It is likely that until this moment in time you’ve been convinced that we have only five senses: seeing, hearing, tasting, touching, and smelling.  This is, after all, what we’ve been taught since, well, I don’t know, forever  I guess.  But why is this so?  What do we mean by “a sense”, and what do these classifications even do for us?  I’ll describe some things I’ve thought about in this regard, and some ways that I see it relating to the study of mathematics.  In doing so, I’ll propose that we in fact have (at least?) six senses.  Don’t worry though—this sixth sense has nothing to do with seeing dead people (I’m hoping a reference to a 90’s movie isn’t too obscure here).

Let me take as a starting point the following seemingly simple question: What defines a sense?  Despite its four word delivery, this is actually quite a subtle issue.  To avoid a lot of the subtlety and leave that for the philosophers, I think we can define a sense to be some faculty that we use to perceive our surroundings.  Surely, all of the information that we gather from the external world is gathered in the form of (at least) one of the five faculties of sight, sound, taste, touch, and smell.  Or is it?

Since “perception” is a very abstract and complex issue to pin down precisely, let me use a different definition of “sense” that is easier to handle (i.e., more concrete), and that also captures what we want from our intuitive ideas about our senses.  Namely, let me define a sense to be a faculty with which we can access beauty.  The astute reader might now remark that our notions of “beauty” are ill-defined as well, which I would agree with.  Thus, let me use this definition as motivation for an even more concrete definition: a sense is a faculty through which we can experience pleasure.  Now, there are still some terms here that are hard to define, but let us take this as our definition and see where it leads us.

Clearly I have limited our definition of “a sense” quite a bit, from being something that is used to perceive the external world (quite a general statement) to something that is used solely to experience pleasure (something quite specific).  Let me first explain the utility of this definition, and then perhaps its motivation will be more clear.

The power of this definition comes from the fact that it is relatively concrete and tangible, yet we can still recover the five senses that we know and love.  In other words, we gain the ability to make forward progress without sacrificing any generality.  Thus, even though I’ve made the definition more narrow, we actually don’t really lose much (see more about this sort of reasoning in the post “What is Abstract Thought?“).  Let me now clarify how it is that we can recover the five usual senses from this more narrow definition of a sense as “a faculty through which one can derive pleasure”.

We can derive pleasure from seeing a beautiful sunset or painting, hearing a Beethoven symphony or the sound of the rain pattering the windows amidst distant rolling thunder, tasting a chocolate soufflé or an icy beer on a hot day, touching the soft fur of a puppy or the lips of a lover, and smelling freshly baked chocolate chip cookies or the top of a baby’s head (yeah, you know what I’m talking about).  Thus, we have properly recovered the five senses that we already know and love.  Moreover, anything that we can perceive from the external world could in theory be used to derive pleasure, and thus focusing on pleasure is a useful (and pleasant) tool, as well as a completely general one.

But are there other ways than these to experience pleasure?  I believe that there is precisely one other way—a sixth sense—to derive pleasure, and that this sixth possibility is perhaps the most useful of them.  I believe that logic is a sixth sense with which we can perceive pleasure, and that believe it or not we are all already familiar with this sixth sense.  Before I mention exactly how we’re already familiar with this sixth sense, let me clarify that I am associating the pleasure derived from a sense with the emotional pleasure derived from the use of that sense.  In other words, I am equating the pleasure of smelling freshly baked chocolate chip cookies with the memory of being a child and smelling the cookies that mom baked every Saturday (or whatever your memory is), so that the pleasure comes from the pleasurable emotions that were brought about by the sense in question.  It is the use of the sense of smell which instigates that pleasurable experience, and I claim that the use of logic can instigate equally if not more profound experiences of pleasure.

I claim that we all already do this.  I.e., we already use and derive pleasure from our sixth sense, we just don’t see it as such (yet?).  For example, whenever we think of “the infinite” we are deriving some kind of pleasure by purely logical means.  We ponder the numbers and realize that there can be no “greatest” number, for we could always add 1 (or 10, or 2,000) to that number.  By realizing that there can be no greatest number, we come to the conclusion that there must be infinitely many numbers.  We are then forced to stand in the presence and wonder of a very beautiful mental construction of the infinite, having used nothing but our sixth faculty of logic.

This, I argue, is precisely what mathematics is—it is the art form whose beauty is accessed through our sixth sense, and whose medium is logic.

Music is the art of constructing beauty through the medium of sound.  A musician and/or composer trains to be able to create such structures, and the listener derives pleasure from those constructions via one of her six senses.  A chef trains to improve his ability to create beauty via the medium (and sense) of taste, and a painter does so with sight.  (As for touch and smell, I don’t know, think of a masseuse/masseur and Febreze, respectively).

In exactly the same way, mathematicians construct beautiful structures, the only difference is that we look upon these structures not with our eyes or ears, but rather with our sixth faculty of logic.  Moreover, the sheer existence of these structures often evokes immense pangs of pleasure in those who look upon them.  This pleasure is just of a different sort than that of the other five senses, but the same can be said about any of the others as well—there is no doubt that sight and sound are too wildly different senses.

So there you have it, my proposal for the existence of a sixth sense.  Don’t be scared to develop it, tune it, sharpen it, and master it—it might just be one of the most important senses we have.