Why Do We Keep Missing Goals?

In mathematics, the word infinitesimal is defined as an arbitrary value close to but greater than zero. What does this word have to do with missing goals in life? Let’s find out.

The Role of Goals in Life

Most of us wish to be doing better in life. More specifically, we sort out areas of interest that we would like to improve in. For some, it may be career related progress in fields of technical or managerial expertise. For others, it might be hobby related progress in sports such as golf or tennis or just learning to play a new music instrument. Although we do not always envisage a clear path, most of the time, we manage to envisage a clear goal associated with our field(s) of interest. These goals in turn drive our intrinsic desire to practice or put in the effort. When we set very high goals, we are likely to end up being disappointed, but still manage more progress than if we had set a lower goal. On the contrary, if we set low bars as goals, we are likely to end up being satisfied, but make limited objective progress (underperformance). So where do we balance our goals? Spoiler alert: The key is not in balancing the difficulty of goals.

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Envisaging Progress Mathematically – Why We Keep Missing Goals

Remember when I told you that we do not always envisage clear pathways of progress? This is because human beings are innate linear thinkers, and the path of progress to a goal is mostly a non-linear process. By this tendency of ours, we aim for goals using linear functions, and when we setup challenging goals, we end up being overwhelmed by the linear forecast for effort required to achieve said goals. In reality, geometric progression takes effect, and the progress is non-linear. Below, you can find an image that explains this phenomenon illustratively (not to any particular scale):

It is shown illustratively above that human intuition (which normally extrapolates by linear progression) grossly underestimates the time required to achieve goals compared against geometric progression.

What’s The Catch Here?

If it were as simple as understanding that progress in general is likely geometric rather than linear, everybody should be nailing their goals. But this isn’t the case. Why is this so? This is because the above illustration only works when progress has continuity. In the absence of continuity, that is, if we introduce breaks in progress, it is likely to look like the illustration below:

As you might have guessed, as progress is likely geometric, so is regression also likely geometric. Each break or discontinuity (mathematical term) in effort / action / engagement leads to geometric regression, which leads to a poor progress path towards the ultimate goal.

Change The Goal To Stop Missing Goals

If our intuition is likely misleading us, and if our original goals are likely overwhelming or underwhelming us, what if we change our goals to achieve continuity instead? In other words, what if the goal is to stay on the task regardless of how much ever little effort we are able to manage per stint? I would not blame you if you remain skeptical about spending a minute a day practicing your guitar. But let us look at the effect of continuous geometric progression using a very simple, yet profound example. Let’s take an exponential function over 365 days (a year), with an effort intensity of 1, 1.01 (0.01 above mean effort), and 0.99 (0.01 below mean effort) respectively. How much do you expect the effort increase or decrease of 0.01 would have an effect in the second and third case respectively? The answer:

 (1)³⁶⁵ = 1

(1.01)³⁶⁵ = 37.783434433

(0.99)³⁶⁵ = 0.02551796445

If you are surprised over the difference you see, it is yet another example of how much our intuition could be misleading us when it comes to non-linear versus linear thinking. 0.01 here represents infinitesimal progression or regression. Why not consider continuous involvement as the goal itself, just for the sake of progress?

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