Letterman did the kind of things during those years that had us graduate students asking each other on many a morning, "Did you see what Dave did last night?" And when Dave did an anniversary show, at least the first few ones, watching was de rigueur. There's an online list of "The 80 Greatest Late-Night Episodes of All Time" and, by my count, 44 of them involved Dave (you need to scroll down a bit when the web document comes up, to see the list).
Granted, some of Dave's stunts appear to have been "borrowed" from Steve Allen's work in an earlier era. But, how can you not love Dave's physical comedy, such as dressing in a jumpsuit covered with probably hundreds or thousands of bits of Rice Crispies and being lowered into a vat of milk, or wearing a suit of Alka-Seltzer tablets and being lowered into a vat of water? (I heard a rumor that during pre-testing of the Alka-Seltzer stunt, a stagehand filling Dave's role passed out from the resulting gases, so Dave had to wear a gas mask when doing the actual stunt.)
From the elevator races, to the "democracy show" where the audience got to vote on which features to implement during an actual taping, to the velcro suit, to "supermarket finds," to riding on a luge sled, the Letterman gems are endless. Though Dave gets less physically involved today on his CBS show (perhaps a result of his health problems), he still gives us such cerebral exercises as "Will it float?," a physics lesson viewers don't even realize they're getting.
Among my fellow Michigan grad students, the one who probably got the most enjoyment out of Dave's antics is Steve Fein, a professor at Williams College since graduating from UM. Back then, Dave's NBC show "Late Night with David Letterman" came on at roughly 1:00 AM on the local Detroit affiliate. Michigan is in the Eastern time zone, meaning "The Tonight Show" (then hosted by Johnny Carson) would be on from 11:30-12:30. Then, instead of putting Letterman on at 12:30 AM, which was plenty late, the NBC affiliate put him on at 1:00, with a half-hour of Barney Miller (and other similar shows') repeats filling the gap.
Rather than stand passively by like the rest of us, Steve called up the NBC affiliate to ask why Letterman didn't come on at 12:30. The answer he got had something to do with local affiliates' being able to pocket advertising revenues for shows aired only in the local market (such as the "filler" rerun), whereas the revenues for a national show such as Dave's went to the national office. Steve got a kick out of many of Letterman's stunts and even was known to imitate one or two of them.
Another feature of the show I find interesting is that, in the early years, there was a fair amount of turnover in the band (known variously as "The World's Most Dangerous Band," "The NBC Orchestra," and "The CBS Orchestra"). Sid McGinnis replaced Hiram Bullock on guitar in '84, and Anton Fig (whom Dave used to jokingly refer to as "Antop Zip") replaced Steve Jordan on drums in '86. Bandleader/keyboardist Paul Shaffer and bassist Will Lee have been there all along. But since '86 (which is 18 years ago, for heaven's sake), there have been no personnel changes on these four instruments (there have been additions to the band, however).
I was a little disappointed that Dave didn't change up the show more when he moved from NBC to CBS, and I recall Steve feeling the same way from our correspondences. The question of what facets of Dave's NBC show he could take to CBS reached the point of absurdity when, as stated in one online biography of Letterman:
"NBC claimed that many of Letterman's gimmicks and jokes, including throwing the pencil at the camera, the top ten list, and Larry Bud Melman, among many others, were 'intellectual properties.' NBC lost, but Larry 'Bud' Melman would now be called Calvert DeForest on the CBS show."
And you think I'm kidding when I say that Dave gave many Michigan social psych graduate students intellectual enrichment during our years in Ann Arbor?
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On a somewhat related note, any longstanding show such as David Letterman's on NBC and CBS, will have its detractors, people who feel the show "jumped the shark" and started heading downhill. The term "Jump the Shark" derives from an episode of Happy Days on which Fonzie, clad in his trademark leather jacket, jumped over a shark on water skis. That, to many, was a signal that Happy Days was seriously on the decline. In keeping with the theme of the Michigan retrospective website, it turns out that the creator of the term "Jump the Shark" (and host of the website and author of the book by the same name) is Jon Hein, a 1989 UM alumnus (to my knowledge, I never met Jon at UM, but with tens of thousands of people there, that's not surprising). People can submit their opinions to the Jump the Shark website on when a given show has started to decline. Here are the entries for Letterman's NBC and CBS shows.