The main preface of Hofstadter's essay is that the way in which expert anagrammists deal with go about solving anagrams has the potential to shed light on a fact about how humans process information. In order to introduce this concept, Hofstadter begins by explaining a phenomenon which he describes as "glomming". The word comes from a "glom", which is an agglutination of letters which are arranged in such a way that they are pronounceable using the phonemes of the language in which the technique is being applied for.
In order to glom, the glommer must first begin to commit to memory the letters they are working with. Afterwords, the letters can be arranged into different gloms in an almost unconscious process. Throughout Preface 2, Hofstadter likens gloms to what he calls "virtual objects". These are objects whose existence is distinct from how it is represented. He uses the analogy of a ball in a video game to convey this point to the reader. A video game ball is represented by pixels on a screen. But the ball itself is not the pixels that represent it, and encompasses much more than the pixels or the hardware underneath them.
Hofstadter makes an argument for why it is important to try to solve the anagram jumbling problem with glomming as a focus for the heuristic approach that the machine takes. His argument can be summarized as an attempt to further understand how the brain operates, rather than to just attempt to recreate what it is able to do. Hofstadter stresses that while mathematical and exhaustive approaches to solving the problem do exist and are superior, they cannot help us in understanding how we ourselves go about solving these mental tasks.
The Hearsay II project was involving knowledge sources that went about their tasks by means of parallel conditions that had precondition checks so that their higher level search processes were not active at all times, saving a lot of processing power. Hofstadter was particularly interested in these precondition checks, even though the researchers themselves seemed to think little of this method, utilizing it without caring much for any implications it might hold. This way of doing things is then likened by Hofstadter to the idea of a parallel terraced scan. This is a method in which multiple searchers and searchees evaluate each other simultaneously to determine where they will end up.