Numbers are all around us, describing our environment, our distances, our height, and our universe. These unique symbols have not recently arrived in our cultures. While so much of our earth was separated into clans, towns, kingdoms, states, and continents the need for communicating quantities, values, and agreed upon trades was low. As we gradually shared ideas and competed for ‘the best’ way to describe our planet, numbers came into being: so many characters and ways of communicating the same things.
Yet, one of the most subtle and powerful additions to our host of math symbols was the concept of ‘nothing’. How could one show the fact that there was ‘nothing’ in the storehouse, or that after payment for services there was ‘nothing’ owed. What about when you had 5 apples and they all were eaten? How do you show that ‘nothing’ was left.
For several hundred years in the BC timeframe many cultures in the Indian/Middle East/Mediterranean were attempting to describe ‘nothingness’. The Mayans in South America had the need for ‘nothingness’ as well.
However, the concept of ‘nothing’ was strongly tied to the beliefs and religions of the time. They questioned the idea of taking the invisible (‘the nothing’) and making it visible. Many forms of idols, totems, special rocks, chants came to symbolize the gods that were such a powerful determinant in each culture. They asked, “Is it permissible to create a symbol for “nothing” thereby making it visible? If so, what value would be this ‘nothingness’?
At this same time our counting systems of the world were emerging as well. We went from a non positional system of numbers (like using tallies, or roman numerals) to a positional one. This means that the numbers 5 and 1 in that order meant ’51’. Since we have positional numbers, the order of ’15’ is different than ’51’, each position representing certain quantities of values. (5 tens and 1 unit; or 1 ten and 5 units). But what if you had the temperature of 102 degrees? If you represented it as ’12’ if would mean 1 ten and 2 units. Hey, what is that zero doing? It is moving the 1 and the 2 apart into their new values of (1 one hundred and zero tens and 2 units). The zero became a place holder to separate the two numbers so that the actual meaning would be correct.
So in math classes today we look at the character (0) in unique ways. It still represents ‘nothing’ and is a place holder to help values be correct. And yet, we still are taught that (0 times 3 = 0). Does it really make sense to ask a student ‘what is 3 quantities of nothing'? It really stretches the imagination to ask if you take the character (0) and divide it into 5 pieces what do you get? Really? Nothing divided into 5 pieces? Why ask the question or insist that students understand this seemingly obtuse axiom. Nothing is simply nothing. Zero is a character that provides usefulness for sure, yet soon looks and begins to act like a number and we don’t question it. Zero (nothing) is truly an exceptional character having both limited visible meaning and usefulness as well as extraordinary invisible presence.
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Are there invisible items that we have placed into our vernacular to provide meaning and definition for us? We have words such as love, patience, kindness, tolerance, joy and many others.
We see the effects of these emotions and outcomes in our human experience.
And at the same time could we have reduced their extraordinary value and understanding?
Is it conceivable that we possess these placeholder words in order to assist us in pointing to their non visible source or our non visible nature?
Yet, one of the most subtle and powerful additions to our host of math symbols was the concept of ‘nothing’. How could one show the fact that there was ‘nothing’ in the storehouse, or that after payment for services there was ‘nothing’ owed. What about when you had 5 apples and they all were eaten? How do you show that ‘nothing’ was left.
For several hundred years in the BC timeframe many cultures in the Indian/Middle East/Mediterranean were attempting to describe ‘nothingness’. The Mayans in South America had the need for ‘nothingness’ as well.
However, the concept of ‘nothing’ was strongly tied to the beliefs and religions of the time. They questioned the idea of taking the invisible (‘the nothing’) and making it visible. Many forms of idols, totems, special rocks, chants came to symbolize the gods that were such a powerful determinant in each culture. They asked, “Is it permissible to create a symbol for “nothing” thereby making it visible? If so, what value would be this ‘nothingness’?
At this same time our counting systems of the world were emerging as well. We went from a non positional system of numbers (like using tallies, or roman numerals) to a positional one. This means that the numbers 5 and 1 in that order meant ’51’. Since we have positional numbers, the order of ’15’ is different than ’51’, each position representing certain quantities of values. (5 tens and 1 unit; or 1 ten and 5 units). But what if you had the temperature of 102 degrees? If you represented it as ’12’ if would mean 1 ten and 2 units. Hey, what is that zero doing? It is moving the 1 and the 2 apart into their new values of (1 one hundred and zero tens and 2 units). The zero became a place holder to separate the two numbers so that the actual meaning would be correct.
So in math classes today we look at the character (0) in unique ways. It still represents ‘nothing’ and is a place holder to help values be correct. And yet, we still are taught that (0 times 3 = 0). Does it really make sense to ask a student ‘what is 3 quantities of nothing'? It really stretches the imagination to ask if you take the character (0) and divide it into 5 pieces what do you get? Really? Nothing divided into 5 pieces? Why ask the question or insist that students understand this seemingly obtuse axiom. Nothing is simply nothing. Zero is a character that provides usefulness for sure, yet soon looks and begins to act like a number and we don’t question it. Zero (nothing) is truly an exceptional character having both limited visible meaning and usefulness as well as extraordinary invisible presence.
===================
Are there invisible items that we have placed into our vernacular to provide meaning and definition for us? We have words such as love, patience, kindness, tolerance, joy and many others.
We see the effects of these emotions and outcomes in our human experience.
And at the same time could we have reduced their extraordinary value and understanding?
Is it conceivable that we possess these placeholder words in order to assist us in pointing to their non visible source or our non visible nature?