[4][5] Each episode opens and closes with bookend segments in which Caltech professor David Goodstein, speaking in a lecture hall, delivers explanations "that can't quite be put into the mouth of our affable, faceless narrator".
[2]Episode 22 solved the Kepler problem — that is, demonstrating that an inverse-square law of gravity implies that orbits are conic sections — using a variant of the Laplace–Runge–Lenz vector, though not by that name.
[2] Footage featuring historical reenactment of Johannes Kepler was purchased from Carl Sagan's 1980 television series Cosmos: A Personal Voyage.
[13] Caltech mathematician Tom M. Apostol joined the Mechanical Universe production staff in order to ensure that the series did not compromise on the quality of the mathematics it presented.
[16] When test screenings to humanities students revealed that their greatest difficulty learning calculus was a weak background in trigonometry, Apostol wrote a primer on the subject to be distributed with the telecourse.
[18] The 1990 science-fiction action film Total Recall used portions of the Mechanical Universe title sequence, in a scene where the protagonist (Douglas Quaid, played by Arnold Schwarzenegger) is offered virtual vacations in locales around the Solar System.
[4] Computer animation presented derivations in step-by-step detail, but rapidly and with touches of whimsy, such as algebraic terms being canceled by a Monty Python-esque stomping foot or the hand of God from Michelangelo's The Creation of Adam.
[20] The goal was to avoid putting the viewers' "brains into a 60-cycle hum", without sacrificing rigor; the creators intended that students could learn the overall gist of each derivation from the animation, and then study the details using the accompanying textbook.
[22] Creating the computer graphics necessary to visualize physics concepts led Blinn to invent new techniques for simulating clouds, as well as the virtual "blobby objects" known as metaballs.
[23] Blinn used the vertex coordinates of regular icosahedra and dodecahedra to determine the placement of electric field lines radiating away from point charges.
[27] The show was one of the first twelve projects funded by the initial $90 million pledge the Annenberg Foundation gave to the Corporation for Public Broadcasting in the early 1980s.
[2] In 1992, Goodstein noted that the series had been broadcast, via PBS, by over 100 stations, "usually at peculiar hours when innocent people were unlikely to tune in accidentally on a differential equation in the act of being solved".
[29]Goodstein and assistant project director Richard Olenick noted:Anecdotal information in the form of letters and phone calls indicates very considerable enthusiasm among users at all levels from casual viewers to high-school students to research university professors, but there have also been a number of sharp disappointments, particularly when Instructional Television administrators have tried to handle TMU like a conventional telecourse.
[2]Similarly, a 1988 review in Physics Today suggested that the programs would not function well on their own as a telecourse, but would work much better as a supplement to a traditional classroom or a more standard distance-learning course such as Open University.
[31] Similarly, a review in the American Journal of Physics, while praising the "technical proficiency of the films", wrote of the animated equation manipulations: "As the MIT students say, this is like trying to take a drink of water out of a fire hose".
[32] A considerably more enthusiastic evaluation came from physicist Charles H. Holbrow, who told Olenick: "These materials will constitute the principal visual image of physics for decades".
[12] A reviewer writing for Educational Technology found the animations "fascinating to watch" and opined that they were at least as effective as what many instructors could manage at a traditional blackboard.
[33] An editorial in the Los Angeles Times called the show "extraordinary" and the animations "splendid", quipping that "if differential calculus is not television's Supreme Test, it would certainly make the semifinals in any competition".
Negative reactions generally had less to do with the intrinsic perceived quality of the episodes than with the time the science-history material took away from content seen as "critical exam-preparing instruction".
[42] Writing for Wired magazine's web site, Rhett Allain cited the series as an example of videos that could replace some functions of traditional lectures.
[47] For his contributions to the field of computer graphics, including his animations for Cosmos, The Mechanical Universe and Project Mathematics!, Blinn received a MacArthur fellowship in 1991, as well as the 1999 Steven A. Coons Award.