CanyonWind wrote:
dannit wrote:
We could measure the size of a persons trousers by a single number: Let x be the leg length, and y be the waist length. Define the size as s = (2^x)(3^y), then we have a unique number for every pair of trousers since numbers only have a single prime factorization. Numbers just indicate the structure
Sounds like your math is more sophisticated than mine. So who has bigger pants, a gluttonous midget or an anorexic basketball player?
Bras, shirts, and shoes are also two variable systems, more complex than intelligence. Would the same apply to them?
Since it's a single variable system, was Einstein more intelligent than Mozart?
One of the topics I study is the concept of measure, what are the fundamental principals of quantifying this like: how long is a line? how much water is in my glass? whats the probability that it rains? They all follow the same principals (For technical detail:http://en.wikipedia.org/wiki/Measure_theory)
The thing is with abstraction that sometimes what we think we understand may actually be tied down by too many assumptions. The question originally was about the ability to 'measure' a bi-variate quantity though a single number. Which I gave you. Now you have re-formulated the question by asking 'Is the measure ordered?' (by ordered I mean that the relation < or > is well defined), this doesn't hold in general theory for specific cases.
So in answer to your question, for any system quantified in size by N variables I can define a single size parameter S = (2^a)(3^b)(5^c)(7^d)...(p^z) where p is the Nth prime number and z is the Nth variable. Remember also that letters can be enumerated as can any finite set of parameters. Suppose I have a random object sized by a number 0-9 and a letter A-E then I can define a size s by s = (2^x)(3^y) where x is the number and y is the number representing the letter. Then say s = 36 tells me that s=(2^2)(3^3) and so our object is sized as 2C, similary s = 144 = (2^4)(3^2) so this object is 4B.
and for your last question: Cannot collect data from either of them so its a matter of debate
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