A quantitative model of human knowledge of the physical world based on the use of various parts of the electromagnetic spectrum is proposed. The model is epistemologically effective in demonstrating limits to what scientific knowledge can provide us about the physical world, thus enhancing for students the potentially exploratory opportunities available in scientific research, based on how little we really know. Additionally, the model provides a pedagogically useful way to engage students in considerations of the role of measurement, scale, and estimation; these features are urgently needed by many students according to international assessments and are particularly important for non-science majors.