I Am a Strange Loop - Douglas R. Hofstadter [45]
Although both video voyages were vivid and variegated, I decided for this chapter to write up a “diary” of the earlier one, undertaken long ago at Stanford, since that’s when I first explored the phenomenon and learned about it step by step. So the story below involves a different television, a different TV camera, and in general an older technology than was used in making this book’s color insert. Nonetheless, as you will see, much of the old diary still pertains to the newer voyage, though there are a few small discrepancies that I’ll mention when I come to them.
Diary of a Video Trip
There happened to be a shiny metallic strip running down the right side of the TV set I was given, and the presence of this random object had the fortuitous effect of making the various layers of screens-within-screens easily distinguishable. The first thing I discovered, then, was that there was a critical angle that determined whether the regress of nested screens was finite or infinite. If I pointed the camera at the metal strip instead of the center of the screen, this gave me what looked like a snapshot of the right wall of a long corridor, showing a few evenly spaced “doorways” (which actually were images of that metal strip), moving away from where I was “standing”. But I was not able to peer all the way down to the end of this “corridor”. I’ll therefore call what was visible on the screen in such a case a truncated corridor.
If I slowly panned the camera leftwards, thus towards the center of the screen and perforce further down the apparent corridor, more and more doorways would come into view along the right wall, smaller and smaller and farther and farther away — and all of a sudden, at a critical moment, there was a wonderful, dizzying sense of infinity as I would find myself peering all the way down the corridor toward a gaping emptiness, stretching arbitrarily far away toward a single point of convergence (the “vanishing point”, as it is called in the theory of perspective). I’ll call this an endless corridor. (Note that essentially this same kind of corridor is also visible in the photo of the self-reflecting mirrors in Chapter 4.)
Of course my impression of seeing an infinite number of doorways was illusory, since the graininess of the TV screen and the speed of light set a limit as to how many nestings could occur. Nevertheless, peering down what looked like a magically endless corridor was much more enticing and provocative than merely peering down a mundanely truncated corridor.
My next set of experiments involved tilting the camera. When I did this, each screen obediently tilted at exactly the same angle with respect to its containing screen, which instantly gave rise to a receding helical corridor — a corridor that twisted like a corkscrew. Though quite attractive to the eye, this was not terribly surprising to the mind.
An unanticipated surprise, however, was that at certain angles of camera twist, instead of peering down a helical corridor punctuated by doorways, I seemed to be looking at a flat spiral resembling a galaxy as seen through a telescope. The edges of this spiral were smooth, continuous curves of light rather than jagged sets of straight lines (coming from the edges of the TV screen), and such smoothness mystified me; I saw no reason why a sudden jump from jagged corners to graceful curves should take place. I also noticed that at the very core of each “galaxy”, there was nearly always a