Predictive Gaps

Origin. Dmitri Mendeleev, St Petersburg University, 1869–1871: the periodic table, and the three elements predicted from the holes in it.

Mechanism. A classification ordered on one variable and grouped on another will, if both are real, have positions that no known member occupies. The orthodox response is to close the table by adjusting the ordering until it fits what exists. Mendeleev's move was the reverse: treat the empty cell as a claim that something is missing, and read the missing thing's properties off its neighbours by interpolation. This converts a taxonomy from a summary of the known into a generator of falsifiable predictions, and it is the step that distinguishes a classification that explains from one that merely files.

Procedure. Order the entities by the variable you believe governs them; Mendeleev used atomic weight. Group them by recurring behaviour; he used valence and oxide formula. Where the two constraints conflict, trust the behaviour and leave the ordering to be corrected later — he inverted tellurium and iodine against their weights. Where a position has no occupant, do not close the gap: name it provisionally after its lighter neighbour (eka-aluminium, eka-boron, eka-silicon), and predict the occupant's properties by interpolating between the cells adjacent to it in both directions. State the predictions numerically, so that discovery either confirms or refutes them. Wait.

Applies to. Any domain with a two-dimensional classification where both axes have physical meaning: a taxonomy with a gap, a product matrix with an unfilled cell, a parameter space with an unexplored region.

Limitations. The gap is only informative if both ordering and grouping track something real — an arbitrary classification generates arbitrary holes, and most classifications are arbitrary. Mendeleev predicted several elements that do not exist (coronium, newtonium in the ether row) with the same method and the same confidence, and the successes are remembered because gallium, scandium, and germanium turned up between 1875 and 1886. The method gives no way to tell in advance which of its gaps are real, and it is silent on the mechanism underlying the periodicity, which was not available until atomic number replaced weight.