I remember, it was long time ago, studying math and physics. Whilst I had no problem in understanding dimensional spaces over the usual 3, as just equations with more than 3 variables, I had problems in physics going beyond the 4th dimension, something you need to do when considering several unification theories (attempts). Strings and superstrings seem to vibrate in plenty of dimensions and that baffled, and still baffles me. 3 and 4 dimensions made sense.
I also could live with 2 dimensions in the mathematical world and a new that a plane was a 2 dimension entity that made sense in theory but in practice, in the physical world, there are no 2 dimensional “objects”. They might be pretty thin but still they extend in the third dimension.
Theoretical physicists (the same breed that told us we might be living in a “n” dimensional continuum -not continuum though in a mathematical sense, since it is a sort of foaming clusters) have speculated that there can be 2 dimensional entities and they called them anyons (do not confuse these with anions, meaning negative ions). That was theoretical speculation in the last century, some forty years ago, 1982.
These anyons would be in between the entities obeying to the Fermi-Dirac statistics (fermions, like electrons -elementary particle, and protons/neutrons -composite particle) and the entities obeying to the Bose-Einstein statistics (bosons, like the photon and the now famous Higgs field/particle).
Fermions comply with the Pauli exclusion principle, i.e. where there is one you cannot squeeze another in (that is why if you hit a wall with your car, the wall gets dented and the car is destroyed, the fermions that made them up cannot merge nicely together). So if we smash, as physicists do, two fermions they actually repulse each other and go their own way (if the smashing force if really strong you may split one or the two fermions in subcoponents that will be flying away). On the other hand, bosons are indifferent to one another, you can look at them as waves and like waves they seem to add on one another (or subtract) and once they have passed the “meeting point” each one keeps going undisturbed as if nothing happened. Well actually for both fermions and bosons the reality is a bit more complicated but I hope you get the gist (and that physicists won’t feel the urgency to throw stones at me).
Theory predicted intermediate entities existing in just two dimensions (and here I got problem in visualising them…) that would behave partly as bosons and partly as fermions.
Now scientists at the University of Leipzig have conducted an experiment demonstrating the existence of these “quasiparticles”.
This is very interesting for physics buffs but it might also end up in furthering the quest for quantum computers since these anyons may be an answer to correcting the mistakes that occur in current quantum computation. This would affect us all, opening the door to alternative way of computation that may be used to solve problems that are too hard for current computational (von-Neumann) paradigm (usually those involving combinatorial aspects, called by gurus NP-hard).
It will likely take a few decades to see practical application of anyons, but so did the practical application of silicon and yet today it will be difficult to imagine a world without “chips”.