I would like Cecil to address this interesting illusion, which anyone may easily demonstrate. Hold your hands in front of your eyes about 2-4 inches away, with your two extended index fingers touching, tip to tip, and focus on the distance.
You will perceive a “sausage” finger interposed between the right and left index fingers. How is this ghost finger produced? There is another illusion that I suspect has a similar basis. Get an empty toilet paper role and hold it in front of the ipsilateral eye and gaze through it at the distance while you hold your other hand, palm towards the other eye. You will see (if you focus right and hold the tube and open palm at the correct distances) a hand with a “hole” in it.
The quick answer is that the brain does all this magic. I suspect that there are more intellectually satisfying explanations that involve detailed analyses of neural circuitry and function. Like why is it that the left half of your brain controls the right side of your body?