Mm, seriously handwaving. I think I have to see this in actual math. I understand the idea behind the analogy, though.
How can I see something that has no mass? How does a wall stop light?
Those last questions look kind of dumb. I guess I am asking is how can something have no rest mass (which would also mean no energy?) have mass when it moves faster? Is it just nothing moving really fast?
You see things the same way a wall stops light. Your eye absorbs the photon (or the wall absorbs the photon). Now energy has been added to your eye (or wall) and it heats up a bit. Your brain registers the absorbtion of this energy and interprets it givng you a picture of what you’re seeing.
Think of energy like a sound wave. Does sound have mass? Nope but it causes the air to compress and decompress which vibrates your ear drum which you interpret as sound. This is an imperfect analogy since light needs no medium (such as air) to propogate but maybe it helps give you a sense of it.