If our space is a surface, it must be contained within a larger space. This idea arose in physics over a century ago, when in 1919, Kaluza derived Maxwell’s equations from Einstein’s equations given another dimension. He essentially unified quantum theory and relativity, but another physical dimension was impossible because another it would make gravity vary as an inverse cube, so the solar system would collapse. Physical realism required any other dimension to be physical, so Kaluza’s promising discovery was ignored. Bearing this in mind, when mathematicians later discovered that light could be explained by a rotation into a fourth dimension, they were careful to call it imaginary, so complex numbers were accepted.
Klein then 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 was also ignored. Years later, string theory resurrected his idea to explain its extra dimensions, but couldn’t explain why nature has extra dimensions that do nothing but make our equations work.
But if physical space is itself a surface, these confusions disappear. Instead of an extra dimension inside space, there is a dimension outside space by which it is observed. Just as a two-dimensional screen needs a third dimension to be seen from, so our space needs a fourth dimension to be seen from. Hence, 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.
They note that this extra dimension is sequestered from our space, so it doesn’t alter gravity or charge (Randall & Sundrum, 1999). If there was another physical dimension, we could walk out of this world, but we can’t, any more than an avatar can leave a game screen. We are contained by space, like goldfish in a bowl, so for us it is the ultimate container, but space as a surface means that it is also contained within something else.