Interpretation of $l_p$ norm inequality If $1\le p\le q\le \infty$, we know that the following inequality holds:
$$\|a\|_q\le \|a\|_p.$$
What could be a possible interpretation of this inequality for a non-mathematician? For example, can we say something like "the $l_p$ norm becomes more robust (or sensitive) to outlying values with the increase of $p$"?

The inequality $\lVert a\rVert_q\leqslant \lVert a\rVert_p$ means that if $\lVert a\rVert_p\leqslant 1$, then $\lVert a\rVert_q\leqslant 1$ or in other words, that the unit ball for the $\ell^p$-norm is contained in the unit ball for the $\ell^q$-norm.
For an interpretation of the unit ball of these spaces, you can have a look here.
