First, I would like to clarify what I mean by "intuitive definition": *an intuitive definition is an informal understanding of a concept which helps to build mental agility, with the possible side-effect of crippling one's ability to imagine the full scope of the concept*.

Next, I would like to clarify what I mean by "effective intuitive definitions": *effective intuitive definitions are sets of intuitive definitions, which, taken together, try to minimize the overall crippling effect of intuitive understandings on imagination*.

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In [this](http://arxiv.org/pdf/1205.5935v1.pdf) document, in section 1.1 the author writes:

> 
> I’d say the best intuitive deﬁnition of a vector is “anything that can be represented by arrows that add head-to-tail.”
> 
> 
> 

I am not convinced that is the best intuitive definition. I think that at the very least, for any concept, the best intuitive definition must be a set of intuitive definitions that is an effective intuitive definition.

In particular I feel that the above proposed "best intuitive definition of a vector" is severely cripples the imagination because it ties down one's imagination to three dimensional space.

**What are some effective intuitive definitions of vectors?**