Extra spatial dimensions are probably quite different to the ones used in the flat-land analaogy.

I see a lot of people using the flatland analogy when trying to describe the behaviour of extra spatial dimensions, however I think it’s important for people to recognise that the extra dimensions described in flat-land are likely not the same as the extra dimensions that (possibly) exist in reality.

The flat-land analogy assumes that any higher spatial dimension is the same ‘type’ of spatial dimension as the other dimensions – namely one that’s linear and extends to the edge of the universe in a similar way to the other spatial dimensions (albeit aligned on an axis that’s perpendicular to the other 3 directions). It’s unlikely that this is the case in reality however, as it would be very easy for us to observe the effects of additional large, extended spatial dimensions if they existed.

If extra spatial dimensions do indeed exist in reality, then they’re likely quite different to the 3 extended spatial dimensions that we currently observe. They’re probably closer to the tightly coiled, circular dimensions that are sometimes hypothesised about in things like string theory, and they would potentially exist at scales below the plank length.

Unfortunately, I find it quite difficult to picture an analogy which can represents this idea in the same way we do with flat-land, but it’s still interesting to think about. If true, then it’s possible we already exist in this extra dimension without realising it. NHI could exist on earth just like us, but be occupying another part of the ‘curve’ on the coiled up dimension – less than an atoms width away from us.