Can anyone tell me where this information was originally published? I have seen several online references to Randy's ideal water profiles but I never saw a mention of the source publication. Thanks in advance.
As there is no such thing as an ideal water profile you are, in effect, searching for the fountain of youth. Learn about the style(s) of beer you are interested in brewing. As part of your research you will find information about the general characteristics of the water each was brewed with. Brew the beer with water that is fairly close to those characteristics and then experiment from there until you hit the optimum (or near optimum) result in terms of your personal optimality criterion.
It's probably also worth mentioning that many of the ion profiles published in books and magazine articles in those days of yore were physically/chemically impossible in the sense that one could not synthesize them at any reasonable pH. In many cases they also represented the water of the region in which the style originated - not the water of the region as treated by the brewers that worked there.