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Many physical constants related to quantized gravity, e.g., the Plancklength, mass, curvature, stress-energy, etc., are nonanalytic in G at G=0, andthus have expansions in powers of G whose terms are progressively moredivergent with increasing order. Since the gravity field's classical action isinversely proportional to G, the path integral for gravity-field quantumtransition amplitudes shows that these depend on G only through the product hG,and are nonanalytic in G at G=0 for the same reason that all quantum transitionamplitudes are nonanalytic in h at h=0, namely their standard oscillatoryessential singularity at the classical "limit". Thus perturbation expansions inpowers of G of gravity-field transition amplitudes are also progressively moredivergent with increasing order, and hence unrenormalizable. While theirperturbative treatment is impossible, the exceedingly small value of hG makesthe semiclassical treatment of these amplitudes extraordinarily accurate,indeed to such an extent that purely classical treatment of the gravity fieldought to always be entirely adequate. It should therefore be fruitful to coupleclassical gravity to other fields which actually need to be quantized: thosefields' ubiquitous, annoying ultraviolet divergences would thereupon undergodrastic self-gravitational red shift, and thus be cut off.

Orthodox quantization of Einstein's gravity: might its unrenormalizability be technically fathomable and physically innocuous?