Why Every Moment Looks Like a Turning Point in Exponential Growth

You're probably familiar with charts like these:

The gist is always the same:

• "Before" growth was slow
• "Future" growth will be fast
• The current moment represents a turning point

One of the assumptions here is that the data is indeed exponential (it could just as well turn out to be an S-curve instead of a J-curve). And in addition the author(s) seemingly know about the future.

Let's ignore reality for a moment and assume for simplicity that indeed the authors are correct and the phenomenon they're writing about is indeed exponential in both the past and the future.

My big annoyance is that while those charts are technically correct, they imply that there is something special about the current moment and that this is THE moment where we switch from slow growth to fast growth.

In exponential growth, there's nothing special about the current moment. You can pick any time period on an exponential graph and those graphs will always look the same!

I will prove it to you.

Refresher on exponential growth

Skip this section if you don't need a refresher on exponential growth

Before we delve into the explainer, let's briefly refresh on what exponential growth is. Exponential growth refers to a pattern of data that shows greater increases with passing time, creating a curve of an exponential nature. In other words, it's a pattern of growth where the quantity increases by a consistent percentage rate over a given period of time.

For instance, if you have $100 and it grows by 5% each year, the first year you'll have $105, the next year you'll have $110.25, and so on. This might not seem like much of a difference at first, but over time, the amount will become significantly larger due to the effect of compounding. This is the essence of exponential growth - it accelerates over time, as the quantity grows based on its current value.

This concept is widely used in various fields including economics, biology, and technology, among others. However, while exponential growth can be a powerful tool for understanding and predicting trends, it's also important to interpret it correctly, as we'll discuss in this article.

Some Data & Graphs

Let's generate some data to illustrate what I mean.

Let's create a data set for 200 data points to represent yearly data from 1900-2100. We use the formula y=r?x to calculate the value for each year:

• x = year
• r = growth rate (I picked a growth rate of 1.5 (150%) for the example but any will work)
• y = the value of whatever the subject is you're interested in.

See here for the data sheet. ALL charts below will use this same data set.

Now let's zoom in on the data for time periods of say 20 years.

Let's start with 1900-1920. Not much seems to have happened before 1910, but look at that growth after 1915, that most have been an amazing period of growth!

Can't wait to look at the period right after: 1920-1940. Not much seems to be happening 1920-1930... But it skyrocketed again after 1935!

So was the first chart wrong? It doesn't seem to flow into this second chart. Did growth slow down?

No, the growth is still the same factor 1.5x. But look at the vertical axis... We're talking about exponential growth so these numbers go up quickly... So quick that in the following charts I'll be using the scientific notation to represent y. So 406561177535215000 will be shown as 4.07E+17.

Ok so there was some impressive growth in the early 1900's, but let's look at the early 2000's, there should be much more growth visible now right?

I assume that by now, you're getting the point: No matter which timeslot we pick, the chart for exponential growth looks the same.

Let's perform a final check by examining the periods from 2060-2080 and 2080-2100:

Same story here.

Please note that the fluctuations you see on the right axis of the charts are due to Google Sheets' arbitrary automatic selection of the maximum value for that axis, but it doesn't influence the shape.

Do exponential graphs ALWAYS look the same?

No. Interestingly, the charts starts to look different when we use different time periods.

If we consider a longer period, it seems like nothing significant will happen in the upcoming years, and we'll have to wait until the 2090s when things will really start to accelerate.

Alternatively, if we consider a shorter period, it seems like there is definitely linear growth, but not much exponential happening here.

So why then do all those "you are now here at this infliction point" graphs look like the first images in this article?

Because the authors in those articles want to trick you in believing that something big happened recently/will happen soon.

And they're not necesserily wrong, it's just that this is always the case when it comes to exponential growth. That's it's main feature. And of coruse they conveniently leave that part out.

Conclusion

While exponential growth charts can be a useful tool for visualizing and understanding trends over time, it's crucial to interpret them correctly.

These charts, by their very nature, will always show a period of rapid growth following a period of slower growth, regardless of the time period chosen.

This can lead to the misconception that the current moment is a unique turning point in terms of growth, which is not the case.

Remember, in terms of exponential growth, there are no actual kinks in the data representing a before and after.

There's nothing inherently special about "today".

The pattern of exponential growth remains consistent over time, and any point on the curve can appear to be a significant turning point when viewed in isolation.

So, don't let these charts trick you into thinking that "today" is a unique turning point. Instead, use them as a tool to understand trends and make informed decisions about the future.

Having said that, remember this Chinese proverb:

The best time to plant a tree was?20 years ago. The second best time is today.

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