The idea that our space is a surface contained within a larger space arose in physics over a century ago, when in 1919, Kaluza derived Maxwell’s equations from Einstein’s equations by assuming another dimension. He essentially unified quantum theory and relativity but another physical dimension made gravity vary as an inverse cube, which would collapse the solar system. Physicalism required any extra dimension to be physical, so Kaluza’s promising discovery was nipped in the bud. In contrast, when mathematicians later managed to explain light as a rotation into a fourth dimension, they were careful to call it imaginary, and complex numbers were accepted.
Klein later tried to rescue Kaluza’s extra dimension by suggesting that it was curled up in a tiny circle that went nowhere, so it existed but did nothing, but this didn’t help. However years later, when string theory needed extra dimensions to work, the idea that they were curled up within our space was resurrected, but why nature made extra dimensions that do nothing but make our equations work was unclear.
However if physical space itself is just a surface, these objections disappear. Instead of an extra dimension inside space, there is a dimension outside it, into which it can vibrate. Just as a two-dimensional screen needs a third dimension to curve into, our space can curve into a fourth dimension, so some physicists now suggest that our world is a slice of a higher-dimensional world:
“Physicists have now returned to the idea that the three-dimensional world that surrounds us could be a three-dimensional slice of a higher dimensional world.” (Randall, 2005), p52.
Note that this extra dimension is sequestered from our space, so it doesn’t alter gravity or charge (Randall & Sundrum, 1999). If Klein’s other dimension was physical, we could walk out of this world, but we can’t, any more than an avatar can leave a game screen. We are then contained by space, like goldfish in a bowl, but if our space is a surface, it is also contained within another space, which will later be called quantum space.