Life Lessons from Math: Sequencing and Pacing Projects—Joseph Kimball and Miles Kimball

In the last year I have written 3 blog posts on one theme:

I was motivated just as much by the practical lessons I was learning myself as by the usual blogging motivation of communicating a cool idea. Projects that only really start having a payoff flow after they are completed are very common, so it matters.

Here is what I feel I learned from writing those 3 posts:

Projects that only start paying off when they are completed should be done at a relatively quick pace, only reined in when the speed with which cost increases with the pace becomes relatively high (technically, that means pushing up the pace until the elasticity of flow cost with respect to pace becomes substantial).
If there are several projects of this type to be pursued in sequence, the pace of the projects sequenced first should be even faster, since a lot is waiting on them.
Unless you have a special justification to do otherwise, focus on only one project of this type at a time. One project that is done pays off better than many half-finished projects!
For the most part, start with the project that has the greatest flow benefit relative to its size.
When two projects have similar ratios of flow benefit to size, start with the one that has the greater flow benefit. (For somewhat subtle mathematical reasons, the ability to adjust one’s pace from one project to the next makes the size somewhat less important.)

My brother Joseph found these three blog posts intriguing. With his permission, let me share what he wrote about the life lessons he drew from these 3 posts. Below are Joseph’s words:

Executive summary: Do one project at a time in your set of projects, do that one as fast as you can, and choose that first project as the one which has the biggest benefit to size-of-job ratio and the biggest benefit to time-to-complete ratio.

In Miles’s post How Fast Should a Project Be Completed? where the project won’t give benefits until it’s complete, the conclusion was to complete the project quickly (as fast as possible without getting excessive). His assumption about learning languages is that he’ll need to learn quite a bit (about 10,000 words in addition to a reasonable grasp of the grammar) to have functional comprehension for reading (with conversational ability as a nice but not necessary bonus if that happens too).

The math in that post boils down to saying that as long as the cost of doing the project at a particular speed plus the cost of delaying the completion of the project is greater than the cost of doing the project at that speed, then there’s space (elasticity) to do the project faster. At some point the cost of doing the project faster may become unrealistic, even if you haven’t hit the limit of the equation. But the greater the cost of delay for finishing the project, the greater the speed to finish should be.

If you’re doing a project that has numbers attached, such as construction (where there are monetary costs for all the pieces, additional costs for speeding up individual pieces, and contract costs for going beyond a specific deadline), it can be fairly straightforward (in the theoretical sense) to plug in the numbers to Miles’ equations and come up with actual numbers for how fast is optimal for that project. If your project is amorphous, such as learning a language, the equations are still relevant, but become fuzzier and more subjective. But even with fuzzy and subjective numbers the conclusion is to do the project as quickly as your circumstances allow.

In the Scrum method of project management [which originated as an element of Agile software development], the team does “sprints” to complete specific tasks towards a larger project. Part of that idea is to have a quick turnaround of a specific small chunk of the project that can be completed, slotted into the larger project, and celebrated. Then the team moves to the next sprint.

In Miles’s post “Sequencing of Projects,” the conclusion was to complete the first project in the sequence as quickly as possible, so the whole sequence gets done more quickly. This is true regardless of the order you do the projects in but is even more powerful if you can find the optimal order.

The graph at the beginning of the post [also shown just above] shows the benefits of the project sequence on the y axis (up), and the time it takes to complete the project sequence on the x axis (right).The curve goes to a limit of infinity at each axis showing the extremes that are mathematically possible (though unrealistic). Each project has a benefit from completing it and a time it takes to complete. You can compute the cost of any project as the rectangle defined by its benefit and the time it takes. If you can shorten the time it takes, the benefit will increase from completing the project.

Shortening a project will increase the cost to complete it, and the limit of the function goes to infinity. Since we are mortal infinite effort is beyond us, so there’s a limit on how much effort we can put into any project. This is particularly true if this isn’t the only project we have going on (which is very normal for us mortals).

Looking at the other arm of the limit, we could theoretically get the same amount of benefit by pushing the time to complete the project toward infinity. However, since we’re mortal there’s a hard limit on how far we can realistically push a project toward this arm. Again, since this is likely not the only project in our life, we need to be cognizant of fitting the other projects into our mortal timeline. There are a number of “projects” that would fit toward this arm of the project graph though such as: daily or periodic health and safety (brushing teeth, yearly physical, putting on your seat belt, checking tire pressure in your vehicle, etc.); keeping a daily journal/diary; periodic check-ins with your support group (significant other, family, friends, etc.). These types of project are never really “completed” but only terminated at the end of our mortal life. This sort of “never completed” project is beyond the scope of what Miles was contemplating in his article but does follow from examining the graph.

I think Miles’s idea that learning a language is kind of all-or-nothing is not a good one. An all-or-nothing project would be more like constructing a building, where you can’t occupy the building until the city inspector has signed off on it. Thus, the building is useless at 99% complete. Language learning seems to me to be more of an elongated S graph with utility on the y axis and vocabulary on the x axis (ignoring grammar in this example). So you get very little utility until you have a good core of vocabulary (at the lower inflection point), then the utility rises pretty quickly until you get to that “10,000 word” level which encompasses all the words in common use (the upper inflection point), then utility increase gets smaller sharply as you add specialty words.

The elongated S graph would also apply to things like sports, where you really can’t do it until you have a base level of knowledge and skill (the lower inflection point), but then you get a lot more out of it as you increase your skill until you hit the upper inflection point. Beyond that upper inflection point you get Olympic or top-level professional performance. An example pertinent to me would be martial arts where a “black belt” rank (or equivalent in whichever art you’re studying) is the lower inflection point, and a “master” rank might be the upper inflection point.

Back to Miles’s concept of learning languages though, once you’ve reached that upper inflection point, it’s more a matter of maintaining that level by periodic practice and gradually learning the specialty words you need. At this point the level of effort you’ll be putting into that language can be reduced to maintenance level and you can begin the next project (learning the next language). If his goal is to learn three languages, then getting that first language to maintenance level as quickly as possible will allow the next language learning to begin sooner. The benefits of having the first language under your belt can start accruing while you work on the next one.

While doing projects such as learning languages can be done in parallel, you’re not going to get to that upper inflection point where you start getting big benefits for any of the projects until much further in the future since you’re splitting the time you’re working on any one project. Also, there’s the possibility of “cross-contamination” by which I mean messing up your work on one or more of the projects due to the incorrect application of effort on one into another. An example of cross-contamination in my life was one year in high school where I took both German and French. Both teachers hated this since I’d mix the German into the French class and vice versa. Doing the projects in parallel increases the delay dramatically thus increasing the total cost of delay in getting the benefits.

As a tangent, let me suggest that one of the benefits or completing one project first (to at least the lower inflection point) is that it will enhance the serendipitous connections between projects. So, if you have enough grasp on the first project, connections can become apparent in the second project as congruent points arise. An example in my life is that I attained black belt in Shaolin Kempo (the art I currently study) more than a decade ago. Shortly after that I took classes in historical European martial arts (HEMA) for a while. I was able to compare and contrast techniques between the arts as I continued to advance in each. This led to an increase in my understanding of both arts because I had enough knowledge of one to make those kinds of connections.

The mantra of “complete the first project, then move to the next” has some exceptions. If we come to a point in project A where we’re waiting for someone else, or some event to occur that’s external to the project, then we can put aside project A for project B until that waiting state resolves. Examples of waiting for an external event might be weather, delivery of a part, another person’s completion of an element of the project you need to integrate into the whole, etc. If we’re waiting for inspiration to occur related to project A (letting your subconscious process what you’ve worked on so far), then putting it aside for project B may be a good move. In some cases during longer projects you may find your mental/emotional cost for continuing project A has risen dramatically, and this may prompt a shift to project B until that excess cost state for project A has resolved (if it doesn’t resolve in what you consider an appropriate time you may want to work with a mental health professional).

In Miles’s third post on this general topic “Sequencing of Projects, Continued,” he gives equations that help us determine which project to do first. The conclusion is that we should choose to be done first the job which has the biggest benefit to size-of-job ratio and the biggest benefit to time-to-complete ratio.

If you have a moderately sized job that’ll give a big benefit when complete, that’s a good candidate for doing first. Similarly, if you have a job that’ll give a big benefit compared to the time to complete it, that’s a good candidate for doing first.

Brushing teeth takes about two minutes if done thoroughly. Immediate benefits are the feeling of clean teeth, and the sense of accomplishment at having completed the task. Long term benefits include less time in the dentist’s chair and lower lifetime dental care costs. The comparison of size of job (two minutes per day) to benefits (many hours, thousands of dollars, and possibly significant pain eliminated over the lifetime) suggests this task should be high on the list of projects for your day.

Exercise is a project that has the type of elongated S curve I described earlier. The benefit of a small amount of exercise – 5-10 minutes per day, which can be as simple as walking around the block and swinging your arms a bit – is big over a lifetime according to the research I’ve seen. The benefit of extensive exercise – 30-60 minutes of medium to high effort– is significant but has a much smaller benefit to time ratio. This suggests that a few minutes of moderate exercise should be high on the list of projects for your day, and that more extensive exercise can be further down on your project list.

Both the benefit to size-of job and benefit to time-to-complete ratios should be declining over the series of projects.

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