Lovecraft suggested that non-Euclidian geometry would drive human brains mad; that confronting realities other than the ONE reality we think we are familiar with would be such a shattering moment that our minds would never recover. His fiction, and the interminable repetition it has suffered at the hands of less-imaginative writers over the years since, works over this theme again and again, and non-Euclidian geometry gets brought numerous times as an example of that sort of mind-shattering alteration to reality.
Things We Were Not Meant To Know.
But non-Euclidian geometry has, so far, driven remarkably few people mad. It turns out that alternate models of reality are not only comprehensible; they're immensely useful.
For non-mathematicians of Lovecraft's time, the early 1900's might well have been around the time when non-Euclidian geometry was first getting considered and talked about, and no doubt there was plenty of confusion as to what it really was and what it meant. The first forms were discovered only in 1823, so it's not crazy that 80 years later it was hitting the non-expert populace.
(basically non-Euclidian geometry is geometry that defines "parallel" differently than what we normally think of as parallel. Sort of. Not a mathematician, over here. Go look it up if you want to know.)
It turned out to be far less shattering than people feared -- no more so than alternate number systems such as irrationals or worse imaginary numbers. It turns out that people are actually pretty good at holding simultaneously contradictory models of the world in their head. Which, when you think about it, is a pretty important skill to possess. That's what any artist or any craftsman does when they create. They imagine a world different from this one, a world in which their novel or server or toothbrush exists, and they act in order to transform the current world into the imagined world.
I recently re-read Douglas Hofstadter's landmark Godel, Escher, Bach: An Eternal Golden Braid, and while deep in exploring Godelian gymnastics I realised again how critical MODELS are to our ways of thinking and seeing. It is the models by which I organize my perceptions that determine my reality -- as I change those models, I change the very world around me. Not to get all freaky and strung-out-60's-ish about it -- but it really is sobering to realise how many of the "facts" by which I guide my own decision-making are in fact models that I've generated about the world.
In response to statements like these (model = reality) people bring up physical issues ("Changing your models won't allow you to walk through walls"), which is fair enough, but you know, not many of the difficult decisions in my life have to do with physical issues. The TOUGH decisions in my life are always about how to handle or communicate with the folks in my life -- and in that arena my models really ARE of critical importance. And having multiple models that I can switch between is as immensely helpful to me as non-Euclidian geometry to assorted mathematicians.
Both Euclidian and non-Euclidian geometries are TRUE. Both describe the world accurately, depending on what aspects of the world I want to model. But the real power is not in using one or the other -- it's the ability to use BOTH, to hold them both in my mind simultaneously, that opens me up to honest, sincere change in myself and my world.
Now the models I use in my head are not easily available for my own review -- I can't print them out in a meaningful way. But I clearly can examine them, even if only incompletely, and I think it's reasonable to assert that I can also examine models that I DON'T use. In a way, that's what I do when I try to understand another person -- I'm trying to comprehend how their model works, so that I can compare it with those of mine that I'm aware of and decide if it offers any advantages.
And I don't go insane when I do. But I think Lovecraft touched on a very real fear of us all -- that by opening ourselves to possibilities, to models other than those that we're already comfortable with, we will imperil that deepest sense of ourselves. We cling to our models, and reject new ones out of hand, because we are afraid that we risk our identity. I know that when I react defensively, as I do so often when someone tries to present a model unfamiliar to me, or one that seems to conflict with ones I have already invested my pride and self-worth in, what I'm really doing is fighting to maintain my erroneous notion that my models are actually my reality. I'm pretending that if I consider alternatives, I will diminish myself, or maybe lose control of myself. When in fact, practicing my ability to hold multiple models simultaneously is really the strongest, most human thing I can do.
H.P. Lovecraft is wrong. Having your mind shattered is a GOOD thing.