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Roger L. Costello wrote:
> What is a "kilometer"?
Ahah.
> Or is it something else? /Roger
A kilometer is just a thing, like a potato, or a person. It's not a
solid object, but it's an amount of *space*, and space certainly exists,
even if you only perceive it as a "nothingness" in which to put stuff.
In your case, the river has a property of 'length', and the value of
that property is a number of kilometers. It's also a (different) number
of metres, miles, attoparsecs, etc.
Mathematically, units are considered to be unknown quantities, sort of.
Eg, if you travelled 10 metres in two seconds, then your speed
(according to s = d/t, speed is displacement divided by time) is 10m/2s
= 5 m/s. It's as if "m" and "s" are variables that you never find the
value of.
So I used to imagine that there was some fundamental unit of measurement
of distance, but that it was Magical and Divine and Unknowable, so we
would work in metres and just multiply our distances by a conversion
factor, "m"  the length of a metre in the Holy Distance Units. Just as
one can never write down a value for "i", the square root of minus one,
one can never write down a value for "m".
This enforces "dimensional consistency". The s=d/t equation is
dimenstionally consistent because speed is measured in "m/s",
displacement is measured in metres, and time is measured in seconds; if
you take all the variables to be one of their particular unit the
equation balances. However, I'm told that Schroedinger's Equation from
quantum mechanics can't possibly be correct because it's dimensionally
inconsistent; the fact that it's managed to predict real physics and be
so useful is just that it's a workable approximation to whatever's
*really* going on down there in atoms.
Saying that the river has a length property of "X kilometres" is pretty
similar to stating that Alaric has an "owns" property of a set including
(but not limited to ;) the value "six pencils". The differences being
that I can lay my six pencils down on a table and they are distinct
objects, while all kilometres are indistinguishable and interchangeable;
because two points are a kilometre apart, there's a potential kilometre
inbetween them; and since there's probably a fairly infinite number of
points in the universe, there's going to be a fairly infinite number of
pairs of them a kilometre apart, so a lot of potential kilometres
around. But we ignore them when they're not useful. And that's only
covering straight kilometres, not the kilometrelong coils we could fit
infinite numbers of into each and every atom's inner electron orbits. We
are interested in how many kilometres it takes to fill the great circle
segment from London to New York when planning a journey, but not as
interested in the fact that one could construct a kilometrelong path
around our circulatory systems.
If one were storing computer data about said river, then "kilometres"
could become a data type  a subclass of "distance" and "number";
putting this information in the type could (given an expressive enough
type system) allow you to instruct the compiler to perform appropriate
conversions if kilometres and miles are added, or to complain if
kilometres and seconds are added without explicit overrides.
"kilometres" might be useful as a CSS class in some document, perhaps
with a:
distance.kilometres:after {
content: "km"
}
...or similar.
> 1. Is kilometer a class? Is 6300 an instance of the kilometer class?
> kilometer class: {..., 6300, ...}
No, definitely not. All that statement says, at best, is that
"kilometres are counted with numbers".
> 2. Is kilometer a function? e.g., kilometer(Yangtze) > 6300
> In general: kilometer(physical object) > number
> "The kilometer function maps a physical object to a number."
Nope  because the length property of the Yangtze is 6300 kilometres,
but the meanWidth property is probably something like 0.1 kilometres.
Both kilometre properties of the same object.
> 3. Is kilometer a property? e.g., a property of the Yangtze River
> is kilometer (this doesn't quite sound right; perhaps there's
> another way of expressing this that is more natural?)
Your definitions in (2) and (3) are equivelant  the existance of a
"property" by the usual definition implies a partial function from
"objects" to "the value of this property for that object".
> 4. Is kilometer a label? If so, then what's a label?
It's a label for an abstract concept  a certain distance, in the
abstract. The *particular* distance from the source to the mouth of the
Yangtze river is called "the Yangtze river", but it happens to coincide
with 6300 arbitrary instances of the abstract distance "kilometre", you
could say.
ABS
