The Miracle of the Shoe-Trees

I've taken some stick about what I'm going to say here, but I believe it needs to be said. After all, "In order for evil to flourish, it is only necessary that good men have unnecessarily wrinkled shoes".

Shoe-Trees - The solution to an age-old problem

Almost everyone in an office job has to wear shoes. Some of us like to wear smart shoes, and some are compelled to because the concept that the texture of your clothing does not influence your ability to do a job has not percolated through the brainpan of their boss (see my paper "The Effect of Khaki Trousers on the Maze Running Ability of Rodents" - Journal of Sartorial Psychokinetics, May 1997.)

It is a poignant aspect of the human condition that using our possessions inevitably leads to their degradation and eventual destruction (See my paper "The Second Law of Thermodynamics and the Inevitability of the Depressive Personality" - Journal of Entropic Studies, June 1993.) To wear shoes is to wear them out. The more we like a pair of shoes, the more we are likely to want to wear them, and the more we wear them, the sooner they succumb to the dings and scratches of daily life. Life is, as has been said before, sad. Absolute shoe preservation is impossible, (ibid.) but there are strategies which we can adopt to slow down their decomposition.

Shoe Preservation Strategies - 1

The Imelda Marcos Approach

This can be summarised:

If N = number of shoes owned
and W = average number of wearing events required to destroy a pair of shoes
and w = average number of actual wearing events per pair of shoes

then:

as N tends to infinity, w/W tends to zero

In fact, as N tends to infinity, the chances of ever finding the same pair of shoes twice tends to zero, so unless you manage to wear-out a pair of shoes in a single wearing event (i.e. W = 1), you will never have to face the destruction of a favoured pair.

There are a number of obvious problems with this strategy. These are:

a) The Storage Problem
As the total number of shoes increases, space required for storage increases proportionally. Eventually, all available space will be taken up with shoe storage space, meaning that the only place available to wear the shoes is a shoe closet. This may reduce the number of occasions when the wearer will want to wear certain styles of shoe, as the requirement for dressy shoes varies depending on the attributes of the location of the occasion for wearing them.

Interestingly, this variation can lead to a chaotic state where the wearer can never decide which pair of shoes is appropriate, and will thus spend all of their time trying each on in turn, never satisfied with the result. This dissatisfaction itself alters the feelings of the wearer as to the most appropriate footwear for the moment, and this positive feedback/chaotic state is impossible to escape. Subtle precursors of this effect can be seen to occur even for relatively small values on N, where as N increases, d (the probability of arriving at a dinner party on time) falls geometrically.

b) The Distribution Problem
This is related to the Storage Problem, but instead of being directly related to the volume of space required for shoe storage, it relates to the time taken to move through this space to retrieve the desired pair of shoes. Clearly, as N increases, the time taken to retrieve any particular pair of shoes increases at a rate dependent on the geometry of the storage space. This relationship also holds true for the converse case, that of returning the shoes to their correct location after each wearing event.

It may be argued that the return of the footwear after a wearing event is superfluous, as if N is large enough, there will never be a need to retrieve that particular pair again. This is a superficially attractive idea but in practice, neglecting to replace the shoes is equivalent to moving the shoes to the current location and leaving them there. This will either eventually result in the filling of the current location with more and more shoes, slowing, and eventually stopping all shoe retrieval, or require the wearer to move constantly through the shoe space to avoid being trapped by the ever growing pile of worn shoes. This movement will reduce the availability of certain parts of the shoe space, constraining the choice of shoes to a greater and greater degree, reducing the effective value of N.

Indeed, not returning shoes, even assuming optimal packing at the point of discard (theoretically, the user can always carry the box around whilst wearing the shoes, though this seldom happens in practice), will increase the effective storage volume of the shoes by a factor of at least 2, further exacerbating both the Storage and Distribution Problems.

c) The Money Problem
As N increases, the total cost of the shoes increases proportionally. This explains why the most successful exponents of this strategy have had the assets of small countries at their disposal.

d) The Cow Problem
The Cow Problem is related to the Money Problem, but relates to the availability of raw materials. This may include, as the name suggests, leather, but in principal the problem applies to any finite supply of material needed for shoe production, such as eyelets or mock-crock.

Shoe Preservation Strategies - 2

The Cleopatra Approach

This strategy is a simple one - increase W (where W = average number of wearing events required to destroy a pair of shoes) by making the effective wear on the shoes per wearing event tend to zero. This is also known as "being carried around everywhere".

Problems also affect this strategy. These include:

a) The Intimacy Problem
Being carried around everywhere implies an intimate physical relationship (though not necessarily in the Biblical sense) between the carrier and the carriee. This problem is further magnified by the eventual need for multiple carriers, as being carried around is usually associated with an increase in the weight of the carriee. This crux of the problem is this: The carrier/carriee relationship requires patience, willingness and physical closeness, but the effect of having to carry someone (especially as they get heavier) is precisely to degrade these qualities of the relationship.

It is not coincidence, in my opinion, that we use the phrase "to drop" when we talk of ending a relationship. I feel sure that this is a folk memory of earlier, more hierarchical times.

b) The Revolution Problem
This is an extension of the Intimacy Problem, in that is involves the willingness of a population to support (!) someone who i) gets carried around everywhere, and ii) (often) has an inordinately large number of pairs of shoes.

Thus we see that this strategy is closely and perhaps fatally dependent on the political history of human civilisation. (See my book - "Let Them Eat Shoes - Footwear and the French Revolution" RKP, 1992.)

(To be continued...)