| 5. The Poincaré Conjecture Introduction
Manifold Poincaré asked whether or not the three dimensional sphere is characterized as the unique simply connected three manifold.
Relation He wanted to solve the equations that define the same mathematical property in relation to a three dimensional sphere, but was unable to provide a singular answer.
Is a three dimensional sphere simply connected or not?
Poincaré assumed that it was at first but he was unable to prove it.
The Problem
The Millennium problem is to prove whether or not the Poincaré conjecture is correct, and to fully explain this principle of simple connectivity in relation to a three dimensional sphere.
The Answer
Conjecture The Poincaré conjecture presents us with two options, either a three dimensional sphere is simply connected or it is not, and asks us to choose one of them.
Dimensional The concept of simple connectivity seems to work for a two dimensional example because the outcome is restricted to two possible opposites.
1. Simply connected.
2. Not simply connected.
Restricted The rules change when considering three dimensions because instead of being restricted to only two potential answers, we are now restricted to three potential answers, no more and no less.
Combination A three dimensional sphere may still be simply connected or not, as it was in the two dimensional answer, but now it may also be a simultaneous combination of the two.
Answers Three simultaneous dimensions require three simultaneous answers in the same way that all other answers to all other questions do.
Simply A three dimensional sphere may be simply connected, not simply connected, and neutral.
Simultaneously.
Conjecture 1. The Poincaré conjecture is true. 2. The Poincaré conjecture is false. 3. The Poincaré conjecture is neutral. Simultaneously.
Am I wrong? I simultaneously oppose, agree with, and neutralise all criticism ad infinitum. My point is literal. There is no point creating a theory of everything that doesn't work. |