Ai Pengya

The two examples on the top of my head of induction and deduction when I came across a student’s question on the discussion board. (Two wierd examples😅but I feel quite funny lol)

First I remembered the math exams in secondary school, especially on sequence questions. One classic problem goes like this: 1, 2, 4, 8, …—what’s the formula behind this sequence? This is an example of induction. I think you’ve probably encountered this word when you were solving similar problems. You employ induction to derive a general expression for specific cases, in this instance, the numbers are 2 to the power of n series. However, what if the following number isn’t 16, but something like 4, 2, or 1…? So there are pitfalls in induction reasoning. Now, consider being given a sequence governed by 2 to the power of n, and you’re asked to find the fifth number, starting from n=0. Here, deduction enters the scene as you work from a premise to arrive at a specific conclusion. However, this approach only holds true for sequences following the 2 to the power of n pattern. It fails when applied to other sequences because the initial premise doesn’t apply, leading to erroneous conclusions.

Another example is the Leaning Tower of Pisa Experiment. We can see how a theory evolves through induction and deduction. Initially, people observed that iron balls fall faster than feathers. Based on these observations, they concluded that greater mass results in quicker descent. This is induction reasoning: people observed many phenomena and reach a conclusion that seemingly holds true for all falling objects. We can call it the “theory” that falling speed correlates with mass. However, when scientists use deduction thinking the same questions, there are issues arise: what happens with two iron balls of different masses? According to the “theory,” the smaller ball should fall slower than the larger one. Yet experiments showed both iron balls falling at the same velocity. So there must be some flaws in the “theory”; it fails to hold up in a specific scenario. Scientists then generate alternative hypotheses (new premises), such as the speed of descent depending not on mass, but on acceleration. These hypotheses gain support through experiments, leading to the development of new physical theories.