of mathematical astronomy by the ancient Greeks in the 1st millennium BC. All ancient astronomical observations were based on visual techniques. Of all the key techniques used in ancient times, the most common in Babylon (most likely the source of astrology) and most other ancient cultures were based on phenomena that occurred close to the eastern or western horizons. MacKinnell opines that it is incongruent to use a modern mathematical approach to the much older constellations that were first described well before these mathematical approaches were invented. The heliacal rising constellation at the vernal equinox is based on the last zodiacal constellation rising above the Eastern Horizon just before dawn and before the light of the approaching Sun obliterates the stars on the eastern horizon. Currently at the vernal equinox the constellation of Aquarius has been the heliacal rising constellation for some centuries. The stars disappear about one hour before dawn depending upon magnitude, latitude, and date. This one hour represents approximately 15 degrees difference compared to the contemporary method based on the position of the Sun amongst the zodiacal constellations. Each age is composed of 30 degrees, therefore, 15 degrees represents about half an age or about 1080 years. Based on the heliacal rising method, the Age of Aquarius arrived about 1,080 years earlier than the modern system. John H Rogers in part one of his paper Origins of the ancient constellations also states that using the ancient heliacal rising method compared to the (modern) solar method produces a result that is approximately 1,000 in advance. Using this approach, the astrological ages arrive about half an age earlier compared to the common contemporary approach to calibrating precession based on modern mathematical techniques. Thus, MacKinnell has the Aquarian Age arriving in the 15th century while most astrologers have the Age of Aquarius arriving in the 27th century, almost 700 years in the future. In popular culture In popular culture, the expression "Age of Aquarius" usually refers to the heyday of the hippie and New Age movements of the 1960s and 1970s. The successful 1967 Broadway musical Hair, with its opening song "Aquarius" and the memorable line "This is the dawning of the age of Aquarius", brought the Aquarian Age concept to the attention of a huge worldwide audience. The 1969 Woodstock festival was advertised as "An Aquarian Exposition in White Lake, New York," while The Aquarian is a New Jersey