Understanding “Enough”

Concept #1: Inputs that are necessary but not sufficient reach a point of diminishing returns.

The implication of this asymptotic increase is that when a positive relationship between input and output is detectable (e.g. imagine sleeping in gives you more energy the next day), you’re on the “not enough” or “enough” portions of the curve. If there’s no detectable relationship between input and output (e.g. imagine drinking coffee isn’t helping to wake you up), you’re on the “more than enough” portion of the curve.

To continue using health as an example output, physical fitness is necessary but not sufficient for good health. At the population level, aerobic fitness is a powerful predictor of mortality. This positive relationship between fitness and health suggests that most of us are not fit enough. Aerobic fitness is improved by physical activity, suggesting that one plausible limiting factor to our health at the population level is that we’re not physically active enough.

Consistent with these considerations, less than 5% of American adults reach the the CDC recommendation of 150 minutes per week of moderate physical activity (about 10,000 steps per day). Graphically speaking, most of us are on the “not enough” portion of the physical activity vs health curve. As for athletes performing much more than the recommended daily minimum of physical activity, it is unclear if there are any additional benefits to their health, consistent with the idea there being a point of diminishing returns in the physical activity vs health relationship.

But let’s consider an additional input variable in our example- diet. Exercise will only do so much for your health if you eat at McDonald’s three times per day. This is essentially just a rephrasing of “necessary but not sufficient”, and there are implications beyond just the existence of a point of diminishing returns.

Concept #2: Increases in any input yield increased maximal output.

Generally speaking, if you increase one input variable, you enable increased returns from all other inputs as well. If you clean up your diet, working out will give you greater increases in fitness. If you improve your people skills, your hard work is much more likely to pay off professionally. Increases in one input increase sensitivity to increases in other inputs. Because any input can become rate-limiting, the theoretical maximum output increases with an increase in any input parameter.

Now here’s where it gets interesting- the reason that this last concept works is because if you increase one input by enough, other inputs then become rate-limiting and fall along the “not enough” portion of the curve. This is true even if those other inputs didn’t actually themselves change. For example, if you’re sleeping 5 hours per night and get zero exercise, the zero exercise part of that lifestyle may be the limiting factor in your health. If you then start running 5 miles per day, the 5 hours per night sleep schedule may then become the new limiting factor to your health, even though it wasn’t previously. This is the basis for continuous improvement- continually finding and addressing each new limiting factor.

Of course, inputs come at a cost. Working hard is, well, hard. Exercise and sleep both take up valuable time that could be used for other productive activities. When you’re focused on getting enough sleep or earning enough money, you want to be as efficient as possible.

For our next analysis, let’s continue working with a two-input, one-output model system, and assume for simplicity that 1) the costs of both inputs scale linearly (i.e. doubling the input also doubles the cost) and 2) both inputs are equally costly. In that case the efficiency of your system can be defined as the output divided by the sum of the inputs.

Concept #3: Outputs are obtained most efficiently when no single input is rate-limiting.

When dividing an asymptotically increasing output by linearly increasing inputs, the resulting curve has a maximum near the point of diminishing returns. In the series conductors model, the greatest flux can be achieved with the least cumulative conductance if all conductances are equal. This produces a situation where control is distributed among the inputs, and changes in any input can be compensated by changes in other inputs.

For a real world example, you’ll make the most efficient use of mental energy at work if you’re focused on the technical and interpersonal aspects of your job each up to, but not beyond, their corresponding points of diminishing returns in productivity. You’ll achieve the greatest improvements in health with the least lifestyle modification if you focus up to, but not beyond, the points of diminishing returns each of diet, exercise, and sleep. If you’re operating efficiently, every input will yield increased outputs, and a minor decrease in one input can be fully compensated by minor increases in other inputs.

In same cases, the costs of your inputs sometimes directly oppose the benefits of your output of interest. For example, although most people get so little physical activity that it’s becoming a major public health issue, the energetic costs of running are great enough that it’s also very possible to run yourself to death. The job duties you’d have to perform to advance may become demoralizing enough to outweigh the happiness that money can buy. In cases like these, it may be more useful to think in terms of net benefit rather than efficiency. Using the same assumptions as before (i.e. equally costly, linearly increasing inputs), the net benefit is the output minus the sum of inputs.

Concept #4: With costly inputs, too much is worse than too litte, but slightly more than enough may still be a good thing.

When looking at this relationship, two things are immediately apparent: 1) too much is worse than too little, and 2) the relationship changes as the costliness of your inputs changes. With a high enough per-input cost, the net benefit may always be negative. The point at which maximum net benefit is achieved also depends upon the costliness of inputs. The maximum net benefit can lie beyond the point of diminishing returns (and thus beyond peak efficiency) in systems with low-cost inputs.

So what does this mean in your daily life? It means, for example, that while sedentarism will kill you years from now, overexertion can kill you today, and yet the maximum benefits from exercise may actually come from mild overexertion. It means that while slacking off will get you fired a few months or weeks from now, trying too hard and screwing up badly can get you fired today, and yet the maximum benefits from hard work may still come from mild overreach.

Generally speaking- way too much is far worse than way to little, but a little bit more than enough may the best of all.

The differences that the degree of costliness make operate such that if you’re sick and the energetic costs of exercise are thus more significant, the maximum benefits from exercise may occur with a less vigorous bout. If a relative just died, the maximum emotional benefits from productivity may occur with a less productive workday. Conversely, when inputs are less costly, the potential benefits of mild overreach increase. The easier it is to increase an input, the more worthwhile it may be to continue increasing beyond the point of diminishing returns.

Concept #5: Focus your energies on inputs that yield tangibly increased outputs.

So far, I’ve discussed the concepts that 1) there will often be a diminishing returns for any single input, 2) increases in a rate-limiting input tend to increase the rate of returns for other inputs, 3) outputs are often achieved most efficiently when process control is distributed among several inputs rather than a single rate-limiting input, 4) way too much is usually worse than way too little, and 5) a bit more than enough may be the best of all.

How do you put these ideas to work in your life? Easy:

In order to improve any of life’s outputs, its useful to focus on one necessary input at a time. If the outcome tangibly improves with investment in the input you’re focused on, double down. I think that most people do this part instinctively, with inputs that require self-discipline being the obvious exceptions.

Where I often see others trip up (and often trip up myself) is with the converse: if investment in the input you’re focused on doesn’t tangibly improve outcomes, it’s time to focus on another input instead. Working 80 hours a week and getting nowhere? Time to try a different approach to the project. Drinking coffee after lunch but still feeling drowsy all afternoon? Maybe it’s time to try taking a walk after lunch instead.

If you can routinely double down on whatever yields increasing returns and shift focus away from whatever doesn’t, you’re well-situated to continuously improve in life. Even if each new input you choose to focus on is chosen at random, your attention will linger where it is most needed, thus continually addressing each new limiting factor. Because there will be some delay before you’ve realized that your returns are no longer increasing, you’ll naturally shift focus when you’ve reached that “a little more than enough” optimum.

In addition to providing a useful heuristic for increasing returns from your efforts, these concepts can also be applied to more abstract problem solving. In my dissertation, for example, we started with the question of why oxygen uptake by exercising muscle is reduced in diabetes. First, we focused on the possibility that not enough blood was reaching the muscle. It turns out that even though muscle blood flow is usually reduced in diabetes, there’s no detectable input-output relationship between maximal blood flow and maximal oxygen uptake in diabetes. Time to look at another parameter, then- what about the muscles’ demand for oxygen? We repeated this process several times until we determined that an inefficient distribution of blood flow within the muscle is the most likely limiting factor.

Concept #6: Think of inputs as outputs in their own right, each with several necessary inputs of their own.

Increasing your investment in a rate-limiting input is not always a self-explanatory process. Let’s say you’re having trouble getting your work done. Maybe you’re perfectly capable of doing the work, and you’re just not actually getting it done. In that case, “work harder” is the obvious way to invest in the rate-limiting input, but it may not always be that easy. Maybe you’re spending all day on the project, but you just can’t make yourself focus on it. In that case, the best input invest in for maximal returns might be your motivation or energy levels. Sometimes you’ll encounter cascades of converging inputs in which the necessary inputs for your desired output have necessary constituent inputs of their own.

As an example of this concept, let’s take a look at the hypothetical model I’ve drawn of converging inputs leading to professional advancement. Start at the top. If you want to advance further in the workplace, you may find that either your level of achievement or other people’s opinions of you are rate limiting. For the sake of the argument, let’s say its a matter of your reputation. Could you improve your reputation more with better social skills or with a better attitude? If attitude is the limiting factor, is that because you tend to give up easily? If so, focusing on improving your persistence may be the optimal strategy with which to achieve greater professional advancement.

For another example, let’s say you wish you had more energy. Personal energy tends to be a function of both physical and mental health. Given that about half of American adults have a chronic disease these days, physical health is likely to be the more common limiting factor among my readers. Physical health requires a good diet and some degree of physical fitness. For the sake of the argument, let’s say you’re eating very well. What’s the limiting factor to your fitness? Maybe you already lift weights. In this hypothetical, the best way to improve your overall energy levels could then be to improve your stamina.

In both examples, you start at the top- what do you really want? What inputs do you need in order to achieve that top-level output? Which input is the limiting factor? What second-order inputs are needed to improve this first-order limiting factor? Which of these second-order inputs is rate limiting? Repeat this process iteratively until you’ve found a self-explanatory, bottom-level input that you can focus on improving. Once you stop seeing returns from this bottom-level input, return to the top level and repeat.