Bertrand's chord, Buffon's needle, and the concept of randomness

Subjective patterns of randomness and choice: Some consequences of collective responses.

“…Preference for the internal part of the given frame at the expense of the margins (barring the corners in some cases) is shared by the responses to all the conditions in Experiments 1 and 2 (Figures 3 and 6) and by many other investigations (Attali & Bar-Hillel, 2003; Dudley, 1982; Kareev & Rania, 2001; Lacey, 1962; Nickerson, 2005; Rubinstein et al, 1997; Teigen, 1983). Henze and Riedwyl (1998, Figure 4.3) present the above mentioned two winning sextets in the British National Lottery of 1995 as they were visually arranged in the lottery ticket in a rectangle of 5 × 10 (without the bottom-right corner cell).…”

“…We hypothesize that the relation between the difficulty of memorizing a pattern -which is the subjective counterpart of its objective complexity (Kolmogorov, 1965) -and the judged randomness of that pattern will be positive. 6) and by many other investigations (Attali & BarHillel, 2003;Dudley, 1982;Kareev & Rania, 2001;Lacey, 1962;Nickerson, 2005;Rubinstein et al, 1997;Teigen, 1983). Henze and Riedwyl (1998, Figure 4 Insert Table 14 about here.…”

“…When the grid was bisected by either a vertical or a horizontal central axis, the numbers of marks were too equally divided between the two sides. Similarly, Nickerson (2005) concluded that perceptual balance, or moderate uniformity of the density over a given area, is a determinant of the degree to which a 2D pattern is perceived as random. The two somewhat contradictory inclinations, to homogeneity on one hand, and to avoidance of edges on the other hand, seem to live side by side in many participants' productions of randomness.…”

“…The same tendency was evident when participants had to guess numbers in a given range (Teigen, 1983). Lacey (1962) and Nickerson (2005) asked participants to draw random chords within a circle. They found that the chosen chords were, on average, longer than those which several legitimate random processes would produce.…”

Five down, Absquatulated: Crossword puzzle clues to how the mind works

“…Evans (2007) referred to this aspect of behavior as reflective of the "singularity principle," which is one of three that he considers descriptive of hypothetical thinking. When attempting to solve a problem that can have more than one solution, people find it easy to accept the first solution they discover and believe it to be the solution, failing to consider the possibility that there may be others (Nickerson, 2005).…”