At the end of the eighteenth century the hasidic movement was facing an internal crisis: to what extent should the teachings of Baal Shem Tov and Maggid of Mezritch, with their implicit spiritual demands, be transmitted to the rank-and-file of the movement? Previously these teachings had been reserved for a small elite. It was at this point that the Habad school emerged with a communication ethos encouraging the transmission of esoteric to the broad reaches of the Jewish world. Communicating the Infinite explores the first two generations of the Habad school under R. Shneur Zalman of Liadi and his son R. Dov Ber and examines its early opponents.

Beginning with the different levels of communication in the teachings of the Baal Shem Tov and the Maggid and his disciples, Naftali Loewenthal traces the unfolding of the dialectic between the urge to transmit esoteric ideas and a powerful inner restraint. Gradually R. Shneur Zalman came to the fore as the prime exponent of the communication ethos. Loewenthal follows the development of his discourses up to the time of his death, when R. Dov Ber and R. Aaron Halevi Horowitz formed their respective "Lubavitch" and "Staroselye" schools. The author continues with a detailed examination of the teachings of R. Dov Ber, an inspired mystic. Central in his thought was the esoteric concept of self-abnegation, bitul, yet this combined with the quest to communicate hasidic teachings to every level of society, including women.

From the late eighteenth century onwards, the main problem for the Jewish world was posed by the fall of the walls of the social and political ghetto. Generally, the response was either to secularize, or abandon altogether, traditional Judaism or to retreat from the threatening modern world into enclave religiosity; by stressing communication, the Habad school opened the way for a middle range response that was neither a retreat into elitism nor an abandonment of tradition. Based on years of research from Hebrew and Yiddish primary source materials, Communicating the Infinite is a work of importance not only to specialists of Judaic studies but also to historians and sociologists.

Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis.

"One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion."—Margaret Wertheim, New Scientist