What exactly do mathematicians mean when they refer to "the data" involved in a construction?


I've encountered this many times and I can usually figure out what's going on, but I am curious about the terminology, how it was introduced, and its connotations.


A concrete example: In pages 35-6 of "Differential Geometry" by R.W. Sharpe, there is a section entitled "Construction of Bundles". The author outlines three conditions that hold for a given $G$ bundle, and then later refers to these three conditions as "data" from which a $G$ bundle can be constructed. This usage confuses me.


Is there a semantic reason why standard words, like "component", "part", or "constituent" are not used?



What is "Data" involved in a mathematical construction?
I don't know. However, this time I won't let that stop me from answering.


If you talk to a carpenter or a craftsman about a geometric or algebraic
construction, they might look at you in a funny way, since your product
is not material. Also (unless you are doing topological surgery or concatenation
of words), you usually don't put parts or components together. Instead you
follow a recipe of low or high level operations applied to things already
constructed, which are as intangible as the result. The stuff you feed to
the operations is some form of structured data, some of it numeric, some
linguistic, some relational. Also during the process, you need to check that
the inputs satisfy appropriate requirements, and/or that the recipe can
guarantee the desired outcome.


That's why I am comfortable with the use of the word 'data', and prefer
it to something like 'component' or 'subassembly'.


Gerhard "Except When It Seems Apt" Paseman, 2013.04.14


