My (late) friend Vic Stenger wrote a book on this, "The Fallacy of Fine Tuning", mostly to debunk Christian misuse of fine-tuning arguments. He analyzes the Hoyle resonance calculation as you do and the stability of the proton. Rich Deem's neutrino mass. Why is gravity so weak. Deuterium abundance. Inhomogeneities in the earlier universe. Rees's "nuclear efficiency" parameter. The book discusses about thirty putative examples of fine-tuning; some serious, some just misconceptions (the speed of light is so fast). Many of his examples are from Martin Rees and Hugh Ross. Hugh Ross has a website where these examples seem to be mass produced: http://www.reasons.org/articles/the-proton-neutron-mass-difference-illustrat... Vic also discusses the speculative, holographic principle answer to why Lambda is so close to zero, but not zero. I'll send you a copy of Vic's book if you like. I think there are some general arguments against the significance of so called fine-tuning. One of them is that there is no canonical measure on these parameters. By expressing fine-tuning in terms of percentage of the measured value, one is implicitly taking the measured value as a scale parameter and assuming values far from it (logarithmically) are equally probable. There's an argument just based on dimensionality, that says if the parameter space of universes has many dimensions and there's a compact life-friendly region, then among all the universes supporting life you're most likely to find yourself on one near the edge of the region. Brent On 5/6/2015 11:47 AM, Warren D Smith wrote:

I'm interested in claims of the kind "the universe's fundamental constants were fine tuned with the goal of supporting intelligent life" and the question of how to assess how valid/crazy such claims are.

One can collect various claims of the form "if constant X were changed to become >Y*X, then the universe would become unfriendly." Please list your favorites. I'd like to assemble a collection.

But usually when I try to do that I get Y-values of, say, 10. Not 1.01, which would be a lot more impressive.

There are certain Christians etc who enjoy collecting such claims, but some of them are misleading (and some are just completely wrong, but I'll ignore those). Two examples:

"The neutron/proton mass ratio is about 1.001 and if it were >1.01 or <1 then life would be impossible." Really this is since the electron is 1836 times lighter than the proton, and perhaps one could argue if 1836 were <750 or >3000 the universe would be unfriendly, but that would be a factor-4-wide range, not factor<1.01-wide.

"The 'Hoyle state' of carbon: the third-lowest energy state of the carbon-12 nucleus, with an energy of 7.656 MeV above the ground level. According to one calculation, if the state's energy were lower than 7.3 or greater than 7.9 MeV, insufficient carbon would exist to support life; furthermore, to explain the universe's abundance of carbon, the Hoyle state must be further tuned to a value between 7.596 and 7.716 MeV. A similar calculation, focusing on the underlying fundamental constants that give rise to various energy levels, concludes that the strong force must be tuned to a precision of at least 0.5%, and the electromagnetic force to a precision of at least 4%, to prevent either carbon production or oxygen production from dropping significantly." But S.Weinberg responds: The crucial thing that affects the production of carbon in stars is not the 7.65 MeV energy of the radioactive state of carbon above its normal state, but the 0.25 MeV energy of the radioactive state, an unstable composite of a beryllium 8 nucleus and a helium nucleus, above the energy of those nuclei at rest. This energy misses being too high for the production of carbon by a fractional amount of 0.05 MeV/0.25 MeV, or 20 percent, which is not such a close call after all.

Weinberg seems to think the only really impressive fine tuning is the Einstein cosmical constant Lambda, which is not zero, but is about 121 orders of magnitude smaller than a naive guess would have been, perhaps due to an amazing almost-cancelation, albeit nobody understands it.

It seems to me even a collection of examples with Y=10 each, still seems impressive if you have enough of them. Here is a quote by Martin Rees about this: "Suppose you are in front of a firing squad, and they all miss. You could say, 'Well, if they hadn't all missed, I wouldn't be here to worry about it.' But it is still something surprising, something that can't be easily explained. I think there is something there that needs explaining."

Is there?

Fred Hoyle's "amazing fine tuning" regarding the energy of the excited state of the carbon atom at about 7.65 MeV above ground, was re-examined by H.Oberhummer, A.Csoto, H.Schlattl: "Fine-Tuning of Carbon Based Life in the Universe by Triple-Alpha Process in Red Giants," Science 289, 5476 (7 July 2000) 88-90. Nucl.Phys. A 688 (2001) 560-562 Nucl.Phys. A 689 (2001) 269-279 "The result is that even with a small change of 0.4% in the nucleon-nucleon interaction strength, carbon-based life appears to be impossible, since all the stars then would produce either almost solely carbon or oxygen, but could not produce both." They argue that Weinberg's analysis somewhat missed the point: if the level moves too much you get no carbon, only carbon and no oxygen, or only oxygen and no carbon. You have to be just right. Sounded cool, except largely retracted after further re-analysis including some of the same authors as before, H. Schlattl, A. Heger, H. Oberhummer, T. Rauscher, A. Csoto: Sensitivity of the C and O production on the 3-alpha rate, http://lanl.arxiv.org/abs/astro-ph/0307528 "when the evolution of the stars as a whole was followed for their entire life, in particular the low- and intermediate-mass stars show fine tuning of carbon and oxygen yields that is more complicated and far less spectacular than found in Paper I. Therefore, the anthropic significance of the 3alpha rate might be considerably less." Oops. Still later review: Ulf G. Meissner: Anthropic considerations in nuclear physics, Science Bulletin 60,1 (2015) 43-54. http://lanl.arxiv.org/abs/1409.2959 ...from which you might guess the latest claim is the Hoyle effect constrains the strong force to within a few-%-wide window, otherwise the universe will be lousy. Making this now all as clear as mud.