Disclaimer: The ideas portrayed here are my personal opinions and if you don’t agree with anything please leave me a comment and I will take a note and try to revisit my thoughts.

This week I am going to talk about a different subject, its about human behavior – my observations and a desire to see everything mathematically. I believe that everything that can be measured can be expressed mathematically and that includes human behavior as well. Those of us who are earning their livelihood through an employment have to deal with a lot of questions on a daily basis, apart from the work related decisions we have to make decisions related to our co-workers (including juniors and seniors). Let’s see if we can define behavior (properties) of our team-mates in mathematical terms.

There are some basic mathematical properties associated with mathematical operations and numbers and they define the rules that govern the output. If we look at the objective of our employment it is also about getting some sort of output. There are some basic mathematical properties and they are listed below:

- Closure Property
- Commutative Property
- Associative Property
- Distributive Property
- Identity Property
- Additive Identity
- Multiplicative Identity

These properties help us a lot (in mathematics) and if you can define these properties for the components and operations in any other field they make your life easier there as well. So let’s start with “Closure Property”.

**Closure property:**

A set of numbers is said to be closed for a specific mathematical operation if the result obtained when an operation is performed on any two numbers in the set, is itself a member of the set. If a set of numbers is closed for a particular operation then it is said to possess the closure property for that operation.

How do we define the closure property for a set of people or team? Well a team will be assumed of having closure property if any operation on that team (training, motivation, guidance or even reprimanding) doesn’t result in anything new. Such teams generally lack the innovative culture and the output from such teams is always the same. Such teams don’t grow or produce something new and are generally handicapped by the tendencies of individuals to stay in the comfort zones.

**Commutative Property:**

The word “commutative” comes from “commute” or “move around”, so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is “a + b = b + a”; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is “ab = ba”; in numbers, this means 2×3 = 3×2.

This property is a property of team members who are flexible enough to be moved around in different roles and they don’t change the equation. This is generally a good trait (although sometimes the expectation might be to have some value added as a part the commute/movement). If you have such dynamic individuals in your team who can be assigned to versatile roles this in a sense adds a dimension to your team dynamics where you have backup for most of your key roles.

**Associative Property:**

The Associative property of numbers states that the addition or multiplication of a set of numbers gives the same output regardless of how they are grouped.

Example – Addition: (2 + 3) + 4=2 + (3 + 4); Multiplication: (2 x 3) x 4 = 2 x (3 x 4).

Associative property of the team helps you in producing outputs where teams don’t rely on output on each other to continue doing their individual jobs. For instance the team might have multiple functional roles and each should contribute to the ultimate outcome, outcome of individual functions should not be dependent on each other.

**Distributive Property:**

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

Example: a x (b + c) = (a x b) + (a x c)

The distributive properties of individuals helps teams to scale by expanding their roles to influence larger portions of the team. Some individuals possess the multiplicative distribution property where in they are able to influence the culture, ethics and attitude of their fellow in such a way that it starts multiplying with the individual skills of the fellows working under their supervision. So if you have such individuals in your team go ahead and bring them up to influence your organizational talent pool.

**Identity Property:**

There are two types of identities

Additive Identity:An identity element (as 0 in the group of whole numbers under the operation of addition) that in a given mathematical system leaves unchanged any element to which it is added.

There are individuals in each team who add no value to any operation, they just are empty placeholders that can be utilized to show numbers but won’t add any value to the output (neither qualitative nor quantitative). Such individuals may or may not be a liability – depending on your organizational structure but they need to be kept in check at all times to make sure that they **don’t try to multiply themselves** because an additive identity when multiplied leads to the product being **Zero**.

Multiplicative Identity:The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number

Example: 5 x 1 = 5, 1000 x 1 = 1000

Individuals who are multiplicative identities don’t add any value to any product, team or equation, their movement in any direction (horizontal or vertical) doesn’t improve anything. There are such individuals who when promoted would not add any value to the team/department for which they become responsible and hence don’t have any impact whatsoever on the output. They are ineffective despite the **Distributive Property** of multiplication. In the long run, promotion of such individuals generally would have negative impacts on your team performance (and there is no mathematical theory that I can think of behind this right now). They are ceremonial figures to say the least and long term liabilities (because they never grow – they always remain at the starting point) at the most.

As I mentioned in the beginning, these are my personal opinions that I have presented here and all are welcome to provide inputs/corrections.

I hope to be back with some technical stuff soon.

Until then…

Pradeep