^{*}

Conceived and designed the experiments: PB PK. Analyzed the data: PB MG. Wrote the paper: PK. Programmed the experiment and supervised data collection: MG. Critically revised the paper: PK PB MG.

The authors have declared that no competing interests exist.

Performing mental subtractions affects time (duration) estimates, and making time estimates disrupts mental subtractions. This interaction has been attributed to the concurrent involvement of time estimation and arithmetic with general intelligence and working memory. Given the extant evidence of a relationship between time and number, here we test the stronger hypothesis that time estimation correlates specifically with mathematical intelligence, and not with general intelligence or working-memory capacity.

Participants performed a (prospective) time estimation experiment, completed several subtests of the WAIS intelligence test, and self-rated their mathematical skill. For five different durations, we found that time estimation correlated with both arithmetic ability and self-rated mathematical skill. Controlling for non-mathematical intelligence (including working memory capacity) did not change the results. Conversely, correlations between time estimation and non-mathematical intelligence either were nonsignificant, or disappeared after controlling for mathematical intelligence.

We conclude that time estimation specifically predicts mathematical intelligence. On the basis of the relevant literature, we furthermore conclude that the relationship between time estimation and mathematical intelligence is likely due to a common reliance on spatial ability.

Circadian rhythms regulate sleep, body temperature, and the functioning of various organs

Our research is motivated by direct and indirect evidence of a tight link (a) between temporal and numerical processing and (b) between even the simplest numerical processing and mathematical intelligence. Several authors have suggested that the processing of spatial, numerical, and temporal information involve either tightly intertwined magnitude representations or a single, common one

More specifically, it has been suggested that numbers are represented along a left-to-right mental number line

In numerical processing, the Spatial Numerical Association of Response Codes (SNARC) effect provides additional evidence for a spatial representation of numerical magnitude. In number-parity judgment (odd vs. even), for example, left-side responses are faster to small than to large numbers, whereas right-side responses are faster to large than to small numbers

Neuropsychological evidence on hemispatial neglect lends further support to the conjecture that numbers and durations are both spatially represented. Hemispatial neglect consists in a deficit in attending to the left hemispace following right inferior parietal lesions

When asked to bisect a line, neglect patients typically display a rightward bias. A striking example of the spatial nature of numerical representations is that neglect patients, while reporting which number falls exactly in between two others, also show a rightward bias on their mental number line. That is, when asked to report which number falls exactly in between 2 and 6, they typically report 5 instead of 4 (

Direct behavioral evidence of interactions between numerical and temporal processing exists too. Some of these interactions may be due to response competition

A skill that requires little if any working memory capacity, or general-purpose processing resources, is numerosity (discrete quantity) estimation. Since it does not involve symbolic processing, it is a very basic skill. Yet, it has been shown to specifically predict mathematical ability, and not other kinds of competence

The experimental procedures were approved by the Institutional Review Board at the University of Padova, and were in accordance with the Declaration of Helsinki (Sixth Revision, 2008). All participants gave their informed written consent to participate in the study.

The participants were 202 naïve students (101 women and 101 men, mean age 22 years, range 18–52 years), who were recruited and tested individually. All participants reported normal hearing.

The experiment was implemented in Matlab (Mathworks ©). The software was running on a Pentium IV computer connected to a NEC Multisync FP950 monitor and an M-AUDIO Fast Track Pro sound card. The output of the sound card was delivered to the subject via Sennheiser HD 560 headphones at 65 dBA pressure level measured at the subject's ear. Sounds presented during the experiment had 16-bit resolution and a sample rate of 44.1 kHz.

Participants performed an auditory prospective time-estimation task (which depends less on memory than a retrospective one

We first made sure that participants knew that one millisecond is a thousandth of a second; next, we presented them a series of tones. The tones were amplitude-steady complex ones, gated on and off with 10-ms raised cosine ramps (to avoid onset and offset clicks), including the first four harmonics of a 250-Hz fundamental. After each tone, participants typed their estimate of its duration in milliseconds. The tone durations were 100, 200, 500, 1000, and 3000 ms (spanning the range of so called

Intelligence was measured with the Italian version of the arithmetic, digit span forward, digit span backward, and similarities subtests of the WAIS-R. The arithmetic subtest involves solving arithmetic problems from easy (e.g., “What is the total of 4 plus 5 apples?”) to relatively hard (e.g., “If 8 machines can finish a job in 6 days, how many machines are needed to finish it in half a day?”). The digit span forward subtest requires the repetition of 3 to 9 digits. The digit span backward subtest requires the repetition of 2 to 8 digits in reverse order. The similarities subtest requires solving non-mathematical problems from easy (“In what way are an orange and a banana alike?”) to relatively hard (“In what way are praise and punishment alike?”). The arithmetic subtest is expected to measure mathematical intelligence, the digit span subtests are expected to measure working-memory capacity, and the similarities subtest is sensitive to general or non-mathematical intelligence.

For each subject, we averaged across the six time estimates for each of the five tone durations. For each of the resulting average time estimates, we then calculated the absolute standardized time estimation error (henceforth

Intelligence tests | Range | Mean | Median | Std. dev. |

Arithmetic | 0–19 | 10.94 | 11 | 3.37 |

Self-rated math skill | 0–10 | 5.47 | 6 | 1.89 |

Digit span forward | 0–14 | 7.88 | 8 | 1.83 |

Digit span backward | 0–14 | 7.18 | 7 | 1.82 |

Similarities | 0–28 | 19.61 | 20 | 3.09 |

Time estimations for the five durations were highly inter-correlated. The correlations ranged from .30 to .83, with an average of .59. Hence, we only considered simple (Pearson) correlations rather than multiple correlations (

Tone durations in milliseconds | |||||

Intelligence tests | 100 | 200 | 500 | 1000 | 3000 |

Arithmetic | −.28 (.000) | −.26 (.000) | −.25 (.000) | −.29 (.000) | −.22 (.002) |

Self-rated math skill | −.31 (.000) | −.31 (.000) | −.30 (.000) | −.19 (.008) | −.10 (.168) |

Digit span forward | −.14 (.040) | −.14 (.045) | −.18 (.011) | −.17 (.013) | −.11 (.125) |

Digit span backward | −.09 (.225) | −.07 (.343) | −.07 (.325) | −.11 (.123) | −.12 (.087) |

Similarities | −.01 (.926) | −.01 (.916) | −.00 (.973) | −.01 (.941) | −.05 (.478) |

When all measures of non-mathematical intelligence (digit span forward, digit span backward, and similarities) were partialled out, all the significant negative correlations between time estimation error and either arithmetic or self-rated mathematical skill remained significant (

Tone durations in milliseconds | |||||

Intelligence tests | 100 | 200 | 500 | 1000 | 3000 |

Arithmetic | −.26 (.000) | −.24 (.001) | −.23 (.001) | −.27 (.000) | −.18 (.010) |

Self-rated math skill | −.29 (.000) | −.28 (.000) | −.27 (.000) | −.15 (.031) | −.06 (.380) |

Digit span forward | −.06 (.392) | −.06 (.367) | −.10 (.142) | −.10 (.171) | −.05 (.488) |

Digit span backward | .04 (.602) | .05 (.490) | .04 (.536) | .01 (.924) | −.04 (.561) |

Similarities | .08 (.289) | .07 (.338) | .07 (.307) | .08 (.285) | .01 (.933) |

Percent absolute standardized time estimation error, at five tone durations, for participants whose arithmetic score fell either in the lowest (open symbols) or highest (closed symbols) tertile. Error bars represent ±1 standard error of the mean.

Our results show that time estimation predicts mathematical intelligence (measured either objectively, via the WAIS-R arithmetic, or subjectively, via self-rated mathematical skill), whereas it is unrelated to two other forms of intelligence—working-memory capacity (WAIS-R digit span) and non-mathematical reasoning (WAIS-R similarities). After we partialled out non-mathematical intelligence, all correlations between time estimation and objectively- or subjectively-measured mathematical intelligence remained significant. In contrast, none of the correlations between time estimation and non-mathematical intelligence remained significant after we partialled out mathematical intelligence.

Brown

Grondin

Electrophysiological and neuroimaging results reveal that the cortical substrates of time and numerical processing show considerable overlap, involving the prefrontal and posterior-parietal cortexes and the intraparietal sulcus (for reviews, see

It is unlikely that one's mathematical ability is related to some internal clock, but mathematical ability does rely on numerical processing

On the basis of our current results, we conclude that time estimation predicts mathematical intelligence. Taking the literature into account, we furthermore conclude that the relationship between the two is likely to be due to a common reliance on spatial ability.

We thank Monica Gammieri and Margherita Maestri for data collection.