Why can't I walk through my wall?

We can’t really measure where the potentiality wave of the atom’s outer electron shell ends, but it is roughly 15 orders of magnitude larger than the nucleon. That would mean that roughly 99.9999999999999% of the atom is nothing but open space. Further, the individual quarks that make up the nucleon of a hydrogen atom stay so far apart that at least 99.99% of its nucleon is also empty space. Quarks may well be point particles like electrons, in which case the whole darned atom would seem to be nothing but empty space.

Jon Ronson relates this bit of humor about the above in his book, The Men Who Stare at Goats.
“This is a true story. It is the summer of 1983. Major General Albert Stubblebine III is sitting behind his desk in Arlington, Virginia, and he is staring at his wall, upon which hang his numerous military awards. They detail a long and distinguished career . He is the United States Army’s chief of intelligence, with sixteen thousand soldiers under his command… He looks past the awards to the wall itself. There is something he feels he must do even though the thought of it frightens him. He thinks about the choice he has to make. He can stay in his office, or he can go into the next office. That is his choice. And he has made it. He is going into the next office… He stands up, moves out from behind his desk, and begins to walk. I mean, he thinks, what is the atom mostly made up of anyway? Space! He quickens his pace. What am I mostly made up of? He thinks. Atoms! He is almost at a jog now. What is the wall mostly made up of? He thinks. Atoms! All I have to do is merge the spaces. ... Then General Stubblebine bangs his nose hard on the wall of his office. Damn, he thinks. General Stubblebine is confounded by his continual inability to walk through his wall.”

General Stubblebine is a man who thinks outside the box. And so am I. What if I hit my wall at relativistic speeds, I think. Maybe I could go straight through then. But then, the light from my office desk lamp hits my wall at relativistic speed, and it bounces off the wall too. Tiny little photons—point particles with no mass, hit a wall of empty space and—after having blithely traveled through a whole bunch of other empty space, they hit my wall and bounce off. Why? Since I am almost entirely empty space, and so is my wall, why won’t knowing that let me walk through walls?