I don't remember where I read this but some information theorist made a distinction between information and command. Information implies something new whereas a command especially if followed without question does not constitute information. So 2 - this is Yes, that is No and This is In that is Out can be seen as commands rather than information. If the Yes/no is an answer to a question i.e. if it is something that is revealed then it qualifies as information. The bit is the simplest answer Yes or No but if it is not an answer, if it does not come from outside of the system then it can only be a command. So the bit is "almost the center of the information age" but I want to say not quite.
2 is a question - the seeking of information but is not information in and of itself. I suppose 3 is the answer. 3 is information.
Well, I'll grant there has to be someone or something for whom the information has meaning. I like the noise/information contrast. I still see a command as a form of information. And in some cases ("freeze!") a matter of life and death, as cops have shot those who literally did not understand this sort of command.
I'm not about to worship the 2, of course, but given my newfound love of numbers, this one seems important, more important than most numbers.
It's the simplest possible base of positional notation. It is the exact discrete "moment" where unity changes to plurality. It's also the only even prime. It also appears again and again in physics, as an exponent.
2 is a question. I'll grant you that. But it is also an answer. "Do you take this man to be your...." "I do."
Then there are those games where someone asks twenty yes or no questions, and must from binary answers (bits), figure out the celebrity being talked of, etc. Then there's that kid's game Guess Who.
Two genders, or at least two gender poles. Negative and positive electrical charge. Two directions in time. The symmetry of the human body. Birth and death. (I guess your 3 reappears if we look at reproduction...but maybe that's included with death, as many insects die after mating...)
I won't snub 3 though. 3 dimensions. Rock Scissors Paper. The Trinity. Or 3 could include an element that is the Union of the other 2.
I should stress that I'm thinking of all the human textual culture that is being represented by bits even as I look at this screen. The logic gates that make this computer process are binary