Hi Tom, thank you for your interest in my treatise. Obviously it is incomplete - just part one however I believe that everything will be much clearer as I move forward with completing the treatise.

I'm unclear as to what you mean by "a bl series is proportional between its elements" vs. "arbitrary increments" could you elaborate?

As for the heuristics you've provided, I'm afraid they are not entirely correct.

Nominal Numbers - Agreed that in general nominal numbers do not follow BL such as zip codes and telephone numbers. The only exception is if there is a crossover such as in asset tagging where letters and numbers are used to be both noimal & somewhat quantifiable.

Ordinal Numbers - here I cannot concur. BL can manifest in ordinals. Why? Because althought they indicate a position - there are still a reflection of the serial quantitative nature of numbers.

Cardinal Numbers - here is the crux of my Treatise and thus is where the heart of BL originates - it is the logical uniliear system underpinning cardinal numbers that causes the effect we currently refer to as Benford's Law. I will show this in future posts.

Other human assigned numbers - depends of if they really fall under the nominal, ordinal or cardinal definitions - but anything that involves the process or mechanism of quantification (adding/subtracting/multiplying/etc.) will follow Benford's Law.

BL conformance does not require multiplication in any form. Logical observance of the 1-9 serial nature of quantities is all that is needed.

Logs are not necessary for BL, however do follow BL.

Scale is useful in easily seeing BL, however scale is not required for BL to exist. BL exists within the set of cardinal numbers 1-9.

I am still focusing on completing this treatise on BL and am therefore holding off on exploring the connection between BL and fractals though I am confident that due to BL being a natural part of numbers and nature being a reflection of numbers, and fractals being a description of nature, they are certainly related.