Some thougts on cartesian products

val bykoski val at
Mon Jan 23 23:28:56 EST 2006

Christoph Zwerschke wrote:
> Bryan Olson schrieb:
>>> Still think there is no such thing?
>> Uh, yes.
>>    The Cartesian product of two sets A and B (also called the
>>    product set, set direct product, or cross product) is defined to
>>    be the set of [...]
>> All sets, no strings. What were you looking at?
> Not only sets. This goes on (anyway "everything is a set"). You can also 
> have the Cartesian product of functions. And you can think of a string 
> as a function from a countable index set I to the set of all characters 
> C. So the Cartesian product of two strings will become a function from 
> IxI to CxC. Since IxX is countable again, this is equivalent to a tuple 
> of 2-tuples of characters which you can also interpret as a tuple of 
> strings with 2 chars:
> "ab" x "cd" = ("ac", "ad", "bc", "bd")
> Do I have eliminated all remaining clarities now? :-)
> -- Christoph

	i think you raised a great issue: a lack of efficient support for 
"combining" objects.  Any language, if has smth to do with reality,
needs that kind of functionality.    The combination dynamics, or growth 
(multiplication) dynamics is a critically important functionality in 
chemistry, physics, biology.  It probably may be emulated by standard 
means such as lists and dictionaries.  If such support is available 
though, this is a sign of mature language designed to cover the 
realistic processes with rich growth/combination dynamics.
	For instance, the dynamics of aperiodic growth that generates a 3D 
aperiodic arrays/structures with the controllable "bits" in each unit to 
be configured by dynamic masks to match the environmental ("boundary") 
conditions would be a significant step in building next-generation 
languages/silicon to support synthesis of realistic 3D structures (and 
functions).  Accordingly, the command "line" may need to be 2D and the 
interpreter be designed to handle/understand not only a (command) text.
	Just reflecting aloud..

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