From the time of early infancy, humans are endowed with the capacity to approximate the number of objects in their visual field, an ability that continues throughout life and may underlie the development of more complex mathematical skills.
For years, scientists have explored how people estimate numerical quantities without physically counting objects one by one, approximating, for instance, how many paintings are displayed on a wall or estimating the number of players on a football field.
Gaining a deeper understanding of how the process of approximation occurs in the brain has become a fertile area of research across numerous disciplines, including cognitive psychology, neuroscience and education.
While researchers have long believed that estimating the number of objects in a visual scene is an instantaneous and parallel process with objects being scanned from one side to another, a team at the University of California, Berkeley, has found that previous scientific wisdom on the subject is incorrect.
Their new evidence, using eye-tracker data, reveals that the eyes capture information by fixating on a visual object and estimating quantities in the center of the visual field.
Writing in PNAS, Samuel Cheyette and Steven Piantadosi, two cognitive scientists, explain that the brain relies on an approximate number system (ANS) that is key to estimating the number of objects.
“Anywhere you see something and can guess at what the value is without explicitly counting is the kind of estimation we studied,” Piantadosi said.
An example, both scientists agreed, could be defined by walking into an empty classroom and approximating 30 student desks. Or being stuck in a traffic jam and estimating through the rear-view mirror how many cars are bottlenecked behind.
They attribute the ability to estimate numerical data to a “serial, foveal accumulator,” which means how many objects are observed in the line of sight, the central visual field. They were able to determine from eye-tracking data that people avoid estimating objects in their peripheral visual field.
“That means I add up stuff one after the other – serial accumulator – based on what I see in the center of where I look, as opposed to the edges,” Piantadosi said.
“So when you estimate the number of cars behind you, you are likely moving your center of gaze around and nonverbally adding up an approximation to the number.”
To understand how viewing objects and estimating an approximate number is processed by the brain, Cheyette and Piantadosi studied 27 people between the ages of 18 and 29, who estimated quantities of dots that were displayed on a computer screen.
The team found that approximating numbers in humans is not a rapid, parallel process as previously thought, but one that clearly involves estimating what is seen in the center of the visual field.
“We say it is serial and foveal, as opposed parallel and global because your estimate is heavily dependent on what objects you look at directly as you glance around a scene,” Cheyette said.
The fovea is part of the retina in the rear of the eye involved in visual acuity. The fovea also is the part of the eye responsible for the line of sight, the line connecting the eye with a fixation point in the visual field.
“People don’t seem to fully account for objects in their peripheral vision,” Cheyette explained.
“This also gets at why we call it an accumulator.
Quantities seem to be accumulated across visual fixations, meaning that you approximately add up objects you glance at, keeping a count of how many you fixated.”
Cheyette and Paintadosi were additionally able to predict participants’ numerical estimates using their visual fixation data.
As the number of dots displayed increased, participants’ mean estimates likewise rose, and estimation errors decreased.
The team also surmises that an approximate number system is conserved across species, and is an ability shared with close and distant evolutionary relatives.
Although eye-tracking data has not been collected on other species, Piantadosi has studied wild baboons and theorizes that they use “an estimation scheme to pick the larger group to follow.
The properties of the system look just like humans estimating numbers,” he said.
Cheyette, meanwhile, suggests that the ability to estimate numbers and make decisions based on approximations is widespread throughout nature.
“An approximate sense of number certainly applies to primates,” Cheyette explained, “but also many other animals—even those whose evolutionary history diverged from us hundreds of millions of years ago.
“For instance, bees and cuttlefish seem to have approximate senses of number, which they use to guide them when foraging and hunting.”
Throughout the course of a day, individuals make decisions on the basis of estimations — Do I have enough gas to get to work this morning?
How long will my afternoon meeting take?
How much bread do I need for the week?
Our decisions regarding what we buy, how we plan our day, and any of a number of other activities are strongly influenced by quantities that we calculate using estimates based on relevant knowledge.
In this study, we assess the cognitive and neuroanatomic basis for deficits in quantitative estimation in groups of patients with focal neurodegenerative disease in frontal and parietal cortex.
Cognitive estimation is the strategic process of generating a mental approximation based on available but incomplete information (Shallice and Evans, 1978).
Beyond the necessary semantic knowledge of the relevant concepts and working memory needed to maintain relevant information in an active state, cognitive estimation requires quantitative reasoning about familiar concepts and probabilistic processes in the face of imprecise information in order to develop a reasonable final estimated quantity (Shallice and Evans, 1978; Bullard et al., 2004).
There appear to be two major components to cognitive estimation: executive resources and number knowledge.
These components facilitate the integration of information from semantic memory using strategic reasoning skills to derive a probabilistic evaluation, a process that is central to cognitive estimation.
For example, when estimating how long it will take to read this article, one must identify and retrieve the appropriate knowledge about reading from semantic memory, and integrate this with quantitative information about reading speed, to derive an appropriate estimate (e.g., it’s an academic article with small font so it might take longer than most reading).
In the current study, we sought to identify the neuroanatomic areas contributing to the neural network supporting cognitive estimation.
Based on functional imaging studies in healthy adults and patients with focal brain damage, we hypothesize that these two components depend in part on two interacting brain regions.
Seem to be of particular importance for cognitive estimation. fMRI studies of healthy adults engaged in tasks requiring probability show activation in dlPFC (Casey et al., 2001).
An fMRI study examining the neural correlates of tactile estimation showed greater levels of activation in dlPFC during a texture estimation task as compared to a nearly identical task not requiring any estimation (Kitada et al., 2005).
Complementary to the neuroimaging evidence, individuals with frontal lobe damage demonstrate severe limitations in cognitive estimation abilities (Shallice and Evans, 1978). Smith and Milner (1984) showed impairment following right-lateralized dlPFC damage in patients with surgical treatment for epilepsy.
To examine the role of dlPFC in cognitive estimation, we assessed estimation abilities in non-aphasic individuals with the behavioral variant frontotemporal dementia (bvFTD), a neurodegenerative condition that is associated with GM atrophy encompassing dlPFC (Rosen et al., 2002; Grossman et al., 2004) and frontal WM disease (Whitwell et al., 2010a).
Symptomatically, bvFTD is characterized by executive impairment as well as behavioral disinhibition and personality changes (Kramer et al., 2003; Libon et al., 2006; Rascovsky et al., 2011; Possin et al., 2013).
We assessed cognitive estimation in these patients to minimize confounds associated with semantic knowledge, visuospatial and language abilities where their performance is generally preserved, but show limitations in reasoning, organization, and social judgment.
Given the collective evidence of estimation deficits in people with executive dysfunction, and the association of these deficits with dlPFC damage, we expected bvFTD patients to be impaired compared to healthy controls in a test of cognitive estimation, and that their impaired cognitive estimation performance would relate to cortical atrophy including at least right dlPFC.
Number knowledge is also necessary to produce appropriate quantitative estimations. This is the domain of knowledge over which cognitive estimations often operate. Numerical knowledge is said to involve an analog number system that depends in part on the representation of ratios between quantities on a logarithm-like number line (Dehaene, 1997).
Some have argued that the representation of precise numbers larger than 4 may depend in part on an external algorithm involving language (Dehaene et al., 1999), although we have shown that number knowledge is compromised in non-aphasic patients with CBS and PCA (Koss et al., 2010; Spotorno et al., 2014). Multiple fMRI studies using a variety of techniques have demonstrated that the parietal lobe, and particularly the intraparietal sulcus and adjacent inferior parietal lobule, play a crucial role in the representation of number knowledge (Piazza and Dehaene, 2004; Pinel et al., 2004; Danker and Anderson, 2007; Nieder and Dehaene, 2009).
This includes knowledge of quantity that is mediated both symbolically by Arabic numerals and non-symbolic representations of number such as quantities of filled circles. Furthermore, the inferior parietal lobule seems to be associate with magnitude and quantitative processing, possible because of the spatial magnitude component involved in these processes.
An fMRI study tested healthy volunteers during number comparisons and showed bilateral activation of the inferior parietal lobes, with higher activation on the right side (Chochon et al., 1999). Dehaene et al. (1999) also found increased fMRI and ERP activation in the inferior parietal lobe during approximation calculations as compared to exact calculations, which they attributed to non-linguistic numerical processing during approximations.
In the present study, we assessed the quantitative or numeric component of cognitive estimation in patients with parietal disease, including CBS and PCA. CBS is an extrapyramidal disorder with involuntary movements associated with basal ganglia disease and a variety of clinical features attributable to parietal disease including apraxia and cortical sensory loss (Murray et al., 2007; Armstrong et al., 2013).
PCA is a variant of Alzheimer’s disease with visuospatial deficits due to parietal–occipital disease (Crutch et al., 2012).
We have shown that patients with CBS and PCA have significant deficits with number knowledge, including impairments on measures involving single-digit calculations and Arabic numeral-dot matching (Koss et al., 2010; Morgan et al., 2011). Numerical and quantitative processing, crucial components of cognitive estimation, are associated with parietal lobe functioning, therefore, we expected that CBS and PCA patients with parietal damage would also show deficits in cognitive estimation.
To evaluate the specificity of the hypothesized frontal and parietal contributions to cognitive estimation we additionally evaluated patients with mild cognitive impairment (MCI).
MCI is characterized by mild memory impairments (Feldman and Jacova, 2005; Albert et al., 2011) and is typically considered a prodromal form of Alzheimer’s disease (Boyle et al., 2006; Gauthier et al., 2006; Meyer et al., 2007). Critically, MCI patients have relatively preserved executive function and intact number knowledge (Zamarian et al., 2007; Aretouli and Brandt, 2010); therefore, despite cognitive impairments and likely neurodegenerative disease, we hypothesize that these patients will have relatively preserved cognitive estimation.
Complex behaviors such as cognitive estimation depend on multiple GM nodes that are integrated by WM projections. dlPFC and intraparietal sulcus hypothesized to play a role in cognitive estimation may be linked by dorsal and ventral WM streams.
The dorsal stream is mediated by the superior longitudinal fasciculus (SLF), and the ventral stream by the inferior frontal-occipital fasciculus (IFO) or some combination of the uncinate fasciculus (UNC) and inferior longitudinal fasciculus (ILF).
To help define the WM projections integrating the neuroanatomic network underlying cognitive estimation, we also obtained diffusion-weighted imaging studies. We expected that some combination of dorsal and ventral stream projections would also be implicated in cognitive estimation by imaging studies.
More information: Samuel J. Cheyette et al. A primarily serial, foveal accumulator underlies approximate numerical estimation, Proceedings of the National Academy of Sciences (2019). DOI: 10.1073/pnas.1819956116
Journal information: Proceedings of the National Academy of Sciences