The Legacy of Zero

The meaning of Zero (0) in mathematics is special and deep. In mathematics, the concept of zero is simply either “nothing” or “a sense of nothing.”

Zero (0) is referred to as शून्य: (0), which means "no measurement" or "no measured quantity". However, zero (0) is also called as खं(0), which means “a sense of nothing”. Whichever the case, both terms (शून्य: or खं) represent the same thing but with a distinct perspective.

What I mean by "a sense of nothing" can be understood through the following example: Suppose you take a loan of ₹500. How much do you truly possess?

In essence, you have nothing. Even though you physically hold ₹500, this amount does not truly belong to you—it is tied to an obligation to repay. This creates a perception of "nothingness," despite the presence of a tangible quantity.

Here, the ₹500 is a physical quantity, which is represented by a positive number 500, but it is counterbalanced by an opposing concept, a negative number. This negative number represents an obligation. It signifies that the physical quantity in hand is destined to be removed or reduced. In this sense, negative numbers here are just representations of actions or conditions tied to the quantity, indicating that it is bound to be diminished or relinquished.

$$0+500+\dot{500}=0$$

But why we used “+” symbol in front of $\dot{500}$?

The answer is very simple. To remove something, you must accept something first. Therefore, writing (-500) as $\dot{500}$ makes more sense and is intuitive to understand that what negatives represent in reality. It looks like abstraction, but it is not.

NOTE: It is not possible to have less than nothing; thus, if there is a measurement of any quantity, it must be acknowledged as something, irrespective of the assigned actions. Consequently, in situations involving inequality, we cannot represent negative numbers as being less than zero, as they convey a concept analogous to positive numbers with opposite perspective.

If you added (+) “n” items to your system and removed (–) “n” items from your system then this equilibrium position is what is referred as खं (Kham) or 0. Hence, 0 conveys the sense of ‘no measurement’ or state where ‘n’ quantities are added, and ‘n’ quantities are removed. Both are analogous to each other.

$$+n-n=0$$

If we say -6 < 0 as “-6 less than 0”, then we are directly challenging our own understanding of numbers that 0 is just an equilibrium position. However, it is more logical to say as “-6 is left of 0”. If you try to stick with that logic of “-6 is less than 0” then zero (0) would lose its own nature and significance. Saying -6 as left of 0 does not convey the meaning that -6 is less than 0. It simply means that we have flipped our representation only, but the quantity itself is greater than zero (0).

Adding a quantity in a system can be represented with positive number and removing a quantity from a system can be represented with negative number. However, whether it is positive or negative, they both points to the same physical quantity that is to be measured but represented differently because we treat the quantity differently (doing different operations).

This idea can perfectly represent or mimic situations where we do have physical representation of negative numbers like in the concept of charge, velocity, force, temperature, height, money, and many more quantities that we observe in nature. Further we will see how these concepts can be explained and represented neatly with this theory.

Now, we have a solid definition for numbers. What they are and what they represent.

Zero, or खं, is essential because without it, other numbers lack meaning. Therefore, zero's existence is fundamental to all numbers, making it the ultimate truth in measurement which makes all numbers and operations possible.