Moore's law in astronomy and why it's over for alien sightings

There's a very compelling reason why we aren't regularly visited by aliens. In astronomy, as in our everyday lives, technology is on the march. In fact, as with computers, every few years new telescopes and their instruments get twice as powerful. This exponential growth in technological capacity means that a PhD student can often perform more science during his or her thesis than their supervisor has in their entire career---which can be embarrassing. But this exponential growth has transformed our knowledge of the universe as our detectors and telescopes continue to get better and better. Astronomical discoveries of things such as supernovae, pulsars, quasars, extra-solar planets and supermassive black holes have all grown exponentially since the first few were uncovered by now-primitive instruments. In my own research field the first pulsar (a regularly repeating series of radio pulses from a neutron star) was discovered in 1967. Initially it was seriously postulated to be an alien beacon. Within a few weeks they realised it wasn't aliens when three other pulsars were found in very different regions of the galaxy. Technology advanced and, within ten years, there were about 100 pulsars known. By the mid 1980s a few hundred. Now they number well over 2,000. Some pseudo-random combination of bigger telescopes, better detectors, more scientists and more powerful computers has led to exponential growth in pulsar numbers for more than 40 years. Indeed pulsar astronomers are equipped with some of the best alien-detecting equipment on the planet, but so far its pulsars > 2000, aliens nil.