Re: What is Aggregation? Re: grouping in tuple relational calculus

David Cressey wrote:
> This is slightly off topic, but here goes:
>
> A long time ago, I learned that there were 4 possible features of a set:
>
> identity, order, interval, and proportion.
>
> Every set we work with in IT has identity, but there may be sets that do
> not: (the set of all electrons?)
> Order has been discussed endlessly (so far) in this NG. I will state that
> sometimes the representation has order, but the set represented does not.
> Interval is basically whether subtraction makes sense or not: (25 degrees
> celsius minus 18 degrees celsius).

Are you suggesting that does or does not make sense? It does; the result is a delta-T, temperature difference, and you can do things with them - such as add them to an absolute temperature - that you can't do with two absolute temperatures.

> Notice that "average" for temperatures is meaningful, although the "sum" is
> not.

You can add an average delta-T to a reference temperature:

   T[ave] = ((T[1] - T[ref]) + (T[2] - T[ref]))/2 + T[ref]

> Proportion is basically whether division makes sense for the set. It turns
> out that, if division makes sense, then so does addition. (distance,
> money).

That's an interesting observation. Time intervals have proportion; so do delta-T's. Dates do not have proportion.

What about absolute temperatures? I'm not sure whether there's a circumstance where the ratio of two absolute temperatures is really meaningful - though it would give some meaning to this star is twice as hot as that star. If the ratio of two (absolute) temperatures is meaningful, this would disprove by counter-example that where division makes sense, so does addition.

> The above is very, very informal. It's just to introduce the idea. I'll
> leave it up to the more formal denizens of the NG to express it more
> formally.

-- 
Jonathan Leffler                   #include <disclaimer.h>
Email: jleffler_at_earthlink.net, jleffler_at_us.ibm.com
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