When hunting for a book on probability and statistics a few nights ago, I stumbled onto a book on Combinatorics bought in 1994 and my honours year thesis.
Combinatorics is a branch in Mathematics that study about relationship. An example will be in a room, there are 3 people - A, B, C. A relationship is defined by A knows B. What is the maximum number of relationships? One could draw 3 nodes representing A, B and C; and lines (also known as edges) connecting the nodes to represent a relationship. The maximum number of lines is 3. Try drawing!
In a very simple way, combinatorics is about counting the different combinations. And when we look about relationships, they are highly complex and complicated matters. So even in the era of supercomputers that we are living in, these computers are not that "super". They have their limitations in counting - recall the time, when your computer "hangs"?
Here in, enter the white knight - "heuristics". Heuristics may look like a big word but essentially, it means common sense.
An example will be in the case of an MRT coin changing machine. Suppose there are only 3 coin denominations - 10 cents, 30 cents and 40 cents. What is the minimum number of coins to disburse for the notes that a customer may slot into the machine? The heuristics way will be to disburse the highest value coin first. E.g. $1 note = 40 cents + 40 cents + 10 cents + 10 cents; or four coins.
Most of the time, the heuristics way will give the correct answer, but not all the time. E.g. $3 based on the heuristics way will disburse a total of nine coins - seven 40 cents (i.e. $2.80) and two 10 cents (i.e. $0.20). However, the minimum number is eight - six 40 cents (i.e. $2.40) and two 30 cents (i.e. $0.60).
Every day, people are inundated with decisions, big and small. Heuristics are one of the many ways that people arrive at their choice. It is not only an area of Mathematics but also of cognitive psychology. Hence, heuristics have been researched to understand the decision making process.
Heuristics serve as a framework in which satisfactory decisions are made quickly and with ease (Shah & Oppenheimer, 2008). Many types of heuristics have been developed to explain the decision making process; essentially, individuals work to reduce the effort they need to expend in making decisions and heuristics offer individuals a general guide to follow, thereby reducing the effort they must disburse. Together, heuristics and factors influencing decision making are a significant aspect of critical thinking (West, Toplak, & Stanovich, 2008). There is some indication that this can be taught, which benefits those learning how to make appropriate and the best decisions in various situations (Nokes &Hacker, 2007).
Several factors influence decision making. These factors, including past experience (Juliusson, Karlsson, & Gӓrling, 2005), cognitive biases (Stanovich & West, 2008), age and individual differences (Bruin, Parker, & Fischoff, 2007), belief in personal relevance (Acevedo, & Krueger, 2004), and an escalation of commitment, influence what choices people make. Understanding the factors that influence decision making process is important to understanding what decisions are made. That is, the factors that influence the process may impact the outcomes.
See Mathematics is alive and is everywhere :)