Measurement and State

What is measurement in Mathematics?

Measurement in mathematics is often not well understood. In the modern context, assigning a numerical value to a quantity is referred to as measurement. However, what precisely do we mean by a numerical value? What defines numerical value, and what do we mean by assigning it? These fundamental concepts must be addressed to adequately define measurement. Before delving into the understanding and definition of measurements, it is important to comprehend the concept of "Quantity" in mathematics.

Quantity

Any tangible or intangible entity, property, characteristic, or abstraction, whether measurable or not, is termed as a Quantity or you can say “Mathematical object”.

Quantities can be classified into three categories:

• तत्व (Tattva): That which can be quantified and possess properties

• गुण (Guna): That which can be quantified but does not possess property but is the property itself.

• प्रकृति (Prakruti): That which cannot be quantified and possess no property.

We will not go much deeper on defining these types of quantities right now but will discuss later in detail.

Defining “Measurement”

Measurement is the process of quantifying a quantity and assigning a specific behaviour or action to the quantified. This process inherently involves selecting a unit and a scale, which allow for the discrete representation of a quantity. Without these elements, measurement cannot take place because measurement always involves interaction with the quantity that you want to measure. I am not delving into this in detail now but will certainly introduce it to you as needed.

What is a “System”?

A system here represents the following elements: Your measurement space, quantified and the behaviour of the quantified. All these elements together make up a system what we call as the “Measurement System”.

State of a System

A state is like a final snapshot of the measurement system. If the final measurement mimics another state, then the measurement must be equal too. Consider a space with nothing in it. Now, an apple appears within this space. This event happens once more, and then one of the apples is removed. What observations can be made about this sequence? What did you observe?