Science is a crowning glory of the human spirit and its applications remain our best hope for social progress. However, there are limitations to existing science and perhaps to any science. The general mind-body problem is known to be currently intractable and mysterious (8). This is one of many deep problems that are generally agreed to be beyond the present purview of Science, including many quantum phenomena, etc. However, all of these famous unsolved problems are either remote from everyday experience (...) (entanglement, dark matter) or are hard to even define sharply (phenomenology, consciousness, etc.). In this note, we will consider some computational problems in vision that arise every time that we open our eyes and yet are demonstrably inconsistent with current theories of neural computation. The focus will be on two famous related phenomena, known as the neural binding problem and the experience of a detailed stable visual world. I, among many others, have struggled with these issues for more than fifty years (1, 2, 3). Somewhat paradoxically, the continuing progress in scientific methods and knowledge reveals that these are both unsolvable within existing neuroscience. By considering some basic facts about how the brain processes image input, we will show that, under the standard theory, there are not nearly enough brain neurons to compute what we experience as vision. Inconsistencies like the ones shown here have had a profound effect on paradigm change in the sciences. More directly, the discussions below suggest possible new theories and experiments. (shrink)