In the historiography of the relationship between technology and theoretical science, electrical communication plays an important role. It was by means of mathematical reasoning based on the new theory of electromagnetism that it was first understood how to extend the range of telephony by inserting self-inductance in the line. This paper surveys developments from around 1880 to 1910, at a time when ‘pupinization’ had become a reality and mathematical physics an accepted part of the research strategy of a few advanced (...) companies in the electrical industry. It presents the confrontation of two different styles of engineering science, on the one hand there was the empirical approach and on the other an approach more mathematical in nature. This paper offers some reflections on the nature of ‘counterintuitive technologies’ and the general relationship between science, engineering and technology. (shrink)