### The Traveling Zero

No, this isn’t the story of how our modern concept of “zero” as value and placeholder originated in India and made its way to us via the Persian scholar Al-Khwarizmi and the medieval Italian mathematician Fibonacci. It’s about how our concept of zero point, the neutral baseline compared to which we define positive and negative, can wander around over time.My grandparents used to have a wind-up clock in their dining room that ticked loudly and chimed every quarter-hour; every time I went to stay with them, that clock would keep me awake long into the first night, but eventually I wouldn’t notice it anymore except vaguely to register the passage of time. After I returned to my parents’ house, the silence of my room would seem bizarrely obtrusive. What was happening was my brain adjusting its perception of normal background noise: in order to cope with a new constant stimulus, it bumped up that baseline so the clock wouldn’t keep demanding my attention. When I returned to a quieter room, my brain registered the silence as some kind of anti-noise.There are a lot of ways to use this traveling-zero phenomenon for good. When you do progressively harder exercise, your body adjusts so that what was once challenging starts to feel easy. If you bump up the speed a little on an audiobook, it sounds normal again after a few minutes and you can bump it up even faster. The becoming-a-salad-eater strategy I outlined a few weeks ago works because once each new level feels normal, the next doesn’t look so hard. And my goal for getting better at time management is to gradually introduce more and more structure to my day, so that I don’t reflexively balk at planning so many things.

In fact, this phenomenon can appear with any kind of learning. I remember when I was young, my uncle corrected my misconception that when you double a number, its square doubles too; in fact, it increases by a factor of four:

$(2\times n)^2 = (2\times n) \times (2 \times n) = (2\times 2) \times (n\times n) = 4\times n^2.$

It was embarrassing to have believed something so obviously false in retrospect. In her book How to Bake Pi, math professor Eugenia Cheng says of the feeling “Oh, now you point that out, it’s so obvious—why didn’t I see that before?”:

Well, as I say to my students, feeling stupid for not having understood something before just shows that you are now cleverer than you were then.

In other words, once you’ve learned new tools for thinking about something, shifting up your baseline level of analysis, it feels more like your past self has gotten stupider than that your present self has gotten smarter. But once you stop to recognize how far you’ve really come, it becomes a lot more fun to keep going!

But there’s a danger to the traveling zero as well. You may be familiar with the idea of lifestyle inflation, the way spending tends to rise with income so that people never seem to feel like they’re making enough: the idea is that when your income is low, you don’t expect a lot of luxuries, but when your income increases they stop feeling like luxuries and more like normal spending.

###### Lifestyle inflation: even if your income increases as in the above graph, it might feel more like the graph below:

You may also have heard that when looking for a new home, people put too much emphasis on features like new appliances and too little on how far they have to drive to work: it’s easy to stop noticing the furniture after a while—your baseline will rise or fall to match them—but you can’t stop paying attention to the drive.

There’s another danger in that when populations are divided, their zeros can drift in different directions. That’s how proto-Germanic became modern German, Swedish, Danish, Norwegian, Dutch, Afrikaans, etc.; in each community, the normal-sounding way of speaking gradually shifted over time, and now these languages are mostly mutually unintelligible.

And if we’re not careful, the U.S. population is in danger of drifting apart ideologically to the point where we cannot understand each other’s world-views; Google searches for echo chamber and filter bubble more than doubled in the past week as people try to understand why there are so many more different-thinking people than they realized. (Check out Blue Feed, Red Feed for a taste of the “other” side, whichever that is.) Several measures have been suggested for how Facebook, a common target of filter-bubble blame, could remedy its feed algorithm by suggesting posts it knows disagree with your views, but I think each of us also has a responsibility to remember that just because what we see appears to be divided into “neutral” and “extremist” doesn’t mean it doesn’t look exactly the same way from the other side.

## 5 thoughts on “The Traveling Zero”

1. Nick says:

Your final picture suggests a 2D projection of René Thom’s cusp catastrophe…

Liked by 1 person

1. I was indeed thinking of the word “bifurcation” as I drew it…

Like

2. Chip Watkins says:

Very perceptive piece–thanks!

Like