An IEUC Baseline system configured for desktop use, would probably provide a large wide format flat panel display possibly with full color 3-d capability (achieved with glasses or preferably a headgear free lens system ), a 6 degree of freedom input controller, speech recognition and synthesis capability, a traditional keyboard, and tablet for sketching.
The display itself would initially be partitioned into two panes, one graphical and one textual, both of which would be remarkably free of clutter. The 6-Degree of Freedom controller would permit the elimination of graphical scroll bars and zooming controls. Selections in the visualization pane could be referenced in the textual dialog with pronouns so one might select several nodes and say or type, "What is the average balance of these accounts?" or "Show me a tree map weighted by citation frequency of the items in this outline."
A zoomable interface paradigm would be employed throughout to eliminate the clutter of today's overlapping windows and virtual desktops.
Thus you would be able to directly invoke a visualization that might require navigating a large number of modal parameter selection dialogs in one of today's systems. You could further simply the interface by invoking expert system support by requesting a "walk through" of some common task.
The system itself would maintain a "discourse model" of what you were talking about to draw reasonable inferences that it could confirm by injecting a confirmatory query into the dialog. At that point you could answer or digress or request an explanation of the reason for the query.
This same interface and level of interactivity would extend to both Explicit End User Programming and Programming By Example as in a directive to the system to "Watch how I group these items".
Documentation with live examples could be call up in the display pane as well making an IEUC Baseline system a digital library of its own design. (See the Inform 7 interactive fiction authoring environment for the closes extant system to what we have in mind.)