In 1951 the Palmer Show Card Paint Company introduced the first paint-by-numbers kits, which were sold under the marketing slogan, “Every Man a Rembrandt.”  The kits, which were essentially coloring books for adults, sold by the millions.  They came with a canvas, brushes and numbered jars of paint in various colors.  The canvas was imprinted with the outline of a picture, sort of like a jigsaw puzzle, with every piece numbered.  By filling in each numbered space with the corresponding numbered paint color, a picture gradually emerged: a landscape, a seascape, a Parisian street scene, a facsimile of Leonardo da Vinci’s “Last Supper” or “Mona Lisa.”

It occurs to me that my digital camera works on more or less the same principle as those old paint-by-numbers kits. There are no spaces to fill in, of course, just numbered pixels — some 12.8 megapixels altogether (12.8 million pixels) in the “classic” Canon EOS 5D camera I’ve been using for the last 20 years or so.  Those pixels are like the tiny dots you’ll see in a newspaper photograph, only much smaller.  The setting I normally use is 300 dpi, or 90,000 pixels per square inch, much smaller than you can see with the naked eye.  Each of those pixels is coded with a number using a binary system, essentially a string of zeroes and ones that translate into many different combinations of red, yellow and blue hues, as well as a grayscale of shades between black and white.  Those zeros and ones add up to every image I capture with my digital camera and everything you’ll ever see on your computer or smart phone.  

While I’ve been content to put a frame around a small patch of reality to create my photographic landscapes, programmers have been building virtual worlds using massive strings of zeroes and ones.  The purveyors of this enterprise boast they they are able to generate immersive photorealistic environments that are indistinguishable from physical reality.  To date, this technology has mostly been used in online computer games.  But it would be naive to assume the rapid advance of generative zeros and ones will end there, particularly if there are potential revenue streams involved.  

Oxford philosopher Nick Bostrum suggests we may already be living in a virtual world without realizing it.  He reasons that computers will eventually be so powerful they will not only generate perfect facsimile worlds down to the last detail but also produce conscious beings to inhabit them.  That, of course, may already have happened, and those conscious beings would be us.  Bostrum argues that an advanced civilization might run large numbers of simulations of their own ancestors, meaning ourselves.  This raises an intriguing question: How do we know we aren’t in one of those computer simulations?  And how could we tell?

I would start with the lint filter in my clothes dryer.  If I open the door to my dryer and pull out the lint filter, I should expect to find lint in the filter with the look and feel of real clothes lint.  Did some advanced generative AI program produce the simulated look and feel of lint?  And if so, why?  What about the soap powder and bleach on the shelf above the washer and clothes dryer? What about each grain of sugar in the sugar bowl on my kitchen table?  Would each grain of sugar taste sweet to the tongue?  What about the contents of every piece of junk mail and every bill stacked up next to my sugar bowl on the kitchen table?  Not to mention the contents of every shelf and drawer in my kitchen, as well as every food item, fresh and frozen, in my refrigerator.  And that’s just the stuff in my laundry nook and kitchen, to say nothing of the rest of the house and the whole of the world beyond, down to the last blade of grass and grain of sand.  What possible motive can there be to write the trillions of lines of code necessary to create the illusion that some computer-generated facsimile of myself exists in a computer simulation of what I like to think of as the real world?

If our world were generated by some sort of algorithm, we would expect to find a mathematical basis for its operations – which, of course, is exactly what we do find. Ancient astronomers noticed that celestial bodies, originally thought to be gods, moved across the sky in precise patterns.  By the second century BCE, the Greeks had developed mathematical tables for predicting solar and lunar eclipses.  They were the first to discern an underlying order and harmony to the universe that could be expressed numerically. “All is number,” proclaimed Pythagoras, a Greek philosopher best known as the discoverer of the Pythagorean theorem.  He meant that in an absolute sense.  He and his followers regarded themselves as a kind of sacred priesthood for whom numbers were divine, replacing the gods of the Greek pantheon.

Little did Pythagoras realize how the maxim, “All is number,” might one day play out in scientific disciplines undreamed of in his day: to time and space, to the properties of light and gravity, to the laws of motion and thermodynamics; and to particles smaller than an atom.  Even though elementary particles violate all the laws of classical physics, they still conform to the laws of probability.  Rather than try to explain the often bizarre behavior of these particles, many quantum physicists subscribe to the “just shut up and do the math” school, which recognizes that quantum physics works, even if no one can quite explain why.  As for any metaphysical implications, physicist Stephen Hawking sniffed, “Mysticism is for people who can’t do the math.”

Even though just-do-the-math may be the rule in the scientific community, the broader implications have not gone entirely unrecognized.  Albert Einstein, for example, wondered, “How can it be that mathematics, being after all a product of human thought, independent of experience, is so admirably appropriate to the objects of reality?”  Echoing  Einstein, fellow physicist Paul Dirac asked, “Why is nature constructed along these lines?” He continued, “One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe.”

Dirac would no doubt have been horrified if anyone had taken this latter comment literally, since he was an avowed atheist.  Dirac and many of his colleagues might fairly be categorized as latter-day Platonists, meaning that they believe mathematics occupies its own separate realm apart from the physical world, similar to Plato’s realm of perfect Forms.  Chief among the current advocates of this view is MIT cosmologist Max Tegman, who believes our reality is based on mathematical structures that exist independently of physical reality.  These modern-day Platonists probably would not go so far as to say that numbers were divine, as the Pythagoreans did.  The universe is somehow constructed according to principles of advanced mathematics with no actual mathematician doing the computations.  So we are left to wonder how these mathematical laws arose in the first place and how they operate upon the universe. Is it from outside the physical world, or are these laws somehow embedded in it?

Meanwhile, in my small corner of the universe, Adobe Photoshop is now offering a “generative fill” tool that can be used to replace portions of a digital image or expand it with essentially made-up visuals.  Photoshop has long been able to clean up minor defects in an image by painting over the affected area with pixels borrowed from the surrounding area.  But Photoshop’s new tool is taking digital “paint by numbers” to a whole new level, making things up as you go along.  Indeed, generative AI programs are already capable of creating photorealistic images without recourse to a camera or photographer.  Flesh-and-blood landscape photographers are understandably nervous about this.  But then again, if Bostrum is correct and we are all just “conscious” algorithms operating in a facsimile world, then the arrival of Photoshop’s generative fill tool is just one long strong of zero and ones worrying about another string of zeros and ones.