It appears that the controversy over whether animal experiments demonstrate a threshold for carcinogenicity from chemicals was due to an error in plotting dose response. A linear (arithmetic) scale for the dose of chemicals obscures effects at doses below those used in the experiment and distorts the effect seen over the range of doses used. Gaddum (Nature 156: 463, 1946) pointed out that, empirically, dose should be on a logarithmic scale to effect a linear quantal response. It now is proposed that this logarithmic relationship of dose to effect has a sound basis in chemical thermodynamics (Waddell, Toxicol Sci 68: 275-279, 2002). When the results of major studies (e.g., ED01, etc.) done in the past were reanalyzed with this in mind using the Rozman et al scale (Drug Metab Rev 28: 29-52, 1996), which has a logarithmic scale down to one molecule (10(0)), unequivocal thresholds were demonstrated. Many animal studies now have been reanalyzed by this procedure (e.g., Waddell, Toxicol Sci 72: 158-163, 2003; Waddell, Food Chem Toxicol, in press; Waddell, Hum Exp Toxicol, in press); these studies show thresholds for carcinogenicity at doses ranging from 10(17.1) to 10(21.92) molecules/kg/day. These results require a complete reevaluation of human risk assessment for carcinogenesis from chemicals and a redirection of basic research to discover the system, or systems, that are overwhelmed at these thresholds.