Knight,
Since you didn’t dispute SUTG’s math earlier in this thread it is intellectually dishonest of you to describe your signal as “simple” in this context.
It may be simple to you, but as SUTG quite ably demonstrated it is not simple from a statistical coincidence point of view. Let me remind you:
Actually, SUTG acknowledges that he is overestimating the probability but he didn’t bother to go through it. When you consider the bandwidth and redundancy of information required for SETI to recognize, bin and characterize a signal in bit-wise terms, especially in view of the frame shift problem, you add several orders of magnitude more uncertainty. SUTG overlooked the fact that you have to encode each of the 29 characters into bits. You can’t just send the letter “A” – you have to encode it. You could use Morse code which is pretty efficient but it is very susceptible to frame shift error – one bad bit and the whole message is ruined (SETI is geared to look at repetitive unusual signals repetitively and find matches). At a minimum, that stretches the required character encoding by at least a factor of 4. So 100^211 is a very conservative estimate. Since I prefer scientific notation that’s 10^422. in case you don’t know, that’s a 1 with 422 zeros after it – bigger than a googleplex (10^100).
OK, now according to
wikipedia SETI can monitor 8 million channels simultaneously with a resolution of 0.05 Hz after stabilization. That 20 bits per second but that applies to each bit and there are 221x3= 663 bits. Therefore, it would take SETI at least 30 seconds to get the message in any particular viewframe. Therefore, performed continuously, SETI can recognize 16 million messages like yours per minute if they exist. That’s 960 million/hour, 23040 million/day, and 8.4 x 10^12 per year. To make the math easy I’ll be even more conservative – let’s say 10^13 per year.
So you’ll have a (10^13)/(10^422) chance per year of seeing your signal by random occurrence. To get to just a 50% probability of seeing a signal due to chance alone you’d have to watch SETI’s monitoring for approximately 10^400 years.
I’m pretty tired and in case I erred I don’t mind using SUTG’s number of 29^211. Gee, I’ll even be more generous to you and say it’s only 10^211. That would still mean it would take 10^198 years to have a 50% expectation of seeing your signal by chance.
Not such a “simple message” is it pal? We take our intelligence for granted but statistically, even seemingly simple messages encode a lot of information.