Seeing the world through log scale
One of the most surprising outcomes of this Covid-19 pandemic is probably a lot more homo sapiens learned to see graphs on logarithmic scale than any high-school math teacher could ever have dreamed of.
But math teachers around the world should not cheer too early. Most people learned to see Covid-19 growth curves on log scale not because they really grasp the essence of exponential growth — but because the curves look less scary when plotted on log scale.
The truth is: most, if not all, of the things that matter in this modern world are better seen through log scale. Those that make sense on linear scales usually don’t matter.
Things that make more sense on log scales are things that scale.
Things that make more sense on linear scales are things that don’t scale.
A few examples of things that don’t scale:
- School grades
- Ranking in restaurant guides
- Graduate salaries
- Post-MBA salaries
- Prices of packaged cereals
- Prices of SUVs
- IQ of a homo sapiens
All of the above are best plotted on linear scale. If plotted on log scale, the samples will clutter into a small dense group of dots. It would not make any sense at all. These are things that don’t scale.
A few examples of things that scale:
- Book sales
- CD sales (before the invention of MP3)
- MP3 downloads (before the invention of streaming services)
- Market caps or valuations of streaming service providers
- Net worths of homo sapiens
- Homo sapiens infected by coronavirus
- Potential collateral damages due to homo sapiens infected by coronavirus
- Additional potential damages due to an unusually low-IQ homo sapiens currently occupying the White House
Plotting any of the above on linear scale, you run out of papers very quickly. The only way to make sense of it is to plot them on log scale.
For example, it might be that for all CDs on earth that sold more than 1,000 copies, there will be 1% that sold more than 10,000 copies.
For those CDs that sold more 10,000 copies, there will be 1% that sold more than 100,000 copies.
For those CDs that sold more 100,000 copies, there will be 1% that sold more than 1,000,000 copies.
For those CDs that sold more 100,000 copies, there will be 1% that sold more than 10,000,000 copies.
There’s no way to fit the samples of the last group (>10M) and the samples of the first group (<10,000) on the same linear-scale chart.
In other words, there’s no way to plot Michael Jackson’s “Thriller”, Pink Floyd’s “Dark Side of the Moon” together with the debut (and final) CD made by a random garage band in Shibuya on a linear-scale chart, coz’ the number difference is more than 10,000 times.
Switch to log scale, you can do so properly, as the difference shrinks to 4 divisions.
These are the things that scale.
I’ll leave it to the readers to do the same brainstorming thinking through the other examples I mentioned as things that scale — especially the last one.
Unfortunately, even though we’re living in a world more and more dominated by things that scale, homo sapiens are not born with brains that understand scalability by default.
When we evolved into homo sapiens 300,000 years ago in Africa, the daily mission of our brains were:
- secure enough meat for the family
- make decisions whether to move to another place that might have more food
- calculate how many storable foods are needed to survive the snowy winter
- estimate how much woods would be needed to keep the family warm in the night and cook the meat
- making split-second decisions to either run or climb the trees upon seeing a wild bear
None of the above are things that scale. It’s therefore safe to say that our DNA does not come with natural understanding of things that scale.
In fact, a huge part of human history remains dominated by things that don’t scale.
The graph above was plotted in linear scale for me to explain the point. As you can see that the World GDP remains flat at the bottom ($0 trillion) for a substantial time for the two millennia, until around 1500 when it started to rise above the floor.
Then industrial revolution happened, coupled with capitalism. The world GDP started to grow exponentially toward the right side of the chart.
World GDP numbers are things that scale.
Note that plotting the graph on log scale, we still see something that look exponential. This is because there are two compounding exponential in World GDP numbers. Both world population and GDP per capita increases exponentially after industrial revolution and capitalism were born.
All economists and most financiers are very familiar with these charts and the rationales behind the compound exponential growths.
But most people from other walks of life have never seen them or thought about them. They mostly observe the day-to-day lives of themselves and their loved ones. What they see is linear changes.
For example, my father was born as the first son of a very poor family. My grand parents didn’t learn how to read and write — my grandpa eventually learned how to read and write the ultra complicated traditional Chinese all by himself — and had to work many different jobs to keep the family fed.
My father studied and worked very hard to get families out of poverty. Eventually allowing a comfortable life growing up for me and my brothers, and comfortable retirement years for my grandparents, who did not have any pension.
I then benefited from this life my father afforded me, continued to study hard and work hard, but also took more risks, which eventually allow me to become a Venture Capitalist.
But when my father and I sat down for a cup of tea to talk about our lives, he would not think about scalability. He would just compare how much “salary” I make (though more correctly, how much my partners and I pay ourselves), how does that compare to the cost of an apartment in Paris, and how were these things in his days.
This lack of understanding of things that scale was fine at my father’s generation, as Taiwan was experiencing hyper growth and evolving into a modern democracy with capitalism.
It does not, however sadly, apply to most Taiwanese of my generation, including my younger brother, who works at the largest travel agency in Taiwan.
Not understanding things that scale would lead to frustration in a lot of people of this generation, including the OccupyWallStreet people as well as many of the die-hard Trumpsters. Despite these two groups of people are probably quite different in their composition, their anger both stem from the lack of understanding of things that scale.
I consider myself a lucky person. Whether in my previous career as an engineer/entrepreneur, or in my current job as a VC, things that scale, or scalability, are at the core of everything we do.
Everyday I am seeing people around me on the way to become millionaires, billionaires or bankrupted. I do not expect to see them pondering on whether to another job that is 2.7km more distant but will pay them 5.71% more annual salary and with a better healthcare coverage — okay I know a better healthcare coverage in US could cost a lot more than the 5.71% salary increase, but still…
Everyday I see these people around me through log scale, just like I see everything in my life.
If you haven’t done so, you should, too.
p.s. For those that are more read, if you find this article reeking pungent odor similar to that of Nassim Taleb, let’s say his 7 books remain my top recommendations for many people.
