Coming Into Focus
Those of us who have working vision know about the phenomenon of focus. Whether we have to wear corrective lenses for our eyes, or whether we have just used binoculars, a telescope, a magnifying glass, or a microscope, we know that small visual details can often be made clearer by adjusting the focus of a lens. Lines, edges, and intersection points look sharpest when they are in focus.
An analogous phenomenon occurs as we learn more details about an event, a situation, an activity, or an area of knowledge. What previously seemed “fuzzy” or vague about it to us seems to become clearer with the acquisition of more detail. But there is also a paradoxical effect in that distinctions that previously seemed clear to us can become less clear as we acquire more detail. What looked like a straight line may, upon sharper focus, look jagged, or look like a series of closely spaced dots, or even look fuzzy.
As the accumulated beliefs and knowledge shared by us humans has grown, these paradoxical effects of focus have happened to us collectively. Observations of our physical, chemical, and biological environments have revealed both more detail and more ambiguity. New telescopes have shown us many new galaxies, stars, planets, comets, asteroids, and moons; but they have also led scientists to question what previously seemed to be fairly clear distinctions between stars, planets, and asteroids. Some small, fairly cool stars are barely distinguishable from giant warm planets, and small rocky planets are difficult to classify as different from large asteroids.
Similarly, old biological and psychological distinctions — between living and non-living things, and between male and female people — have become less clear as we have learned more detail about the chemical basis of life and heredity and as we have learned more detail about the chemical, physiological, and neurological bases of human sexuality.
What makes the paradox of detail even more interesting is that there seem to be two very different sources of detail, which I will call “observed detail” and “generated detail”. Examples of observed detail are what scientists study when they make astronomical observations, collect biological specimens, study properties of chemical molecules, and observe interactions of sub-atomic particles. This is an example of observed detail derived from one of the Hubble Telescope Ultra Deep Field images of distant galaxies:
See https://en.wikipedia.org/wiki/Hubble_Ultra-Deep_Field for more details.
Examples of generated detail include the digits of the number Pi, the ratio of the circumference of a circle to the diameter of the circle (from http://www.math.com/tables/constants/pi.htm):
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 …
and fractal sets, including various exceedingly complex-looking visual fractal patterns that can be generated by simple algorithms. This is an example of generated detail from the Mandelbrot Set, an image generated by a simple mathematical algorithm:
See https://en.wikipedia.org/wiki/Mandelbrot_set for more details.
What distinguishes generated detail from observed detail is that it is difficult, or perhaps impossible, to learn anything specifically useful by examining more and more of generated detail, but examining more and more of observed detail is helpful to learning more about the phenomena behind the detail. Mathematicians can use deterministic algorithms to generate more and more digits in the limitless fractional expansion of Pi. The digits may seem to show interesting patterns, but knowing more of those digits tells us nothing else that is useful about Pi or anything else. Similarly, generating more and more visually detailed depictions of fractal sets really reveals nothing more that is specifically interesting about those sets, or about the process by which they are generated, even thought they reveal endlessly changing visual patterns that have the same fascinating quality as those in a kaleidoscope.
I propose that the distinction between generated details and observed details extends to the distinctions between fiction and non-fiction writing, between abstract expressionist art and representational art, and between theory and experiment in science, except that in those cases systems of generated details may be intended in some way to approximate, match, or predict systems of observed details. Writers of fiction often try through their characters to teach us about ourselves as people, artists try to convey emotional qualities that we are incapable of expressing with language, and theologians and scientists, each in their own way, develop theories to explain our human existence.
Even in mathematics, the seemingly most exact and abstract area of human knowledge, the mathematician Kurt Gödel has proven that no finite axiom system is capable of providing a theory that can distinguish all of the true statements of mathematics from the false statements of mathematics. In many particulars even mathematical truth is uncertain or arbitrary.
So where does that leave us? Some people may prefer to explore systems of generated details, and create new ones, such as more and more elaborate fantasy worlds, for the surprises and other pleasures that process can provide. Other people may prefer to explore systems of observed details, such as astronomy, physics, chemistry, biology, and neurophysiology, for the surprises and other pleasures that pursuit can provide. (In many ways those activities can be similar in terms of human enjoyment.) Still other people may prefer to explore parallel systems of observed and generated details, such as theoretical and observational sciences, to see how closely those systems correspond in their details and can be kept in correspondence, by changing the theoretical systems, as new observed details emerge.
An important thing to keep in mind in all of those pursuits is that only in limited, finite systems does everything come perfectly into focus. In most systems new details can always be observed or generated.
Let us hope, as humans, that as more details about ourselves and our environment come into focus, we may learn more that is useful to us collectively in order to survive and thrive cooperatively within the limits of our environment.