# max(), sum(), next()

Mensanator mensanator at aol.com
Sat Sep 6 20:22:07 CEST 2008

```On Sep 5, 10:45�pm, Steven D'Aprano <st... at REMOVE-THIS-
cybersource.com.au> wrote:
> On Fri, 05 Sep 2008 22:20:06 -0400, Manu Hack wrote:
> > On Fri, Sep 5, 2008 at 1:04 PM, castironpi <castiro... at gmail.com> wrote:

<snip>

> [The rest of this is (mostly) aimed at Mensanator,

Ok, I see where you're coming from.

> Fundamentally, the abstract function "sum" and the concrete Python
> implementation of sum() are both human constructs. It's not like there is
> some pure Platonic[1] "Ideal Sum" floating in space that we can refer to.
> Somewhere, sometime, some mathematician had to *define* sum(), and other
> mathematicians had to agree to use the same definition.
>
> They could have decided that sum must take at least two arguments,
> because addition requires two arguments and it's meaningless to talk
> else. But they didn't.

Ok. But the problem is they DID in SQL: x + Null = Null.

Earlier, you said that an empty box contains 0 widgets.
Fine, empty means 0. But Null doesn't mean empty. Say
your widget supplier just delivers a box and you haven't
opened it yet. Is the box likely to be empty? Probably
not, or they wouldn't have shipped it. In this case,
Null means "unknown", not 0. The number of widgets you
have on hand is Null (unknown) because inventory + Null = Null.

SQL will correctly tell you that the amount on hand is unknown,
whereas Python will tell you the amount on hand is inventory,
which is incorrect.

> Similarly, they might have decided that sum must
> take at least one argument, and therefore prohibit sum([]), but they
> didn't: it's more useful for sum of the empty list to give zero than it
> is for it to be an error. As I mentioned earlier, mathematicians are
> nothing if not pragmatists.
>

Here's a real world example (no ivory tower stuff):

An oil refinery client has just excavated a big pile of
dirt to lay a new pipeline. Due to the volume of the
pipe, there's dirt left over. Ideally, the client
would like to use that dirt as landfill (free), but it
must be tested for HAPS (by summing the concentrations of
organic constituents) to see whether it is considered
hazardous waste, it which cas it must be taken off site
and incinerated (costly).

In MOST cases, a HAPS sum of 0 would be illegal because
0's generally cannot be reported in analytical tests,
you can't report a result less than it's legal reporting
limit. If ALL the consituents were undetected, the sum
should be that of the sum of the reporting limits, thus,
it cannot be 0.

Can't I just use a sum of 0 to tell me when data is missing?
No, because in some cases the reporting limit of undetected
compounds is set to 0.

In which case, a 0 HAPS score means we can confidently
reccomend that the dirt is clean and can be freely reused.

But if the analysis information is missing (hasn'r arrived
yet or still pending validation) we WANT the result to be
UNKNOWN so that we don't reccomend to the client that he take
an illegal course of action.

In this case, SQL does the correct thing and Python would
return a false result.

> --
> Steven

```