How can the logical structure of a genetic genealogy be encoded in a hexadecimal representation?

Question

Hexadecimal is a standard of computer coding because it can be used to represent arbitrary Boolean structures and Boolean algebra in succinct strings of characters.

A representation of a Boolean logic mapping to hexadecimal values can be seen in the appendix of the draft for genetic genealogy I have been working on: https://docs.google.com/document/d/1Hrsu3fTj0JL38DPXZ12U7u5ygQmjhDBkwbxIBXz9DhY/edit?usp=sharing

https://en.wikipedia.org/wiki/Hexadecimal

https://en.wikipedia.org/wiki/Logical_connective

https://en.wikipedia.org/wiki/Hasse_diagram

 

Suppose for the sake of argument and as an exercise to the reader that we want to encode two people's genetic genealogy for comparison purposes but only enough information for each person's parents. So like my brother and I.

Comments

Following.

Answer 1

This is a very interesting line of thought, the problem I see is that genetic data in not binary. It could be represented that way, but comparison math designed for booleans may not lend the desired results. I have not quite delved the depths but I would tend to represent the data in base 4, or more likely as pairs of binary digits.

As to your thought experiment with you and a bother's DNA, full siblings share all the same ancestors. Comparison between them will show their relation but will not provide enough info to analyze any other relationship. With the exception of the X,Y, and MtDNA which would match and would be traceable.

I am fascinated by this idea and I may work on it through the day and post more.

Comments

While my brother and I certainly share the same ancestors, we do not share the exact same sets of genetic data. A comparison of our autosomal and X chromosome DNA would not be without differences, so (ME == BRO) is false in general. (ME BITWISE_AND BRO) would produce a string that is not 0 and not MAX.

While genetics and genetic genealogy are certainly not base 2, it is possible to always reduce a base-n representation to a base 2 representation when n is a natural number, so there is an equivalent hexadecimal representation of the complex of relationships between my brother and I, our ATCG/{Autosomal, X chromosome, Y chromosome, Mitochondrial} set, and our parents.