In prior blog posts, I wrote about Identity--how to know if a book in the Library contains true facts/data about a historical event (past or future, no matter how distant)--Identity *is* the eloquent (and important) word to describe how this symmetry operates. Knowing that the book is true historically requires a look at symmetry.

That which is symmetrical would rely on Group Theory, which gives us four properties, as Mario Livio suggests in his book, *The Equation That Couldn't Be Solved*. Those properties include:

- Closure (any two members produce a member)
- Associativity (combinations do not change the product)
- Identity Element (an object that combined with any other member of the group leaves the member unchanged; zero is one example)
- Inverse (every member has its inverse, resulting in the Identity Element as the product)

If a book being read by a library patron says it is a book written for them specifically as a forensic report on certain historical events in the correct time frame:

- With combination, each element of the group produces only other elements of that group;
- Orderly despite perspective;
- Suggests it is written for the reader as a forensic report of facts/data;
- Invites dismissal of group elements to invalidate continuity;

Then that book is indeed an accurate representation of history, no matter how far in the past or the future. In the blog post from August 17th, one month ago, I mentioned that the Well-Ordered Principle tells us that no matter how rich a set of axioms/operations are, they will still be incomplete, undecided. For some mathematicians, unless constructed, a number is indiscriminate, undecided, and to their perspective, fiction. What does this mean to the above four properties?

Property #1 says that each element combined with an element of the group produces only other elements of the group, but how then might the Well-Ordered Principle put a wrinkle in that particular property, let alone the set of four? We'll find out over time.

*Quite Literally Yours,*

*The Librarian*