# TimeWise: How to Spend Your Leisure Fruitfully

# Why Are You Reading This Right Now?

Of all the things you could have chosen to do at this moment, you chose to read this. Why? And after reading this, you'll choose another activity. Perhaps walk your dog or cook dinner. With every such choice, you traverse in time one branch in a tree of forking possibilities. How do you decide which branch to take?

You’re reading this right now presumably because you think you’ll get some personal value from it. You can quantify that value, in principle, by assigning a real number called **utility** (from Economics) to it. The higher the utility, the more value you get. But while you're reading this you're also depriving yourself of the utility of doing one of the many alternate activities available to you. That is the **opportunity cost** of reading this now. In theory, if you had perfect knowledge of how much value you get from each of the infinite ways in which you can spend every moment of your time, you could define a personal utility function of time for each possibility. Then, the answer to the question "what should you do now" simply becomes do that which increases the utility to you the most. In other words, choose the path of steepest ascent in the space of utility functions. Actually things are more complicated. For example you may want to maximize utility over your lifetime rather than in this instant (otherwise you would never choose to save for retirement, for example).

Your choice to spend your time reading this article hopefully does provide some utility to you, but surely it does not provide the greatest increase in instantaneous or lifetime utility. Nor is it feasible to precisely measure the increase in utility due to this activity or any other. So is this discussion purely theoretical and you are doomed to a random walk in this bewildering space of choices? I hope not. You can in fact glean a practical strategy from these insights: curb the scope of the optimization and instead balance your time judiciously across core dimensions that you personally value.

# How Would You Like To Spend Your Time?

For most of you, much of your time is already spoken for. For example you have to wake up at a certain time to get ready for work and to get your children to school, you have scheduled meetings and appointments, you have to eat, and so on. If you are fortunate, there are breaks in your day and then you get to choose what you do. How you spend that leisure is an unfettered choice for you to make.

What guidance can you use to make that difficult choice? Start by choosing a small set of **dimensions** that you would like your leisure activities to cover. For example, my dimensions are *exercise *(body)*, thought *(brain)*, meditation* (calm)*, culture *(beauty)*, fun* (enjoyment) and *relations* (social). The dimensions should be non-overlapping so that an activity can be decomposed into contributions to one or more of the dimensions. If you’re familiar with linear algebra, you can think of an activity as a *vector* in the space of your chosen leisure dimensions. The magnitude of the vector is a measure of how strongly the activity contributes to the dimensions. The same class of activity (e.g. going for a run) can contribute differently to the dimensions for different instances of the activity (e.g. yesterday’s run versus today’s run), depending on the how the particular instance transpired (e.g. you ran uphill yesterday and on flat terrain today, so yesterday’s run would have a higher contribution to the exercise dimension compared to the contribution from today’s run). For a given activity you subjectively self-assess the components of the vector i.e. how much the activity contributed to each of the dimensions. A useful way to calibrate the dimensional contributions is to consider your peak activity for each dimension (e.g. a 6 mph run is my sustained peak for the exercise dimension). Then, for an activity, estimate what percentage of the peak can be attributed for each dimension (e.g. a neighborhood dog walk has a ~20% exercise component for me). Here are some examples:

Each activity instance consumes some amount of time in a day. The component of the activity vector along each dimension determines the equivalent time spent on that dimension. So, from the example above, if you play 100 minutes of soccer, that is equivalent to 90 minutes of *exercise *(since 0.9 * 100 = 90), 70 minutes of *fun* (since 0.7 * 100 = 70) and 50 minutes of *relations* (since 0.5 * 100 = 50).

Given the history of time spent on each dimension, we can determine an average daily time spent on that dimension. The average should be a weighted average such that older contributions to the dimension are less significant than more recent contributions (e.g. I need less exercise today if I played a hard game of soccer yesterday as opposed to a week ago). An activity attenuates with how long ago you did it. Model this attenuation as an exponential decay with a *half-life* for each dimension. A half-life of D days means that the contribution from from an activity D days ago is half the contribution from the same activity today. In this way you can compute an **exponentially weighted moving average** of the daily time spent on each dimension.

Now that we have formulated leisure dimensions, how an activity contributes to the dimensions, and how we can summarize a daily time spent on a dimension (taking into account the full history of contributions to the dimension), we’re ready to turn our attention to the utility function that determines the value we get for the amount of time we spend on a dimension. Define a **utility function** for the leisure time spent on each of the dimensions:

Each utility function should have the following properties:

1. There should be an optimal amount of time at which the utility of spending time on that dimension is maximized. Any further time spent on that dimension should reduce the utility. This property accounts for the intuition that too much of something is bad. Also, there's an opportunity cost to spending more time on a dimension at the exclusion of other dimensions.

2. There should be diminishing returns the closer you get to spending the optimal amount of time on a dimension. This accounts for the fact that the more you’ve neglected a dimension the more value you’ll get by spending time on it.

A simple function (by no means unique) that satisfies the above properties is

If you’re familiar with calculus, you can see from the first and second derivatives of the above function how the two required properties are satisfied. The rate of change of utility with time shows that the utility increases as the time spent goes from 0 to the optimal time, reaches a maximum at the optimal time and then decreases if more time is spent on that dimension. The rate of the rate of change shows that the utility “decelerates” as the time spent goes from 0 to the optimal time.

Now you have all the ingredients to help guide how you should spend your leisure:

- Choose a small set of non-overlapping leisure dimensions.
- For each of your leisure dimensions, configure the half-life that attenuates old activity contributions to that dimension. Shorter the half-life of the daily weighted-average, the more frequently you want to spend time on that dimension. For example, I value some kind of physical exercise every day so I choose a half-life of 1 day for my exercise dimension.
- For each of your leisure dimensions, configure the maximum utility of contributions to that dimension. Higher the maximum utility the more you value that dimension. Only relative utility values between different dimensions matter, the absolute utility value does not. For example, if you value exercise twice as more as fun you can choose 100 for the maximum utility of exercise and 50 for the maximum utility of fun.
- For each of your leisure dimensions, configure the optimal weighted-average daily time spent on that dimension. For example, I choose a daily average of 40 minutes of exercise per day and contributions from dog walks, running, cycling, etc. help me reach that goal.
- Track each leisure activity that contribute to one or more of your dimensions: the activity date, duration and magnitude of the contribution (compared to the peak contribution) to each dimension. For example, a 30 minute run on a certain date with a 80% contribution to exercise (since you ran slightly slower than your peak pace) and no contributions to any other dimension.
- Compute your current point on the utility curve for each dimension, using the computed weighted daily average of time spent on each dimension.
- When leisure is available to you, consult where you currently are on the utility curve for each dimension and choose an activity that will increase the utility most significantly. For example, given the following snapshot of my leisure history, I’ll most benefit from an activity that is thought intensive (for example, writing this article).

# How Can You Use This?

How can you easily track your activities, their contributions to your leisure dimensions, the exponentially-weighted-average time spent per day on each dimension, where on the utility curves you lie and how you can increase the utility the most? To get you started, I’ve created a Google spreadsheet (link) that you can make a copy of.

There are two visible sheets (‘Activities’ and ‘Dimensions’) and a couple of hidden ones for calculations and auxiliary data. The yellow-highlighted cells are modifiable. Use the ‘Dimensions’ sheet to configure your own leisure dimensions. It is seeded with the default set of 6 dimensions described in this article. You can change the existing dimensions and define up to 10 dimensions according to your personal goals. For each dimension you should specify the half-life for the exponentially-weighted-average time spent, the maximum utility and the optimal daily-average duration.

Use the ‘Activities’ sheet to log your leisure activities, view where you are on the utility curve for each dimension and which dimensions you should spend more time on to increase the utility to you.

So give it a try and see if this helps you lead a more balanced, fulfilled life (at least in leisure). Here’s to being time wise!