I guess wildcat should be the one to respond, but --
Xander said:
The whole series of 1,2,3,4,5,6,7,8 is based upon the assumption that what preference means is the areas in which you have the most capability. It's a forgiveable assumption esp for an NT where competence and confidence are partnered so closely. Why would an NT who is soo bad at SF use it more than absolutely necessary? Well what happens if preference means "regularly engaged in"? In other words if you are an INTP do all those outbursts of illogical behaviour tinged with feeling and out of context mean that you use SF quite a lot?
Well, I think yes, it does. However the use would be ineffectual and harmful to say the least, because the INTP isn't well equipped to act as an ESFJ. It's important to note that even though the idea and the table consist of numbers 1, 2, 3, 4, 5, 6, 7, 8 they still talk about the eight functions and the associated personality theory. They would be meaningless without the interpretation -- i.e molding them into a familiar mold within the mind's eye. 4, 7, 6, 1 signify the INTP. They add up to 18, one half of all functions added up. 9 is key because it's any one dichotomy. ESFJ is therefore 36-18 = 18 = 8+3+2+5. However the key point as illustrated above by elfinchilde is the subtraction. Take an INTP, subtract the INTP (natural preferences indeed) from the INTP's full "potential", 36, and you get ESFJ, the shadow and inherently undeveloped side of the INTP's personality.
Now as the table probably doesn't work too well based on only four preferences doesn't this mean you need to sort out the foundation before constructing the house?
If I'm getting this correctly, that's the whole point. The four preferences were never a foundation because they utilized just four functions, whereas every person has all eight within them (the deal with 9x4 = 36) and this is something MBTI also agrees with. Wildcat's table is conceived to work with all eight functions. In fact it's probably something MBTI-interested people should take a look at because it's really quite "liberating" and makes sense! (And for once, explains the cognitive processes test's results.)
Oh and I know you're looking at the maths between types and so forth but you've yet to state any found correlations or patterns beyond the numbers themselves. Now you chose the numbers so any patterns existing between them are irrelevant unless they mirror patterns in the functions themselves.
The patterns fundamentally are not that different from those that the MBTI already contains. It's simply enlarged.
For example, 4-function system:
INTP > Ti Ne Si Fe < ESFJ
And the complete 8-functional representation per wildcat's system:
INTP > Ti Ne Ni Te Fi Se Si Fe < ESFJ
Or something simpler, the I-E contrast:
Four functions:
INFP > Fi Ne Si Te < ESTJ
ENFP > Ne Fi Te Si < ISTJ
Eight functions:
INFP > Fi Ne Ni Fe Ti Se Si Te < ESTJ
ENFP > Ne Fi Fe Ni Se Ti Te Si < ISTJ
To link to your analogy, looking at the light bouncing off the mountain only tells you what you see, what light reflects and not what the mountain is. Ergo you are studying what the numbers tell you about the numbers and not about what the numbers represent. For that you have to approach the mountain and get in touch with what it actually is.
The interpretation is what the numbers represent...