Imperial numbers and Measurement - Circular Measurement

Basic:

Imperial measure owes nothing to any Earth system of measurement. The Imperial system was designed in an already scientific and technological era for much the same reasons Earth's metric units were designed - to simplify a complex system of historical measures.

The numeration system is base sixty - 3 times 4 times 5. This makes numbers more easily manipulated than previous systems. It works upon the same positional basis as our Hindu-Arabic system, and the same concepts apply, with multiples of 2, 3, 4, 5 and 6 (and 10, 12, 15, 20 and 30) having intermediate importance in thought between the unit and the system base of sixty. For all units, the digital places are described thus:

Prime: 60 times the base unit

Square: 3600 times the base unit

Cube: 216,000 times the base unit

Fourth: 12,960,000 times the base unit, and so on.

For fractional numbers, iprime is 1/60th of the base unit, isquare is 1/3600th, ithird is 1/216,000th, ifourth is 1/12,960,000th, and so on. If there's an 'i' in front of the multiplier, it relates to a fractional number.
For situations requiring more precision than a single digit, the spoken convention is to specify the magnitude of the leading digit, and following digits are presumed to be immediately decreasing in magnitude. "Two minutes thirty" can be two and a half minutes of time, or two and a half light-minutes of distance. "Seven ithirds fortysix fourteen" would be seven 216,000ths, forty-six 12,960,000ths, fourteen 777,600,000ths of the relevant units. If the relevant digit is a zero, the zero is spoken, so "seven ithirds zero fourteen" would be seven 216,000ths, zero 12,960,000ths, fourteen 777,600,000ths of the relevant units

Most of the time, measures are context sensitive in translations to English. For instance, a range is assumed to be given in distance units, a mass or weight in terms of mass units, and so on. In Technical, the fact of what you are measuring requires the units of measurement to match, and this has, over time, leaked over to conversations in Traditional as well. In Mindlord, everything is context sensitive anyway, and nobody uses Concept for technical or technological purposes, as the 'language' is entirely unsuitable for that purpose.

Circular measure

The Empire uses a system of degrees, minutes, and seconds much like Earth. The major difference is that the imperial circle is 60 degrees, not 360 like Earth. There are still sixty arc minutes to an arc degree and sixty arc seconds to an arc minute This makes circular measure an easy, straight-forward conversion of six to one. In mathematical graphing, zero (and sixty) is straight up, not to the right. In navigation, zero (and sixty) is straight ahead, thirty is directly behind. The convention is to use the current orientation of the ship or observer to establish a 'horizontal' axis, which is stated first and measured in degrees minutes and seconds left of current direction faced, so fifteen degrees is directly to an observer's left under current orientation, fortyfive is to the right. If the measurement is negative, it's measured to the right of current orientation, so for example, directly to the right can also be expressed as minus fifteen. The vertical axis is established in the same way, and measured the same way. Note that unlike Earthly spherical coordinates, this gives four acceptable solutions for a direction, although degrees left by degrees up is most standard.

Some common Earth angles, and their imperial equivalents:

180 degrees = 30 degrees imperial
90 degrees = 15 degrees imperial
60 degrees = 10 degrees imperial
45 degrees = 7 degrees, 30 minutes imperial (usually spoken as "seven degrees thirty" or "seven thirty" if context and magnitude is established)
30 degrees = 5 degrees imperial
15 degrees = 2 degrees, 30 minutes imperial

(Only mathematics can hope to describe eleven dimensional work such as Interstitial Vector. Technical and Mindlord both handle it reasonably well, but no Earthly language can be anything approaching both clear and accurate in this regard, so I'm not going to try)