Return-Path: Message-Id: <9204040427.AA22397@relay1.UU.NET> Date: Sat Apr 4 04:26:24 1992 Reply-To: CJ FINE Sender: Lojban list From: CJ FINE Subject: Thoughts on measurement and errors X-To: Lojban list To: John Cowan , Eric Raymond , Eric Tiedemann Status: RO X-From-Space-Date: Sat Apr 4 04:26:24 1992 X-From-Space-Address: cbmvax!uunet!CUVMA.BITNET!LOJBAN 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