The Calculus of Dressing

Appendix 2.

Back in the installment Chapter 70, called “Keeping Your Balance,” we looked at the concept of weighing specific style variations, each against each other, to achieve a harmonious whole within a single outfit. To help visualize this, I devised a graphic representation of the continuum of balance as a three-dimensional cube, each of the axes standing for one range of opposites—the Continuum Cube.

That was all well and good for an overview, but it was the stripped down, basic version – there’s actually more to the theory than what I posted there! I gave a more complete view in my published works, but here in the Appendices I am going to share with you the fully-realized, advanced theory.

The complete theory of balance is visualized scientifically here by use of a four-dimensional theoretical construct of the Continuum Cube—a Grand Unified Theory of dressing well, if you will, that graphs every possible option of menswear for every possible circumstance.

There have been numerous philosophical postulations over the years concerning the art of dressing well. To those we can now add a mathematical theorem, a graphic distillation of the musings of D’Aurevilly, Wilde, Bulwer-Lytton and de Balzac, which clarifies and concretizes their ideas in a clear way: that dressing well is an ethos, an attitude and outlook on the world that just happens to be reflected in its external appearance. The most obvious aspect of your appearance is your refinement of the art of dressing well: to be correctly and impeccably attired in any given situation. As Brummel said, “If John Bull turns to look after you, you are not well-dressed, but either too stiff, too tight, or too fashionable.”

Let’s start with the idea of formality. You have an innate sense of the degree of formality of any outfit you might be called upon to wear. You wear nicer clothes to church than you do to work, and nicer clothes to a wedding than you do to church; and if you were playing golf, you would be dressed better than if you were playing tennis. If you were to graph all the different sorts of clothes you wear, you could represent them as a line, with the dressiest at one end, and the most casual at the other. We'll call the two extremes “formal” and “sporty.” What we would have is a bit of geometry: a line. It would look like this:

Notice that from any point on the line, you could choose something more formal, or sportier (you could also call it “casual” or “informal.”) Our line extends forever in both directions, as lines do, but that won't do for us; for you can't go on increasing formality forever.

The solution is to make the line asymptotic and the end-points as a limit, which can be approached infinitely closely, but you actually can’t truly “get there.” Reaching the limit is relativistic—the closer you get, the further you have to go, and the harder it is to get there. One limit is the point beyond which you can't get any more formal. That point represents the dress suit: for white tie and tails is the most formal thing a man can wear in the Western world. In other cultures it may take a different form, but the result is the same.

Logically, at the other end is an asymptotic limit beyond which one can't get more casual – which, it stands to reason, is being entirely naked. (Why is this, you may ask? Patience…we'll discover why soon.)

So our line segment, our X axis, if you will, looks like this:

Every element and article you wear fits somewhere along this line. The goal is an average between two extremes that is not too far out of the range of “normal” for your particular place and circumstance; whether this is attending a wedding or shopping for groceries. In other words, for any point on the line, any deviation on one side of the point must be weighed carefully against its variation on the opposite side of the point, to achieve a harmonious whole. The problem in today's world arises when a man doesn't know what to wear at all, much less how to find what an average value is, and even less how to work the extremes to maintain that balance properly.

As an example: everyone has at some point been subjected to such aberrations as a tuxedo jacket that has been paired with sneakers, or a patterned shirt, or a loosely-knotted long tie, or a silly hat, or sloppy jeans. Their misguided thinking is that a dinner jackets' formality will be offset by the other things, and the average will be dressy-casual.

This doesn't work in practice, because the attempt to balance two variations is increasingly unlikely to create a harmonious average the farther apart those extremes are. In fact, dinner dress is so extremely proscribed, it takes very little to push its balance to a place of informality: all that is needed are minor alterations to detail, like a subtly-colored boutonniere, a flash of pocket square, a rakishly-designed waistcoat, or even the material of the jacket itself.

It seems pretty easy so far, doesn't it? Well, we have another line, which describes another dimension of being properly dressed: the difference between “town” and “country” wear. Whilst the “Formal/Sporty” line describes the differences in the purpose and cut of your clothes, the “Town/Country” line is concerned with your clothes' color and pattern: for mens' clothes should properly match the environment in which they are worn. A “town suit,” for instance, is plainly cut and conservatively tailored, with smooth fabrics and dark colors, usually in shades of black or blue: the colors of steel and iron and concrete, the textures of glass and chrome and macadam.

A “country suit” tends toward the rough tweeds, pebbly or textured fabrics, in browns or greens, in plaids, checks, or other patterns, with details like collar tabs, elbow patches, or flapped pockets: the colors and textures of nature, with details that reflect outdoor pursuits.

This line, too, has two asymptotic limits, and those limits are of necessity the same as with the formality continuum: the most “Town” you can get is a dress suit of white tie and tails, and the most “Country” is not dressed at all. The two scales that we have seen operate independently of each other: for every point of formality, there can be applied the complete range of values in possible color and pattern. We can graph these against each other on an X and Y axis.

Most men have a passing experience in the art of color and pattern matching. At its most basic, it is an intuitive reflex. A dark suit needs a light shirt and a bright tie, for instance; or else the suit looks muddy and somber. A light suit looks better with a patterned shirt of a darker color, and so on. Making informed decisions regarding pattern takes more experience, but is also largely intuitive. Matching a plaid shirt with a plaid tie may look busy if they are in the same color range and size, especially if paired with a plain suit; but a suit with a subtle pattern paired with a very light plaid shirt and a very strong plaid tie may look very handsome indeed. It's all in the balance created between the factors.

If we were to graph every possible combination of these two groups of extremes, we would discover the result is the limit of a square, each point of which describes one individual shade of purpose and cut, color and pattern.

Dressing well now becomes a matter of determining your purpose and location at any given time, charting that point on the graph, and making your clothing suitable to that point on the X-Y axis. The closer the average effect of your clothing is to that point, the more “correctly” you will be seen to be dressed. On this square, the front right-hand corner, representing maximum values of Town-Formal, would represent the dress suit; and the rear left corner, representing maximum values of Country-Sporty, would be nudity. (This latter corner, naturally, is to be avoided if you desire to be a well-dressed fellow.) The relationship of all four factors taken together is the balance of your outfit.

Where the axes cross, (we'll call it point 0,0) is a theoretical neutral outfit that is all-purpose, neither too dressy nor too sporty, that would not look too out of place either in the city or out camping. This theoretical middle-of-the-road outfit would not be a panacea that would be instantly accepted anywhere, mind you! It would, rather, be bland porridge, neither one thing nor another, and you would likely be seen everywhere as not quite fitting in, no matter where you were or what you were doing. The neutral point at the center of the graph is not a target at which to aim – it is a sinkhole to be avoided!

Before we continue, let's look at some examples of how to use the scale as we have constructed it thus far.

You can adjust the balance to your immediate purpose, by changing a single detail to adjust the point along both axes. A matching three-piece looks official and professional for a business meeting, and would occupy a place well in the Town scale, and moderately in the Formal scale. Simply change out the matching waistcoat for a tattersall version, and the outfit looks less stuffy for an evening out, by skewing the point both towards the Sporty and Country.

You can also make an adjustment to either scale independently. Running to the auto-parts store to buy an oil filter and spark plugs in a suit and tie may raise some eyebrows, but you can keep the same point along the Formal continuum and slide the Town continuum strongly into the Country realm with a hardy tweed jacket, open-collar shirt and dungarees: the message is that grungy business is at hand. A seersucker suit, loafers, and a bow tie looks fine on the boardwalk, firmly in the Sporty-Country quadrant, but you wouldn't wear it to church without skewing it into the Country-Formal quadrant.

These basic style decisions can be complicated with variable factors such as the time of year and the immediate weather conditions. For instance, on a bright day, a pair of tan trousers may look fine with a mid-gray plain weave jacket; but on an overcast day, it would appear too Country, and a darker gray herringbone jacket to skew it slightly towards the Town side may look better. In the heat of summer, a shirt and tie may look overdressed in lieu of a simple polo shirt under your jacket; but in the fall, going without a tie may result in an underdressed appearance.

Now that you've gotten familiar with the two-axis system of clothing balance, we'll add a third measure to the continuum. Just like the other two, this third balance factor operates independently, and can be applied to every point in the square. This scale will be applied to your clothes' style and detail.

At one end, we have the historical extreme – the traditional, conservative, classic styles. At the other end, the contemporary extreme – the avant-garde, imaginative, futuristic, and innovative styles. We'll place this continuum at right angles to the other two, along the Z-axis: and call the extremes “Historical” and “Innovative.” Simply, the further along the “Innovative” direction you go, the further away you get from tried-and-true style trends.

When we graph every possibility of style against our other two measures, all the major factors of sartorial balance are accounted for and can be reduced to three continua. These continua can be visualized and plotted against each other as axes on a three-dimensional graph.

This is the Continuum Cube. Any point within this cube is defined by our three balance factors. The continuum is the limit of a cube; it is not unbounded on all sides. The ideal, as it was with the two-axis plane, is not the intersection of the axes at the exact center of the cube. Near the external faces of the cube are the limits of perspicacity, where clothes become costume. And just as you've seen with each individual scale, and also with the X-Y axis, the X-Y-Z axis has the same oppositional value, viz., the “Fully Dressed Point” at maximum Town-Formal-Historical is counterbalanced by its logical opposite at maximum Sporty-Country-Innovative – the “Fully Undressed Point.”

Let's use the Continuum Cube now to briefly demonstrate how skewing works along all three axes. We'll start at an easy point to visualize: the top right corner of the cube that pegs all three scales for formal, town, historical wear. Of course, it's the dress suit again: bespoke tailcoat and trousers, boiled-front shirt, pique Marcella waistcoat, stiff detachable wing collar, white tie, and patent leather pumps, with all the accompanying studs, links, straps, braces, and buttons that go with it. You can't get more Formal-Town-Historical than that. It's a very exacting and unforgiving point on the cube, right at the end of the limits, and must be followed precisely, because right on the apex of the cube is where it belongs.

Because of its precarious position, the dress suit is easily knocked off its apex by the addition or alteration of any detail. A simple boutonniere will skew the outfit slightly down the X axis, ever so slightly away from Formal. Substitute balmorals for pumps, and the skew jumps further down the Sporty scale, as well as the Country, and even slightly Innovative, and just like that – you're off the face of the cube and into the interior. This lone example also demonstrates why proper white tie is as exacting as it is.

Why is nudity the “Fully Undressed Point,” and not, say, swimming trunks, or even underwear? Because even swim trunks are subject to variations in sportiness, color, texture, and historicity, all of which will place it somewhere within the boundaries of the Cube, even if it is just adjacent to the apex. There just isn't a garment that is the opposite of a dress suit: as the limits of the axes are reached, the options of the furthermost point dwindle down, until the point of the apex is...nothing.

The apex and surface points are for our purposes theoretical: since a limit by definition can never be reached, you won't be dealing with the extremes on the faces of the cube. You will be dealing with any number of factors that will average into a value somewhere in the middle interior of the continuum.

Now, the three-dimensional Continuum Cube only works as far as the physical aspect of your clothes – but as we’ve found, how you wear your clothes, your degree of insouciance and panache, has an effect on where they skew on the Cube as well. This is of particular interest, as a properly insouciant attitude is integral to being perceived as well-dressed. So we must bring another axis in play – a W axis, at right angles to the other three, to make a hypercube.

What’s that you say? You’ve no idea how that works? Well, let’s work through the progression mentally. Take a point, and put another point at right angles to it. (Since a point has no dimension, technically “right angles” is any direction at all, but we’ll call it “right angles” for the sake of consistency of the illustration.) These two points form a one-dimensional figure: a line segment. It runs in one direction—length. Now take a line segment, and put four of them at right angles to each other such that they define an area. You have made a two-dimensional square: it runs in two directions—length and width. Now take six squares, and put them at right angles to each other so that they define an area. You have a cube now: three dimensions, three directions—length, width, and depth. Of course, here on your computer screen it’s merely a shadow of a three-dimensional form, but your brain recognizes it as a cube, even though all the sides aren’t the same length and the angles aren’t ninety degrees.

So far so good, but now it gets tricky. Continue the pattern: two points, four lines, six squares – now what? Of course, eight cubes; at right angles to each other such that they define an area of four dimensions. The problem comes when we try to imagine the W-axis, at right angles to the X, Y, and Z axes. What’s after height, width, and depth? The best we can see is a three-dimensional shadow, reduced again to two dimensions on your screen – a mere shadow of a shadow.

Because it is so devilishly hard to imagine a four-dimensional hypercube, and even more difficult to represent it on a two-dimensional computer screen, I won't even attempt to include it graphically. That fourth dimension represents the manner of the method and attitude of wearing your clothing and the degree of precision of its physical execution. At one limit, we have nonchalant, detached, easygoing, and breezy. At the other extreme, calculated, purposeful, precise, and severe. 

Graphed against the other 3 axes, the limit of Nonchalance coincides with the “Fully Dressed Limit” of Town-Formal-Historical, and the limit of Precision coincides with the “Fully Undressed Limit” of Sporty-Country-Innovative; thus, the closer to fully dressed one is, the more nonchalance is required. Contrariwise, the more casual your clothing, the more precision is required to offset the ever-present danger of slovenliness.

This presents a useful method of representing the fourth dimension of the Continuum Cube in relation to the other three directions. We know the limits of Nonchalance/Precision coincide with the limits of the other three continua, and we know each three-dimensional point is subject to the complete four-dimensional variance. (If this is befuddling, just reduce the exercise by one dimension: every single point on the two-dimensional graph of Formal/Sporty and Town/Country is subject to the entire scope of the Historical/Innovative variation.)

If the four extreme limits located at opposite apices of our hypercube (the F/T/H/N and the S/C/I/P limits) are then connected by a line, it will also pass through the midpoint of the W, X, Y, and Z axes, (at 0,0,0,0,) and a new axis is created: what I shall call the DANDY AXIS. (Dandy in its historical sense: as representing the apex of the art of dressing well from a holistic mind/body standpoint.)

Quite simply, for any circumstance, the most elegant mode of dress will exist at some particular point along the Dandy Axis, wherein all four continuua shift together in an equalinear progression. All four factors will then be in harmony, no one variation will stand out among the others, and for any given situation there exists a correlating given point on the Dandy Axis wherein you will assuredly be properly dressed, and John Bull will be given no reason to turn his head to look after you.

The relationship of the Dandy Axis to the four directional axes W, X, Y, and Z can be easily illustrated by separating the four dimensions out and placing them alongside each other, as scales on a slide rule. The Dandy Axis is represented by the movable cursor, which intersects all four axes perpendicularly along congruent points. This is a handy mental tool for determining correct dress: when only one factor is known, the other three are immediately apparent. In other words, for any given known Purpose (X-axis,) the proper relative degrees of Location (Y-axis,) Tradition (Z-axis,) and Execution (W-axis) are revealed in their correct place.

But now, back to the Continuum Cube itself. The Dandy Axis is the average of all the values at each point of the cube. This is an important relationship: for at whichever point in the interior of the cube you may find yourself, that point will always be perpendicular to a correlating point somewhere along the length of the Dandy Axis, as well as set a certain distance apart from it.

The Dandy Axis is thus very useful in revealing instantly, in a relative way, both “how dressed” you are, as a function of the point along the Dandy Axis' length, as well as any deviation from the proper standard, as a function of your point's distance from the Axis.

It can also be a useful compass, to give you an “absolute value” of just how dressed you are compared to any other point in the Continuum Cube. Let's take an example, and a rather obvious one, that demonstrates graphically how “more dressed” doesn't necessarily equate to “more clothes.” First, we'll take a tee-shirt, flip-flops, and cargo shorts, and plot its point within the Cube.

This graphic is looking straight down along the Dandy Axis, through the cube, to its S/C/I/P apex. The cube has been “sliced” through our point on a plane perpendicular to the Axis, resulting in the small tetrahedral figure. The size of the tetrahedron indicates that our point is close to the “undress limit” of the cube. Note, too, the distance of our point from the Dandy Axis.

Now, let us compare this to a different point, this one representative of a polo shirt, Bermuda shorts, and boat shoes.

This outfit covers the same amount of skin, and fulfills the same function, as the previous one. Its relative position in the Cube, skewed toward the Historical and Formal ranges slightly, cause it to sit perpendicularly to the Dandy Axis further along its length from the “undress apex,” (indicated by the larger size of the tetrahedron; due to the larger “bite” of the cube the cut has taken) and closer to the Dandy Axis itself: resulting in being “more correctly dressed,” with the same amount of clothing. (This assumes the optimal dandy values along the W axis for each point, as well.)

With practice, you can keep the Continuum Cube in your minds' eye as you decide what to wear, place a target point within the cube along the Dandy Axis, and choose clothes that will average into that target point. By looking at what you wear in this theoretical way, and fitting it into this matrix, you needn't be operating solely on intuition and guesswork, and you will have a solid guide for making wise sartorial decisions that will never inadvertently hit wide of the mark, by being too showy, anachronistic, or situationally inappropriate...or as Brummel would say, “too stiff, tight, or fashionable.”

Click here to go back to the installment that this Appendix references.