Josef was born to an impoverished Jewish family of tradespeople who placed a high value on education. He was the uncle of the Austrian-British philosopher Karl Popper. After a highly religious early education he was sent to the German Polytechnikum Prague. Four years later he the started at the Imperial Polytechnikum, Vienna to study Mathematics, Physics and Astronomy. However, despite doing well, the Concordat of 1855 enabled the Vatican to impose restrictions to Jews, and so he could only support himself by taking on low paid menial work.
After graduating from the Vienna Polytechnikum, Popper-Lynkeus worked for two years as an engineer in a private firm. From 1862 – 1866, he tutored and occasionally lectured, and from 1867 - 1897, he privately pursued various inventions. In 1868, he contrived a system of gaskets to prevent the buildup of scales on the inner walls of steam boilers. This and some other inventions prepared the ground for his work in engineering, physics, and social and moral philosophy – independently of establishment and closed academic groups.
Popper-Lynkeus's ideas were innovative for his time. In engineering, he thought of the possibility of electric power transmission, the conversion of mechanical energy of waterfalls and rising tides into electrical power (1862). In physics, he thought of the mass-energy relation (1883) and the idea of a quantum of energy (1884), the principle of unavoidable distortion of the parameters of objects under investigation by measuring instruments. In psychology, he thought of the interpretations of dreams based on analysis of the conflict between the social consciousness of an individual and his or her animal instincts (short story Dreaming like Waking, 1889). Several years before Theodor Herzl, in the work Prince Bismarck and anti-Semitism (1886), Popper-Lynkeus came to the conclusion that the Jews could be saved from anti-Semitism only if they possessed their own state. He considered creation of such a state an urgent need, and that the type of regime in the beginning did not matter, that even a monarchy would be satisfactory.
The aforementioned short story was included in the collection of philosophical stories under the common title Fantasies of a Realist, which was published in 1899 and ran through twenty editions. Since then, Popper-Lynkeus used the pseudonym Lynkeus – after the keen-sighted watchman from the Argonaut's ship, appearing also in Goethe's Faust. Three of the many ideas Popper-Lynkeus suggested in this collection were:
Popper-Lynkeus mentions the great power that music has over the masses. He stated that marching music often serves as a support of tyranny, transforming the masses into a paste anything can be made from. This idea of Popper-Lynkeus is similar to an idea of Leo Tolstoy, who said, "Those who want to have more slaves should compose more marching music."