Data sets with high dimensionality such as natural images, speech, and text have been analyzed with methods from condensed matter physics. Here we compare recent approaches taken to relate the scale invariance of natural images to critical phenomena. We also examine the method of studying high-dimensional data through specific heat curves by applying the analysis to noncritical systems: 1D samples taken from natural images and 2D binary pink noise. Through these examples, we concluded that due to small sample sizes, specific heat is not a reliable measure for gauging whether high-dimensional data are critical. We argue that identifying order parameters and universality classes is a more reliable way to identify criticality in high-dimensional data.