John, (01)
I think you may have misunderstood my point (though I am not sure the value
of pursuing this). (02)
> CP> So, as you probably know, studies in pre-literate Mesopotamian
> > mathematics show that these cultures did not have a notion of number.
> > In other words, they did not have a clear notion of 1, 2 or 3.
>
> I very strongly doubt that. A few isolated tribes, such as the Pirahã, do
not have
> a system of counting, but that is an extremely rare example. See, for
example,
>
> http://www.newyorker.com/reporting/2007/04/16/070416fa_fact_colapinto
>
> CP> One can track when the idea was introduced. In the early writing,
> > three sheep were signed by three symbols for a sheep. Subsequently >
there
> was one symbol for 3 and one for sheep. (03)
The point is not that they had no notion of counting in sense of the Pirahã
- rather that they did not start off with our current abstract notion of
numbers.
The evolution of this is preserved in their bullae.
Originally they used symbols (pictograms) for sheep in their bullae - and
naturally started off representing three sheep with three sheep symbols.
Over time they developed symbols for numbers and so represented three sheep
using the numeral 3 and the symbol for sheep. (04)
One can make a similar history for the development of the numeral zero. (05)
> Writing certainly changes many things, but the point I was making is that
the
> level of sophistication by illiterate people was extremely high. All the
ancient
> civilizations from the Nile to China were founded thousands of years
before any
> of them had a system of writing. (06)
My understanding is that writing evolves to support civilisation
(http://en.wikipedia.org/wiki/Civilization seems to make the same point -
Writing, developed first by people in Sumer, is considered a hallmark of
civilization and "appears to accompany the rise of complex administrative
bureaucracies or the conquest state."). Your comment suggests that these
cultures were civilisations for thousands of years before they started using
writing. But not my area of expertise. (07)
Chris (08)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: 27 March 2010 16:35
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Inventor of the Web Gets Backing to Build Web
of
> Data
>
> Chris,
>
> CP> I think you may be underestimating some of the post-language changes.
>
> Writing certainly changes many things, but the point I was making is that
the
> level of sophistication by illiterate people was extremely high. All the
ancient
> civilizations from the Nile to China were founded thousands of years
before any
> of them had a system of writing.
>
> Just look at Stonehenge, with its careful alignment to the sun and moon,
its
> huge stones that required some technology to move, and the number of
people
> that had to be organized in order to do the moving and constructing. But
they
> were all illiterate.
>
> As another example, consider the Polynesian navigators who crossed
thousands
> of miles of open ocean from Tahiti to New Zealand to Hawaii to Easter
Island.
> Some of the old timers preserved an oral tradition of how they navigated,
and
> they gave a demonstration while observers with GPS systems watched. And
they
> were amazingly accurate.
>
> CP> So, as you probably know, studies in pre-literate Mesopotamian
> > mathematics show that these cultures did not have a notion of number.
> > In other words, they did not have a clear notion of 1, 2 or 3.
>
> I very strongly doubt that. A few isolated tribes, such as the Pirahã, do
not have
> a system of counting, but that is an extremely rare example. See, for
example,
>
> http://www.newyorker.com/reporting/2007/04/16/070416fa_fact_colapinto
>
> CP> One can track when the idea was introduced. In the early writing,
> > three sheep were signed by three symbols for a sheep. Subsequently >
there
> was one symbol for 3 and one for sheep.
>
> The Romans wrote I, II, and III. But they also had words 'unus', 'duo',
and 'tres'.
> Those Mesopotamian systems were used by merchants for long-distance
trading
> before they had cuneiform symbols for the words. I'm sure they were just
as
> sharp at bargaining in the bazaars as their modern descendants.
>
> CP> We have the remnants of this is the different bases we use for
> > counting different things (e.g. hours, minutes). Japanese still > has
residual
> different numerals.
>
> Sure. And we still use Roman numerals. But note that the words for the
> numbers from 1 to 100 are the best preserved terms in all the
Indo-European
> languages. Those languages diverged from a common source over 7,000 years
> ago -- thousands of years before any of those languages were written.
>
> There is a very good reason why the numbers are so well preserved:
> merchants who spoke different dialects had to understand the spoken
numbers
> because they didn't have written numbers.
>
> CP> My view is that the human mind is to some extent plastic and
> > it can learn things like numbers that have a big effect on its >
functionality.
> There is an analogy with a computer, where one > could argue that its
hardware
> is fundamental (in some sense) but > it also makes a big difference what
> software is loaded.
>
> I certainly agree with that. And I also agree that writing has a strong
effect.
>
> CP> My only reason for pursuing this is that if these kinds of
> > claims are correct then the introduction of computing should >
correlate with
> some conceptual changes - fundamental or otherwise > - and maybe some of
> this ontology stuff has a part to play in it.
>
> Yes, I believe it can have some effect. But as I said in my previous
note, the
> strongest effect is the nurturing by parents (and other people) during the
first 3
> to 5 years -- a time when most children are still illiterate and those who
have
> learned some reading haven't yet been strongly influenced by it. Some
> influences, such as TV, can actually have a negative effect, largely
because they
> reduce the amount of direct human contact.
>
> By the way, that article about the Pirahã tribe has some other important
> implications for ontology. The following observation is significant for
the ways
> of thinking about individuals and time:
>
> New Yorker> Committed to an existence in which only observable >
experience
> is real, the Pirahã do not think, or speak, in > abstractions - and thus
do not use
> color terms, quantifiers, > numbers, or myths.
> >
> > the Pirahã perceive reality solely according to what exists within >
the
> boundaries of their direct experience — which Everett defined > as
anything
> that they can see and hear, or that someone living has > seen and heard.
“When
> someone walks around a bend in the river, > the Pirahã say that the
person has
> not simply gone away but > xibipío — ‘gone out of experience,’ ” Everett
said.
> “They use the > same phrase when a candle flame flickers. The light ‘goes
in and
> > out of experience.’ ”
>
> In short, the Pirahã seem to classify observations about people and candle
> flames in the same way -- somewhat like my simple observation language
about
> Kermit the frog.
>
> John
>
>
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