Science, Maths & Technology

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Invention and innovation: An introduction

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# 11.5 Step 4 – act of insight

Suddenly an insight suggests a solution, or the means of achieving a solution, to the inventor. Legendary examples include Newton observing an apple falling from a tree and having his insight into the laws of gravitation or Archimedes leaping from his bath and running naked through the streets shouting ‘Eureka!’ (‘I've found it!’). These vivid images point to the fact that creative ideas can occur when someone is not consciously trying to solve a problem.

These acts of insight are not only dependent upon the state of mind of the inventor, however, but also on the circumstances in which they occur. The image of Archimedes’ moment of insight is familiar. Archimedes realised, allegedly as he lowered himself into his bath, that there was a relationship between his weight and the volume of water displaced.

Archimedes became excited because he realised this could provide him with a solution to a problem set for him by Hiero II, the ruler of Syracuse on the island of Sicily. Hiero had had a new crown made but suspected that his metal workers had stolen some of the gold and substituted it with a gold-silver alloy; so he wanted to know if the crown was pure gold or partly silver. Archimedes, a Syracusian mathematician and specialist in applied mechanics, realised that if the crown was partly silver it would be less dense than pure gold, would be bulkier for its weight and therefore would displace more water when immersed. As a consequence he had discovered a principle that would help him to determine whether the king's crown was pure gold or a mixture of gold and silver.

In his book The Act of Creation, Arthur Koestler (1989) points out that at the critical moment Archimedes was able to make the connection between two previously unconnected trains of thought that his mind was processing (incubating) simultaneously. Nobody before Archimedes had brought together those separate ideas and if those particular circumstances had not pertained – thinking about the crown problem while taking a bath – that particular eureka moment would not have occurred. It might have occurred to someone else on another occasion because the history of invention shows that many minds are often working on the same problem (remember Edison and Swan on the electric light), but it is possible that many such moments have passed unnoticed for want of the necessary conjunction of inventive mind and propitious circumstances.

Koestler comments that rather than the mental achievement being to draw that particular conclusion, the achievement was actually in bringing together the two apparently unconnected ideas – a process he calls bisociation. Bisociation is one example of what is called associative thinking, which can lead to inventive solutions to problems. There are other ways of bringing together associations of ideas, knowledge and techniques from different areas: adaptation, transfer, combination, and analogy.