Phil Robertson's Omega/Constant

We've all been treated to endless discussion of the Phil Robertson flap related to his interview in GQ. The "endless" property of this debate inspired me.  Perhaps it's not actually computable.

In that spirit, I am reminded of the newest "physical" constant available - the one named for Gregory Chaitin. The abstraction of this constant is Chaitin's Omega - it's an infinitely repeating binary fraction ( each subsequent bit maps to 1/pow(2,x ) for each x in the natural numbers ). Each bit is a yes/no answer to whether or not a particular set of instructions terminates on a particular Turing Machine. 

http://mathworld.wolfram.com/ChaitinsConstant.html

The current value of Chaitin's Constant is known to  64 bits and has  a decimal representation of 0.00787499699 Why no, that's not 1/127 and why would you think such a thing? Sheesh.

So allow me to introduce Phil Robertson's Omega. Each bit represents the answer to the recursive proposition R(x) "Is x bad?" where x is a concatenation of "Is" and a  repeated string of "of intolerance". We simply textually substitute the nonsense "Is of" with "Is" for clarity's sake (I suppose you can tolerate the "Is of" if you *want*, but I know what I'll do, by golly).

 For example, R(0) is ... nothing, undefined  ( shame on you for even *thinking* that - "Is" isn't much of a sentence, now), and R(1) is "Is intolerance bad?", R(2) is "Is of intolerance of intolerance bad?" and so forth.

Wait, get that extra "of" out of there... thanks - "Is intolerance of intolerance bad?" says R(2).

So I think we can all agree that R(1) is true. That gives us a first pass value of 0.5 . Calculation of the remaining bits is left as an exercise for the reader.

With any luck, tens of gigabytes of Internet bloviation per second will now be replaceable by a nice compact single decimal constant.  Use it wisely!