Twenty-One Views of Uncertainty

by Glenn Blakeslee

part 1 of 2

We rolled the dice because God could not, or would not.

We placed twenty-one boxes on the plane. The boxes, each crafted from a variety of materials using all of the tools available, were arrayed in the shape of an equilateral triangle, six to a side and six within. On the featureless surface of the plane the boxes seemed to stretch to the horizon.

At each of the boxes we placed the insubstantial arcana, the realm of symbols invented by man in the study of numbers real, whole, and imaginary.

We stood before the first box, at the apex of the triangle. Beyond the first box was a row of two boxes, then a row of three, and so on until the final row of six. The first box was relatively unadorned, built of a plain unfinished wood, sides roughly screwed together with number ten slotted wood screws. The lid was fastened along the back edge by a rusty thick piano hinge, latched along the front by a corroded gate hasp.

On the surface of the plane, at the left front corner of the box, floated the symbol for Planck’s constant, a stylized h with a crossed ascender.

We approached the box with caution. This was the first of the series, and caution was warranted. Inside the box uncertainty ruled, a subtle force, unblazoned and quiet, insubstantial and yet possibly firm to the untutored touch.

Some of us advocated a direct technique, approaching the box casually with no apparent formal or leading attitude, and flicking over the rusty bale of the hasp with a force equal to three pounds per square inch or less, spread over the two inch leading edge. They argued that this should not disturb equilibrium, as true equilibrium could not be disturbed. Some of us argued for a more regimented approach, securing the lateral lanes of consequence by presenting a rough symmetry, or at least by standing in front of the box on our own two feet and assuming a forceful, unapologetic air.

A quorum was quickly reached, and we decided that a proper approach needn’t be decided on; that uncertainty might well serve on the exterior of the box as well as the interior. As a consequence, we waited for the impulse of a truly random event.

This was difficult, as the featureless plane had been selected exactly because it was featureless.

After a while some of us started to respirate more fully than others, in the hope that increased agitation of the molecules surrounding us would effect an event. Some of us passed gas. After an indeterminate amount of time one of us, probably Lawrence, fainted onto the top surface of the box, causing it to tip on its side. The force of the upset caused the lid to slowly creak over to one side, opening, and together we peered into the interior of the box.

Inside the box, something furry and white stirred and stretched and emerged. An enormous Persian cat, face classically quashed, stared at us with cool green eyes, and then slowly padded away toward the nonexistent horizon.

Finished with the first box, we were now at the second row, a row of only two boxes. Which box was the second box, the box that we would go to next, had not yet been decided.

An argument broke out involving variations of the left-right, east-west nature of the decision before us. The more clear-headed among us argued that to consider geographic or cultural determinacy as a form of logic was fuzzy-headed, that the soft sciences needed to be left out of the task before us. Then Lawrence noticed the cat.

The cat sat on the box at the right.

We approached the cat, and the box beneath it, and for the first time since we’d begun our venture we made a unanimous decision. We all screamed at the cat. The cat stared at us, flicked its oversized tail twice, and jumped behind the box. The box on the right it was!

The box was constructed of fine hardwood, inlaid with curlicued filigree, fastened with finely etched silver hardware. The box was aromatic: it smelled of solidity and unshucked pecans. Near the front of the box two parallel lines appeared to be etched into the surface of the plane — the equal arcana. With no hesitation we quickly approached the second box and, again with no hesitation, unclasped the latch and lifted the lid.

The big white Persian cat lay on its side at the bottom of the box. The Persian cat looked and smelled dead. We all blamed Lawrence.

In hindsight it appeared the second box might have actually been the third box. We were not sure who was responsible for the mistake: the cat, or Lawrence, or the massed potential of our indecisive, weathervane consciousness.

The third box was similar to the first, built of hardwood with precision hardware binding its edges and securing the lid of the box. The third box, however, seemed to have been stressed in ways unimaginable to those of us observing from the plane. There were deep, creased striations running at a diagonal to the squared-off bounds of the box. The striations were black and ragged, made by forces that we had not witnessed and could not understand. The creases seemed to crackle.

At the front right corner of the box the pi arcana, a curvy little stonehenge of a symbol, drifted just below the surface of the plane.

The third box opened just as easily as the second. The scent of flowers wilting and of burning dung rose to meet our collective senses. Inside the box was a spherically symmetric potential, the edges of its mathematically-charged envelope fusing nearby particles as their attempts to dodge and spin were obviated. The potential sparked and glowed. Inside the potential, clutching his knees to his chest with arms clothed in one of his famous but now quite dirty sweaters, was Albert Einstein.

His head was shaved and he had a large silver hoop earring, as large as an American Eagle silver dollar, piercing the stretched lobe of his right ear. We were certain it was Albert Einstein because of the bushy white mustache. He appeared to be agitated, but it was hard for us to determine this at first because of the inherent chroma shift of the potential, and also because we had ruled out physiological effects, such as secretion, as another trick of the soft sciences.

“He’s sweating, and crying and screaming for his mother,” Bob observed. “In the German tongue,” he added.

The fourth box presented a problem similar to the problem encountered approaching the third box. So far in this endeavor we had solved the approach question in a semiclassical manner: approach the box neither formally nor casually, merely approach it and let events unfold as they may. The problem here was not so much in approach as in order.

The middle box of the third row represented a new regime of order, if we chose to make it one: some of us noticed an internal triangle of six boxes, with the middle box as the apex. Their plan was clever, and they argued that it would save us time, as if time were ever an issue.

Their plan called for some of us to move through space, independent of the others, and to take up a position next to each of the six boxes of the internal triangle. At a signal each of the boxes would be opened, hopefully exactly simultaneously, and the state of their contents observed and recorded.

The manpower required for this feat was not an issue, as we were at least six squared in number and constantly reproducing. Those of us opposed to the plan could only raise more prosaic concerns in response. How would the signal be made over the vast distances involved? Should the boxes be opened without first consulting each corresponding arcana?

Lawrence moved to the front of the discussion. He was forceful and righteous in his presentation. Had we bothered to actually consult the arcana in any of the previous experiments? “As for the signal,” he said, “I will take care of that,” and he moved off through the array of unopened boxes to stand at the apex of the inner triangle.

Five others separated from us and moved off to join Lawrence. We stood with the wreckage of the opened boxes behind us, and watched as the subset of six gathered and conferred. We knew that this was a great moment, and each of us was giddy with excitement, whether we approved of the methods or not.

Lawrence gestured, and the others moved to their proper locations. They dwindled with distance, became indistinct, yet we knew where and who they were, and we could see them clearly. Time elapsed as it should, and we waited, and then the moment arrived. Each stood at his box, and each received a signal from Lawrence and began the business of preparing lids to be opened: pulling pins, moving levers, twisting knobs, extracting hold-bars and set-screws. Lawrence gave the final signal.

Proceed to part 2...