I don&#x27;t think that&#x27;s a serious restriction.<p>Firstly - in general it&#x27;s trivially true that you have probability 0 to cleanly embed a high dimensional space into a 2&#x2F;3 dimensional representation <i>over the set of all possible high dimensional data</i> - yet <i>interesting</i> data often does have lower-dimensional structure.<p>Secondly - so what? Can you think of plausible scenario where this assumption does <i>not</i> hold and it&#x27;s possible to generate a low-dimensional embedding?  If it&#x27;s impossible to embed, then it&#x27;s not an algorithmic problem if you fail to find an embedding.