Cage's work from the sixties features some of his largest and most ambitious, not to mention socially utopian pieces, reflecting the mood of the era yet also his absorption of the writings of both Marshall McLuhan, on the effects of new media, and R. Buckminster Fuller, on the power of technology to promote social change. HPSCHD (1969), a gargantuan and long-running multimedia work made in collaboration with Lejaren Hiller, incorporated the mass superimposition of seven harpsichords playing chance-determined excerpts from the works of Cage, Hiller, and a potted history of canonical classics, with fifty-two tapes of computer-generated sounds, 6,400 slides of designs, many supplied by NASA, and shown from sixty-four slide projectors, with forty motion-picture films. The piece was initially rendered in a five-hour performance at the University of Illinois in 1969, in which the audience arrived after the piece had begun and left before it ended, wandering freely around the auditorium in the time for which they were there.  Also in 1969, Cage produced the first fully notated work in years: Cheap Imitation for piano. The piece is a chance-controlled reworking of Erik Satie's Socrate, and, as both listeners and Cage himself noted, openly sympathetic to its source. Although Cage's affection for Satie's music was well-known, it was highly unusual for him to compose a personal work, one in which the composer is present. When asked about this apparent contradiction, Cage replied: "Obviously, Cheap Imitation lies outside of what may seem necessary in my work in general, and that's disturbing. I'm the first to be disturbed by it." Cage's fondness for the piece resulted in a recording--a rare occurrence, since Cage disliked making recordings of his music--made in 1976. Overall, Cheap Imitation marked a major change in Cage's music: he turned again to writing fully notated works for traditional instruments, and tried out several new approaches, such as improvisation, which he previously discouraged, but was able to use in works from the 1970s, such as Child of Tree (1975).  Cheap Imitation became the last work Cage performed in public himself. Arthritis had troubled Cage since 1960, and by the early 1970s his hands were painfully swollen and rendered him unable to perform. Nevertheless, he still played Cheap Imitation during the 1970s, before finally having to give up performing. Preparing manuscripts also became difficult: before, published versions of pieces were done in Cage's calligraphic script; now, manuscripts for publication had to be completed by assistants. Matters were complicated further by David Tudor's departure from performing, which happened in early 1970s. Tudor decided to concentrate on composition instead, and so Cage, for the first time in two decades, had to start relying on commissions from other performers, and their respective abilities. Such performers included Grete Sultan, Paul Zukofsky, Margaret Leng Tan, and many others. Aside from music, Cage continued writing books of prose and poetry (mesostics). M was first published by Wesleyan University Press in 1973. In January 1978 Cage was invited by Kathan Brown of Crown Point Press to engage in printmaking, and Cage would go on to produce series of prints every year until his death; these, together with some late watercolors, constitute the largest portion of his extant visual art. In 1979 Cage's Empty Words was first published by Wesleyan University Press.  In 1987, Cage completed a piece called Two, for flute and piano, dedicated to performers Roberto Fabbriciani and Carlo Neri. The title referred to the number of performers needed; the music consisted of short notated fragments to be played at any tempo within the indicated time constraints. Cage went on to write some forty such pieces, one of the last being Eighty (1992, premiered in Munich on 28 October 2011), usually employing a variant of the same technique; together, these works are known as Number Pieces. The process of composition, in many of the later Number Pieces, was simple selection of pitch range and pitches from that range, using chance procedures; the music has been linked to Cage's anarchic leanings. One11 (i.e. the eleventh piece for a single performer), completed in early 1992, was Cage's first and only foray into film.  Another new direction, also taken in 1987, was opera: Cage produced five operas, all sharing the same title Europera, in 1987-91. Europeras I and II require greater forces than III, IV and V, which are on a chamber scale.  Already in the course of the 1980s, Cage's health worsened progressively: he suffered not only from arthritis, but also from sciatica and arteriosclerosis. He suffered a stroke that left the movement of his left leg restricted, and, in 1985, broke an arm. During this time, Cage pursued a macrobiotic diet. Nevertheless, ever since arthritis started plaguing him, the composer was aware of his age, and, as biographer David Revill observed, "the fire which he began to incorporate in his visual work in 1985 is not only the fire he has set aside for so long--the fire of passion--but also fire as transitoriness and fragility." On August 11, 1992, while preparing evening tea for himself and Cunningham, Cage suffered another stroke. He was taken to St. Vincent's Hospital in Manhattan, where he died on the morning of August 12. He was 79.  According to his wishes, Cage's body was cremated, and the ashes scattered in the Ramapo Mountains, near Stony Point, New York, the same place where Cage scattered the ashes of his parents, years before. The composer's death occurred only weeks before a celebration of his 80th birthday organized in Frankfurt by the composer Walter Zimmermann and the musicologist Stefan Schaedler was due to take place. The event went ahead as planned, including a performance of the Concert for Piano and Orchestra by David Tudor and Ensemble Modern. Merce Cunningham lived another 17 years, dying of natural causes in July 2009.  Cage's first completed pieces are currently lost. According to the composer, the earliest works were very short pieces for piano, composed using complex mathematical procedures and lacking in "sensual appeal and expressive power." Cage then started producing pieces by improvising and writing down the results, until Richard Buhlig stressed to him the importance of structure. Most works from the early 1930s, such as Sonata for Clarinet (1933) and Composition for 3 Voices (1934), are highly chromatic and betray Cage's interest in counterpoint. Around the same time, the composer also developed a type of a tone row technique with 25-note rows. After studies with Schoenberg, who never taught dodecaphony to his students, Cage developed another tone row technique, in which the row was split into short motives, which would then be repeated and transposed according to a set of rules. This approach was first used in Two Pieces for Piano (c. 1935), and then, with modifications, in larger works such as Metamorphosis and Five Songs (both 1938).  Soon after Cage started writing percussion music and music for modern dance, he started using a technique that placed the rhythmic structure of the piece into the foreground. In Imaginary Landscape No. 1 (1939) there are four large sections of 16, 17, 18, and 19 bars, and each section is divided into four subsections, the first three of which were all 5 bars long. First Construction (in Metal) (1939) expands on the concept: there are five sections of 4, 3, 2, 3, and 4 units respectively. Each unit contains 16 bars, and is divided the same way: 4 bars, 3 bars, 2 bars, etc. Finally, the musical content of the piece is based on sixteen motives. Such "nested proportions", as Cage called them, became a regular feature of his music throughout the 1940s. The technique was elevated to great complexity in later pieces such as Sonatas and Interludes for prepared piano (1946-48), in which many proportions used non-integer numbers (1 1/4 ,  3/4 , 1 1/4 ,  3/4 , 1 1/2 , and 1 1/2  for Sonata I, for example), or A Flower, a song for voice and closed piano, in which two sets of proportions are used simultaneously.  In late 1940s, Cage started developing further methods of breaking away with traditional harmony. For instance, in String Quartet in Four Parts (1950) Cage first composed a number of gamuts: chords with fixed instrumentation. The piece progresses from one gamut to another. In each instance the gamut was selected only based on whether it contains the note necessary for the melody, and so the rest of the notes do not form any directional harmony. Concerto for prepared piano (1950-51) used a system of charts of durations, dynamics, melodies, etc., from which Cage would choose using simple geometric patterns. The last movement of the concerto was a step towards using chance procedures, which Cage adopted soon afterwards.

Answer this question "what are the names of some of his early pieces?" by extracting the answer from the text above.
Most works from the early 1930s, such as Sonata for Clarinet (1933) and Composition for 3 Voices (1934), are highly chromatic and betray Cage's interest in counterpoint.