirom brightness equivalence increases as the the reversed sign of y’ implies an inversion. tness ratio of trt : objects, e’s r~/r~, he relative brighthtness P ~ujv~l~n~e,AB, is found to be

n ar’ in [46], except for the minus sign; e added since thl; diflerences & and E’ (fig. 32) take which implies like si ns of the deviations AR and of LIP and ta 61 and [Xl], the relationship

is obtained. In accordance with

ing, complete compensation (y’ = ai’) deviation in [I 131 disappear; in the case of no compensation (y’ = 0) the brightness deviation equals the deviation of the illuminat cans, Au = - tan ~51’I- ta The value of A, 1 decreases as the val tan y’ increases; as already mentioned, here the inversion is hidden (as an inversion with respect to magnitude). 61 The relative brightness deviation of the objects is subjectively determined and may be denoted AfIns;in the same wxy, Au0 will be the relative devi&ion of their environments, since this deviation is objectively determined. The relationship between the brightnesses can then be written :

Here the first inequality expresses that both deviations will always go in -__the same direction (having the same sign); the second implies that 61 In the case of experiments on contrast, however, there is no inversion; by taking tan aci’= 0, equation [113] gives d B = tan y’, Fig. 33 shows that the range of the A-experiments decreases as the value of tan (xi’ decreases; in the limiting case of tan arl’ = 0 this range completely disappears, the inverse correspondence of da and tan y’ being replaced by the above direct correspondence.

240

W.

MQED

the subjective deviation will always be smaller than the objective deviation. The relation [114] applies to bo kinds of experiments, those an constancy and those on contrast. 6s The consistency of [t14] wi.th conclusion II, as well as the hidden inversion, has been shown. However; nothing in the relationship between the Cghtnesses itself points to an inversion; thus, [114] could as an independent principle, not to be compared with concl The crucial point which then arises is : which concluaon must be considerfcd to he the real one? In other words: is there an inversion fundamental in the comparison of the A and &experiments or not? From the present point of vie,w, the answer must be that the inversion is fundams:ntal, and that the statement about the brightness relationship cannot re;.Ily be considered to be R principle of perception. The argument is that in ?erceptia;ll the ultimate end is to perceive objecfs: stimuli, however, can never be an object of perception, they are not perceived at all. The objects must be described by their intrinsic values which are independent of the il.ncidenta! illumination, but in the brightness ratio t&i&L the intrinsic part refry is still intermingled with the factor e’ referring to the illuminations. The latter can be considered to form a field of potentialities (section 5.1 l)$ which have not yet been realized -leaving open the possibility of realization in different ways. In perception the subjective equality of two cards can indeed be obtained i-2 two different and oppositely directe ways, their brightness deviations being in both cases the same and goi in the same direction, and, moreover, aZw the brightness deviations of the ewiron objects goi’ng in boifhcases in the same direction. Even under the latter conditio.ns, it is possible to match a card in the one semi-field with a card of caitherhigher or lower white-value in ,the her semi-field, depending on which way the brightness deviation of environmen of the cards has been objectively realized (conformin to the A or of experiment). In order to visualize the above, graphs of the brighr:Pl;ss deviations are shown (fig. 33’); the values of these deviations have been calculated by mcaias of [113], taking constant values of tan LQ’. ---6~ From [113] the brightness deviation AgOwill follow if tht: two cards are taken to ‘be identical with their backgmmds, or if at least equivalence occurs (7’ = #?1. The vabs dB0 = - m dcil’and &jo = bn /I’ are then found ill the cases of experiments A and B, B* respectively.

241

Fig. 33. Domain of results (brightness deviations). A B, B+ tan y’ Qn

experiments cv constancy, identical backgrounds; experiments QLIcontrast, identical illuminations; xelative deviation of corrected white-values, relative deviation of objective brightnesses.

raphs are, of course, 1imite.I by the extreme values &. 1 of the relative deviations tan y’ and rl~~ which (letermine the common terminal points (-+=1, +- 1) and (-- 1, -- 1). Bcty one half of each curve has to be calculated, since the points of the other (symmetrical) half can the values of ( tan y’ ( and 1 d B 1; by [ 1131, be found by interchan ’ namely, a set of hyperbolas is determined, and the mid-points of the segments in fig. 43 lie on the (common:1 axis of these hyperbola;. The complete set of curves, their parameter tan LX~’ varying from 0 to + 1, would fill up a triangular doaain, the boundaries of which are segments of degenerated hyperbolas. The base of the triangle is the locus of the experiments B, B* (tan lxr’= 0); the two other sides are determiaed by the value tan CX~’ = 1.

242

H.

W.

K.

MOEI.

A second set of curves, symmetrical to the former in respect of the lin4: for tan pli’= 0, would arise from values of tan dci’ varying from CGto - I:, the corresponding experiments would be realized if, in a symmetrical room, the opposite windtaw were used.63 The two trian domains form together a square, the universal domain of all possible results of all possible experiments. In the A-experiments only part of each curve can be realized, limited by the ideal values, (tan 1,‘) = tan obi’and (LIB)= -tan (or’,marked on *7, .xes ofco-ordinates by the curve itself. Thus, the area of the (square) domain of the A-experiments is half of that of the triangular domain. The uplper limits of the 8 and B*-experiments cannot directly be seen in the dialgram, since here all the line segments coincide; they are determined by the corresponding limits of the A-experiments if a standardized arrangement has been used. In fig. 33 the mean values of tan y’, given in table 23 for tan lyl’ = .OO, .43, and 80, have been indicated on the respective graphs for these cases (no shading, slight and heavy shading); the ranges have also been marked on the curves, by means of the extreme values of tan 1’ shown in fig. 3 It can then easily be seen which experiments must be \:ompared in order to find ckar examples of ambiguity of the objective stimulus, where the objects in experiments on constancy and in experiments on contrast woul~clh:we the same brightness deviations going in the same dire&on. Of course, if the brightness deviations of the objects are to have the :&&me: direction, the same must hold for their environments-as follows at once from [114]; in fig. 33, where the graphs of the A-experimenss end of the B, B*-experiments are determined by one and the same Carmula ([113]), the A-experiments must indeed be compared with the R*-experiments, if the deviations, dg are to have the same sign. Moreover, by com:)aring the ranges marked off on the graphs, it can be seen that A and B*-experiments of the same value LIB can only be anticipated if d B k:s between the limits - -18 and -. 50. (the lower limit of range A1 and the upper limit of IF). Thus, in table 20 only the experirc cnts of va’iues tan y’ \vithin the range - ,18 to - 30 are to be eon ridered; they must be compared with all the Al-experiments in t&1(: 21, and with the few As-experiments of values tan y’ > 30 83 For practical reasons these experimentswere criticized in section 5.6; theoretically, however, they must be admitted in view of the intermediating function of the B-experiments in the completed id:eal model of the arrangement (fig. 27b).

243

T IIIA TABLE

25 - matched values of &.

+ -27 - ‘19

29 19

34 14-15

5

.239 .163 .402

$ .23 - .23

27 21

32-33 15

51 6

.200 .202 .402

+ .I6 w .30 - .31 - .32

21 32

2S? 2s

4 7

.140 .269 __-. _. .#9

9 9

13 0

4 9

.124 .291 .415

w-w g&--W

- .34 =_ .34

15 15

17-18 4-5

2a lti

.089 .306 .395

w-w IF-W

w-w b--W

- .34 - .34

+ .I0 - .34

-A0 ---. 40

17 17

19-20 7?

24 10

.091 ,306 -.397

13 13

14-15 1

aif 12

.034 .367 .401

b-b b-W

-. 44 -.46

-I_.56 - .46

29 29

37-40 16-17

9& 12*

.544 .436 ,980

b-b b-W

- &45 - .46

-+ .55 -=‘.46

3 17

20 3

17 14

“527 ,415 ,942

- .51 - .48

-+-.49 - .48

25 35

35-36 24-25

104 1%

,467 ,450 ,917

b-b b-W

- so - .50

+ so --so

13 27

26+27 14

13 13

,477 ,475 ,952

A1.n experiments on constancy; Bl,s,a experiments on contrast; w, g, b backgrounds; ds relative brightness deviation of the cards, tan y’ relative deviation of corrected white-values; n&I,) number of the card in the darker (brighter) semi-field; An difference of card numbers ns, and nL; x object ratio (= rL/rDh

244

H. K. W.

MOED

in table 22. Examples of ambiguity, thus found, are given in table 25 for different values of dB. h each example two experiments, of type A and B*, have been compared? their brightness deviations being the same, or nearly the same. The values of dg in the B*-experiments could be seen at once from the values of tan y’ in table 20, whereas for the A-experiments they had to be calculated, by means of 11133,from the values of tan y’ in tables 21 and 22. C3ef course, to find corresponding experiments, the diagram could have been used-horizontal lines of constant value dg would intersect the graphs A and B* at corresponding points. In each series of A-expetimerr.ts one special case rises, represented by the mid-point of the gr concerned (the vertex of the hyperbola); tEiis point, lying symmetri in rerqect of both axes o co-ordinates, is determined by equal vah~~ a; 1 /s .a 1 and tan y’. In the tables these special cases occur in examples 2 and 11, where four equal values of 1 AB 1 and 1 tan y’ 1 arise (in ::xperiments AI, Bz* and AZ, Bs*); in example 10 nearly the same occurs. In columns nD and nL the osiginal card numbers have been given, namely, of the cards which where found EObe subjectively the same, and in cases of interpolated values the card numbers of both imperfect mat&s (they can be found from tables 10-12, by means of the evaluations in table 1). In alli the examples the differences dn of the card numbers referring to experiments of type A and type B* go in opposite directions. Generally, four cards will be necessary in the two experiments cornpare& apart from the interpolations (examples 1and 2). In other examples, however, the ambiguity of the objective stimulus is more conspicuous: the same card in one of the semi&Ids has then been matched with cards of both higher and lower white-value in the other semi-field (exarqpite 3, where nL is the same, alld examples 8 where nD is the same in both experiments compared). In example e same card lying in tb,: darker or in the brighter semi-field could in both cases be matched with a card of lower white-value in tFdeother semi-field. Finally, in the special cases, where the value of 1 tar? y’ 1 in both experiments is the same, only two cards would be needed, the cards being interchanged in the two experimer -Qcompared. In examples 10 aad 11 this has nearly been realized: cards 25 aad 35 formed one of the t,wo best matches in both experiments compared (AS and Bs*) ; in the same pair of experiments card 27 could be matched with cards 13 and 14 differing less than 4 %.

~CONSTANCY AND CONTRAST

IIIA

245

The last s:olumn in table 25 shows the logarithmic values of the ratio x of thh%reflection factors of the objects; in section 5.4 this ratio has in short :,een indicated as ‘object ratio’. The sum of t.he values 1 log x 1, the signs being disregarded, is about the same in al: the com,483 -&-.005; in the comparisons The two constant values can be rences of the illuminations in the e experiments Al, and .943 in the relationship, that appears to occur between the subX, arises from the selection of the values jectively determined val com~~red~the pairs A, formed under the condition that the subjectivity detcr~~incd brightness deviations, JnS, must be the same. The relationship can then be writter,:

ity of [I 151 can easily be proved by means of fig. 32b. In that figure the directed line segment E’ indicates the logarithmic differc ewe of the illuminations in an experiment on constancy, and thus its length will be / log e’ 1~.The line segment I’ represents the partial com*

pensation of the illumination difference, by the diffr:rent reflection ts; its length equals 1log x IA, which is the first term factors of the in [l IS]. The se ent B represents the logarithmic brightness difference +of the objects, in the A-experiment as well as in the corresponding W-experiment (the brightness deviations of the experiments A and B* pared must be the same, and, consequently, the brightness ratios arithmic values). l-iowever, in the IF-experiments the re identical and thus the brightnesses aI e in direct proportion to the reflection factors; it then follows that the segment B, which 4. 32b refers to an A-experiment, at the same time determines the directed line segment r that would occur in a diagram of the corresponding B*-experime:t, its length being I log x IR*. Summarizing the above it follows that the illumination difference 1 log e’ ) in an experirr *nt on constancy is broken into two parts, equalling the object difference 1 log x 1 of the A-experiment and of the correspond-

246

H. K. W. MCf?D

ing B*-experiment of the same brightness deviation d.&, respectively’ The opposite darection of the two p?arts shown in fig. 32b corresponds to the opposite direction of the object differences in the two experiments compared. It will be clear that the special case found in the A-experiments a partition of 1 log e’ 1 into two equal parts--the o brightness ratio will then have the same value, and, canseque rektive deviations tan y’ and 1Ag 1 will be the same eqaipartition of f log e’ ( is found in example 2 (I log x in experiments & and Bs*), and in examples 10 and 11 .412 &- .005 and .463 & .Q13 in experiments A2 an values in cases Al and A2 would have been ,201 i\nd ,472. From the ambiguity of :thieobjective stimulus it appears cannot fully be descr[Sed by a relationship between t e brightnesses only. The brightnesses, however, may be useful in analyzing the pr~~ss of perception and in the comparison of experiments, namely, by their function as the intermediate between aspects of reality whi,n in a direct way cannot be compared (see section 5.10).

8.2. Contrast Deviations riments in section 8.1 In the examination of the results of the e have: been considered, the brightness deviations OTthe objects compar but not the relations of contrast of the objects and their environ The diagram thus obtained (fig. 33) shows indeed a ccrt s,incethe different experiments on constancy are distingui graphs, whereas all the graphs of the experiments on contrast coincide. Any point in the diagram refers to a definite value of the deviation of illuminations, tan ai’, since only one graph goes through a @he ‘segment of the rectangular hyperbola being Nly determined by its limit kg poin Ls, the axis, and one more point given); tan (xl’, th meter of the graph, is uniquely determined. However!, from a point in this diagram, indicating the brightness deviation of two objects, nothing can be said about the backgrounds of these objects; the brightness difkrence of a pair of cards, of given illuminations, is completely independent (in an &jective sense) of the surroundings of the cards. The counter-part of the diagram in fig. 33 would be a diagram where the same asymmetry occurs, the A and B, W-experiments being inter-

CONSTANCY

AND

CONTRAST

IlIA

247

iven point would then uniquely determine the value of the de~i~ti~n of backgrounds, tan B’, but nothing would be known out tan ,%i’.The latter indeterminateness would arise if, Instead of ttle the ~~~~t~onsof contr st of the objects and their environ~ns~d~red; th ns are determined by the (intrinsic) rials used9 which are independent of the d of the brightnesses produced by these 0 star with, the ~ountera~art of fi . 32 will first be shown; since the iven an easy survey of the relationships in fig. 33, tisipatcd in the present case. Conforming to the nsch, the new dia ram will be found from fig. 32 by a s; moreover, the version stated in the present concluobserved _

(a) no com~n~tion

(b) partial compensation

(c) complete compensation

Fig. 34. Compensation of the difference in background. R logarithmic difference log WI/~&J log G in background, *.. r logarithmic difference log rl/rz = log x of the objects, z +

logarithmic difference log CI/CZ = log c of contrasts.

In fig. 34 the directed line segment R indicates the logarithmic differ- log Rn, of the backgriinds, just as the corresponding . 32 represents the logarithmic diRerence of the illuminations E’. In both figures, these segments referring to the objective conditions of the experiments are (subjectively) divided into two parts; one of these parts is the logarithmic difference of the objects, r in fig. 32, -* . 34, Here the inversion can be seen: in the A-experiments the differences of the objects and those determined by the objective conditions go in opposite directions, whereas in the ,B *-experiments the two differences go in the same direction. aIn? the neutral concept of c mpensation cpn be applied, and, of course, it, both cases the uncompensated part of the objectively given {differencegoes in the same direction as the whzle of it. In fig. 32

Ht. K. W. MOED

248

this part of the illumination diflerencc produces the Pogtirithmic bright-

ness difference B of the objects; in fig. 34 the non-compensated part of
I1161

*-

4-

4-

folicws, which is a short notation of [Ma]

log

Cl

- log C’s= (Tog RI - log Rs) - (log 1-1-_ log Q),

and thus

I.1171

log

Cl -

log

c2

=

log Rr/n - log

Rzlr2.

Thus, in the present symmetrical system of description, the relation of contrast of any object and its surroundings is objectively determined by

PM

C = R/r,

and the contrast ratio, c, of two objects by

The value R/r refers to the two components of a complex whole, formed by the object and its environment (section 5.13); therefore it should not be called a constrast ratio (i.e., a ratio of two contrasts compared)-it objectively describes the relation of contrast itself, as it at the moment is given in perception by the one complex whole. Only in comparison with a second whole will a ratio of (two) contrasts arise, two objects then being observed in succession. From [118] it follows that the relation of contrast of the object and its surrounding,s takes tht form of a polarity: in logarithmic measure the relation ma;r be described as log R - lo r, whereas the reverse form would not be usable. This result is independent of any accepted positive directior in the diagrams, and is not impaired by an interchange of the two semi-fields; it eventually arises from the relationship X > r c c --II. e4 III section 5.1 the difference of log r and log R was already considered to be one of the measures which, would virtually be usable for measuring contrast. 11201

A9

and r in [116]. The latter relationship, of ~&xlusion IIB (section 7.9, which derived from the subjective judgments of the cards ents. Thus the uniqueness of senst in the entirely determined---objectively, it would be ounds and cards of greater difference v~rs~on in the description (either the direction versed, or the value R/r in [I I$] had to be ntrast the object and its environment are 8s subjectively a polarity occurs, has been 5.13.

d alr~a~iy in

Iln the l~~er~t~~rhe ~~~tr~~~r~~ 8s re ards the description of’ contrast by using objective Or ~~~j~t~v~term9 can easily be recognized. The subjectivep&.rity ~ieemsmost clearly to be expressed by the common terms ‘object’and ‘hound’. The action CRthe subjecthas been described by Brticke as follows: “Das Princip arbc auf unser Urtheil tiber eine andere. .“; des Contrastes,d.h. der Einwi *

’ and ‘inducirte Farbc’ are then used (3; may here indicate objective and subjective colour,

uishes two fields, ‘das kontrastleidcnde Feld’ and ‘das kontrasterregende R&l’ (11; p. 2701; here in both cases the term ‘Feld’ seems to be used in the objective sense. if, moreover, the methods of physics are applied, instead of the uniquely directed action given by the polarity comes a two-sided interaction between comparable elements: Ebbinghails mentions the problem of the ‘wcchselseitigen ; p, 10041; Meriag devclopes his ‘Thearie dcr Wechselwirkung Contrasteinfl im samatisehan felda’ (9; p. 159-210). In many cases the controversy between differenttheoriesof contrast might eventa the above opposition of terms, the phenomenal unity given in broken up irl the description and envisaged either from the side of

the subject or from the side of the abject. he contrast ratis can be iven the same form as thr brightness ratio; the lwttes may be written &lx, where et is the corrected illumination ratio, E’+?& and x the object ratio, vr,/vrj. If the background ratio, &p?s, is denoted as G, then the contrast ratio can be written G/x, where Thus8 brightness ratio and contrast ratio both take the form X zzz r&. of a cross-ratio, i.e., the ratio of two single ratios; one of the single ratios is the object ratio, the other refers to one of the objective ~ofi&ions--in case of the brightness ratio the illuminations, in case of the

:250

H. K.

W. MOED

r:ontrabt ratio the backgrounds. In this correspondence, however, the inversion is hidden: in the definition of the brightness ratio the semi-fields in e’ and x are interchanged, whereas in the definition of the contrast ratio the semi-fields in G and x correspond. TO m rlr the differ~~~e~ the ratio r in the first case may be written x- and in the second as the sign in x- indicates the inversion of the object values in the e

ments on constancy (shown by their reversed direct sign in x,- indicates the correspondence of direction between the differences of the objects and those of their environments, occurring in the e:lperiments on contrast (fig. 34). ‘The signs here are not algebraically used, but they only serve for correlating the results of the experiments. In the B,B*-experiments on contrast the value of r in fi between two ideal limits equalling 0 ar/

* I _-pectiveyy; from the figure

(and From formula [116]) itc then follows?hat the contrast difference C *Nil1always be smaller than the Ideal value (C) in fi ~ 34a, determined b: r121:1

(C)== R, r=G=Y tc+-

However, since l.he illuminations in the B,IS*-experiments are Identical, the ideal limit I! (= log R1 - log J?$ will have the same value as the logarithmic briihtness difference of the backgrounds; as shown in the foregoing section this will always be valid if corrected values of the objective brightnesses are used. Thus it has been found that the contrast difference C will always be smallell than the logarithmic bri difference g the backgrounds, if the illuminatioils are identical; the two differences ga iz the same din>ction. The above tinding, however, also holds in the case of different illuminations, the backgrounds lacingidentical, as in the Alexperiments. Formula l116J applies to that case as ~~11,since it contaib?s only the intrinsic L values of the materials, r and lit..which are indepenclent of the incidental illuminations; if the backgrounds are identical the formula gives: 112421

C=-r, W=O. .+4.” fFrom fig. 32 then follows that in the A-experiments the logarithmic contrast difference of the objects also goes in the same direction as the logarithmic brightness difference of the backgrounds (which equals E’ in this figure), the former difference being smaller than the latter. c-

ND CONTRAST HIA

arithmic

251

difference implies a greater

aller relative deviation, the clbove can be summarized

iild in excrements on contrast the lies in the bri hter semi-field; the bjects is smaller than the relative r en~,ironme~ts. etermined brightness deviation of the 3 dnO; if the relative deviation of contrast, is denoted as Ace, then the above

e

A cs < 1.

Here the first i expresses that both deviations will always go in the same di the same sign); the second implies that the subj~tiv~ de~~~ati~nwill always be smaller than the objective deviation. In [123], just as in [t 141,the inversion is den in the method used for measurin the object differences in the c riments. In the diagram of co-ordinates r the deviation tan y’ of the ues is zero for any point of the tine o of object identity; the deviation increases as the angle y’ increases. The zero value of the deviations of the C-values is give&l by the tine c of direct contrast equality (fig. 16); any point of this line indicates’ the equatity of the contrast values of two objects: &/rr = R&s,

y’ = rc;‘,

as follows from 124%.Since the P% ‘s tie bet Neenthe lines c and o (conclusion IIt), the relative deviatio from contrast equivalence increases le /Y -_I_y’ increa 9; the reversed si n of 7’ implies an inversion.“B In the A-experiments, however, there is no inversion of magnitude: 1rlc 1 increases as y’ increases, as follows from [I 221. 6s The equality of tha contrast values in [124] complies with the term ‘direct

contrast equality’ introduced in section 5.1 for the line c; this term refers to :he physical measurement of the equality of contrast values determined by line c, just as tht: term *brightness equality refers to the physical measurement of the equality of brightnesses determined by the non-corrected stimulus line s. In the objective

252

H. K. W. MOED

T!le consistency of [123] with conclusion II, as well as the hidden inversion, having been shown, the same remark can now bc made as

in the case of the brightness deviations. Just as formula 111 the relation [123] for ~1c cannot be considered to be a rea, 1 ception. The inversion must be adhered to as a fundamen teristic distinguishing the results of the experiments on con those on contrast; moreover, in the relations of contrast of the ~~~~~t~ and their environments the intrinsic values of the objects are intermix Mith the values of the incidental conditions--;G:re the bat Elhc relations contrast, expressed by the value 19/r, m well be expressed the brightness values of the object and its b since the illumination of the object and its surroundings can to be the same. The brightness of the card stimulates t the effect that a..~,>objectis realized in perception, whereas th does not. The latter remains the potential (===not realized) component in the complex whole for .zzd by the object and its environment (section 5.13), ieaviog open the possibility of realization in the contrast relation with the object in different ways. In perception the subjective equality cf two cards can indeed obtained in two different and oppositely directed ways, their contrast dleviations being in both cases the same and going in the same direction, and, moreover, also the brightrlessckviatiom c)f the enviroments o$ the objects going ilr both cases in the sawe dirwtion. Even under the latter condition, it is possible to maitch 3 card in the one semi-field with a card of either higher or lower white-value in the other semi-field, depending on which way the brightness deviation of the environments of the cards has objectively been realized (conforming to the A or B,B* type of experiment). In order to visualize the above, gra.phs of the contrast deviations are shown (fig. 35); the values of the IJeviations have been calculated by means of the following relationship, derived from the contrast ratio C:

WI description of the experiments, however, brighthess deviations are to be referred to ‘brightness equivalence’, arrd, analogous to this, the contrast deviations may be referred to ‘contrast equrvalence’. The latter term can be understood by observing that the BE’s on line c are (objectively) equtfalent to the ideal point C on that line, the common value of the contrast ratio being unit) ; any deviation from this value 1 (thus from the equality in [124])implies a deviation f?om the equivalence to the zero pole C.

253 tten

ows that the conditions ing replaced by tan /I’ only &me objective condition e any value without affecting +orn this it follows that backgrounds and as well as all the

Domain of msults (contrast deviations). rinmts on constancy, identical backgrounds; A B, B* experiments on contrast, identical illuminations;

tan y’ relative deviation of corrected white-values, AC relative deviation of contrasts.

254

a, xc. w. MOED

formulae [113] and [126] give values AB# an as the objcstive deviation Am* in fig. 35 the deviation Ar: has the same sign as tan y’, the latter having the same sign as the objective deviation tan p’ (conclusion IIB) ; in fig. 33 tl Lb3 deviations AB and tan y’ have unlike signs, but the same holds for tan y’ and tLe objective deviation tan ix’ (conclusion UP,: -thus AB and tan a’ wiil have the burns The ob.jective deviations will be obtained by tak formulae for Ag and AC; in that case there is no co (logarithmic) differences B and C in figs. 32a and limits, equalling the objeztivelyWgiven di fences, and the same holds for the relative deviations. Of course, this again will valid for any experiment, the brightness deviations being fully determined by the illuminations, and the contrast deviatims grounds, if the cards are identical. From [125] it follows that the deviations AC wiil be zero if the vafue of the contrast ratio is unity, the condition of which is the equality tan y’ = tan ,!Y([126]), conforming to [124]; there will then be complete compensation of the objectively given difference (fig. ,346). By taking tan fi’ = 0, i.e. identical backgrounds, forrriula [126] gives AC= - tan y’, conforming to [122] for the logarithmic differences. Ihis linear equation for AC gives in the diagram where tke points referring to experiments with located
255

23 25

14 29

9

4

.316 .151 T4k7

-w b-b

-

‘18

-

.ts

-s .34’ +‘ .I8

I5 23

4-5 27

w 4

.306 .159 .465

3

-” .33 t. As;

13 19

3 24

10 5

,301 .163 .464

-- .20

4

5

-- .20

-- .32 i_ .2O

27 5

19 Ii

8 6

.292 .174 -.466

-- .21 .- .2f

-- .31 -+-.21

21 21

12 26

9 5

.283 .187 .47O

6

(

Bl* Al

-- .22 _I .22

25 32

17 35-36

8 3&

.268 .198 .466

7

-

-25 .25

- .27 $ .25

9 I1

1 18

8 7

.243 .224 .467

8

-- 27 - .2?

I_s .25 -t- 427

19 19

12 26?

7 7

.226 .244 ,470

9

- .32 e .32

-- .2Q -t- .32

5 0

0 9

5 9

.I77 292

--

A69 & relutive contrast deviations of the objects, l%r other symbols see table 25.

Table 26 has been set up in the same way as table 25: in each example of ambiguity two experiments, of types B* and A, are compared. Pn table 26 the contrast deviations are the same, and here again the

H.

256

K. W. MOED

differences of card numbers iq the A alrd W-experiments go in oppodte &e&ions. The magnitudes of these di about the same, in two expeiiments c experiment in fifig-35 lay 0x4 t axis of the hyperbola--this word grvc eqt& values of tan y’ and d& and, i that case, orljy two cards w~ul be necesxary in the two experiments. In the experiments act no example of this particular case occurs, but it is nearly o comparing the experiment A* in example 7 and cards 1I and 12 are here matched with cards 18 and 19 rcs~tiv~ly ; the values of AC, which shou bt: the same, differ ,02, and the values of lue .235 they should have (i.e., half of 1 log x 1 differ .Ol from the t I

log &/-&).

In a few examples only three cards arc used in the two experimc~ts compared: in no 9 the same cal*o lying in the darker or the bri semi-field could in both cases be matched with a card of lower whitevalue in the other semi-field; in nos 5 and 8 the same card lyia one semi-field could be matched with cards of both higher an white-value in the other semi-field. In the last column of table 26 the accuracy of the matchin according to the relationship [127]

1 log

1.

X In* -+- / log X I* == I log 6; ] u+, Acs = constant,

which is analogous to [ 1151used for checking the matchings in table 25. 271 can easily be understood ‘by me is observed that in the matching of experiments the value C in that +Egure must eqlual the value [422]), The exact . 3;1.(see formul value of log G (== log RI/&$ wzuld be ,471, its av~ra e value in table is .467 .& .002. Summarizing the above it follows that the bat round difference into two parts, ( log G I in an experiment on contrast is brokx4~ equallirlg the object differences 1 log x 1 of the ~-ex~rim~~t and the ding A-experiment of the same contrast deviation d cIl, respectively. These object differences (r and P in figs. 32 and 34) go

correspor

in opposite directions, when the objec;vely &en differences have the same direction; this arises from the inversion shown in fig. 3:. By combining the results of the

two

last sections the ambiguity of the

object in the one semi-

ness deviation of their the same direction; moreover, the value ay be the s;.me in ablee 25 and 26. amples 5 and 6, table 25) the magni-

ns could be made e object in the one semi-field and that out of a series of adaptations uld be matched,

the same), mokover, one of their two parts (dne or dcs being the e other part will also be the s me--and thus dcs or ABE. In and dnor would have in both deviations, ABy, y the same directions, but also the same magnitudes! 8.3. , O@cz~tive Generally, t h a uniform distr

V&e and the Objecgive Stimulsls tination of the experimental room will not produce on of light throughout the room; in experiments on tions even imply the asymmetrical (sideways) the experimental arrangement and thus a gradient of light eneral case the physical value of the illumination, ured by a ~zonventianal, constant unit, should be distinguished easured by a variable ?!nit depending an the whole o lumination. The more general concept, i.e. the ‘objective’ value llumination, was found to be the proper measure in the objective description of the present experiments on perception; by using this value, exceptions from general statements were precluded in section 5.5. 6s M The term ‘objective’ will bxe be preserved for the corrected values; they are determined with respect to the objectively given whole, whereas the physical values refer to parts of that whole.

258

l-4. K.

W. MQED

In the same way, the des:ription given in section 8.1 was simplified by the choice of the corrected, objective brightness as the variable;

a unification of theory was obtained by the elimination of exceptions which would arise if the physical brightnesses were used. The above distinction of values entails the n~~ssity to di between the physical ‘sknulus’ and the objective one in the and perception of objef:ts. If, in analysin the stimuli are to be considered, then the more ge the objective stimulus, :;hould be: used in the description. At any point of the illuminated field the unit value of the objective brightness must be taken in direct propocrion to the objective unit value of the illumination at thatt point; thus, the objective stimu1u.s is defined in relation to the whole stimulus field, its measure depending on the unity of this whole (just as the objective unit valur: of the illumination, see section 5.5). A physical device for de tec:!ing ‘objects’ can only measure the physical ‘stimulus’, i.e., by ‘obsert’ing’ a part of the field that has been substituted for the whole. The human eye can be used in this physical way (section 5.1$, but its natural use implies an unrestricted view of the whole field-hence the definition of the objective stimulus as a field-variable. On the other hand, by a comoination of photo-electric cells it would be possible to balance the effect of the light gradient (as well as the variation of the general il,iumination) in the measurement. Bn general, however, the distknction of the physical brightness (the ‘luminance’) and the corrected, objer:tive brightness should be observed, especially in all cases where the deviation of the illuminations, ‘t;anIX,has to be corrected in view of the gradient of light. As an example of the above distinction, reference is made to the relationship ai = -- cxof the non-corrected lines s and t (R is discussed in section 5.10 in purely physical terms. By the same token tte relationship CX~’ == - CG’af the corrected lines s and t could be obtained, but then the correctecl, objective values of the illuminations snd the brigknesses shoulld he used; in the latter case the luminance would have to be distinguished from the corrected, objective bri the objective stimulus. In experiments in the open, where the light gra.dient is zero, the use of the objective value of the illumination, which is a relative value, is still to be preferred-variations of the general illumination are then eliminated a priori, by the variation of the unit value. According io a principle given by Jaensch (11; lp. 311) these variations would

cl the results of extolments on conszancy and on contrast. times be found in which both the alues could be used in the description. For the contrast and 1241 reg the corrected, the physical as s background te-values of a card ~llumjnation intensity; of course, the und does not then depend on the tion. However, it would be only f the brightness in this case too. eve, it follows that in the description of experiments on Contras&it would be adequate always to distinguish the physical brightness value. The o tive value of the ifhrmination is fully deterrmined, namely by the ratio E/E0 = E’,

VW

where &I is the intens y of the undisturbed illumination at the point eonsider~d (no shadin screen being used). ‘The ratios E/E0 imply a ht gradient, and so they were used in correction with re the corrected illumination ratio; as mentioned above, they are also c~~p~nsa~ed with respect to variations of the geseral illumination. Moreuvcr, a further unification of theory is obtained, the two conditions, bae k rounds and illuminations, both being characterized numbers, R and E’ respectively. 67 htness value presents a remarkable contrast to the lue of the illumination, in that it cannot be fu ly determined in the ~)bje~~iv~description of the experiments. In ordel to define its unit value, the illuminated field is regarded as having been replaced by ea uniform field havit3g the same reflection factor throu~;howt. At any the field the unit value of objective brightnes, can then be considered to be she brightness of the uniform field at that point, if the illumination is not disturbed by a shading screen, thus having the , If I& is the reflection factor of the substituted uniform intensity -.-__ _ by using the jectivevalues of the illuminationscan the universal domain of Uluminations k: described; e.g., the physical value EOin the case without shading still c3epeudcon the general illumination, but the objective value will always be 8’

Only

WE0 = 1.

.%a

H.

K. W.

MOED

geld, and r that of the actual field at the point consi would be dete objective brightness ;&ere E/El, = E’, and thus

Here, the value of Ab of the substituted field a change in this value would proportio valu~esin ‘the description, in the same way illumination of the room would produce an br&htnesses. 68 At the same time, it has be%n found that the obj~~v~ brightness is measured by dimensionless numbers, ust as the obj valves of the illuminations, E’. In the formulae for the relative deviations, only ratios of the v occur ; since the value I;tzis then eliminated, as well as any propo~ionality factor, these deviations are fully determined1 and the same logatrithmic differences (e.g., the relative deviation BB in [112] and the logarithmic difference B in fig. 32’). With respect to all Thuse fully defined numerical values the terms ‘objective brightness’ and ‘objective stimulus’ may be used interchangeably. The correctic\a of the physical values has been carried out ’ with a view to the, fiunction in perception, the objective values referrin to the given objective whole. A further distinction, e. ., in ‘distal’ and ‘proxima? variables (described by Brunswik, 5; p. 6), would imply a regional subdivision of the objectively given whole and thus a return to the physical point of view, 8.4. The Miw r Modt?l Brunswik, in his classifica,tion of vari distinguishes ‘exteern;!l stimulus variables’ fro variables’, whic:~ two sets are conside chains; the met liating links of the chains are formed by ‘or variables’. In a model o this scheme the mediatin organism is repro sented bs: a lens; a rlumber of rays, each of them indicatin train of events, enter the lens at the stimulus side and leave it at the a Of course,by axecdditional caxlitioa the substitutionc&d be made fully debd; for instance,the condition might be imposed that the substitutionshould not change the total anwunt of reflectedlight within the ibid of vision.

261

he rays emanate from an initial focus and they are nal flus by the double convex on the work of

ut no direct (causal) relation shown that the Iens model mirror model’. er ~b~~~ive or subje e terms in the description of ity is d in two different ways, main’ f objective or subjective owever~ only one reality appears in the phenomena ‘objective’ or ‘subjective’-on the contrary e subjective reality should (indirectly) be ta it: they are both to be described so as to com$y with the ame way, when making comparisons oniy ence value for the identity ctive system of description referred ts it: objects can be C+ so as to comply with it, e its own identity. e9 ram the above tt would follow that in perception the objet tive and the subjective were connected by phenomenal unity, in the description by the idea of identity; however, the tmity cannot be perceived. nor can the identity be directly described, thus the direct way from the one other is completely barred. Just as in the Brunswlk Model there are two opposite wets of variables here, but instead of a mediatine 8 freely tr~~$~ttin the train ofevents, a barrier is found to exist, in perption as well as, with respect to the train of thought in the deswiption.70 the optical counterpart of a lens--a mirror--a model can that would apply to the present method of description. A mirror indeed acts as a barrier, since the light touching its surface is reflected mstead of being transmitted; moreover, its function as a so In close telation to the idea of identity, the concept of ‘in between’ can be applied to both objective and mbjective relations (see section 5.6). 70 The report of the experimental evidence with respect to the existence of a barrier zone had to be postponed to the next part of this paper, where the general experiments will also be discussed.

262

H, K. W. MOED

reflector fits, in well with the train of events which can be observed in experiments on perception. When thti: objective stimuli are ‘touching’ the subject a behavioral ~ reaction of tnat subject is reflected bat into objective subjective, perceptual response (e.g., subjective COPOUT) any reality value in the objective system and can there referred to as ‘virtual’. Here the term ‘virtual” is borrowed from the physical model of a mirror, but is used in a wider sense; to the perceptual model, the term would adequately desc in which the subjective variables are to be handled in system of description, as well as the objective variables in the subjective system. With respect to subjective reality the functions of the minor are th same as in the case of objective reality, the ‘real’ and the ‘virtual’ bein interchanged. The subject directs its attention towards the object, from which, when it is ‘touched’, an impression is reflt:cted back into subjective reality. The origin of the objective stimulus, however, cannot have realtty value in the subjective system and can therefore only be descri as ‘virtual’. Since the objective and the subjective systern are separated from each other, it follows that the mirror must be ‘in between’
CONSTANCY AND

CONTRAST IPA

263

and subjective reality. Contrary to the relativity of the this whole is given in an absolute way ity’ and ‘identity’ forming the barrier oth the objective and the subjective r~f~~r~dto that absolute whole and both ed by it in an ~b~o~ut~way-the ideal limit, however, tw~~~~two wholes, and conse tw~as~d~d~esswould arise and the mirror, ht seem to be double-faced and n itself. However, this apparent in fact only arises om the observer’s taking in succession the nd the subjective point of view. ing to these two possibilities n in the model: the mirror takes here the form of a double-mirror, consisting of two planes which visits directions. When using this model, however, it should that its duplicity is only relative; in an absolute sense the mtrror is 0~1~and from this oneness it follows that the two sides are in fact. identical. fn geometrical terms: there must be a one-to-one relationship between the points on the two sides of tne mirror--each point on the identified with a definite point on the other side. one side is to Since the functions of the mirror as a barrier and a. reflector are the same with respect to the objective and the subjective whole, the form af the two reflecting planes in the model must be the same witih respect to both wholes. Thus, if these planes were curved, their curvatures site directions; in that case, however, there would en the two planes and the mirror would indeed be uently, the mirror i:n the model must be perfectly plane, witksu$ any curvature, and without any spatial separation of its two faces. only an initial rough outline of the mirror model a few short-cuts in the description :;till have to be amplified on.71 Firstly, the objective stimulus will not really ‘touch’ the subject itself, neither can the object really be ‘touched’ when it is envisaged by the 71 Only the mirror itself is described;the two spaces will be discussed in section 9.2 and chapter 10.

the mirror in the perceptua’l tivct reality its function

a& would be formed terminals cannot

ORt.k two ~~~~~ of the double-mirror respectively the mkrer could possibly be ‘touched’. ascription of the mirror model still ve” and the ‘subjmive’ are completely separated not di&y wrqarable, it has still to be explained the same model-of course, by also representing the barrier ii1 the e reasons. ‘wking around the mirror” would be so far as it implies a direct way from the one into the not directly represent objective, y ~ssibilities. Im the foregoing. et with, namely, in the concept mirror a ?rue image of the object could be obtained. priori. In the same way, the model coulii’ be ve !,ystem as the renl one, but it ccruid just

266

H.

JL

W.

MOED

as well be used in the opposite sense and would then represent the subjective s,ystc:m; thus, in fact, there are two models in one. ‘T?Kmirror itself detcrmines$ geometrical relationships only, which called neither belong to objective no: subjective reality, but could th the ‘ideai’-they are determined by truth in the abstract sense. which objective and the subjective car be referred to this ideal thus forms a mediate betweer two systems which cannot di tlY compared. To make this cles?r, again a comparison with a common mirror may be made, the phyt;ical modei of which is shown in fig, 36.

Fig. 36. Phyr ncal

mirror model.

M mirror; E real eye-point, 1 rei 1 iIl’Ii3ge;E* virtual eye-p&It,

/*

virtual mage.

Fig. 36 is well known fron textbooks on physics, Gth the exception of the second ‘eye-point’ EJ , Sy this completion the whole fi symmetrical vvitlhrespect co t re plane of the mirror ; of course, there is symmetry in a geometrical !ensc$only. Functionally there is no symmel try, since only one half of t le model can be realized. Assunrin that the ie+fthalf were realized, then the right half would remain virtual -it could be realized if a double-mirror were used and envisaged from the other side of its plane. Thus, by using a double-mirror, the physical model would be completely sym’metrical, in so far as the same person Could use the mirror in two symmetrical ways in succession. 1 and I* m the real and the v+tual image, respectively (if the left half of the figure is realized); E and E * may be called the real and the virtual

The two images

show 8 point-to-point correspondence, ing formed by projecting the same nd E* respectively. Thus, the metrically, in a symmetrical way, n in the mirror; for that reason e term may be applied to the two represent the eye of one and the r in two symmetrical ways in

istinguishing of ‘physical* and define physical wholes in the al devices beams of light are ht tines without any regional subdivision. Each beam forming its terminals; in these is ern~tt~d~ reflected, refracted or absorbed. For the present purpose such a continuous train of events between two discontinuities may be called a physical whole. The straight lines depicting 36 indicate two such physical wholes, I -+ M e separated by the discontinuity M, namely, the ardting the different wholes In phy:,icali science the discontinuitie are studied and y causally dete’rmine aws the connection between the wholes is restored in thz description. Thus, besides the distinction of separate wholes there is a train of thought going in the direction of ter’ wholes; for the present purpose an ‘objective’ whole may be d as a complete train of events having its one terminal at the eal) terminal at the mirror plane of the perceptual modei, 73 Objectively then, the realized part of fig. 36 will belong to one whole: there is a direct ~~~~ll~al)train of events running from I to E. The dk74 AS mcntianad irr the description of the perceptual model, the real and the ective terms are replaced by subjective terms. virtual will intorch case of the physical model in fig. 36: the terrr!s T!ris provce skw to ’ and ‘virtual’ irniip used in physics are objective terms-in subjective terms the image I would ba virtual and I* real, since: only the latter image is seen by the

subject. lls In the same wry, a ‘subject&’ whole may then be defined as a compbte ‘train Of events’ having its one terminal at the subject and its other (ideal) terminal at the mh~or

plan0 of tile perceptual model.

268

H. K.

W.

MOED

continuity shown in the figure where the (physical) rays are broken does

not form a break at all in that objective whole-the reflection against the mirror is a fully determined link in the causal chain, just as the other links (otherwise, no law of reflection would be known). Therefore, in the objective model (fig. 39, the direct connection of I and bY a causal chain of events is repj:e:;ented by a single strai t line, just 8s the physical wholes in fig. 36.

M

Fig. 37. r)bjective mirror model. M mirror, E eye-point, I given image,IE twin a,f stimuli, EA train of action, A identical image, A’ deviating ima

Point E, representing ir, :ig. 36 the human eye, is in fig. 37 the ideal terminal of the causal train I + E; as mentioned before, on the one hand this point where the mirror is ‘touched’ will never be reached by the causal chain, on thl: other hand it must be considered to fully deiermined .

The reflection by the physical mirror in fig. 36, the refraction by the lens of the eye aqd the, absorption by the retina, as well as the tram+ mission by the optical nerves, are links in the causal chain, but it would not make sense to represent them by points in fig. 37--for this would again introduce regional subdivisio.as in the \ybjective whole and would thus be a return to the physical point of view. Ph>zic41;, the links of the causal chain must be distin&shable by a typical constant; by means of that constant the chain considered can be isolated from a causal network as a separatla whole (for instance,

n of an organism). In perception this constant will be iven image: throughout the causal chain nothing to or lost of that image-any loss or addition (e.g., c) is to be considered as an irmperfection in the chain. ed on by the causal train in the form of certain s; for i~st~nce~ in the optical part of the train mined by the spatial position of the points of the y Jac~~sch, in his experiments on constancy the absolute values, but only the ratios of the brightness to be important (11; p. 311). ive rise to a changed view of the function of an energetic value, ‘causing’ some effect when ‘tou it appears as a dimensionless nship. The causal train appears then to be determined by a final namely, the projection of that relationship on the plane of the mirror at the ideal terminal Therefore, the given definition of the objective whole may be corn ted by the condition that the characteristic relationships at the terminals I and E of the train should be identical. In perception only the relation between the dimensionless values at ant; considerations about the terminals I and appears to be im y and the diRerent causal links wou refer to the movement itself of the train of events and belong to the domain of physics. Line EA in fig. 37 represents a second train of events, namely the action reflected back into objective reality. ere the same difference with a physical reflection occurs as has already beet4 mentioned with respect to the concept of coincidence in perception and in physics. Since in the ideal terminal E no causality occurs, here no ri id ‘law of reflection’ will be valid-the dimensionless n E cannot causally direct the train of events E -+ A, but it ‘acts’ as an ideal model. For instance, a subject copying a sheet of numbers may indeed give a ‘true copy’ of the original, but there might equally well be a number of errors. There is only one final result of the action (point A in the figure) that would ‘truly’ reflect the given original; an infinite number of deviations would be possible (apart from probabilistic considerations as to their realization). The one ‘true’ image would result as if the whole process were determined by causality--as z$f a rigid ‘law of reflection’ were valid at point E. Therefore in fig. 37

I-L rc. w. MO

270

this ideal case is depicted in the same way as a physical reflection a a real mirror would be ind.ic:lte;l; any deviation from this ‘standa is then to be indicated by c&ation fro the standard reflection in the mode!! (e.g., by the dolted line EA’). In fig. 37 the termir als I and ,A are indicated at the plane of the mirror; in the ideal case descr and IZA representing two clifS3rentobjective wholes are then s in reldtion to 8 perpendiculsr to the mirror plane, and point exactly halfway on the (indirect) ?ath from I to A. If the act A did not truly reflect the image !’ , the symrletry in the model would be distu I n the case of a physical reflecticIn against a real mirror, the component of the movement of the l”gM in Lhedirection of the not show any discontinuity at tl e point of reflection same might be said with respect to the perceptual model: in the ideal, symmetrical case there wi.J be pprfec L continuity along the mirror plane at point E (fig. 37), but any &via &ionfrom that case would imply a discochlnuity in the dire&an of *ille mirror plane. ‘6 This break in the continuity z:L:ng the mirror plane would then clearly indicate perception and action as two different wholes in objective reality, whereas in the idea1 case these two wholes would function as if they were one. In the example given, wile; c: the subject copies a sheet of numbers, the result would be identical with the original as far as the numbers themselves are concerned- -apart from the incidental realizations of these ideal contents on twk) sheets of paper. The latter, in a way, are Wo screens on to which the same image has been projected. Thus, from an ideal, absolute pcint of view the identity would appear as a unity, but in a relative sens: dupl city appear;; to occur, as shown in the following scheme. -----_

I ----_

Epgn-------

~4.-.__~~_~_~

S&ml~ III

In this scheme points I and A represent two identical images; the relation of identity is incicated symbolically by the equality of the w The musal trainof events will actually not reach p&t E, but the movement ikdf may go on (as a train of thwght). ASwill be shownin the sequel,a discontinuity

&cYocclirsin Ihe QlcWHkWnt i tsdf.

COWRAST

IIIA

271

int E. Two different points dependent on the given which does not depend (3r~~~t~vepoint of view, E&l, the images I of the (finite) distances the absolute point of view, aba, ist~n~~s would be the direct unity, + 1, on, as if they were one. r case would seem to be obtained if in the t of transparent paper, series of numbers could --however, there wo ne ‘screen only, name!y, the uld a copy be obtained, the e figures into meaningless ction of the ideal contents ssary either to recognize ct is performing the act, of the ideal model there would be a sheor mechanical guidance f identity can be used cnerslized, objective sense. sense only, not in ealized but it may be bsolute point of view, lly determined as an idea! limit. For instance, indicated ORthe line actually drawn in the scheme, deal limit which could eve.- be reached if a movement along the line were continued in thought outside the ~c~er*~~,The movement could go in the direction indicated in the scheme, or in the opposite direction; in both cases the same r~~ch~d~therwise the absolute point of view would

izes that in objective reality the identity only appears in an indirect way : as a duplicity of two ages, observed from a point the identity is barred: th:: midway between them. The direct way absolute pain of view lies at infinity, and from the relative point of view an inversion in the form of a half-turn is implied in the process of identification--no direct unification would be possible. A few examples may serve to elucidate the above. In the present experiments on constancy and contrast, the subject stands halfway

2’72

H. K. W. MOED

between the two half-fields *aIone side of the ‘tableau’. Especially very young subjects make almost a half-turn when they are looking at the two objects in succession, b It generally the inversion is not so conspicious. It can, ho?vever, ~iways be recognized by a generaii the concept of ‘midway bet:veen’. In scheme III this betweennes~ is given in its most simple for-n, but generally a complex is 0 the inversion and a constant component perpencomponent showin& tficuIh.r to the former. Looling at the two cards in su ssion, the component of :h: line of ‘-viewdirected towards the point midway between the objects remains constant, whereas the other component (from the mid-point toG7%rd:* the objects) shows the inversion. In the comparison of objects the ?ubJe:t is 8 mediatin taking 3 midway position. 111other cases the subject himself identifies with another person; the sL
CQN3TANCY AND GONIRAST HIA

273

but no unification would be obtained; to half-t urn would be necessary. idence cotrld be obtained by a half-turn d the axis of symmetry, lines IE one. Any deviation AA’ (fig. 37) a%one line; since only dimensionA (as mentioned relative deviation of the objects or model will be applied to the present

the ~bjcc%ive model to the matching of cards, one ina!‘, the other being exchanged until the most copy of that nal has been obtained: In the ~ideal) standard case two identical cards would be obtained, Of course, no ide~%itic~tion will be possible until the matching of cards en finished; in the final stage, then, the cards being compared but ndled, a problem arises as to the nature of rhe train of action EA. The solution of this problem has led to a symmetrical description of A. Both trains Imply a ovement, which in objective reality is considered to occur in a ‘field of action’; the action itself can be described as ‘touching’. The latter term has already been used in the caJe of the stimulus train, JE; in a virtual sense it might be said rhat the subject would be touched (by the object), but in objective reality an ideal terminal point is given, represented by point E on the mirror plane. In perception, however, esides a receptive function an active function occurs, which in the case of cutaneous perception directly implies neralized sense this term may equally well be used to ‘touchin cscribe ohe action in the other cases, where the terms ‘to look at’ and ‘U.Jlisten to’ are usually applied. 34 Virtually, the object would be touched by the subject, but in objective zality an ideal starting point is given, which is represented by point E on the mirror plane. At this point E the dimensionless relaoior:ships transferred by train IE and projected on to the mirror plane are received; from E they are transferred by ________*___

generalized concept ‘to touch’ has been applied to the receptive ‘Das Erlebnis der kiirperlichen Beriihrung ist die empfangende Funktim ldes L&xx, die t,ich in den Einzelsinnen nach Sensibilittitsgraden abstuft’ (29; p. 151). 77

By Klages

the

function in perception:

2784

H. R. ‘Y. MOED

EA and eventually projected on to object A, where they cab be compared with the corresponding relationships of A itself. train

Experimentally a direct indication was obtained that in the c~mpariso the one card is virtually laid on top of :he other and that here only relationships are important. In experimenrs with different subjects, at the subject asked to correct the positlorl of a card, saying that by its deviation. ?c appeared that the experimenter, in exehan unintentionally gi,ren it a minute angular deviation from its correct position. special invcatigatior, It was then found that a very small angular deviation irritating disturbance 19 the performance of the experiment. With greater deviations the efkct &appeared; however, it reappeared when the difference in position of the ‘L’WIO rectangular cards compared became about 90 degrees: a small deviation from that value again gave some disturbancp. 14 parallel displacement of the card, out of the centre of the half-field, did not have any effect at all. Apparently, a dimensionless measure (the angle) is important here, whe linear measure (the lengths of the sides of the cards, or the amount of parallel displacement) does not aflect the experiment.

In the experiments two cards are looked at in turn; in the stand case the turning-point will lie midway between (in time)--there is then complete spatial symmetry and no reason why one of the two identical cards should be looked at for a longer time than the other. In physical terms, the spa?ial symmetry would imply symmetry in time; objectively, however, there is no causality: the temporal symmetry COU!~ be disturbed, one card being tntentionally looked at for a longer Fime than the other.‘* Therefore, an ideal standard case may be defined where the obs$rv is perfectly balanced-s ifthe symmetry in the spatial comditio causally imply the symmetry in time; looking at the cards in 8 way can be expected to constitute a near approach to this ids The successive reflections occurring in the ideal standard =ase are determined objectively in the space-time diagram shown in fi In this figure two identical objects A and B, looked at in turn, are indicated in a row A-B-A-B in the direction of the co-ordinafg of time in the order of their appearances in the field of vision. The turnin are represented by the eye-points E lying midway between thl in time. Points E lie on the mirror plane and the co-ordinate of space indicates the objective istanG from that plane; thus, row EEEE determines -_ ?* An incidental observation showed that the results of the experiment may be afkted

by inteti!ional asymmetry in time.

Y AND

I

i

I

C33mparisonof &j&a

CONTRAST

1IIA

275

-f-lJ-ll

- reflections in objective reality.

dentical objects, E eye-point.

the (absolute) zero. If represented the sensorial eye, a rslative zwo in space WSUM be obtained; in that C;W the distance of the objects from the eye can be measured directly and will be the same for both objects (owin to the spatial symmetry of the experimental arrangement). Another point of the optic tract will give an additional ‘dkance kd by the causal train, which cannot be measured directly but II in bath cakes will be the same; the latter applies also to the ideal the mirror plane, which cannot even be localized in space but

~~ve~h~les$ must be considered to be fully determined. The entire ‘objectives distranct: of the objects from the mirror plane is thus found tl? the same for both objects; in the diagram this constancy is represented by the constant distance of the rows AB and IX. gure the trains of events, running in both directions between plane and the objects, are indicated by straight lines--just . 37 and for the same reasons. A reflection occurs not only al. the eye-point, but also at the object observed : the movement is oscillating, going to and fro in the field between the mirror plane and the objects. Of course, just as has been found with respect to the reflection against the mirror, the reflection against the object will not be determined in a causal way-the object does not emit rays of light because it is looked at! In the ideal case of two identical objects, however, by each

train the Same dimensionless relationships will be passed on and all the reflections will occur as if they were causally determined. l-or that reason the refiection in fig. 37 has been dspicted as if it were a physical reflection; from fig. 38 it can now be seen that the ideal reflection not only {WI, but ntwst be represented in that way, as follows geometrically from YOWS AB and EE bci 119 parallel and points E lying midway between the objects in time. The stimulus trains and the trains of action make the same an with the perpel~dicular to the mirror plane; it follows then that all the time intervals shown in the figu-e will be the same. The interval can be measured by observiii g the eye-movements of the subject; apart from the unknown scale factor of 1%~co-ordinate of space, she entire diagram in 5g 38 is then objectively (lztermined. Fig.. 38 shows that the concept of ‘touching’, used with reference to percqtion, differs from the physical concept implying coincidence in spacf, and time. In objective reality there is no direct touching of the mirror and the objects; this would be impossible since the causal trains &J sot actually reach the ideal iimit in objective space. Moreover, there cannot be coincidence in time, sin?‘* the movement in the field beuwet:n the mirror and the objects cannot go in opposite directions a.t rhe same time. I’he coincidence in direct touching implies causally determined reciprocity (if P touches Q, then Q touches P); the reciprocity of touching shown in 5g. 38, however, is not determined that way, but is given as a potsib&y only. For instance, one may hear something, but not listen; one: m-mylook at something without actually seeing it. On the one hand, freedo n instead of rigid cause ity is obtained here; on the other hand, .?wing to the time-delay the organism could be damaged by extreme l;tirn~~li-tlleref~)re at intermediate points of the causal trains the possibility is given to reduce the delay by causally determined reflections (reflext1s). f in rig. 38 the two objects compared were not identical, tlieir distances from the mirror plane would still be the same; thus, rows AB ana3HI in the figure would still be parallel. Moreover, in all the experiment<, performed a certain periodicity appeared to exist when the crrds were looked at in suosession, with incidental break-downs of that regu& ity.

CQNSTANC‘X

AND

CONTRAST

UIA

277

r, must have changed in the figure; since the d by the objects A and B being different, it is to be -point E in the successive observation will e objects ia time. Only the converse has so in time the result of the cited (see note 78) y observation of the eyet check would be possible. d those of action will then make different r to the mirror; since the slope of the straight indicates the velocity of the movement, it oints of r~fl~ction a jump in that velocity will occur. y of the movement (apart from the reflection) since in physics a refraction also jump in tile velocity (of light). Generally, then, in the coiaparison of two objects there will be reflection aud refraction, but in the ideal standard case of two identical objects only reflection occurs ections shown by t e objects in fig. 38 entail that here also the receptive function and the active function must be distinguished, or, in oth-:r words, the passive and the tive ‘side’ of each object. c shows, in the comparison of o objects the active side of cct is compared with the passive side of the other object, and vice versa. However, since the objects are identical, nothing in the figure would change if the objects B were replaced by objects A, i.e., when the same object A was observed for a longer time in succession. In that case the active and the passive side of the same object would be compared. Thus, not only can two objects be found to be identical, but also the identity of one and the same object can be recognized, in principle, same series of observations. It is indeed well known that by looking fixedly at the same object (without any periodicity) the recognition of identity would be aRecked; as observed by Hering the object changes its appearance Pnd eventually even disappears (9; p. 265-266).‘” The receptive function of the ob;:ct, constituting its passive side, can be ascribed to a certain ‘it’ receiving the trains of action. The other _._-_ ‘@

_

On the other hand, upon a sudden in’ erruption in objective reality the reflections

in subjective realty do not stop at once, but they produce the well-known after-images.

278

H. K. ‘Pa. MOEB

side of the object see ns to be self-active, since here the stimuli emanate. Mowever, in objective reality no real self-action is found; on closer examinatii3n each so-called self-action Iproves to be instance, the cards in the experirrents emit rays of illuminated-it is their reaction t) ihat illumination. I a, mass particle can only react when, by outer force, i change it”; motion. Therefore the active function of the object may ascribed to a self-reactive prrizciple-in short: the ‘self’ of ths object. Thus, the ‘identity’ (Dfa single object refers to the unity forme the ‘it’ and the ‘self’--in short: the unity of the object ‘it-self”. a,gain, only the inverse unity can be observed : by trains of stimul trains of action, going in opposite directions, the object is envi from two opposite ‘sides’. When trying to observe the object from one ‘r~ide”only, nothing at all will be seen : the object disappears. In the same way, in the comparison of two identical objects, the ‘it’ of Lhe one object will unite with %C ‘sdf of the other object. Were again the result of this unification cannot be observed directly : a functional whole is formed showing two functions of opposite sense. The difference between this and the case of a single object is that, here, owing to the different location of the objects, the inversion implied in the identification is in a way depict sd in space : the two objects form symmetrical images with respect to th:: point midway between, or--in the generalized sense of ‘betweenness”-with respect to the eye. In fig. 38 the inversion is also depicted by a different (spatial) location of objects A and B, but here this is ahought to represent a different location in time. Just as actually in space, the objects could be unified by a half-tarn around the axis of symmetry (in fig. 38 by foldin paper aEmg the #dash-dotted line through point E), but then the objects disappear from sight . In the fc regoing it was found that identification implies a functional inversion, which can. be df:scribed in terms of space or of time and cGn be depicted in space (with the exception of the result of the unification). In the identification of objects the inversion is conditioned by the reflections against the mirror at the eye-points E lying midway between the objects compared; in the same way, in the identification of the eyepoints the inversion is condition by the reflections against the objects lying midwny between the successive eye-points in time (in fig. 38 two eye-points can be unified by folding the paper along the dash-dotted

mrn~~ry going through the object midway between). Conseque~tly, the identity of the eye-point can only be recognized if stimuli t as that of the object can only be recognized if the matched the ideal reflections will n. The inversion and the full recogniwill then also Yaedisturbed, with respect to the objects under standard conditions will the will not perceptibly affect the identiit follows that the identity of both the subject) and of the object can only be reis observed; this recognition will generally o objects are matched; even the possibility of ref no stimuli at all are received. It is indeed a well-known fact that generally matchings in experiments on constancy or contrast are not wholly satrsfactory, ar .~i that the complete absence of stimuli entails a loss of personality. . 37 in fact one period of the diagram in fig. 38 is shown; the contents of both fi ures are e%entially the same, since in fig. 38 merely r~~etiti(~~s of the same period are given (even in the case of two objects not being identical). Applied to a single object, fig. 37 shows explicitly its two ‘sides’, 1 represeWing the active side of the object (the ‘self’) and A the passive side (the ‘it’ of the object). The two sides of t object are indirectly connected in perception by the causal trains I and EA; the direct connection by means of a causal train (which had to be indicated by hk line AI) is not possible and thus a gap is seen in the figure between A and I.80 However, by means of an eye-paint at infinity of the mirror plane a direct conneet,ion would be possible; as shown in scheme III, this ‘absolute eye-point”, Eabs, would give a direct unification. In the figure this virtual process of identification, which cannot be described in causal terms3 is indicated by the dashed line AI. By virtue of the identification, - _._.-__----__ 80 Hereagain it would follow that points I and A must be indicated at the same distance from the mirror; otherwise, a causal train could be depicted connecting these pokts directly and touching the mirror at a re!*\tive eye-point (by producing the straight line IA towards the mirror plane).

280

E-X. K.

W, MOED

going in the direction ‘it’ + ‘self’, a closed circuit is then obtained; one circulation in that circuit may be considered to constitute the ‘single observation’. The single observation defined here is one out of a series, isolated by abstraction from the continuous process. The complications implied in the starting and in the terminating of the entire series of observations are not considered here; the model (fig, 37) depicts a continuous movement only, which in the periodic diagrawl (fig. 38) would be ‘quasistziollary’. The ‘single comparison9 may, then, be defined by two single observatio:ns in succession (of tix same, or, generally, of two different objects). In fig. 38 the single comparison consists of two periods in succession; if one period is laid on top of the other, by a parallel movement in its plane, fig. 37 is obtained (the circuit being closed by the identification)*i. Thus, a single comparison is defined by two sucozssive circulations in +he mirror model. Generally, an.’arbitrary number, of single observations is represented by the same number of circulations in the model, which can be thought to ha.ve arisen from that number of periods in fig. 38, all of them depicted on top of each other. The passive function in A (the ‘it’) will then refer to each of the two objects in turn, and the same &err&ion will apply to the at’:tivefunction in I (the ‘self”); the reflection against the mirror!, however, will always refer to the same eye-point E, all the observsliiona being prxformed by the same observer Each eye-point in fig. 38 is the mid-point of one period; it lies at

the Gntre uf a single observation. The different eye-points in the figure all refer to the same eye and ithe periods will thus refer to the: function of that eye. Two successive periods must then be demarcated in time by at least one moment where, in one way or another, the normal function of the eye is blac*ked out. The same conclusdon is found, from another point of view, by considering fig. 37. In that figure the gap A-I in the circuit I-E-A has been bridged by the ‘virtual process of identification’ mentioned earlier. Nrtually, here the adirect unification of images A and I would occur, and, from the given examples, it may be anticipated that the result of this ticzion cannot be perceived. The molnentary black-out may be 81 of came, the perMs in fig. 38 murgtthen be measuredbetweentwo succe=live objectsin that figure.

CONSTANCY

AND CONTRAST EIIA

281

located at the point where the dotted line AI. is intersected by the symmetry line of the figure, thus at the centre of the identification. ck-out will not be perceived as such, since the unity n, in a way, be perceived. 82 observation implies two non-causal moments, 38 by the points where the reflections against the object and against the mirror occur, and in fig. 37 by the points of the circuit on the symmetry line of the model. At the eye-point the limit of objective space is reached by the moveh the physical space in which that objective space has been depicted does not terminate here. At the object the objective time (i.e., time with respect to the observation of the object) is limited, though physical time (in which the objective time can be thought to be ‘depicted’) goes on. Still another difference may be observed between the reflections against the objects and those against the mirror. At the objects two different ‘sides’ are functionally determined in perception; in thought their identity may be recognized, but in perception only the inverse unity is given, the two cd sal trains going in opposite directions. At the eye-point the two causal trains do not determine two different sides: in perception this point is given as a unity, where the two different functions are combined (on the s me side of the n-irror). It is the only point where the original unity of he phenomenon is still present, when phenomenal reality is broken up in thought into two different systems of reality; broken away from the original whole, the eye-point still allows a distant view of that whole-in perception. kIowever, in perception phenomenal unity is only given in an indirect way-as the inverse unity---as if reality had two ‘sides’. The inversion is introduced by thinking: the one dye may turn ‘inwards’ or ‘outwards’--CIS if there were two eye-points, the ‘inner eye’ looking inwards and the ‘outer eye’ looking outwards (o course, the latter ideal point is to be distinguished from the outer sense organ). In fact,

88 The periodic character of perception found here complies with the description

@en by B&son of the general character of perception, intellection and language: ‘le m&car&me de notre connuissance usuelle est de nature cin6matographique’ (24 ; 305).

p.

282

H. K. W. MOED

it is not the eye that is turning, but here the entire system of thought has its turning-poitit, allowing the description in either objective or subjective terms. Tierefore, in the description in objective terms, the inner eye can only be virtual; in babjec%ve terms the outer eye is virtual. As mentioned in section 5.17, the description in objective terms and the description in subjective terms are bound together by the idea of identity, which is directly known. In the model this is represented by the two Zeal points on Dpposite sides of the mirror, indicating the outer eye a ;Id the inner eye; in perception the identity of these eye-points is B?~ctly given. ln the further devellopment of the model the difficulty is that two different: systems of description should be combined, i.e., represented by the same model. It is true that the term ‘virtual’ would be adequate in handling the subjective values in the objective system, but first the solution of the principal difficulty has tlo be found-the choice of a special term does not imply any solution at all! A direct solution would clearly be impossib!e : in objective reality the different physical wholes could be combirred to greater wholes, the discontinuities separzuing the wholes being studied in physical science and the connections being restored in the description by causally determined laws; eventually then the ideal limit, the objective whole, wouli!d be approached; no science, however, could ever restore the unity of the objective and the subjective whole, the barrier here being the consequeme of abstract thinking applied to the given phenomena! The direct unification of the two systems is thus impossible, but conversely the way in which the-; have separated may be traced; in the following this will lead to an indirect solution of the given problem. The splitting-up of the phenomenal whole into two separate systems implies the general problem: to understand that a whole could give two new wholes-in fact then a part has been substituted for a whole! In the given general form the problem ztay be studied by means of LDZ~ given example; here the physical mirror model in fig. 36 will be used. This figure shows in a striking way how to understand that a whole, when broken into parts, may give wholes again. Objectively, here, the tract I-M-E indicates one causally determined whole; in the figure it has been broken into two wholes, indicated by straight lines running from a disccn%inuity at the one terminal to a discontinuity at the other

CONSTANCY AND CONTRAST XIIA

283

terminal : the wholes I -+ E and I + E*. However, only pati of each whole has been realized, the other part remains virtual; thus, actlrally the new wholes are on y part of a whole, but virtually they may be considered to be who1 oreover, the figure shows that the virtual part of a new whole is the (mirror) image of the missing part-it is, as it were, the ‘scar’ of een broken off. The forming of new w ales in figure 36 can be considered to be preceded by a duplication of the ori nal into two conjugate wholes, I-M-E and I*-Me-E*, where M* in the nigure coincides with M. Each of the new wholes then takes part of the one conjugate and part of the other. his may be compared with in fission in biology, where the forming of new wholes is preceded by duplication of the essential parts of the cell. The cenformity here found may indicate that a general solution to the given problem has in fact been obtained. In fig. 36 the physical wholes IM and ME have been completed by the virtual image of the part that is broken off from the original whole IME. In the same way and by the same methods the objective whole image of the part that is in fig. 37 has been completed by the virt broken off from the original whole. Thus, es IE and AE are virtually produced at the rear side of the mirror*s; from the objective point of view it is indeed possible to continue the movement depicted in fig. 37 by a train of thought which would virtually go outside the domain of objective reality. The ‘scar’ of what has been broken off seems to recall of another reality---what is not actually found in objective reality is at least felt to be missing there; by this feeling the train of thought can be directed even where causality is lacking. Thus the movement in the direction I -+ E can be thought to have a continuation as if a certain ‘it’-which can never be realized directly in objective reality-would eventually receive the given image. In the same way the movement in the direction E -+ A can be thought to be the continuat,on of a preceding movement, czsif the action originated in a certain ‘wlf-acting principle’ which can never be realized directly in objective reality. 84*85 88 This is not merely copying the physical model, since the generalizationis impliedthat the observation may be ‘true’ or not. The latter ideal case has been depicted in the objective model by the coincidence of the eye-points at the two sides of the mirror. 84 In subje&ve terms one is free to act (or not to act) within the limits set by

284

H. K. W 0 MOED

From the foregoing it follows tha! the objective and subjective reality

can only virtually be combi ed in the same model; actudly there are two models, the objective one in fig. 37 where the eye is turned ‘outwards’ and the objective whole is considered to be ‘real’, and the subjective model in fig. 39 where the eye is turned *inwards’ and the subjective whole is considered to be ‘real’.

M 9

Fig. 39. Subjective mirror model. M mirror, E* eye-point, I* given image, A* identical image, 1*-E*, E*-A* inner movements.

At first sight figs. 37 and 33 seem to be quite similar; however, there is a fundamental difference. In fig. 37 objective reality has ueen depicted by means of paper and pencil, which are clearly attributes carrying the mark of the objective; subjective reality has been indicated in that figure by its (inverse) ilmage. In fig. 39, however, by the same objectively ,giv/znmeans subjective reality should be depicted as a reality, which is clearly impos:‘ble. 0nl.y the hand of an artist might transcend the limits given by objective reality here, and depict the inner movetnents of a subject, but within the limits of science this would not be pcxible. Therefore, m fig. 39, just as in fig. 37, subjective reality is represen .ed in -PI objecxive: reality. Of course, the reactions of a person may be studied, but the ‘1he is not uxrsiderextas the subject, but its an object (of investigation); moreov r, any ‘causality’ found would only be US if. 85 .In both cases, the transgrekon of the barrier would imply a jump k t’lought, one iink being mikng here.

CONSTANCY AND CONTRAST IIIA

285

an indirect way, as the inverse image. The entire model in fig. 39 is then inverted; a’t the right-hand side of that figure a second inversion arises from the objective reality eing considered to be virtual, and, since the two inversions neutralize eh other, here objective reality is depicted in 8 direct way, just as in fig. 37. Summarizing the above it follows that in figure 37 objective reality is depicted as real, in a direct way; subjective reality as virtual, in an indirect way. In fig. 39 subjective reality is indicated as real, but in an indirect way, objet ive reality as virtual, in a direct way. In fig. 39 the ‘it’ and the ‘self’ of the subject are depicted at the same distance from the mirror plane, just as in fig. 37 the ‘it’ and the ‘self’ of the object, and for the same reasons (see, e.g., note SO). NO reason, however, WUS found why these distances in the objective and the subjective part of the models should be the same, and also in the physical model the i’wo parts of each whole differ. Thus, the only remaining possibility is that the ratio of the objective and subjective distances from the mirror represents a personal constant; this would comply perfectly wi; h the foregoing remarks about the formation of new biological wholes, Biologically, only the whole formed by the parts is fixed, but not the parts themselves taken fro each of the two conjugates. Similarly, fig. 36 could be drawn in different ways, the entire length of the linear wholes IE* alld I*E being fixed, but the parts taken by these wholes from the two conjugates IME and I*M*E* differing. The distances from the two terminals of each train to the mirror would then in generaI be different, but the total of the two distances would be fixed. In the same way, in figs. 37 and 39 the total of the two distances, i.e., of the objective distance (between the parallel IA and the mirror) and of the subjective distance (between I*A* and the mirror), may be considered to be fixed--in a way, it represents the gap between the subject and the object resulting from the splitting-up of phenomenal unity by abstract thinking. Virtually, the eye-point is between the object and the subject, but the two distances may differ: thinking, though universal, is only individually performed and each person may split up the phenomena in h?,s own way- the one individual will in his tho’ughts stay at a smaller distance from subjective reality, the other from obj,ective reality. Since only one of the two systems of thought would be possible at the same time, here, a direct method of measurement would be provided by comparing the frequencies of objective and sub.ilective

284

H. .i_. W.

MOED

terms in speach and in writing. The higher frequency would illpiicate a smaller ‘distance from the corresponding ‘side’ of reality, the s)bj,jzctive or the subjective. The ratio of &e frequencies of objective and subjective terms may directly ble compared with the results of experiments on constincy and contrast, measured by absolute methods (section 9.1) and repres&ed by m#eansof the mirror model (sections 10.1 and 10.5). This uew field of investigation has not yet been explored, but ai1 indirect indication of the practical workability of the theoretical statements has already been obtained, and a short report is given below. In the fforegoing it has been shown that in the formation !sf new wholes any distribution of the parts taken from two conjugates may occur. Statistically, then, it may be anticipated that a great number of these who’les would show an even distribution, the individual diRert:nces being bahlmced in the average. Only by a bias could this even balance be disturlbed; hawever, the splitting-up of phenomenal un3ty crises from abstract thinking which is principally unbiased--though in andi’vidual thought deviations may occur. Thus, on average an even (virtual) Gpartition of the original whole may be anticipated. The ideal casz of perfectly balanced perception (and thought), Mhich would be ,tbz universal standard, is then defined bjl the even di:tribl tion of subjective and objective terms in thought, and in perceptitjn $1 the unbiased point of view with respect to the two ‘sides’ of reality, the objective and the subjective; in the model thie latter is representecl by the distances of the eye-point from lines IA and I*A* being :he s&me, i.e., half of the total distance. Indeed, in a generalized experiment, performed by six different subjects, the average factor 0.50 & 0.15 was found; of course, further investigations will here be necessary. By applying abstract thinking to the given phenomena, immediate experienoe of reality is replaced by observation from a certain dista,~ce. In other words: ‘immediate touching’ is replaced by ‘general. ted touching’, i.e., the distant action implied in perception. Distant, actions also occui’ in l&y-’ ,zcs (e.g., that of a magnet); in l.le past they gave rise to considerable difficulties in the description. The o&e of physics would be to describe causally determined! links of

CONSTANCY AND CONTRAST IIIA

287

trains of events; these connections imply in fact coincidence in both space and time (direct touching). 86 The generalized touching implied in the ‘action at distance’ led to ction of the concept ‘field’, in order to bridge the spatial the ‘distance’. The gap in time can be bridged by a ‘movement’ in space, but all efforts made to find a medium carrying that movement are found to be useless. However, as observed by Bergson, the movement does not imply something that is moving (‘le mouvement n’implique pas un mobile’-25; p. 163). For the given purpose, then, the description of the trains of events may be considered to be complete by using the concepts of ‘field’ and of ‘mot-ement’. In objective terms the field has already been indicated as ‘field of action’; in subjective terms it may be ca” ad ‘field of experience’. With respect to the movement the terms ‘outer movement’ and ‘inner movement’ might be adequate. In the subjective model, the ‘self’ is the given image of the subject; from here a train of inner stimuli arises which would virtually result in the outer action-actually, however, the mirror is touched. From the inner eye-point a movement is then se t back into subjective reality, where it is experienced by a certain ‘it’ that may be recognized as being identical with the self; the latter movement would arise virtually from something outside subjective reality. Here again, deviations from the standard case of ideal reflection would produce disturbances in the recognition ot identity. The forming of the objective and subjective wholes has been studied by means of fig. 36; the same figure may now serve to find the relation between the objective and the subjective model. The conjugate of the whole IME in fig. 36 is virtual; however, since ---__

86 Thus, at each non-oat&l1 link of a train of events the perception of the connec-

tion will be obscured either in time or in space; however, this will not be perceived itself (as a break in the train) since in the other dimension perception goes on. For instance, the two non-causal links occurring in each single observation will imply a blurr in space (when the two sides of the object in perception are interchanged) or a momentary black-out in time (when the two sides are unified). The blurring is most conspicious when two objects are compared (instead of a single object being observed) : the two sides which interchange are then located differently in (physical) space; however, even then the blurr itself is not perceived as a break - perception is not blacked out in time.

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a double mirror is used, the virtual may here be called potential: it COU~~ be realized-by a real eye placed at E s(and a real image given at I The double mirror itself would allow thl: realization of i .I’%conjugate of any given whole IME; thus it implies sheer potentiality. In the fi however, only one particular whole IME is given and the realization of its virtual image would give a fully deter,mined whole. Thus, the viral F’sa potentiality in which the form of the actual has l

already been given.

The ‘new’ wholes I + E* and I* -+ E in fig. 36 are partly realized, Fartly virtual. Here again, the virtual already contains the form of the actual; this form corresponds to that cf the realized part of the other whole, lying symmetrically at the other side of the mirror (of course, this correspondence implies the inversion given by any relation of sym.metry). Conversely, the realized part of each new whole corresponds to the virtual part of the other whole; in thf: latter the form of the actual has been preserved. In the isame way, the form of the objxtive whole which is given actually in fig. 37 is preserved in the virtual part of the subjective model in fig. 39; here this form is indicated symnctrically on the other side of the mirror. The same conespondence of fc rm is shown with respect to the subjective whole, which is virtual in fig. 37, and real in fig. 39. The relaltionship between the two modeIs being defined, an attempt will now be made to Scombine them. The two models are relative only: they are determined with respect to the relative eye-point E,E *. Thus, at least the condition that their combination should not show any absolute change, i.e., with respect to the absolute point of view (see scheme III) must be set. Under this condition, the direct combination of the two models is found to be impokble: by pnoving one diagram in its plane it can be made to coincide with the other; however, the ‘processes’ AI and A*I*, determined by the absolute eye-ptxnt at infinity of the mirror, will then go in opposite directions, whereas in figs. 37 and 39 their directions are the same. Thus, in the same two-dimensional space, the models cannot be combined; however, it would be possible to combine them by going outside that space. To this end, one of the diagrams is turned around line M untl it lies upside down. In other words, the two models can be combined by drawing them at opposite sides of the paper, just opposite to each other; the paper itself then serves as the barrier!

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ere, the answer is obtained to the query raised before in this section: ‘walking around the mirror’ does not imply a direct connection between the subjective and the objective; on the contrary, it implies going outside the space in which the model has been given. For practical reasons the two models may nevertheless be drawn on the same side of the paper; in using the model it should then be remembered that one half is virtual, but would be actual at the other side of the paper. In this way the perceptual mirror model in fig. 40 may be used; it visualizes the ideal case of perfectly balanced perception, the distances from IA and I*A* to the mirror being the same. t Eabs

Fig. 40. The mirror model of perception. E outer eye, A-I the object ‘it-self’; E* inner eye, A*-I* the subject ‘it-self’; M mirror, Eabs absolute eye.

In the model the ideal case of perfect coincidence has been shown (the case in which one stands ‘eye to eye’ wvith truth); moreover, the standard case of ideal reflection is represented. The ?;wo halves of the model are clearly conjugate, just as two mirror images: the mov.,ments take the same direction parallel to the mirror, but in the direcL_n perpendicular to the mirror they show a reverse of direction. The ob.ject-side and the subject-side of reality, IA and I*A*, may be called conjugate complexes : the interpretation of points A and A* (the ‘it’) does not show a reverse of sign, but the interpretation of points I

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an J I* ds~:s(the ‘self-reacting’ and the ‘self-acting’ principle, respectively). In common language the difference of the two selves is recognized : the term ‘self~~sealization’ always refers to the subject, never to the object. The entire diagram is determined with respect to two eye-points, the relative one lying on either the one or the other side of the mirror, and the absolute eye-point, lying at both sides of the mirror at the same time (the absolute is not implied in the splitting-up of reality, but, on the contrary, the two relative systems of thought should be referred.to it). Tbe absolute eye-point is self-identical--a relative eye-point will never directly correspond to it; thus, the two planes of the mirror are connected at infirnity.87 The diagram shows two triangles, each consisting of two movements determined by the relative eye-point, and the identification, which is absolutely determined (by the point Eabe at infinity). The form of the complete diagram is that of a chiasmus -a cross-arrangement implying an inversion. The inversion implied in the model can be recognized in common experience, namely, in the distinction and location of the front and rear side of an arbitlrary object. The order of these two sides shows an inversion in space, if compared with the order of the corresponding two sides of the observer. The terms used to indicate the two sides of the obsel*verare functionally deterrnirled, the order from back to front going in the direct ion of vision. At tble object the same order goes in the opposite direction; here it is also funcGonally determined, namely, with reference to the usual position of the object when looked at. Thus, the inversion ocmcurring here is functionally determined with respect to perception. In some cases, for instance if the “wrong’ side of a picture were observed, the inversion would not follow from the usual indication of the two sides of the object ; however, by considering the pibcure as an object only (its function as a picture being abstracted), this side might still be called the [momentary) front side. In other cases, for instance, that of a billiolrd-bidl, there is no functionally determined front and back, but still the momentary front and back would show the inversion. 87 The identity of the absolute eye-point cannot directly be assessed,but only ia the Indirect way implying an inversion: in scheme III point EBBScan be approached by two movements going in opposite directions.

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Of course, the inversion described here is to be distinguished from that implied in identifications; an additional interchange of right and left will then occur, as mentioned before.ss The general inversion shown by any object is that of a mirror image; looking at the object can be compared to looking in a mirror: right and left are not interchanged, nor top and bottom; it is in the third direction, perpendicular to the mirror, that the inversion occurs. The inversion shown in the model is borrowed from the physical model in fig. 36, without any generalization. This might seem to be illegitimate physicahsm; however, the further development of the model has shown that a generalization does occur, namely, with respect to the two spaces at opposite sides of the mirror. Objective space and subjective space are found to be ‘curved’, in opposite directions with respect to the (plane) mirror. Mathematically, this follows from the nonlinear, hyperbolic scale found in section 5.17 with respect to the domain of objective reality (see chapter 10). As mentioned before, subjective reality cannot be represented in the mbdel by the same (objective) means as objective reality; it has been indicated in an indirect way-as if it were o ective. In the interpretation of the model an inversion would be necessary, which can be performed by mathematical means. 13ne point of this interpretation may be shown here, namely, that the standard case of ideal reflection does not change. The point on the straight line I*A* in fig. 40 determined by the horizontal symmetry line of the model may be called the ‘subject-point’ (and the corresponding point on IA the ‘object-point’).*9 The point at infinity of J*A* (and of IA) would be the absolute eye-point Eabs. Four remarkable points are then given on the same straight line: the subject-point, Eabs, I* and A* (or, on IA: the object-point, Eabs, I and A). By these four points a so-called harmonic relationship is determined, and the same applies to the rays going from the relative eye-point 88 Generally, no identification will occur, object and subject being clearly distinguishedin perception* in the case of identification, the subject projects itself into the virtual space at the rear C.le of the mirror-the inversion described in the above is then directly experienced as a half-turn made in thought. se It will be remembered that at the centre of the identification AI (at the objectpoint) the two sides of the object would unite; in the same way, at the subject-point, the subject may be considered to form a unity.

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towards the four points; this relationship can be described by a crossratio, of value - 1. The harmonic relationship is not impaired by the invertjlon: the cross-ratio would take the inverse value, l/-l, and would still have the value - 1; again the standard case of ideal reflection would be obtained. In common language the harmony experienced here is indicated by axpre:ssions such. as: to be ‘in tune with the infinite’ or ‘in harmony with oneself’. Finally, tlhe case where not only reflection but also refraction occurs will be discussed. Deviations from the standard case are objectively given by deviations from identity of the two objects compared; subjectively, disturbances in the recognition of identity are directly experienced and i&dicated by expressions such as: ‘to be out of oneself’ or ‘not to recagnize oneself’. Of course, these expressions refer to the relative point of vie:w only; if in fact no identification occurred, the process of observation, as indicated in the model, would be disturbed itself, which is not a,.ctually rhe case. By ccnsidering again the four particular points on !ines IA and I*A* already mentioned, a striking conclusion could be drawn. The four points, in the order given, correspond to the four points in scheme 111. In this scheme it can be seen that the point at infinity would not only give the dir(ect unity with respect to the two points at the same distance of ErelS,but wits respect to an_~two points. Thus, all objects must be considered to be identical with respect to the absolute point of view; in the same way all subjects are identical. Apparently, there is no ‘process iof identification’, but the identity is given a priori; the only ‘process’ here consists in r:liminatfng all that disturbs or prevents the recognition of identity! From the relative plaint of view there are differences between the subjects, as well as beltr-veen the objects; however, though the images may be defective, from the absolute point of view they are all the same, carrying the same ideal1 contents.90 ~---

Part Mb

will appear in a subsquerst issue

e”

From l&erelative point of view, any comparison implies a ‘substantial’ base, of invariant ~alut:(section 5.16). From the absolute point of view, the fundamental identity found in the above may be the base of any comparison: of objects, observed by the same subject (e.g., in physical experiments), or of subjects observing the same object (in psychological tests). From the relative point of view the differences are ‘accidental’, from the &solute point of view they are ‘relative’.