Analysis of Ss' performance on linear syllogisms and of their assignment of spatial directions to nonspatial ordering relations led to the conclusion that thinking about abstract orderings depends on the construction of spatial representations. In making these constructions, people proceed more readily in a downward than in an upward direction, and in a rightward than in a leftward direction. They also end-anchor. These principles account for the results of otherwise inexplicable variation in difficulty among linear syllogisms. Some ordering relations ("better" and "worse") have a fixed tie to a vertical axis in people's cognitive space, whereas other relations ("lighter" and "darker") are not so tied. Detailed consequences of such differences were predicted and observed in reasoning tasks. Implications for social cognition were discussed, particularly concerning the previously observed predilection for single orderings and the indications that the linear ordering is a preeminent cognitive good figure.

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Rippled noise is constructed by delaying a random noise and adding it back to the original. Iterated rippled noise (IRN) is constructed by repeating the delay-and-add process. IRN produces a two-component perception, i.e., a buzzy tone with a pitch equal to the reciprocal of the delay and a background noise that sounds like the original random noise. The perceived tone/noise ratio increases with the number of iterations. The effective tone/noise ratio in IRN sounds with 1–16 iterations was measured in a discrimination matching experiment; each IRN was paired with a range of standard sounds, having varying proportions of a broadband noise and a complex tone, to find the point where their perceived tone/noise ratios are the same. The experiment shows that the tone/noise ratio of the matching standard increases 3.8 dB per doubling of the number of iterations in the IRN stimulus. Spectral models of auditory perception explain the pitch of IRN in terms of peaks in the region of the first five to eight harmonics of the reciprocal of the delay. However, the matching data are unaffected when the sound is high-pass filtered at the twelfth harmonic of the delay—above the region of resolved harmonics. We show that a wide range of time-domain auditory models can explain the discrimination matching data by applying autocorrelation, either to the IRN waveform, or to the neural activity patterns produced by the cochlea in response to IRN waves.

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