Sets or pairs of incompatible observables, such as momentum and position, play a pivotal role in a wide range of distinctly quantum effects and applications, including quantum cryptography, the Heisenberg Uncertainty Principle, quantum state tomography, and Bell’s inequalities. In particular, in quantum physics, we are prohibited from precisely measuring the values of incompatible observables, a fact that is at the heart of the nature of the quantum state. In this talk, I will explore an assortment of strategies that simple-mindedly attempt to circumvent this prohibition. Motivated by these naïve strategies, we experimentally investigate the use of weak measurement and optimal quantum cloning to perform joint measurements on photons. The direct outcome of these measurements are, depending on the strategy, the wavefunction, the Dirac distribution, and the density matrix of the measured quantum system. Consequently, these naïve strategies provide new ways to characterize quantum systems and to understand the very entities that we are measuring, such as the wavefunction.