On (N + 1) & (1.01^365)
Good theory is hard. Linear or non-linear, the only constant is change
“There are decades where nothing happens; and there are weeks where decades happen” – Vladimir Ilyich Lenin
This post touches on the inevitable in everyone’s lives - change. At times, change can happen very suddenly in our lives (dynamic change). Other times, change is gradual, but we might have a hard time accepting or adapting to it.
Change is not always for the “good” - change just is. Change can be good or bad, but how we interpret our life’s events have nothing to do with change itself. Change is the default state of life.
There’s two types of change: linear/static change (not an oxymoron), and also non-linear/dynamic change.
N + 1 (Static Change)
Measuring Progress
The formula N + 1 - take what you have (where you are in life), add one to it (make small change), end up slightly better than you were before.
If your long-term goal is to walk 10,000 steps/day and your current average is 5,400 steps/day, you could aim to walk 5,401 steps the next time. Linear growth, predictable outcomes, measured progress.
Sounds great in theory, but the formula is slow in helping make meaningful progress, in practice. After a year, you’re only walking about N + 365 steps more than you did a year ago - way shy of the goal of walking 10,000 steps/day.
Going the Right Direction
The one-in-60 rule is a rule used by pilots and sailors to gauge how much they should course-correct, if they notice they’re not on-course to their destination.
The rule states that for every 1 degree a plane/ship veers off its course, it misses its target destination by 1 mile for every 60 miles travelled.
Just 1 degree, visualized:
This means that if navigation system was not entirely calibrated, being even 1 degree off from the starting point would lead the plane/ship to end up in a completely different place.
After 100 yards, you’ll be off by 5.2 feet. Not huge, but noticeable.
After a mile, you’ll be off by 92.2 feet. One degree is starting to make a difference.
If you veer off course by 1 degree flying around the equator, you’ll land almost 500 miles off target!
The point here is that a small difference in action, accumulated over a very long time-horizon, makes a huge difference.
1.01^365 (Dynamic Change)
Doing just 1% more everyday, brings you 37x further from where you started.
Doing just 1% less everyday, makes you 1,500x worse from where you started.
While linearity is nice and predictable, the world is non-linear in many ways, and largely unpredictable. Whether it comes to growth, recovery, healing, or even death, you’ll notice that we don’t always change in predictable way:
Humans change a lot as we grow from ages 0 - 25, but our development slows down after that.
If you get a cold or flu, you’ll feel pretty knocked out at first, but will mostly recover in the first few days. The last few days of recovery will be slower than the first few days.
Clients feel better after varying numbers of therapy sessions. The number of sessions you attend doing psychotherapy are not at all predictive of how much better you will ultimately feel. People feel better at different rates, and in a non-linear pattern.
Death can be unexpected. A turkey that gets to eat lots of food everyday might think it is healthy and living its best life, when suddenly it meets its death.
We Make Clocks, Not Time
Theory is our way of attempting to understand the world. Ordinary people and scientists alike have theories about how the world works, all of the time.
Psychology is full of different theories - different ideas and models that try to capture some universal truth about our values, beliefs, personality, behaviours, mental health conditions, ways of healing, and ways of being.
Every therapist has a theory of healing, every standardized test or measure aims to identify some trait believed to be true and of significance.
Humans love thinking that we know what we’re doing. I think theorizing and attempting to predict things as complex as human behaviour, only really makes humans feel better about ourselves, and it might help us sleep a little better at night.
While Psychology and other social sciences have matured over the decades, the replication crisis sheds light on the idea that most proposed theories, even when backed by empiricism and data, don’t seem to hold the test of time.
Why is that?
My theory: Perhaps the simplest problem with our method of theorizing and doing science, is that we use static methods to capture dynamic, human behaviour.
Whether researchers are using standardized tests, statistical analyses, self-reported measures, even brain scan data, most research studies report some evidence for some measurable effect in a given group of people sampled at a specific geographical location tested at a specific point in time.
Of course most research isn’t going to replicate!
When are people ever in the exact same state and circumstances twice?
It’s easy to overlook, but the fact that humans are dynamic and unpredictable is what makes life fun and interesting, in the first place. Otherwise, what separates us from computers and our coming AI overlords?
What makes prediction, understanding change, and measuring progress difficult though, is that we collectively need to learn to think about complex problems non-linearly, and leave our linear thinking heuristics at the door.
While this article tried to linearly lay out the problem of prediction, change, and progress, learning to think about the world non-linearly might be more helpful, but is easier said than done.
