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I'm not sure...I would go with: the atoms in the chair are strong, so empty space is less important because of the weight distribution. Also, my guess would be that the empty space is mainly in an area that doesn't support your weight.

The newest theory to answer this is applied to "How do the stars and planets hang where they are?" See: Dark matter. It is believed now that it is dark matter that holds things together.

I was watching a show on National Geographic that mentioned atoms being mostly empty space. They asked this question but in the context of a batter hitting a ball. The nucleus of an atom is enveloped by electrons which repel other electrons. They also said that because of this, nothing can actually ever touch: there is always a slight gap between objects. The sensation of touch is actually you feeling the repulsion of the electrons.

EDIT: From what I understand the ratio of empty space to solid space between the nucleus of an atom and it's electron is almost an exact ratio in size and distance of the Earth to the Sun. The electron's rotation is what keeps two objects separate. However, if something were vibrating at an entirely different frequency from another thing, it would be capable of passing right through it. The speed of the electron is so extreme that even light is reflected off of it's surface making an object appear to be solid. There are many theories involving alternate dimensions and realities that vibrate on other frequency ranges, exist at the same time and place as we do, but never affect our reality.

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