There is a clear need nowadays for extremely large data processing. This is especially true in the area of scientific data management where soon we expect data inputs in the order of multiple Petabytes. However, current data management technology is not suitable for such data sizes. In the light of such new database applications, we can rethink some of the strict requirements database systems adopted in the past. We argue that correctness is such a critical property, responsible for performance degradation. In this paper, we propose a new paradigm towards building database kernels that may produce \emph{wrong but fast, cheap and indicative} results. Fast response times is an essential component of data analysis for exploratory applications; allowing for fast queries enables the user to develop a feeling" for the data through a series of painless" queries which eventually leads to more detailed analysis in a targeted data area. We propose a research path where a database kernel autonomously and on-the-fly decides to reduce the processing requirements of a running query based on workload, hardware and environmental parameters. It requires a complete redesign of database operators and query processing strategy. For example, typical and very common scenarios were query processing performance degrades significantly are cases where a database operator has to spill data to disk, or is forced to perform random access, or has to follow long linked lists, etc. Here we ask the question: What if we simply avoid these steps, ignoring" the side-effect in the correctness of the result?