This paper defines a new way to assess the scientific value of Einstein’s special theory of relativity by defining a concept called irksomeness. This follows by converting the adjective irksome, meaning vexatious or troublesome, into a noun. We will call a theory irksome by the following definition: An irksome theory is one in which each of its component demonstrations makes sense or is rational, but the theory as a whole makes no sense or is irrational. Hence a theory, such as relativity, which is a very good example of a theory possessing this characteristic, is irksome or possesses irksomeness, if it satisfies the above definition. An irksome theory is recalcitrant in that its inconsistencies, anomalies, or paradoxes refuse to be tamed or effectively eliminated. It is also irksome when its concepts can not be clearly defined in a way such that there is a consistent agreement regarding its essential truth claims.