In telcraft, a scoring is a thought which mainly stands for howmuchness. Some kinds of scorings are whole scorings, broken scorings, and "true scorings" and "dreamt scorings" (although in truth, "dreamt scorings" are no more dreamt, nor any less true, than "true scorings" are).
Among the whole scorings are one, two, three, and so on; those scorings which are dealt with in the deed of scoring itself. "None" or "emptiness" is also a whole scoring. Those scorings which are greater than none are called laden scorings. For each laden scoring, there is a matching nimble scoring (from "nim", meaning "to take"), which is less than none: these scorings are called nimble one, nimble two, and so on. Emptiness is neither a laden scoring nor a nimble scoring.
A broken scoring is made by breaking a whole scoring into another whole scoring. Thus, if three is broken into two, the outcome is three halves (or one and a half), a broken scoring which lies between one and two.
The true scorings include the broken scorings, as well as those scorings which lie between broken scorings. There is no broken scoring which, when manifolded by itself (or foursided), yields two; in other words, the fourside root of two is not a broken scoring. Instead, the fourside root of two is a scoring which lies between broken scorings; thus, it is a true scoring.
The dreamt scorings are made by putting in a new scoring, called i, whose fourside is nimble one. Every dreamt scoring can be written as a true scoring, together with the manifolding of a true scoring by i. Thus, 2 + 3i ("two with three times i") is a dreamt scoring.
Laws of scoringsEdit
All kinds of scorings follow some known laws. The weightiest among these are:
- The Linking Law of Eking: for all x, y, and z, (x + y) + z = x + (y + z).
- The Linking Law of Manifolding: for all x, y, and z, (x * y) * z = x * (y * z).
- The Swapping Law of Eking: for all x and y, x + y = y + x.
- The Swapping Law of Manifolding: for all x and y, x * y = y * x.
- The Dealing Law of Manifolding over Eking: for all x, y, and z, x * (y + z) = x * y + x * z.
- The Sameness Law of Eking: for all x, x + 0 = x.
- The Sameness Law of Manifolding: for all x, x * 1 = x.