Something occurred to me over the weekend. This argument was inspired by Douglas Hofstadter's Godel, Escher, Bach, although when I first read it I didn't connect it to religion.
In several places in his book, Hofstadter states that the "inherit" meaning of messages depends on the interpreter of the message. For example, if you had a vinyl record but not a phonograph, it would be difficult to understand the message contained on the disc. (It should be possible, by the way, to connect a pin by string to a styrofoam cup, and move the pin along the grooves to hear the music. Please don't try this, or at least use a cheap record.) Similarly, writing on paper must be in the right language (and the right size) for people to understand. Otherwise, a translator or a microscope might be needed. The most famous case of this is of course the translation from Egyptian hyroglyphics to a modern language, through the Rosetta Stone.
On a similar vein, messages which make clear they are messages are easier to understand than messages which are hidden. This seems obvious, but it in fact has great applications. Invisible ink is useful precisely because people don't know there's a message there; even if the message was written in plain English, the average person would have trouble extracting the meaning from that. Another example: I could chew on my pen in different ways during an exam to signal answers for multiple choice questions. My intended audience would know what those symbols mean, but to other people (most importantly, the teacher) the chewing would be merely random. (Again, I would ask you not to try this, but if you do, you have to first solve how to signal the question number, or at least the start of the sequencing.)
Hofstadter then brings up an interesting consequence: assuming this is true, JS Bach would be easier to understand than John Cage to aliens. I quote, "Intelligence loves patterns and balks at randomness." Just as the teacher couldn't see the answers because it was thought to be a random gesture, John Cage's music is too random for aliens to deduce there is an intelligence behind it (putting aside the medium of storage). Bach's music, with clear rhythm and variation and repetition and pattern, would be more readily picked up as the product of intelligent beings.
Reversing the context, if aliens are sending us messages it had better contain patterns. If the aliens are sending us random noise, it would be hard to distinguish it from the background noise of the universe. I'm no expert in this area, but I assume SETI uses some kind of pattern recognition (or anomaly recognition) to detect messages. Underlying that is the assumption that aliens will be conceying in a distinguishable manner.
Here's the twist: if in the background noise of the universe we find patterns and therefore claim that there are intelligent beings out there, how should we treat the patterns in plants, animals, and ourselves? Could it be a message from God?
Note: I just learned that SETI does not in fact look for patterns, but looks for radio signals which nature could not produce. The existence of this signal would therefore indicate the existence of equipment necessary to generate it, hence extraterrestrial intelligence. I'm not sure what the theological equivalent would be. It was fun for a while, eh?