Uncanny sums and products may prompt “wise choices”: Semantic misalignment and numerical judgments

Automatized arithmetic can interfere with numerical judgments, and semantic misalignment may diminish this interference. We gave 92 adults two numerical priming tasks that involved semantic misalignment. We found that misalignment either facilitated or reversed arithmetic interference effects, depending on misalignment type. On our number matching task, digit pairs (as primes for sums) appeared with nouns that were either categorically aligned and concrete (e.g., pigs, goats), categorically misaligned and concrete (e.g., eels, webs), or categorically misaligned concrete and intangible (e.g., goats, tactics). Next, participants were asked whether a target digit matched either member of the previously presented digit pair. Participants were slower to reject sum vs. neutral targets on aligned/concrete and misaligned/concrete trials, but unexpectedly slower to reject neutral versus sum targets on misaligned/concrete-intangible trials. Our sentence verification task also elicited unexpected facilitation effects. Participants read a cue sentence that contained two digits, then evaluated whether a subsequent target statement was true or false. When target statements included the product of the two preceding digits, this inhibited accepting correct targets and facilitated rejecting incorrect targets, although only when semantic context did not support arithmetic. These novel findings identify a potentially facilitative role of arithmetic in semantically misaligned contexts and highlight the complex role of contextual factors in numerical processing.

HANDWRITTEN ADDRESS INTERPRETATION: A TASK OF MANY PATTERN RECOGNITION PROBLEMS

A gradation of pattern discrimination problems is encountered in interpreting handwritten postal addresses. There are several multiclass discrimination problems, including handwritten numeral recognition with 10 classes, alphanumeral recognition with 36 classes, and touching-digit pair recognition with 100 classes. Word recognition with a lexicon is a problem where the number of classes varies from a few to about a thousand. Some of the discrimination techniques, particularly those with few classes, lend themselves well to neural network classification, while others are better handled by Bayesian polynomial and nearest-neighbor methods. This paper describes each of the discrimination problems and the performances of each of the subsystems in a handwritten address interpretation system developed at CEDAR.

A Fibonacci-like Sequence of Composite Numbers

In 1964, Ronald Graham proved that there exist relatively prime natural numbers $a$ and $b$ such that the sequence $\{A_n\}$ defined by $$ {A}_{n} =A_{n-1}+A_{n-2}\qquad (n\ge 2;A_0=a,A_1=b)$$ contains no prime numbers, and constructed a 34-digit pair satisfying this condition. In 1990, Donald Knuth found a 17-digit pair satisfying the same conditions. That same year, noting an improvement to Knuth's computation, Herbert Wilf found a yet smaller 17-digit pair. Here we improve Graham's construction and generalize Wilf's note, and show that the 12-digit pair $$(a,b)= (407389224418,76343678551)$$ also defines such a sequence.