The Mathematics of Work

Introduction

The purpose of this paper is to present, in a quantitative yet practicable sense, the definition of work and—more importantly—the determining factors and components of influence. The qualitative goal is the identification of factors (procedural, environmental, and otherwise) that can be manipulated or mitigated to yield the maximum work with the greatest certainty.

Definition of Terms

First, we must define our terms.

W = Work (the doing of work)

H = Home

W_FH = Working from Home

S = Sales

Y = Support Systems

E = Effort

G = Going to work (i.e., presence at Work)

P = Part-time Attendance

M = Meeting

V = Day Off (Vacation)

X = Pregnancy

BB = baby (bébé)

D = Desk (i.e., presence at one’s Desk)

W_FD = Working from Desk

W_WD = Working while Drunk

Gold Master Goal Matrix

To introduce the context in which Work and its determining factors will be examined, we present the Gold Master Goal Matrix (GMGM):

Objective: Work & Increase Sales
Case	Likelihood Yield Index
1) Go to Work → Work, ↑Sales     presupposed elements: Functioning Equipment Access to Decision-makers and Customers	8
2) Work from Home → Work, ↑Sales     presupposed elements: Functioning Equipment (same as in #1 above) Access to Decision-makers and Customers (almost the same as in #1 above)	7
3) Work from Home → Work, ↓Sales     presupposed elements: No Functioning Equipment No Access to Decision-makers and Customers	0

The GMGM was designed to show the probability that the various circumstances outlined will yield the desired outcomes as stated in the Objective. Case 1 illustrates the highest probability of goal achievement via Going to Work, having the presupposed elements in place, with the yield of Work and Increased Sales. Case 2 show that Working from Home can—with the presupposed elements in place—have a likelihood of yielding the desired results that is only slightly lower than that of Case 1. Case 3, however, shows that Working from Home without the presupposed elements in place has no likelihood of yielding the desired goals, and is effectively equivalent to a Day Off.

Formulas

Work and Home

The GMGM leads us logically to a number of mathematical statements that clarify and delineate the concepts suggested by that groundbreaking matrix. The first of these is the basic premise that working from home without actually working is equal to simply being home. This is represented by the following equation:

W_FH – W = H

Since we know, as a given, that home is not the same as work,

H ≠ W

then we can also draw the following conclusion:

W_FH – W ≠ W

Further, we can prove that working from home without working is, in fact, not working from home:

W_FH – W ≠ W_FH

While some have postulated that going to work is tantamount to working (a position known as the Schultz Principle), the closest that one can come to this claim is the statement that going to work may be highly correlated with working, represented as follows:

G ≈ W

Effects on Sales

Here we examine the relationship of the elements to the objective of increased sales. This relationship is based on the product of the core sales factor (S) and the work-related variables. Let’s look at some formulas that illustrate this idea.

First, we know that sales generated by work are greater than sales generated by simply being home (without working):

S(W) > S(H)

We have already established that W_FH – W = H, so we can further conclude that sales generated by working from home are greater than sales generated by working from home without working:

S(W_FH) > S(W_FH – W)

An obvious additional conclusion is that sales generated by working are greater than sales generated by working from home without working:

S(W) > S(W_FH – W)

A hypothesis which is highly regarded (though as yet unproven mathematically) is the idea that sales generated by working (at work) are greater than or equal to sales generated by working from home. This is known as The Simon Principle. The major challenge to The Simon Principle (also known as The Mami Hypothesis) is based on the contention that sales work done from home can be more productive than that done at work. While The Simon Principle does indeed allow for sales work done from home being equally as productive as that done at work, it has not been augmented to accommodate the possibility of sales work done from home being more productive than that done at work. Here is The Simon Principle:

S(W) ≥ S(W_FH)

The logical flaw in The Mami Hypothesis is that it excludes the demonstrated case that sales generated by working from home can be less than sales generated by working. Nonetheless, it remains a popular concept among lay people, so for your edification, here is The Mami Hypothesis:

S(W) ≈ S(W_FH)

The Value of Support Systems

Support Systems (Y) are those elements that provide the infrastructure and raw materials to allow workers to achieve their goals. These include, but are not limited to, telecommunications and computer equipment, physical access to coworkers, files and data, and product samples.

The Hermit Theorems present the following, starting with the idea that working from home in the absence of support systems is not actually working from home:

W_FH - Y ≠ W_FH

More pointedly, working from home without support systems is not equal to working:

W_FH - Y ≠ W

And perhaps most boldly, working from home in the absence of the support systems is equal to being at home:

W_FH - Y = H

Please note, however, the Cubicle Corollary, which makes the critical distinction that the mere presence of support systems is not tantamount to work:

Y ≠ W

This is a pitfall to which too many succumb. Rather, it is the product of support systems and effort that yield work, as stated by the Exertion Corollary:

Y * E = W

Upon This Desk I Shall Build My Work

The Amber Desk Corollary is an extension of the Hermit Theorems that focuses on the locus of work within the workplace. In it, proximity to the desk (defined as D) is shown to be a key element in the accomplishment of actual work:

W_FD – D < W

The colleague who is not at his or her desk is effectively separated from the essential element of the workplace, which can be equated with working outside the workplace, i.e., from home:

W_FD - D = W_FH

Some theoretician’s have gone so far as to propose The Absentia Hypothesis, which posits the rough equality of allegedly working from the desk but actually not being at the desk to simply being at home:

W_FD - D ≈ H

Reproduction and Production

Working from home in the presence of offspring is characterized as an exponential exacerbation of work impedance in the Apy Theorem, which illustrates the significant negative effect that such an environment has on work output:

W_FH + BB = - (W²)

Drink Up, Dreamers, You’re Running Dry

While substance abuse is certainly a disease, that sad reality does not ameliorate its deleterious impact on work, as put forth in the Boyle Principle:

W_WD = -(W¹⁰)

There have been debates in other academic papers as to the relationship between the Boyle Principle and one of the generally accepted definitions of Work (i.e., Work = Force * Displacement), specifically with respect to whether it is the Force or Displacement that has the negative value. While the position of our authors is that it is the Displacement that has the negative value, this issue can be debated more extensively in another forum.

Conclusion

Among the numerous factors affecting and influencing the generation of work, there are certain theorems which, if dutifully considered, will serve as consistent predictors of work yield. In service of stated goals (increased Sales, in the example of the GMGM), the application of these theorems can be extremely valuable. While various factors can impede the practical implementation of the principles suggested by the theorems, ignoring their significance presents a serious risk to the accomplishment of goals as outlined.