[TheOtherHobbes]

Scientific units are:

1. Standardised. 2. Defined by a numerical relationship to observable physical constants, like c, by definition.

Desk widths aren't a scientific unit. You can only measure the ratio of width to height by reference to a standard unit like the metre, which in turn is based on a constant observable quantity - the distance travelled by light in one second.

You can pick your derived units using any relationship to c - like the distance travelled in 3.2 seconds. But that's still a derived unit, not a fundamental observable unit.

And ratios are dimensionless because they stay the same whatever derived unit system you choose, as long as it's consistent.