Re: Phone game: Gleem

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

>
>
> >Date:         Fri, 29 May 1992 14:50:37 BST
> >From: CJ FINE <C.J.Fine%BRADFORD.AC.UK@CUVMB.CC.COLUMBIA.EDU>
>
> >> Why?  As I understand it, since (mathematically) 9/10 = .9,
> >> {sofi'upano} means exactly the same thing(s) as {piso}.  Nowhere does
> >> it say that one type of fraction may be less precise than the other.
>
> >NO NO NO NO NO NO!!!!
> >This is elementary metrology. In arithmetic, 9/10 = .9,
> >but in physics, or applied maths, or the real world, they are not the
> >same, because they imply different standards of accuracy. As I said in
> >an earlier mail, all measurements (and hence all numbers used as
> >quantifiers) have an express or implied accuracy. If Lojban is not to
> >reproduce the scientific implications of using decimal and vulgar
> >fractions, then we must state explicitly what accuracy is to be applied,
> >and will need to use my "accuracy" operator a lot more.
>
> Um, I'm sorry, but I've never seen .9 used to mean anything other than 9/10
> (barring cases of different bases, of course).  I'm fairly sure it's not
> through lack of exposure; I was a physics major for two years (before
> changing to computer science) as an undergrad, and did a concentration in
> mathematics, studying both applied and theoretical.  (I'm not trying to
> wave credentials at you; I just don't want to be accused of not having
> taken any coursework in the topic under discussion).  I suppose I could see
> someone saying "point nine" when he really means "roughly point nine", but
> imprecision is not implicit at all in the fact that he chooses to use a
> radix point rather than a fraction, nor vice-versa.  I'd rather see your
> "precision" operator everywhere than be told that .9 != 9/10
>
Clearly this needs some more explanation on my part.

There are a number of different ways in which we use numbers, such as:
1. Counting objects
2. Measuring
3. Indexes (eg street addresses)
4. Arbitrary labels (eg road numbers, computer models)
5. Elements of an abstract structure (arithmetic, number theory).

I suspect that 1 & 2 are far more common than the others, though I
cannot demonstrate this. Certainly they are historically prior.

I claim that ALL uses of a number for counting and measuring involve an
explicit or implicit precision.
This seems counter-intuitive when applied to counting small sets. If I
say there are three people here, it does not seem sensible to talk about
the precision. But note that if I say there are 100 people, I may or may
not be being precise, depending on the context. If I have exactly 100
seats to fill, then the precision of my count must be 1, whereas if I
have drink for 100, the precision may well be 5 or even 10. I do not
believe it is practical to determine a lower limit to where this
uncertainty may creep in: I think it is more useful to say that there is
*always* a precision, which may depend on circumstances, and which
shrinks to 1 for a small enough count.

I further claim that if Lojban is to be useful, all numerals used as
quantifiers or as arguments of measurement selbri should be considered
to have a precision, whether expressed or not. I am not saying that the
size of this precision is to be determined by purely linguistic default
(any more than that unexpressed tenses are to be defaulted in a
particular way). But I am saying that the precision should be considered
to be there.

Next I observe that in scientific custom, in the absence of an explicit
precision, the number of quoted places (or significant figures) is used
to specify the precision. Thus a measurement of 2.3 implies the range
[2.25,2.35), while 2.30 implies [2.295,2.305).
 This system is not fully satisfactory (in particular it is not clear
for integers: is 2300 precise to 100, 10 or 1?), but it is customary,
and of course it can be overridden or supplemented by express precision.

Vulgar fractions are not commonly used in scientific contexts. To me,
they do not seem to have a definable precision in the way that decimals
do. But in an impressionistic sort of way, they have a precision of the
size of the denominator - thus 2/3 is anything from 1/2 to 5/6 -
anything that is not so far away that it is 1/3 or 3/3.

[Note that, because of the accident that 10 is the base of our number
system, this particular example does not give very different results.
9/10 is effectively the same as .9. But in general this will not be so].

[Note also that the difference I am talking about is also observable in
another context, viz telling the time. For some purposes, it is
appropriate to be precise to the minute, but frequently we are concerned
only to the nearest, say, five minutes.
	The traditional way of telling the time "Five past three",
	"Twenty to eight" is normally associated with the latter
	precision [we *can* say "thirteen minutes past six" but
	it's less common, and most people would say its "Five to
	ten" for any time from 9.53 to 9.58].
	The newer method - 9.53 - is more precise, and it is my
	belief that often the precision is unwarranted and even
	distracting. That is why I have a watch whose main dial
	is rotary.]

This is my reason for claiming that fractions are not equivalent to the
numerically equal decimal, and urging that this be the case in Lojban
too.
I also urge that we explicitly recognise that all numbers used as
quantifiers or as arguments for measurement selbri have a precision.
(There may be other contexts that require this too).

			kolin