Although I'm not familiar with Johnson's scholarship, as someone who studies mostly medieval history, I'm naturally skeptical of claims about how great the Renaissance was. Like everything else, the periodization is problematic (did it start in Gutenberg in the mid-1400s, or with Petrarch in 1370s, or with Dante in 1320s, or...), and part of that has to do with a geographic split -- things that we associate with "Renaissance" happened in the North later and in different ways than in Italy.

But if you're going to stick with a one-period Renaissance, you should also pay attention to the Carolingian Renaissance or the Renaissance of the Twelfth Century -- both periods in which we're discovering powerful intellectual advances. In general, most people have dismissed Europe prior to the printing press as a pure backwater and Dark Ages -- but this doesn't wash with the developments spurred by Greek and Arabic knowledge filtering back to the West, in logic with Abelard in the 12th century and in physics continuing with Grosseteste and Bacon to Bradwardine in the 14th century. A number of people have argued that the ongoing Commercial Revolution helped spur a more exact and mathematical view of the world. Even if art's what you want, the development of perspective by Giotto and Cimabue came way before the 15th century. Margaret Wertheim's Pearly Gates of Cyberspace, which Katz liked, has a lot to say about perspective.

Besides, if you're looking for the cultural impact of technology, why restrict your focus to the Renaissance? Some of the most important technologies were introduced to Europe centuries earlier, such as the watermill (which was around in late Rome), the stirrup (which enabled shock combat on horseback), the heavy plow (which enabled the tilling of the fertile northern soils), the new horse collar (which allowed horses to pull the plows without choking to death), and the three-field system of planting beans to replenish the soil (which increased the food supply by half, added protein to the diet of the poor and resulted in an immense expansion of European population). All of these had vast social consequences -- not perhaps as culturally sexy as the printing press or Michelangelo, but with far greater impact on people's lives. Personally, I'd rather that the Net's effects be more like the former than the latter.

If you're interested in the subject of medieval learning, math and technology, I'd recommend Alexander Murray's Reason and Society in the Middle Ages and Lynn White's Medieval Technology and Social Change -- although the latter has come under fire for White's tendency to worship the stirrup. I've also heard good things about Jean Gimpel's The Medieval Machine, although I haven't read it.