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:

  1. Closure (any two members produce a member)
  2. Associativity (combinations do not change the product)
  3. Identity Element (an object that combined with any other member of the group leaves the member unchanged; zero is one example)
  4. 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:

  1. With combination, each element of the group produces only other elements of that group;
  2. Orderly despite perspective;
  3. Suggests it is written for the reader as a forensic report of facts/data;
  4. 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