You Can't Hold Things Steady In Time

Life Aug 17, 2021

Life is not static. It's constantly changing. My engineering mind sees the world in terms of rates of change: if you don't grow something, you lose it.

Rarely will you be able to preserve something. Instead you will either gain more of it or lose some. Trying to freeze something in place is futile.

This can range from skills to knowledge to finances.

Either you are using a skill, practising it regularly, and growing your ability to perform it. Or you are losing the skill as it fades into memory.

Likewise money tends to be up or down. Either growing your assets through income and appreciation, or leaking money through expenses and inflation. Positive or negative rates of change, but not zero, not stationary, not a flat line.

To maintain something's level you need to put in repeated work. Otherwise it languishes.

The Bumpy Curve of Using and Losing a Skill

There's this obnoxious limitation of humanity called the forgetting curve. It posits that people forget newly acquired knowledge within days or weeks without repeated exposure to the material.

If you take a lesson from the forgetting curve, it should be that spaced repetition helps you retain skills and knowledge. If you've ever been told "practise makes permanent" you hopefully know that the repetition combats the decline of your skills.

If you're periodically using a skill, what you end up with is a bumpy curve of your skill over time:

Every rising section is use/learning and every falling section is disuse

A few things become apparent with this graph. One is that there's an average level of skill you have, somewhere between your peak performance and trough of performance.

Another thing is that there's a warm-up period where you shake off the rust and reacquaint yourself with your skills. This is a factor into why it's often faster to make a prototype and then the real thing, rather than diving straight for the final product.

Rates of change make up your skill curve, so if you know some pre-calculus you know that there are turning points and inflection points.

What is the Turning Point and the Inflection Point?

Turning points are easy to spot. They're simply where you reverse the direction of a trend:

The local peaks and troughs are turning points, where the curve reverses direction

You might start off gaining, but at some point you stop working on your skill and it starts to atrophy. This spot where it changes from positive to negative rates of change is the turning point.

Inflection points are a little more tricky to think about. They're the spot where "curvature changes sign."

If you look at the slope of the graph below, you'll notice that it starts off steep, goes flat, then gets steep again. That's a changing curvature, going from negative to positive:

The slope of the line goes from decreasing (levelling out) to increasing (growing faster) at x=0

This kind of point can crop up when you plateau with a skill. For a short while you may be stuck, not getting better nor worse. Then you have a breakthrough and start improving again.

Plateaus and inflection points are also a core component of S-curves. Though the S-curve's inflection point is not stationary. I have a whole article talking about the S-curve and some implications here:

The Sigmoid Function in Business aka the S-Curve
There’s much talk in the FIRE world about exponential growth. Yet that is only half the story, because in the real world the sigmoid reigns supreme.
Plateau shaped growth trends are a consequence of the Sigmoid Function

What Rates of Change Mean For Finances

It's easy for me to get sucked into the world of personal finances, where we nerds discuss the differences between savings rates like 15% and 50%.

Examining the nuance of savings rates is only helpful after you've attained the agency stage of financial independence. When you're just starting out, it's more important to say whether you're moving in the right direction or not.

That's the first question for rates of change in finances: are you growing or shrinking your net worth?

If you are dwindling and burning down assets, then you desperately need to reverse course. That's a turning point. Otherwise if you are growing, you are in a good position.

There might be ups and downs to your finances, especially if you work something unreliable like contract work. What matters is that you're able to see past the random walk to see the overall trend upward or downward.

Then as you get further into the positive territory, you have to ask yourself how well you're doing. Are your finances speeding up or slowing down with inflection points? Have they hit their maximum speed?

Is there more you could be doing? Is it even worthwhile to do more, or are you content?

You should always keep a critical eye on your finances. You need discipline to keep it growing, because the alternative is to let it dwindle to inflationary pressures and lifestyle inflation.

It's one thing to say that you have "enough," and stop working to grow your assets. Yet it's another thing entirely to turn away from discipline and feedback loops.

You should always be asking yourself questions.

Questions to Ask for Retirement: A Taxonomy of FIRE Strategy
FIRE is simple as at the core it consists of two goals: cut your expenses, and grow your income. To explore these nuances to strategy, I’ve come up with a few questions that help classify different FIRE strategies.
Question your financial strategy to make it better



Mistress of the Home, responsible for all matters financial. A loving Domme tempered with ambition and attention to detail.