On Sep 30, 2009, at 11:02 AM, Joe Collins wrote: (01)
> Pat Hayes wrote:
>> On Sep 29, 2009, at 10:30 PM, Joe Collins wrote:
>>> Pat,
>>>
>>> > Well, actually, it is. It means 'the same as'. It does not mean
>>> 'nearly
>>> > the same as' or 'not the same as, but so close that I can't
>>> measure the
>>> > difference' or 'very likely very close to' or any of these other
>>> > notions. Equal means *equal*. If A=B then there is *one thing*
>>> with two
>>> > names, not two things that are very close.
>>>
>>> You are correct in that approximately equal, not being transitive,
>>> can not be an equivalence relation.
>>>
>>> In that case, I must conclude that
>>>
>>> > 1 m = 1.00 m : true or false?
>>>
>>> is false
>> ?? I am gobsmacked, both by the conclusion and by the logic. Why is
>> 1 only approximately equal to 1.00 ? The bare numeral '1' refers
>> to the number one. The decimal numeral '1.00' refers to the sum of
>> the number one, zero tenths and zero hundreths. I believe if you do
>> the addition, that also comes to one.
>
> To quote again from the SI standard, ISO/DIS 80000-1, "Quantities
> and units"
> ----snip----
> 7.3.3 Error and uncertainty
> When a number is given without any further information it is
> generally interpreted so that the last digit is rounded with a
> rounding interval equal to 1 in the last digit (see Annex B). Thus,
> for example, the number 401 008 is generally assumed to represent a
> value between the two values 401 008,0 ± 0,5,
> i.e. between 401 007,5 and 401 008,5.
> ----snip----
>
> Not a hallucination, just reading the standard I thought we were
> trying to capture (which, being educated as a physicist, I already
> knew before reading the standard). (02)
Well, OK, but then please can we all clearly indicate in these
messages what sense we intend to give to expressions such a numerals?
I wasn't expecting that the actual notation of mathematics would be
revised for this ontology. If we are to understand numerals in this
way, then Gunther's question was in fact much more complicated than it
appeared to be. In particular, it was not about the truth of an
equation, as it appeared to be, since 'equations' involving 'numerals'
with the above understanding are not in fact equations at all, but
statements of equivalence between existential assertions about numbers
being in interval ranges. I would strongly urge that we NOT do this,
whatever the SI standard says; but if we do, then please, all of us,
state all use cases, precise questions, etc., in completely
unambiguous terms. If you want to ask whether the interval range [0.5
1.5] is equal to the interval [0.995, 1.005], please phrase the
question that way, not as an equation. The answer to that question, by
the way, is clearly NO. As you can see, these answers tend to be
clearer when the questions are posed with enough precision. That is a
reason why ontologies are often useful, by the way. (03)
Pat Hayes (04)
>
> Regards,
> jbc
>
>
> --
> _______________________________
> Joseph B. Collins, Ph.D.
> Code 5583, Adv. Info. Tech.
> Naval Research Laboratory
> Washington, DC 20375
> (202) 404-7041
> (202) 767-1122 (fax)
> B34, R221C
> _______________________________
> (05)
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