Math and Our Brain

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How does math originate in the human brain?

Human brains have been developed by evolution to make meaning out of patterns. Our brains are &ldquo;meaning-making&rdquo; machines. We do not easily accept that any pattern could have occurred by chance or randomly. Hence, we look for causes. We try to connect the cause and the effect by some logic. This is the beginning of intellectual development.

The human brain developed the intellectual ability to identify, extend and reproduce patterns that they saw in the environment around them. Patterns help the brain to categorise sensory data and organise it for understanding. Through this, the brain developed a unique ability to understand abstract ideas. Understanding patterns also helps in predicting and avoiding dangers. Hence pattern recognition is vital for life.

Two patterns which were recognized early was magnitude (as size) and shape.

A sense of magnitude or size is very essential for all living beings to survive in the world. The idea of size comes in various forms. Estimating the breadth of a stream to be jumped over, the size of an opponent or herd of animals, the distance &amp; speed for catching a prey are all instances of such survival skills. All living beings have acquired basics of these skills through the process of evolution. If a species had not acquired this skill they would have died out. The level of development of these skills depends on the environment in which the being lives. For instance, the sense of smell in animals is far superior to that in humans.

Shape helps us to differentiate between friend &amp; enemy, edible &amp; poisonous and to maintain our sense of direction while travelling.

The sense of magnitude developed at a faster rate &amp; to a sophisticated level in humans due to superior social, economic and cultural practices developed by them. A developed human society cultivates, hoards, trades &amp; fights with other cultures. Hence it develops the necessary math to plan battles &amp; seasons for cultivation and document trade transactions. It also helped them to dig canals, measure produce and build sophisticated structures.

Measurable &amp; Countable Magnitudes

We sense magnitude in 2 different ways - as a measurable quantity or a countable quantity. These can also be understood as answers to “how much?” and “how many?”.

Human history tells us that sensing magnitude in terms of size, weight, length &amp; height has been with us from our pre-human stages. These can be called &ldquo;measurable quantities&rdquo;. Volume or weight of a bag of rice, area of a farm, distance to the next village, the time remaining for sunset are examples of measurable quantities. In all living beings &ldquo;measurable size&rdquo; is the more easily understood aspect of magnitude. This is apparent in the many words in daily language which deal with size like big, small, large, tall, short, bulky etc.

The idea of measurable quantities gradually developed into ideas like volume, length, area and weight. We could say that though a lake was longer than another, its area was smaller. Or that though one tree was taller than another, it was thinner. Most of these estimates were either subjective or based on measures related to individuals. A bag of rice that a child could lift was lighter than one which it could not lift.

But there is yet another means by which magnitude is measured – as a countable quantity. This helps us to sense that we have more fingers than eyes. But sensing magnitude in terms of &ldquo;countable quantity&rdquo; developed much later. Hence a sense of number (as in seeing that we have five fingers) is a recent development and may be not more than 15,000 years. Hence the idea of number is more difficult for children to grasp than the ideas of size. Language also adds to this problem.

Research has proved that a rudimentary number sense or “how many” develops in children as early as six months. Children of age three & four have the ability to perceive quantities up to five, perceptually, without counting! Hence numbers one to five are also called Perceptual numbers.

We interact with pour environment, more in terms of "how much" than "how many". Possibly the need for a judgment of "how many" did not arise until our possessions increased. But in the last century, the need for understanding "how many" has increased very rapidly. So we are still struggling to shift from perceptual numbers to understanding very large numbers. May be that is one reason, math is a difficult subject.

Words used to describe &ldquo;measurable quantities&rdquo; are much older. When the concept of &ldquo;countable quantities&rdquo; developed, many of the same words were used to denote both measurable and countable quantities and the exact meaning had to be derived from the context. For example the use of &ldquo;more&rdquo; can mean both measurable (serve me more rice) as well as countable (give me more fruits).

It takes some experience &amp; maturity for a child to realise that a basket of few coconuts is &ldquo;less&rdquo; than a handful of nuts! The coconuts may be &ldquo;more&rdquo; in terms of weight but they are &ldquo;less&rdquo; in terms of number!

The idea of countable quantities is a very powerful aspect of intellectual development. It is this which developed into number sense, counting, numbers, operations and the entire discipline of math!

Though numbers were developed later, they, through the math of measurements &amp; measuring units, gave exact meaning to measurable quantities! The idea of more and less was sharpened by using numbers to specify and compare them. A bag of rice which was a measurable quantity was converted into a countable quantity like 5.2 kgs! A bag weighing 5 kgs was understood to be less (lighter) than a bag weighing 10 kgs.

Parallelly identification by shapes, led to the study of their properties and relations. This developed into geometry.

In summary, the evolutionary skill of sensing magnitude as size or shape developed in humans into a sense of numbers, measurement and shapes and developed into the discipline of mathematics.

We should also see here a vital difference between mathematics and language. Language changes from place to place and can be learnt only by listening to others. But ideas in math develop from our observation of our body and the environment. Mathematics developed by different civilisations tend to be similar, even though there have been no interactions between them. It is an internally developed discipline helped by logical thinking. It is a product of our human evolutionary development.

In that sense, math should be easier to learn than languages!

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