Let $M$ be a smooth, finite dimensional manifold of dimension $n$, and let $m$ be the minimal dimension for which $M$ admits a smooth embedding into $\mathbb R^m$.

**Question:** Does every Morse function arise from a height function in dimension $m$? Formally, is every Morse function $f: M \to \mathbb{R}$ of the form: $$f: M \hookrightarrow \mathbb{R}^m \stackrel{\pi}{\to} \mathbb{R}?$$