## How Errors Lead to New Discoveries

In the book "Where Good Ideas Come From", the author Steven Johnson mentions some stories on how errors lead to new scientific breakthroughs which I think would be interesting for radio/wireless enthusiasts. The first among them is what laid the foundation for electronics and radio broadcasting. Audion (Triode) Vacuum Tube In the summer of 1900 a twenty-seven-year-old aspiring inventor named Lee de Forest moved to Chicago, rented a one-room apartment on Washington Boulevard, and took a day job translating foreign articles on wireless technology for Western Electrician magazine. The translation work was informative: a major exposition on wireless technology that

## A Real-Imaginative Guide to Complex Numbers

June 18, 2020 On a cold morning in August 2015, I narrowly missed a train to my office in Melbourne city. With nothing else to do in the next 20 minutes, my mind wandered towards an intuitive view of complex numbers, something that has puzzled me since long. In particular, I wanted to seek answers to the following questions. (a) What is the role of the number $\sqrt{-1}$ in mathematics? What sets it apart from other impossible numbers, e.g., a number $k$ such that $|k|=-1$? (The origins of this question might lie in how I cut apple slices for my

Recently, IEEE Communications Society published an article “What will 6G be?” Some of the important points it highlighted are the following. More spectrum is needed for more bits: As with all new Gs, more spectrum is needed to entertain more bits ðŸ™‚ Sometimes I wonder where exactly we have made a phenomenal progress in delivering orders of magnitude higher data rates. According to Gerhard Fettweis, several bands between 100 and 300 GHz show some promise. Bits/s/$m^3$: Since the success of a company is measured in the revenue generated, and not exactly the bits delivered per second, the real focus is