Working with the set of real numbers

Chris Angelico rosuav at gmail.com
Thu Feb 13 05:17:36 CET 2014


On Thu, Feb 13, 2014 at 2:31 PM, Steven D'Aprano <steve at pearwood.info> wrote:
> "The former South African apartheid government did not respect the
> Universal Human Rights of blacks."
>
> Under your strict interpretation, we would have to say that even a single
> example of the apartheid government respecting even a single human rights
> of a single black person would be sufficient to disprove the claim.

Right. A common interpretation of that statement would be that, by and
large, one can see a parallel between "people whose rights are not
respected" and "people with black skin". The existence of a single
black person whose rights are respected, or a single non-black person
whose rights are not respected, doesn't change that; if there are X
million black people whose rights are not respected, and Y million
white people who are treated like people, and the converses are
measured in thousands, then the statement would be considered valid.

(That said, though, if there *were* a black person whose rights were
respected, then it would be highly notable. I don't know if there had
been such a case with .za, but there were - if you'll forgive me for
Godwinning - a very VERY small number of Jews who held high position
in Nazi Germany, and who were not harmed because they were of too
great value to lose. It's notable because respecting a single person
of a category of people considered "sub-human" effectively disproves
the notion that "all X are less than people". (If one Jew is worth
keeping around, how can you say that Jews are, by definition,
subhuman? If one black woman can hold a highly respected position in a
university, doesn't that prove that black people and women are just as
intelligent as white males?) But, notable or not, it doesn't change
the fact that Nazi Germany *as a whole* considered Jews *as a group*
to be insignificant, and that the apartheid .za govt treated
black-skinned people *as a group* to be insignificant.)

So where does that leave computers and reals? Well, it comes down to
descriptors. Suppose there were a place where all people are treated
perfectly fairly, UNLESS a white-skinned person is male and aged
between 13 and 20, in which case he is considered guilty until proven
innocent. Does this place treat males and females equally? Not really.
But it's also not really accurate to say that "men are mistreated by
the law", any more than it's accurate to say that "IEEE floating point
handles real numbers". I certainly would not say that an integer type
"works with real numbers", simply because it's almost completely
useless to say that - since it's such a tight subset of them.

ChrisA



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