Titchener’s ⊥ in context 1—delimited, discrete monomotif patterns, line arrangements, and branching patterns

Abstract

Three experiments tested the effects of the presence of nontarget ⊥s on Titchener's (1901) ⊥-illusion. Experiment 1 used patterns of four separate ⊥s, Experiment 2 used branching patterns in which four ⊥s were stuck together, and Experiment 3 used patterns of four triangles or four beehive forms for which the ⊥ could be seen as a skeleton. Three independent samples of 12 observers each had to haptically indicate the lengths of target lines and verbally judge the relative lengths of the two lines of target ⊥s. The illusion to judge or indicate the ⊥'s undivided line as longer than its divided line survived throughout except for the branching patterns: here, haptic indications did not differ between the two types of lines. Specific features of these patterns and of the ⊥ itself may be responsible for these effects.

Titchener’s ⊥ dissected

“…Thus, the net percent amount of the illusion was 2.41 %, which is quite in the range of what had been seen with individual, nondissected ⊥s (Landwehr, 2009(Landwehr, , 2014, as well as with ⊥s arranged in discrete, cyclically symmetric 4-⊥ patterns (Landwehr, 2015a). When computed separately for the three gap sizes, the illusion amounts were 3.71 %, 1.43 %, and 2.00 %, for 3, 10, and 16 cm, respectively.…”

“…3): Across gap conditions, it may have been easier to judge the length of the ⊥'s upstroke than that of the ⊥'s cross-stroke. This idea can be related to the broader study of the effects of different contexts (Armstrong & Marks, 1997;Chapanis & Mankin, 1967;Landwehr, 2015aLandwehr, , 2015b or, more specifically, of "framing" (Houck, Mefferd, & Greenstein, 1972;Prinzmetal & Gettleman, 1993). The idea is particularly intriguing for the haptic data, since indications for the upstroke hardly differed at all across gap sizes, whereas those for the cross-stroke were critically affected (Fig.…”

“…Visual data, as before (Landwehr, 2009(Landwehr, , 2014(Landwehr, , 2015a(Landwehr, , 2015b, were analyzed by fitting psychometric functions. Function parameters were derived from the binary logistic regression routine of SPSS, and points of subjective equality (PSEs) were obtained from the cross-points of the functions for longer and shorter judgments, plotted against an abscissa defined by the difference in length of the two parts of the dashed ⊥−figure (cross-stroke minus upstroke; cf.…”

“…In several experiments (Landwehr, 2009(Landwehr, , 2014(Landwehr, , 2015a(Landwehr, , 2015b, I have shown that the ⊥ illusion, albeit in a weaker form, also occurs in the haptic domain when observers visually inspect the stimulus and then haptically signal line lengths by spreading the thumb and index finger appropriately (cf. Gibson, 1966).…”

“…Gibson, 1966). Attempts to influence the illusion(s), by rotating the ⊥ into lateral or oblique positions (Hamburger & Hansen, 2010;Künnapas, 1955;Landwehr, 2009Landwehr, , 2014 or putting it into different contexts (Landwehr, 2015a), met with limited success. The illusions even persisted in triangles and catenary-derived forms (Landwehr, 2015a, Exp. 3), suggesting that the T-junction as such does not even have to be optically specified for the illusions to occur.…”