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Examines the logical and intuitive paths humans take to solve complex problems and reach goals.
If you were trying to find a specific person in a stadium of 50,000 people, would you check every single seat one by one, or would you look for the section where their friends are sitting?
An algorithm is a methodical, logical rule or step-by-step procedure that guarantees a solution to a particular problem. Think of it like a mathematical formula or a computer code. If you follow the steps perfectly, you are mathematically certain to reach the correct answer. For example, to find the area of a rectangle, you always use the formula . While algorithms are highly reliable, they are often slow and cognitively demanding. In the real world, we rarely have the time to calculate every possible outcome using a rigid set of rules, which is why our brains often look for shortcuts.
Quick Check
What is the primary benefit and the primary drawback of using an algorithm?
Answer
The benefit is a guaranteed correct solution; the drawback is that it is extremely time-consuming and labor-intensive.
Because our environment moves fast, we use heuristics—simple, efficient thinking strategies or 'rules of thumb.' Unlike algorithms, heuristics do not guarantee a solution, but they allow us to make judgments and solve problems quickly. For instance, if you are looking for milk in a grocery store, you don't walk down every single aisle (algorithm); you look at the signs above the aisles and head toward 'Dairy' (heuristic). This speed comes at a cost: heuristics are prone to cognitive biases and errors in judgment. We trade perfect accuracy for 'good enough' speed.
You have lost your car keys in your house. 1. Trial and Error: You start at the front door and look under every single object in the house, moving systematically from room to room. 2. Heuristic: You think, 'Where was I last?' and 'Where do I usually put them?' You check the kitchen counter and your jacket pocket first. 3. The heuristic approach is much faster but fails if you happened to leave the keys in an unusual spot, like the bathroom.
Quick Check
In the 'Lost Keys' example, why is checking the kitchen counter considered a heuristic rather than an algorithm?
Answer
Because it is a strategy based on probability and past experience rather than a systematic search of every possible location.
Sometimes, we don't use a step-by-step process at all. Insight is a sudden and often novel realization of the solution to a problem. It contrasts with strategy-based solutions. Brain imaging shows that just before an 'Aha!' moment, there is a burst of activity in the right temporal lobe. While trial and error is a process of trying various responses until one is successful (often represented as a learning curve where errors decrease over time , or ), insight happens all at once. It is the difference between grinding through a puzzle and suddenly seeing the hidden pattern.
You are presented with a grid of nine dots. You must connect all dots using only four straight lines without lifting your pen. 1. Most people fail because they use a heuristic that assumes they must stay inside the 'square' formed by the dots. 2. Trial and Error often leads to frustration as users repeat the same failed patterns. 3. Insight occurs when you realize you can draw lines outside the perimeter of the dots. This 'thinking outside the box' is a classic example of breaking a mental set through insight.
Which problem-solving strategy is most like a computer program following a strict code?
If you use a 'rule of thumb' to solve a physics problem quickly, you are using a(n):
Insight-based learning usually involves a gradual decrease in errors over several attempts.
Review Tomorrow
In 24 hours, try to explain the difference between an algorithm and a heuristic to a friend using the 'grocery store' analogy.
Practice Activity
The next time you are stuck on a puzzle, stop and ask yourself: 'Am I using a rigid algorithm that isn't working, or do I need to look for a new heuristic?'