Functional fixedness for defining problems

Initial caveat: I have very little formal education in psychology or other cognitive sciences - just a couple classes in college. I read the guidelines in the site FAQ, but I'll understand if this question isn't right for this site.

My background is in mathematics, and over the years I've taken an interest in those aspects of cognitive psychology that pertain to problem solving with the hope that I would develop an awareness of my own cognitive biases and strategies for overcoming them. One that I latched onto is functional fixedness, which as I understand it is the inability to discover uses for an object other than the obvious purpose for which it was designed. For instance, functional fixedness might inhibit a person from observing that a hammer can be used as a weight because they can't see past its ordinary function of hammering nails.

Functional fixedness affects our ability to solve a problem effectively with a given set of tools. I am wondering if there is a similar concept (with accompanying literature) which describes the inability to define a problem differently from how it is normally defined.

• A standard example from mathematics involves the classical impossible ruler-and-compass constructions (such as trisecting an angle). If one views these as geometry problems then it is extremely difficult to understand why they are impossible, but everything becomes much clearer if they are viewed as number theory problems.

• High frequency trading provides another good example: for a long time people viewed algorithmic trading as a software problem - write an algorithm which recognizes a good trade as fast as possible. But high frequency trading really took off when somebody instead viewed it as a geography problem - if everybody has really fast algorithms then the person who is physically closest to the exchange (as measured by the length of the wire over which information is being transmitted) is the winner.

Is this a recognized phenomenon, and has it been studied systematically?

• Commonly known as (the inability to) 'thinking outside of the box', no? :) Nov 7, 2017 at 9:11
• So, you are asking why it's hard to reduce one problem to another (if reduction exist) from mental view? Nov 8, 2017 at 12:17

What you are describing is called mental set. The following extract is from this excelent article.

A mental set is a tendency to only see solutions that have worked in the past. This type of fixed thinking can make it difficult to come up with solutions and can impede the problem-solving process.

For example, imagine that you are trying to solve a math problem in your algebra class. The problem seems similar to ones you have worked on previously, so you approach solving it in the same way. Because of your mental set, you are unable to see a simpler solution that might be possible.