Tai Chi is backed by a set of ideas that help a person perform the forms in the proper physical way and to get the most benefit from each form. This set of ideas was developed by Master Thanh Cao Nguyễn. The set is known as the Thirteen Principles of Zenobics Tai Chi.
The information about the Thirteen Principles is provided by permission of Duke Nguyễn. The “Just for fun” part below is strictly my comments.
1. Keep a serene countenance. 
2. Do the form the slower the better. 
3. Keep continuity with no interruption. 
4. Keep the mind empty and the head erect as if suspended from above. 
5. Distinguish between Yin and Yang, the negative and positive. 
6. Keep a flat chest and back. 
7. Maintain a pliable waist. 
8. Keep shoulders and elbows low. 
9. Use your brain, not your brawn. 
10. Coordinate the movement with abdominal breathing, and synchronize movement with all parts of the body. 
11. Form a new habit of renewing yourself with every moment of each day. 
12. Purify your mind-body and achieve inner peace in outwardly moving form. 
13. Be here now to achieve harmony of the mind and body, and attain the three-fold goal: Truth, Goodness, and Beauty. 
Just for fun:
After reading the Thirteen Principles over the course of a few months, I noticed a pattern of sorts pertaining to the numerical order of the list.
One must use a little imagination for my “discovery”, but if we look at six of the thirteen principles, we can see a correlation between the capital letter “U” and the human torso.
The six principles that I’m talking about are 1 (face), 4 (mind and head), 6 (chest and back), 7 (waist), 8 (shoulders and elbows), and 9 (brain).
We start at the top of the body with 1, proceed down to the midsection with 4 and 6, turnaround at the midsection with 7, and then go back upward to the head with 8 and 9. Fantastic discovery, huh? eh?
Also, I’ve noticed that #7 is unique in that the number seven is the midpoint of numbers 1-13, and the waist is the midsection of the human body.