The Mathematics of Social Sciences
Let's take a simple generalization of the human mind being a combination of 2 elements namely - Good & Evil. All the people in this world would have different combinations of good and evil in their minds. We can draw parallels with numerous ancient oriental philosophical concepts like Yin & Yang (Combination of 2 opposing elements) and Om (Combination of 3 elements A,U,M).
Here, x & y are the proportional weights of white & black respectively.
For different values of x & y, I will get different shades of grey.
Situation 1 - No possible combinations!
Imagine you come across a question as absurd as, "What combination of black and white will give you RED?"No matter what combination of black and white you mix on your palette, you will never get red. Hence, such a situation has no solution.
Situation 2 - Infinite possible combinations!
As it can be seen above, we can have multiple possible combinations of the 3 colours to arrive at the fourth colour. We can either mix only white and black and none of medium grey, or take a portion of medium grey and add some more black to it to make it dark grey. If we were to include the possibility of having negative values (i.e, if it was possible to remove some colours from a mixture), we would be able to get infinite solutions!
Now, let's calculate the grey areas of human mind
Let's ask a fundamental question - "What makes me content with my life?"
As a social scientist, I would think of various elements that lead to contentment in life. These elements could be having a job that you love, having a positive family life and earning handsome money.
Linear algebra comes into picture here because the level of contentment in my life would be a linear combination of these 3 elements in some proportion!
For some people, earning good money may be more important than doing something you love. Such people end up doing a job that they hate doing just because it pays them well. For some people, family happiness may be much more important than job satisfaction. Such people may end up doing something they hate just in order to keep their family happy. Instead of just guessing what element could be important in a society, we can use the magical wand of Linear Algebra to precisely find those proportions!
For illustrative purposes, let's assume that we are trying to find these proportions among a homogeneous group of 28 year old, male, graduate, working professionals in Bangalore. In order to find the combinations, we need to measure the individual elements. We can measure the following 4 questions using a 100 point scale where 0=Not at all and 100= A lot:
Q1. How content are you with your life?
Q2. How much do you like the work that you are doing?
Q3. How much higher do you think is your salary as compared to what people get at your age & experience?
Q4. How positive/ pleasant is the overall mood of your family?
We administer these questions to 3 people and their responses are as follows:
Name
|
Work
Likeability
|
Paycheck
Handsomeness
|
Family
Positivity
|
Life
Contentment
|
Ayush
|
40
|
50
|
10
|
27
|
Bharath
|
20
|
60
|
40
|
38
|
Chandan
|
60
|
30
|
50
|
49
|
As it can be seen, the data that we receive will always be in a tabular or matrix form. Each column stands for a variable captured in a question. Since we are trying to find the importance of each variable on the final variable of Life contentment, we will carry out combination of columns as follows:
On solving this system by linear algebra methods, we arrive at the solution of x=0.3, y=0.2 and z=0.5.
This gives us the solution that family positivity is given more importance, followed by work likeability and paycheck.
With the help of linear algebra, we can find out what is the main driver of contentment. Similarly, this tool can be applied in calculating any other measurable linear combination in this world.
We know that the human brain is made up of grey cells and the human mind is also made up of shades of grey. Mathematics can be used to quantify the human mind and yes, we can calculate more than just 50 shades of grey!
Moral of the story: Embrace mathematics, even if you claim to be a qualitative researcher because beauty lies in integration - the linear combination of qualitative and quantitative research!
Linear Algebra helps us visualize beyond the physical 3 dimensional space through the column-vector concept. Once we are able to visualize multiple dimensions, we may get closer to solving Einstein's dilemma here:






