Perceptual Numbers

We experience these numbers in our surroundings and as parts of our body. The basic idea of one possibly gets triggered as we see ourselves separate from others. We have 1 head, 2 eyes/ ears/hands/feet, 4 limbs (when we crawl) and 5 fingers. We also see & hear these numbers being used when we constantly interact with our family members & animals in the neighbourhood. Hence the patterns formed by these numbers get internalised by us.

We internalise, possibly as visual image patterns, 1 as a dot, 2 as 2 dots or as a line joining the dots, 3 as a triangle, 4 as a rectangle (impressions of 4 feet of animals as they stand on the ground) and 5 as a palm with 5 fingers etc. The image patterns may differ from person to person but the "understanding" is that of a particular number. These ideas have also found a place in our language as when the number five is referred to as "fist" or panja.

Numerosity Module in the Brain

Neuroscientists studying conditions like dyscalculia, propose that the brain seems to have a separate centre for recognising "magnitude as a countable number". We have studied this aspect in the chapter "Math & the Brain".

Possibly the ability to instantly recognize small countable magnitudes was also necessitated by the process of evolution.

Subitizing

When we see collections of numbers from 1 to 5, may be our mind matches the actual scene with the mental pattern and recognises it instantly as that number. This ability is known in math literature as "subitizing".

A human child has to ability to identify its mother's voice in a roomful of talking adults. It can also identify many adults by their faces. These are extremely complex tasks as scientists who have worked on making computers recognise faces, have realised.

If children can perform such complex tasks, identifying a collection up to 5 as a visual pattern should not be very difficult. Glenn Doman of The Institutes for the Achievement of Human Potential in the U.S., claims that the human mind can also be trained to recognise even collections much larger than 5 by training. This idea has already been accepted for a long time in language learning as "sight reading".

Perceptual numbers are the base on which number sense is developed. Both are very critical in learning math in school.

Two Distinct Numerosity Modules

Results of research published in Nature Human Behaviour on 2 October 2023, seem to indicate that there are two distinct numerosity modules - one for quantities up to four and the other for quantities between five & nine.

Experts feel that the finding is relevant to the understanding of the very nature of thinking.

Research seems to show that neurons specializing in numbers of four or less responded very specifically and selectively to their preferred number.

However neurons that specialize in five to nine, however, responded strongly to their preferred number but also to numbers immediately adjacent to theirs.

For example, neurons specific to three would fire only in response to that number, whereas neurons that prefer eight would respond to eight but also to seven and nine.

Number Perception in Animals

We will see later, in the chapter "What is Number Sense" that even birds, bees & fish seem to have a rudimentary sense of numbers for small numbers.

This is very similar to the perceptual number skills of human children.

Multiple Names for Numbers

An interesting fact from history is that most languages have multiple names to indicate the idea of two, like brace, pair, both etc. This is an indication that these words were in use much before the emergence of the concept of two as a "number".

Another such name is "score" which stands for twenty. It could have come into use as it is the total of all our fingers and toes. It could also indicate a time in history where twenty was used as a base instead of ten.

The "number sense" about these numbers had evolved before these were seen as "numbers" which could be counted, written and operated upon.

Need for Counting

The art of counting was probably invented by humans to identify numbers associated with large collections which cannot be "seen" at one glance.

Discrimination of Small Differences Between Large Numbers

However, a research study by the Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, USA and published (2023) in the Journal of Numerical Cognition, seems to suggest that given enough opportunities, people consistently perform better than chance on discriminating tasks even when the numerical difference is extremely small. An abstract of the relevant paper is copied below.

"Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an above-chance rate, this prediction has rarely been empirically tested for any psychological dimension, and never for the domain of number perception. In an experiment with over 400 adults, we find that observers can distinguish which of two collections has more dots from a brief glance. Impressively, observers performed above chance on every numerical comparison tested, even when discriminating a comparison as difficult as 50 versus 51 dots. Thus, we present empirical evidence that numerical discrimination abilities, consistent with SDT, are remarkably fine-grained."