On Sep 29, 2009, at 10:30 PM, Joe Collins wrote: (01)
> > Well, actually, it is. It means 'the same as'. It does not mean
> > 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 (02)
?? 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. (03)
> > Why? I don't think our ontology is intended to be restricted to
> use only
> > by physical scientists.
> I don't either. The SI/VIM standard on quantities and units is,
> however, a formalized scientific theory. If, in trying to capture it
> in an alternative mathematical form for use in computing systems it
> no longer makes sense to physical scientists, then it no longer
> makes sense that relates to the real world.
> It is then of no real use to anyone.
> > IMO, this is all beside the point. The question as posed does not
> > mention accuracy or measurements or anything else. It simply asks
> > whether 1 is the same as 1.00. And I think the only possible
> answer is,
> > yes. (If I were being a computer scientist, I could hallucinate the
> > integer/FP distinction onto this question, and then the answer would
> > depend upon the programming language I was using; but this very
> fact is
> > evidence that this is not the intended meaning of the question,
> The question as posed is ill defined: there is no definition of the
> symbols. If we just take it as given without further definition, i.e.,
> > 1 m = 1.00 m : true or false?
> then *WE* must say false, simply because "1" and "1.00" have
> different symbols. (04)
No, that is a logical mistake. The question wasn't about the symbols,
whether '1 m' equalled '1.00 m'. (05)
> To say otherwise without further definition of what the symbols mean
> is to be tacitly adding some kind of additional meaning which is not
> explicitly defined. (06)
We have to assume some meaning or the question is meaningless. In
fact, there isn't even a question to be answered.
> I was trying to expressly add a reasonable meaning.
> In either case, now I say FALSE and FALSE.
> Let me recall your response:
>> Depends on whether you consider 1 = 1.00. In other words, its
>> nothing to do with meters. But I'd say, yes. (On the grounds that
>> I presume this is meant to address issues of precision in
>> quantity specifications, and I believe they should be relegated to
>> another topic.)
> Were you doing that "hallucinating" thing when filling in the
> missing meaning here? (07)
I was guessing, true. (08)
> Regards, /:^)
> Joe C.
> 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
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