Thoughts on measurement and errors

[CJ FINE <cbmvax!uunet!BRADFORD.AC.UK!C.J.Fine>]

Some thoughts on measurement and errors.


We have a couple of ways of specifying measurements at present.

  ti mitre li vo
  this measures-in-metres the-number 4 (in some direction)

or, as an equality sentence:

  le se mitre beti du li vo
  the measurement-in-metres of-this is the-number 4

We can also make explicit the act of measuring thus:

  ti se merli filo mitre be li vo
  this is measured (by somebody) as thing-measuring-metres the-number 4

or

  ti se merli fili vo lo mitre
  this is measured (by somebody) as the-number 4 on-scale the-mass-of
things-measured-in-metres

or even

  ti se merli fili vo

if the units are conventional.

Again we can put this in equation form:

  le te merli beti du le mitre beli vo (not sure if this is right?)
or
  le te merli beti du livo


What if we want to specify an accuracy?  One way is to add a range to
the numeral in any of the above examples:

 ti mitre li vo su'i ni'upinonomu bi'o ma'upinonomu
 this measures-in-metres the-number 4 + [-.005 interval +.005]

(note that neither "su'i ja vu'u" nor even "su'i jonai vu'u" is right -
we really mean an interval).

This method can apply to any of them:

  le te merli beti beifolo mitre du li vo su'i ni'upinonomu bi'o ma'upinonomu
  the measurement of this on-the-scale-of-metres is the number  4 +
        [-.005 interval +.005]

I would like to propose a couple of alternative ways of doing this -
both are extensions to current definitions.


1. Give "merli" a fifth place - "with accuracy x5" - which can either
be a range, or a reference to a standard.  Thus

  ti se merli zo'e livo lo mitre li ni'upinonomu bi'o ma'upinonomu
  this is measured as 4 in-scale metres with-accuracy +/- 0.005

I think this is important - defining measuring without a place for the
accuracy is unscientific.

2. Provide a new operator (I'll use xe'i):
  y = xe'i x1 x2 [x3] y is a measurement/range, nominal x1, lower bound
x1-x2, upper bound x1+x3 (x3 defaults to = x2)

  ti mitre li vo xe'i pinonomu

Of course "xe'i" is roughly conveyed by "na'u xe merli", but the
operands are wrong.

Other things you can do with these suggestions:

  ko'a merli lo selci fulo mitre beli geini'uze
  He measures cells with an accuracy of 1E-7 metres

  ta minji co merli folo tergutci li geini'uxa
  that is-a-machine for measuring on-scale subunit-of-foot
        with-accuracy-the-number 1E-6
  That's a micro-inch gauge

  la dan. merli leni curve li sobipixace'i xe'i pinopamu fe'a pinorere
  Dan measured the purity as 98.6% [-.015 +.022]

(It is not clear, except from extra-linguistic deduction, whether these
error values are -.015%+.022% or -1.5%+2.2%.)


One more, only slightly related point:

I cannot think of any possible occasion when "+/-" should be translated
"su'i ja vu'u". It is nearly always specifying a range "bi'o". The
major exception is in algebra, when specifying roots of equations, as
in John's example in the mex paper.  Here there are two choices, with
slightly different meanings, appropriate to different contexts.

When solving a particular equation, we may say

li xy. du li vei va'aby. SI'U JONAI VU'U dy. ve'o fe'i ty.

(where dy. is the discriminant and ty. the denominator - can't be
bothered to write them out). This means that x (that we want) is one or
the other of the numbers specified by those connected expressions.

As a general statement of mathematics (eg when you would use the
identity operator rather than equals), I think the appropriate
connective is either "jo'u" or "ce".

I'm not sure quite how either of these work.  If "ce", it is the
operators that are constructed into a set, so I don't know whether that
can be 'exported' to create a set of values. If so,
li xy. du lu'ali .... su'i ce vu'u ...

I think "jo'u" may work, but I'm not certain.  Suggestions, anybody?

                        Kolin