The Knowledge for Use logo

This logo, the first three letters of the word "knowledge," was developed in 1972 to symbolize many aspects of the project.  Its stereogram version is almost certainly a first; it has adorned the bottom of our stationary since early 1972, seven years before the invention of this stereoscopic technique according to one book on my bookshelf.  Here is a JPEG version, enlarged and repeated, because I haven't found a way to make the original size (about a half inch high) work on the Web:

This stereogram, which was typed out on a typewriter, has two "levels" of images.  The first level shows the "k" and the "n."  With eye-crossing, the "k" is raised, and the "n" is lowered, with respect to the background.  (In this presentation, you also see the second level plus a repeat of the first level—because the stereogram-logo is repeated.)   The second "level" shows the "o," except it takes the form of the oriental Yin-Yang symbol.  Yin-Yang symbolizes complementarity, a logical equivalence—but that equivalence is, more often than not, misinterpreted as a mutual exclusion, especially by those who uncritically accept this subtlety from an exotic culture while not "seeing" its deeper meaning.

(When the image is as large as this, eye spreading might be a little difficult.  This presentation is easier to see with eye crossing.)

Random dot stereograms were studied at Bell Telephone Laboratories in the late 50's and early 60's by Bela Julesz, a radar engineer.  Julesz was interested in seeing through the "snow" on radar screens.  He ended up doing the pioneering studies of the perception element  now known as "stereopsis."  It's the interpretation by our brain of  the difference between the images from our two eyes because our eyes are a few centimeters apart.  Our brain interprets that difference as depth.  (It's only a minor aspect of our depth perception.)

Stereopsis blindness was difficult to detect.  The stereoscopic patterns  in the above diagram can be detected only through stereopsis.  If you are stereopsis blind you cannot detect the "message"  which in the above pattern is the raised and lowered objects you see stereoscopically.

The entire pattern is composed of three nearly identical parts, side by side.  No stereoscopic information can be conveyed by any one of the three.  Each is, by itself truly random.  The message is conveyed by the very slight differences between the parts taken two at a time.

something virtually unknown
This is one example of "complementarity," a concept that has been recognized repeatedly over historical time, but which is frequently misunderstood--or, more often, simply missed.  The theoreticians who developed quantum mechanics, Niels Bohr and Erwin Schrödinger, for example, frequently saw it.  Wave-particle duality and the "conjugate" pairs of variables in the uncertainty principle are examples of complementarity.  What gets persistently missed is the inseverability of the parts; the incompleteness of one part without the other(s).  A random-dot stereogram is something else until both parts are present.  A measurement of position-momentum is similarly incomplete when only one–either position or momentum–is there, and strange nonsense can get dumped out of the mathematics when we try to use an incomplete measurement.  The electric field and the magnetic field are a complementarity, and Einstein's special relativity resolved some of the strange nonsense that gets mathematically dumped in our laps when we don't understand that.

(June 22, 1999)  As you see, this page is under construction.  We will demonstrate the similarities between the development of stereopsis and the development of "perceptions of the abstract," the intuitive senses for relationships important to understanding science, relationships that include, for example, ratio and proportion, extrapolation to limits, distinction between necessity and sufficiency, etc.  In stereopsis, you should see exemplars for some of the slippery concepts Piaget introduced: such as "equilibration between assimilation and accommodation."


Quantum Jumps
Quantum Jumps
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