The n-tuple Training Notation

In the last post I introduced a new notation for organizing training distribution.  Here I would like to expand on this idea.  First we need a few definitions.

Definition 1:  An n-tuple is an order collection of n numbers.  Ex: (1,3,5,2) is a 4-tuple.
Definition 2:  A positive rational partition of 1 into n parts is an n-tuple whose sum of entries is 1.  Ex (1/2,3/4,0,1/4) is a partition of 1 into 4 parts.
Definition 3:  A training n-tuple is a partition of 1 into n parts in which each entry represents the portion of training time spent on a single type of training.

Examples of Training n-tuples:


There are training n-tuples of size 0 and 1 that aren't that useful so we'll start with larger sizes.  A training tuple of size 2 (or ordered pair) could have entries representing strength/power and endurance(including "resistance" as discussed before).

Example 1:  (1,0) represents only training strength and power
                     (1/2,1/2) represents equal time spent on strength and endurance.

There are a few useful examples of training 3-tuples(triples).  A climbing only training triple would involve (strength, power endurance(resistance), endurance).  A triple could also include cross training: (strength, endurance, cross training).

Example 2:  (1/4,1/2,1/4) represents one quarter of training time spent on strength and endurance and one half of the time spend on resistance(for the triple of type 1).
                     (2/5,1/2,1/10) represents 2/5 on strength, 1/2 on endurance, and 1/10 on cross training.

One can create arbitrary training n-tuples by ordering the entries from the least to most number of moves, then adding cross training at the end.  A version of the training 5-tuple was discussed last time.  The largest useful training n-tuple I can imagine would be the training 8-tuple:

(c1,c2,c3,c4,c5,x1,x2,x3)

c1:  Short power

c2:  Long Power

c3:  Short Resistance

c4:  Long Resistance

c5:  Endurance

x1:  Cross Training: Strength

x2:  Cross Training: Metabolic Conditioning

x3:  Cross Training: Endurance

Creation of smaller training n-tuples from this 8-tuple can be done by combining some of the above types of training or leaving them out all together.  If I were teaching a course in climbing training I would assign you, the reader, to create 5 different training n-tuples(leave them in the comments if you like).  

Why?

Some of this is for sure overkill, but if there is anything I've learned from studying math is to take an idea and extend it to its logical conclusion.  Later we will explore a periodized training schedule taking advantage of training n-tuples.