But I'm reasonably confident that Professor Hawking never said anything about "one part in a trillion trillion trillion trillion trillion" of anything. And if he did, it had nothing to do with the "fine tuning" fable.
No, I was just citing a reputable source for the general claim. I believe the specific claim in question ('trillion trillion....'), for what it is worth, comes from Hugh Ross, The Creator and the Cosmos, 3rd ed.
However, Krauss, in his paper, "THE END OF THE AGE PROBLEM, AND THE CASE FOR A COSMOLOGICAL CONSTANT REVISITED" has said something along the same lines:
Lawrence Krauss writes:
The question then becomes: Which fundamental fi ne tuning problem is one more
willing to worry about: the flatness problem, or the cosmological constant problem? The
latter involves a fi ne tuning of almost 125 orders of magnitude, if the cosmological constant is
non-zero and comparable to the density of clustered matter today, while the former involves
a fi ne tuning of perhaps only 60 orders of magnitude if one arbitarily fixes the energy density
of the universe at the planck time to be slightly less than the closure density.
source. Of course Krauss doesn't believe this implies a fine tuner, either. He gives his thoughts in a particularly interesting way in a video that can be watched
here
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