Re: "I, User" (re numbering schemes)

Subject: Re: "I, User" (re numbering schemes)
From: Paul Goble <paulg -at- COL -dot- HP -dot- COM>
Date: Mon, 22 Nov 1993 21:14:23 GMT

Bonni_Graham_at_Enfin-SD -at- relay -dot- proteon -dot- com wrote:

: Why? Because if I see a reference to page 450, I have a pretty good idea
: of how thick 450 pages are -- I can almost go right to it on the first
: shot. BUT, where is page 8-8? How can I make a good ballpark guess,
: when chapters are of uneven length?

That sparks an idea. Since we don't have statistically significant
data, let's use the time honored academic technique: apply theory!

#WARNING Begin theoretical computer science

With chapter-by-chapter numbering, a user will use something like a
binary search algorithm:
1. open to a page
2. decide whether to go forward or backward
3. open to a page halfway between the current page and the
previous guess
4. if not found, goto 2

The time taken for a binary search among n pages is O(log_base_2(n)).

With serial numbering, the user can use a direct access/hashing
algorithm: guess where to open, then, if necessary, flip a few pages.

The time taken for such a technique is O(constant), or, more specifically,
O(1 + average guessing error).

#End theoretical computer science

The conclusion: IF people are good at guessing how thick a given number of
pages is, THEN serial numbering is more efficient.

Related conclusion: if serial numbering is best because of this reasoning,
then chapter tabs (but not bleeder tabs) are a hinderance because they slow
down both thickness-guessing and page-flipping.

This matches my experience: if I use a table of contents, index, or
cross-reference, so that I know the page number, I find pages best with
serial numbering and NO chapter tabs. On the other hand, sometimes I
enter a book via the chapter tabs (usually because it has a crummy

Next question (I think see an undergraduate thesis topic coming...): Does
anyone have statistics on how often typical users use tabs vs. an index
to find information?

--------======= * =======--------
Paul Goble
Hewlett-Packard Colorado Springs Division
Learning Products Engineering
paulg -at- col -dot- hp -dot- com

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