|discussion of basic notions of arithmetic-by-inspection|
Chinese multiplication, so-attributed, is simply to cut the multiplier by halves (an easy process) and truncating the occasional fractional half, while doubling the multiplicand (also easy), first adding it to the running product cumulation (initially zero) whenever that truncation occurs, until the multiplier is exhausted equalling zero: it is quite simply binary multiplication, least significant bit first, though in decimal notation it appears tedious, compared to digit-by-digit decimal multiplication.
We'll examine more processes in this simple chine-arithmetic method, arithmetic-by-inspection, which under scrutiny may be already familiar. First: measurement on a graduated ruler.
In the early attempt to use a graduated rule to much precision, such as a measuring stick or a mechanical slide-rule, at some visual precision the reading becomes untested or inexact - verification by magnification usually does not exist in the early stage, and when it does become possible, it then usually replaces the less resolving method, and the process of refinement iterates. Typically the half-way position between two closely spaced graduations is indistinct, while the end-points are barely distinct. That is, (0,1) are distinguishable but (0.0, 0.5, 1.0) are not all certain: At some level of precision the number is estimated not by equality, but by distinguishability: and this will extend to generally statistically evaluated results, when a numeric answer is good, but the adjacent numeric possibility(s) is(are) not necessarily inapplicable, but just more off-centered on the tail of some mensurability distribution. Distributions overlap, and we need a consistent notation for indicating precision, or conversely, numeric spread.
We show here that the general Gaussian normal distribution can be used but over a different basis - and has an interesting simplification: e-pi*x2/s2/s : s=sigma - with graduations at half-sigma steps. And at this arrangement, the normal distribution looks very triangular.
[arithmetic needs to be checked]
A premise discovery under the title,