It's unfortunate that the enneatype writers have seemingly limited themselves to the concepts of aggressive, compliant and detached types within Karen Horney's work. Opportunities for applying other insightful aspects of her work to the enneatypes are missed. In discussing the idealized image in her book Our Inner Conflicts, she offers what can be seen as an interesting comparison between enneatypes 7, 4 and 1.

The idealized image can be described as:

...the creation of an image of what the neurotic believes himself to be, or of what at the time he feels he can or ought to be.

She then goes on to describe three attitudes that can be seen as an interesting comparison between enneatypes 7, 4 and 1.

If the neurotic's interest lies in convincing himself that he is his idealized image, he develops the belief that he is in fact the mastermind, the exquisite human being, whose very faults are divine.

Although the above quote may talk to a narcissistic extreme, it does give some insight on the enneatype 7 tendency or preference to see themselves in light of their potential instead of realized self.

If the focus is on the realistic self which by comparison with the idealized image is hightly despicable, self-derogatory criticism is in the foreground. Since the picture of the self that results from such disparagement is just as far removed from reality as is the idealized image, it could appropriately be called the despised image.

The above quote alludes to a contrast that seems to be at the forefront of enneatype 4 self-image - a contrast between the idealized image of self and the despised image of a defective self. It's interesting to note that both are not real, yet the enneatype 4 may at times harbor a hopelessness of attaining their idealized image (a feeling which can be evoked from envy) and an identification with the despised image (unlovable, incompetent, etc.).

If, finally, the focus is upon the discrepancy between the idealized image and the actual self, then all he is aware of and all we can observe are his incessant attempts to bridge the gap and whip himself into perfection. In this event he keeps reiterating the word "should" with amazing frequency. He keeps telling us what he should have felt, thought, done. He is at bottom as convinced of his inherent perfection as the naively "narcissistic" person, and betrays it by the belief that he actually could be perfect if only he were more strict with himself, more controlled, more alert, more circumspect.

The perfectionistic attitude of enneatype 1 is well described by the above quote. Whereas, enneaype 7 tends to identify with the idealized image (idealized image maintained through positive thought), enneatype 4 leans more toward the despised image (hopelessness of realizing the idealized image and feeling of abandonment), enneatype 1 often operates from an attitude toward perfecting the self into the idealized image.

Once understood well enough, the enneatypes provide a good map for organizing and understanding personality and psychological concepts that don't originate from the Enneagram personality system. However, twisting those concepts to fit the Enneagram symbol's properties (i.e., triads, inner lines, etc.) is something to avoid if accuracy of the original concepts are not to be lost.