The Laboratorium
January 1998

On Smileys and the Conservation of Parentheses


Many authors [Le98] have noted local imbalances in parenthesis counts, in multiple contexts. The feature of this imbalance most noted by these authors has been the consistent bias towards an excess of "left" parentheses [figure 1], rather than vice versa.

Figure 1
( )
A "left" parenthesis A "right" parenthesis

This imbalance is considered surprising, since theory predicts that parentheses obey a conservation law akin to that for electic charge. When local violations of the conservation principle are observed, authors have attempted to maintain the theory by positing the existence of other local violations, of opposite sign, sufficient to bring the overall count to zero. Phillips [Ph96] and several other independent authors, noting the consistent bias towards "left" parentheses in the Corwin-Sczarba Cluster, predicted a substantial deposit of "right" parentheses at the further extreme of the Cluster. To date, however, no evidence has emerged to support the existence of such a cluster; indeed, almost all such efforts to detect these "dark parentheses" have been unsucessful.

Shan [Sh97] and several others have observed, in the context of smileys, the predominance of "right-facing" smileys over "left-facing" ones. [Figure 2] However, since no conservation law had been posited for smileys, this fact was not considered remarkable. Indeed, it arose from surprise at the discovery of the "left-facing" variety, and the attempts to position it within the taxonomy of previously classified smileys.

Figure 2
(: :)
"left-facing" smiley "right-facing" smiley

The crucial link in this puzzle, however, cames from two closely-related observations made by Fong [Fo98a, Fo98b]: (1) that smiley conservation could be established through the alternation of smileys of both varieties, and (2) that the "right-facing" smiley could be regarded as an alternate form of the "right" parenthesis, an observation which easily extends to the other varieties.

The smiley imbalance is towards the "right" variety -- exactly the opposite of the imbalance in observed parenthesis counts. Under the bijection described in [Fo98b], the surplus of "right-facing" smileys can thus be regarded as a previously-overlooked but substantial deposit of "right" parentheses, making smileys the fabled "dark parentheses." This hypothesis supplies appealing answers to a great many open questions. It provides an explanation for the failure of the results previous parenthesis-measuring experiments to obey the conservation of direction. It explains why no similar disparity has been measured for the case of squre brackets and curly braces -- neither is a key component of smileys. And in its unification of previously distinct marks under a single elegant conservation law, it represnts a bold new direction in puncuation physics.