Question

Is there a way to separate open Mathematica notebooks so that they don’t share any variables? How about making it so some variables are shared but not all?

Answer 1

Yes, there is. I recommend reading documentation related to Mathematica contexts. In a nutshell, all variables belong to some context (namespace), and all variables can be accessed via their fully-qualified names of the form “ContextName`varName”. If you just use “varName”, Mathematica will search contexts in $ContextPath (try evaluating the variable $ContextPath to see what it is), and will use the first context where it finds that variable. In addition, each notebook specifies a context (stored in the variable $Context) where all its variables are stored (unless fully-qualified name is used).

By default, for all notebooks the context is “Global`”. Also by default, $ContextPath for all notebooks includes the “Global`” context (as well as “System`” and some others). The net result is that variables are shared across notebooks, and this can rather quickly become annoying. However, there’s an easy solution. To create a “private” context for a notebook, evaluate the following:

SetOptions[EvaluationNotebook[], CellContext -> Notebook]

This notebook will be assigned a unique context (evaluate the variable $Context to see what it is). Also, global context will be removed from ContextPath (try evaluating $ContextPath before and after the SetOptions[...] above to see what’s going on.)

[Update: As pointed out by rcollyer on the new Mathematica stack exchange, to set this option as the default for new notebooks, do the following: open the Options Inspector (Ctrl+Shift+O), change the scope (in the dropdown on the top) from “Selection” to “Global Preferences”; on the left expand the nodes Cell Options -> Evaluation Options, and change the CellContext setting to “Notebook.”]

Now, here’s how to create a shared context:

Begin["SharedContext`"];
varShared1 = "Shared string";
End[];

Alternatively, you could’ve just typed

SharedContext`varShared1 = "Shared string";

Now you can either use the fully qualified names (“SharedContext`varShared1” will work in any notebook), or you can add the context to $ContextPath:

AppendTo[$ContextPath, "SharedContext`"]

If you do this in all notebooks, varShared1 will become visible without a fully-qualified name.

To summarize, context work a lot like many other search paths. However, there are many subtleties (for example, if a symbol has already been defined in some other context, the Begin[“SharedContext`”]/End[] block might not work as you expect — the existing context of the symbol will be used instead of SharedContext`), so I recommend a healthy dose of experimentation and perusing the docs.