# [PD] CVs

Simon Wise simonzwise at gmail.com
Sun May 22 10:29:14 CEST 2011

```On 22/05/11 06:22, Bryan Jurish wrote:
> On 2011-05-20 16:05, Simon Wise wrote:
>> On 19/05/11 23:12, Bryan Jurish wrote:
>>> On 2011-05-19 14:01, Simon Wise wrote:
>>>> That is which numbers are directly perceivable, without some more
>>>> abstract mathematical mapping to guide us?
>>>
>>> Zero ;-)

> Sorry; that was intended as a joke --

yes of course, but it also seemed a good place to rephrase some of the ideas I
was trying (perhaps not so clearly) to articulate!

It is also interesting to consider the fact that words for zero as a number are
so recent in languages that we can try to identify when and where they first
came to be used. It puts another slant on the distinction between numbers and
other ways of expressing some simple quantities. "Nothing" isn't a number,
"Zero" is, because we have included it in our numbering system. Likewise the
words in the languages I mentioned for "one" "two" "three" "many" may be more
like the word "nothing" than the word "zero".

> "Pair" is a word of English, and a highly ambiguous one at that -- it
> might be an ordered pair, an unordered pair, a pair of pants, a pair of
> aces, 'a pair' (aka "couple"), or whatever.  Yes, it's semantically and
> pragmatically complex.  The (abstract) number "2" plays a pretty heavy
> role in all of its sense I can think of at the moment, though.

yes, this complexity and how closely it relates to the number "two" compared to
how a kind of paired-ness can be thought of, and perceived, as something
distinct from "two", is exactly what I am trying to think about.

Looking at a group of three things they also form a triangle, something which is
also closely related to the number "three", yet also is not a number. Does the
word "three" in the above language have more in common with "triangle" than "3"?
It would take much careful and interesting research to begin to answer this.

How large an integer can we perceive in a way analogous to these? It seems to
that for most people it may be five or six, but for some unusual people it is
well over 50.

> but I'm not sure what you're getting at.  Do you
> mean the semantics usually associated with the feature (singleton vs.
> non-singleton set) -- it's kinda cool that zero tends to get lumped in
> with plurals in English (but usually not in German); not sure how other

yes, in the sense that singular it is the way of representing one thing as
opposed to not-one, a counting that goes "one" "many". The German usage spoils
this idea a bit, as singular in this case does not mean "one of". Quite a few
languages, at least from this region, can form the plural by doubling the noun.

> I think I see what you're getting at, but I'm not sure where it's going.
>   I'll accept the "directly perceivable" term for current purposes, but
> there's whole heckuvalot more going on in our heads (brains&  associated
> processes) when we look at and identify a small set of like items as a
> set-of-N than I'm accustomed to calling "direct", and that's just the

That is why looking at the language structures is interesting, I am suggesting
that sometimes looking at what is encoded in the most basic, oldest parts of
human language may help think about what is directly perceivable in the sense I
am thinking about, and it is exactly the presence of language forms addressing
small numbers that suggest they are something else than small positive integers,
add that to the "52"example and it seems that "small" in this case may be larger
than I would have expected.

> It's a unary predicate, i.e. an intransitive.  It takes a single
> argument.  It returns a truth value; albeit in at least one common sense
> of 'exist' that value depends on the evaluation index (possible world /
> place and time of utterance / speaker / etc).  I'm talking about the
> kind of existence which is independent of the current index, i.e.
> __necessary__ existence: existence in every possible world.
>
> Sorry, that was probably annoying.  Yes, different people use the word
> in different ways with different connotations.

not annoying at all, different more or less precise usages get in the way and a
few definitions certainly help decide whether a disagreement is about the
meaning of the question or the answer.

> Warning Will Robinson Danger -- I think what's special about small
> numbers is special to humans, and not to the numbers as such (i.e. as
> abstracta).  I think 2 (e.g. as the cardinality of the set {0,1}) is
> pretty special from an abstract standpoint as well (binary numbers
> simulating alphabets of arbitrary finite size, that darned Turing (1937)
> again), but I'd guess that the ease of small-number recognition is
> probably just a contigent human-specific brain-related phenomenon along
> the lines Chris sketched...

I am suggesting that the size of small sets are not only describable by numbers,
they can also be described as a named patterns. No things, A single thing. A
pair of things. A triangle of things .... when these descriptions do not need to
form a potentially infinite series of counting numbers, they don't even need to
be ordered. They just need to be recognisable as a quality of the set. How big a
set has a perceivable distinct pattern certainly depends on the brain doing the
recognising, my point though is that these patterns, words, whatever, do not
need to be ordered to have useful meaning. They do not need to be labelled by
numbers. Numbers are of course a very useful way to map those patterns, so
useful it is easy to forget and abandon any unordered set of descriptions for
these patterns in groups.

> Data pending... unfortunately the guy I know who would probably be able
> to help me out is probably himself wandering around Australia collecting
> that kind of data at the moment...

sounds very interesting discussion could result

> There's a thing I feel obliged to point out here which aspiring
> linguists get to know as the "Sapir-Whorf Hypothesis" (unrelated to
> Start Trek): basically it states that `if you can't say it, you can't
> think it', and it's been pretty much totally discredited by now; i.e.
> just because you don't have a word for it doesn't mean you can't
> perceive it / think it / know it / talk about it (indirectly).

that it wasn't only the language that was being described, for example the story
about the river and the isolation went into various other details, and the
isolation between nearby groups of people was very striking in many ways.

Certainly wandering way off-topic here ... though ordering, numbers, their
mapping to quantities and the encoding of these quantities and the
interpretation of them is very much on-topic for pd in general.

Simon

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