Take a look at the image again. The "space" an atom takes up is mostly empty. Not only that, points out Dawkins, but electrons are so widely spaced that they are more accurately thought of as flies buzzing around football stadiums.
Our perception that objects are solid is therefore a figment of our imagination and does not conform to how things really, well, are.
There. We really can walk through walls. Its just a matter of reordering how we see things. Hey don’t take my word for it. Listen to the Ted podcast "Queerer than we suppose".