Perceptual Numbers

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Some Numbers Can Be Seen as Patterns

Imagine a situation where you see a few of your friends standing at a distance in a group. Do you really need to count in order to see that there are 3 in that group? No. This is because we can see that there are 3 friends, much like we see that an animal is a cow or a buffalo.

We have already seen that numbers from 1 to 5 can be "seen" or "perceived" even by children, without the need to count much like they recognise their mothers from a groups of ladies. Hence these are called Perceptual Numbers - numbers which can be perceived.

This perception happens as we have internalised several quantities as "things arranged in a pattern".

They are the earliest numbers encountered by us in our lives. The idea of Number starts developing by seeing numbers up to 5 in various contexts around us.



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 the important skill of "number sense" is developed. Both are very critical in learning math in school.

Number Perception in Animals

We will see later, in the chapter "Discovery of 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.

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