When members of an online, distributed learning community revealed that understanding local patterns of communication purpose and form was key to learning how to operate in this environment, we turned to writers on genre and persistent conversation for help in understanding the basis of this community. We derive from genre literature the idea that radicals, that is root characteristics, of presentation exist in computer-mediated environments and define important aspects of conversation via such media. We propose three radicals of presentation that revolve around speaker-audience relations and identify areas of concern for communicators engaging in persistent, online conversations: visibility, addressing primarily speakers’ concerns with the means, methods and opportunites for self-presentation; relation, addressing the speaker’s concerns with the range and identity of the audience, and audience members’ concerns about relations with each other; and co-presence, addressing concerns relating to the temporal, virtual, and/or physical co-presence of speaking and listening participants.

Going forward from Northrop Frye, we derive from genre literature the idea that radicals, i.e., root characteristics, of persistent conversation exist and can help define important aspects of such conversations. We identify from longitudinal interviews with members of a distributed, computer-supported learning environment three dimensions of interactivity that revolve around speaker-audience relations. We propose three "radicals of presentation" in persistent conversation: Visibility, the means, methods, and opportunities for presentation, addressing primarily speakers' concerns with the presentation of self; Relation, the tie between speaker and audience, and among audience co-participants, addressing the speaker's concerns with the range and identity of the audience, and audience members' concerns about relations with each other; and Co-Presence, the temporal, virtual, and/or physical co-presence of speaking and listening participants, addressing concerns about being with others at the same time and place, and giving and receiving immediate feedback. We conclude with implications for social and technical design.

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Practical mathematics in the early modern period was applied to such fields as astronomy and navigation; cartography and surveying; engineering and military arts, including gunnery; and especially banking and mercantile trade. Those who have written about practical mathematics make no mention of medical applications in their surveys, although there were many cases where physicians set up as mathematical practitioners. 1 This article examines medical applications found in practical mathematical literature up to the end of the seventeenth century in England.While instruction in the medical applications of mathematics are scarcely to be found in earlier English publications, we shall see that a sudden minor outburst occurred in the 1650s, when three separate arithmetics appeared with chapters on ''the composition of medicines''. These chapters were each associated with a mathematical operation called ''alligation'', a term which means ''tying together''. There are two main types of alligation: ''alligation medial'' for simple problems and ''alligation alternate'' for use when varied quantities and elements are to be mixed. It was the technique called alligation alternate that was adapted specifically to the composition of medicines in these arithmetics.Alligation was a relatively advanced arithmetical operation, presupposing a knowledge of the rules of proportion. As such, alligation was usually presented near the end of arithmetical texts. Most commonly the examples used to explain alligation involved grains, metals, wines or spices. A typical use of alligation alternate would be to determine the appropriate quantities to mix of various elements each having a different price in order to concoct a mixture destined to sell at a desired unit price. For example, say you are a grocer and you have ample quantities of wheat, rye, barley and oats, which sell respectively for # Alvan Bregman 2005

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