FrankMak
We are all taught to accept that units of measure have to be defined. The International Bureau of Weights and Measures (BIPM) is the keeper of the kilogram and meter, and the Consultative Committee on Units (CCU) provides recommendations on how various units are to be defined. In their 2005 report, the CCU stated,
QUOTE
the consensus that now exists on the desirability of finding ways of defining all of the base units of the SI in terms of fundamental physical constants so that they are universal, permanent and invariant in time.

2005 CCU Recommendations

The July/August 2011 edition of IEEE Potentials contains a paper with the title, A Methodology to Define Physical Constants Using Mathematical Constants.

The concept described in the paper identifies a fundamentally different way to apply mathematics to physical law. Those with IEEE membership or associated with an institution that has a membership can read/download the paper from: A Methodology to Define Physical Constants
The paper is on the second page of the Contents.

The IEEE publication has a classic image of Euclid on the first page of the article, which IEEE slightly altered; the technical material is identical.

The concept uses the relationships of a fundamental physical law and basic geometry to define two basic units of measure.

FrankMak
For several years I carried on discussions with various individuals about the concept of mathematically defined units. One very technically accomplished individual stated the following about SI units:
QUOTE
They are totally anthropocentric, arbitrary, and non-natural base units, from the POV of physical law.  From those four arbitrary definitions of quantity of stuff we get these weird numbers attached to such universal constants of c, G, hbar, and epsilon0.

The values defined in the Methodology will not resolve the remaining dimension problems with G, hbar and epsilon0, but they provide a non-arbitrary starting point.

I have attempted to communicate with BIPM, but they never respond.
FrankMak
Basically, the concept presented in the paper affirms that the mathematics that we use has a direct link to physical law. If the correct values are selected for the physical law-mathematical relationship, it allows the base units of measure to be identified.
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