If you’ve read this blog for long, you know that my work is a combination of math, statistics, and computing.

I was looking over my records and tried to see how my work divides into these three areas. In short, it doesn’t.

The boundaries between these areas are fuzzy or arbitrary to begin with, but a few projects fell cleanly into one of the three categories. However, 85% of my income has come from projects that involve a combination of two areas or all three areas.

If you calculate a confidence interval using R, you could say you’re doing math, statistics, and computing. But for the accounting above I’d simply call that statistics. When I say a project uses math and computation, for example, I mean it requires math outside what is typical in programming, and programming outside what is typical in math.

One of the case studies in Michael Beirut’s book How to is the graphic design for the planned community Celebration, Florida. The logo for the town’s golf course is an illustration of the bike shed principle.

C. Northcote Parkinson observed that it is easier for a committee to approve a nuclear power plant than a bicycle shed. Nuclear power plants are complex, and no one on a committee presumes to understand every detail. Committee members must rely on the judgment of others. But everyone understands bicycle sheds. Also, questions such as what color to paint the bike shed don’t have objective answers. And so bike sheds provoke long discussions.

People argue about bike sheds because they understand bike sheds. Beirut said something similar about the Celebration Golf Club logo which features a silhouette of a golfer.

Designing the graphics for Celebration’s public golf club was much harder than designing the town seal. It took me some time to realize why: none of our clients were Schwinn-riding, polytailed girls [as in the town seal], but most of them were enthusiastic golfers. The silhouette on the golf club design was refined endlessly as various executives demonstrated their swings in client meetings.

Image credit: By Source, Fair use, https://en.wikipedia.org/w/index.php?curid=37643922

Interesting passage from Small is Beautiful: Economics as if People Mattered by E. F. Schumacher:

Nature always, so to speak, knows where and when to stop. There is a measure in all natural things—in their size, speed, or violence. As a result, the system of nature, of which man is a part, tends to be self-balancing, self-adjusting, self-cleansing. Not so with technology, or perhaps I should say: not so with man dominated by technology and specialization. Technology recognizes no self-limiting principle …

We speak of natural growth more often than natural limits to growth. Maybe we should consider the latter more often.

Schumacher’s book was written in 1973 and seems to embody some of the hippie romanticism of its day. That does not make its arguments right or wrong, but it shows what some of the author’s influences were.

The book’s back cover has an endorsement describing Schumacher as “eminently practical, sensible, … versant in the subtleties of large-scale business management …” I haven’t read the whole book, only parts here and there, but the romantic overtones stand out more to me, maybe because they contrast more with the contemporary atmosphere. When the book was published, maybe the pragmatic overtones stood out more.

Kevlin Henney’s keynote at GOTO Copenhagen this year discussed how project time varies as a function of the number of people on the project. The most naive assumption is that the time is inversely proportional to the number of people. That is

t = W/n

where t is the calendar time to completion, W is a measure of how much work is to be done, and n is the number of people. This assumes everything on the project can be done in parallel. Nobody waits for anybody else.

The next refinement is to take into account the proportion of work that can be done in parallel. Call this p. Then we have

t = W[1 – p(n-1)/n].

If everything can be done in parallel, p = 1 and t = W/n as before. But if nothing can be done in parallel, p= 0, and so t = W. In other words, the total time is the same whether one person is on the project or more. This is essentially Amdahl’s law.

With the equation above, adding people never slows things down. And if p > 0, every addition person helps at least a little bit.

Next we add a term to account for communication cost. Assume communication costs are proportional to the number of communication paths, n(n – 1)/2. Call the proportionality constant k. Now we have

t = W[1 – p(n-1)/n + kn(n-1)/2].

If k is small but positive, then at first adding more people causes a project to complete sooner. But beyond some optimal team size, adding more people causes the project to take longer.

Of course none of this is exact. Project time estimation doesn’t follow any simple formula. Think of these equations more as rough guides or metaphors. It’s certainly true that beyond a certain size, adding more people to a project can slow the project down. Kevlin gave examples of projects that were put back on track by reducing the number of people working on them.

My quibble with the equation above is that I don’t think the cost of more people is primarily communication. Communication paths in a real project are not the simple trees of org charts, but neither are they complete graphs. And if the problem were simply communication, then improved communication would mitigate the cost of adding people to a project, though I imagine it hardly does.

I think the cost of adding people to a project has more to do with Parkinson’s Law which says that people make work for each other. (The aphorism form of Parkinson’s Law says that work expands to the time allowed. But the eponymous book explains why work expands, and it is in part because people make extra work for each other.)

I wrote about a similar theme in the blog post Maybe you only need it because you have it. Here’s the conclusion of that post:

Suppose a useless project adds staff. These staff need to be managed, so they hire a manager. Then they hire people for IT, accounting, marketing, etc. Eventually they have their own building. This building needs security, maintenance, and housekeeping. No one questions the need for the security guard, but the guard would not have been necessary without the original useless project.

When something seems absolutely necessary, maybe it’s only necessary because of something else that isn’t necessary.

One of the themes in David Ogilvy’s memoir Confessions of an Advertising Man is the importance of selecting good clients. For example, he advises “never take associations as clients” because they have “too many masters, too many objectives, too little money.”

He also recommends not taking on clients that are so large that you would lose your independence and financial robustness by taking them on.

I have never wanted to get an account so big that I could not afford to lose it. The day you do that, you commit yourself to living with fear. Frightened agencies lose the courage to give candid advice; once you lose that you become a lackey.

This is what lead me to refuse an invitation to compete for the Edsel account. I wrote to Ford: “Your account would represent one-half of our total billing. This would make it difficult for us to sustain our independence of counsel.” If we had entered the Edsel contest, and if we had won it, Ogilvy, Benson & Bather would have gone down the drain with Edsel.

This sort of thinking was very much on my mind when I was preparing to leave my last job to strike out on my own. As Nassim Taleb discusses in Antifragile, a steady job seems safer than entrepreneurship, but in some ways it’s not. With one big client, i.e. an employer, you are less exposed to small risks but more exposed to big risks. Your income doesn’t vary per month, unless it suddenly drops to zero.

In addition to looking for good clients, Ogilvy shares several stories of letting go of bad clients. I have yet to resign from a bad client—I haven’t had any bad clients—but I value the option to do so. The option to resign from a project makes it less likely that you’ll find yourself in a project you wish to resign from.

They say that doctors make terrible patients, but in my experience consultants make great consulting clients. The best are confident in their own specialization and respect you in yours. They get going quickly and pay quickly. (I’ve only worked for consultants who have small companies. I imagine large consulting companies are as slow as other companies the same size.)

Sometimes consultants working in software development will ask me to help out with some mathematical part of their projects. And sometimes math/stat folks will ask me to help out with some computational part of their projects.

I started my consulting business three years ago. Since then I’ve gotten to know a few other consultants well. This lets me offer a broader range of services to a client by bringing in other people, and sometimes it helps me find projects.

If you’re a consultant and interested in working together, please send me an email introducing yourself. I’m most interested in meeting consultants who have some overlap with what I do but who also have complementary strengths.