Query optimizers depend heavily on statistics representing column distributions to create efficient query plans. In many cases, though, statistics are outdated or non-existent, and the process of refreshing statistics is very expensive, especially for ad-hoc workloads on ever bigger data. This results in suboptimal plans that severely hurt performance. The main problem is that any decision, once made by the optimizer, is fixed throughout the execution of a query. In particular, each logical operator translates into a fixed choice of a physical operator at run-time. In this paper we advocate for continuous adaptation and morphing of physical operators throughout their lifetime, by adjusting their behavior in accordance with the statistical properties of the data. We demonstrate the benefits of the new paradigm by designing and implementing an adaptive access path operator called Smooth Scan, which morphs continuously within the space of traditional index access and full table scan. Smooth Scan behaves similarly to an index scan for low selectivity; if selectivity increases, however, Smooth Scan progressively morphs its behavior toward a sequential scan. As a result, a system with Smooth Scan requires no optimization decisions up front nor does it need accurate statistics to provide good performance. We implement Smooth Scan in PostgreSQL and, using both synthetic benchmarks as well as TPC-H, we show that it achieves robust performance while at the same time being statistics-oblivious.