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I'm currently interested in just the principles involved in the radio signal scenario... and what conclusions inductive reasoning leads to.

I don't think it would be proper inductive reasoning to see a PNRS is caused by some intelligence, another PNRS is caused by intelligence, and to induce that the third PNRS is probably caused by some intelligence. There are unknown possible ways to generate a PNRS, and they cannot be ruled out simply because experience shows a couple other examples. This feels like the political approach to space shuttle launches about 10 years ago. Back in the day, designers speced the space shuttle to be safe for launch within a certain range of temperatures. Florida has uncooperative weather and often goes outside the safe range. Politicians wanted the shuttle to launch because it's good for elections. So, they pressure the upper management of NASA to launch outside the designed safe range. This happened a number of time without problem. At some point, management decided that the designers were wrong, and that a couple of launches outside their declared safe range meant that the real safe range was much wider. This continued for a few more launches until a space shuttle exploded on launch because it was too cold. If you shuffle a deck and pull 3 or 4 face cards in a row from the top of the deck, you can't really make any sort of probability measure as to what the next card will be. it could be a deck of only face cards. It could be many full decks. it could be a stacked deck. probabilities can't be determined off of a few rolls of the dice. two cases showing the PNRS was from an alien planet is not enough to make any sort of real probability estimate on the third PNRS. This is playing on a ""gut feeling"" that people have when they're playing roulette. casino's will post the last 20 rolls. Some gamblers will see these numbers and look for some sort of ""pattern"" and bet based off of that, on the ""gut feeling"" that the roullette wheel has some bias. They may even win a few times. But the casino is better off if the wheel is truly random, so any ""patterns"" is purely coincidental.  "