Category Archives: Math

My Dictum and Your Blind Spots

In Thinking Fast and Slow (one of my 5 behavioral economics must-reads), Kahneman lays out the memorable idea that “What You See Is All There Is.” He explains it nicely in a brief interview:

WYSIATI means that we use the information we have as if it is the only information. We don’t spend much time saying, “Well, there is much we don’t know.”

These are the famous unknown unknowns that I’ve written about— the gaps or blind spots you wouldn’t think to look for. These are so important that I think it’s worth updating Asimov’s Dictum: “The most exciting phrase to hear in science, the one that heralds new discoveries, is not “eureka!” but “that’s interesting…” “Similarly, Potok’s Dictum is that whenever you’re planning, evaluating, or decision-making:

The most exciting phrase that heralds good decision-making is not “here’s the answer” but “oh, I hadn’t thought of that.”

Whenever a new idea, perspective, or fact appears, treat it carefully and feed your inner pigeon so that you learn to keep generating them! A useful addition to your cognitive toolkit would be a set of ways to find those blindspots you would otherwise totally ignore. Here are a few I’ve thought of or seen elsewhere:

  1. Explain it to a child
  2. Ask a third party with “middle-level” knowledge of the issue: not an expert, but not a child.
  3. Find a new taxonomy to organize everything you know about the issue — the “worse” it seems, the better. For example, if you’re planning a project chronologically, try to list all the aspects of the project by department or division instead.
  4. Perform a premortem: ask yourself “If this project fails spectacularly, what will have caused it?”
  5. Twiddle the knobs a la Daniel Dennett’s must-read advice about Intuition Pumps, or Polya’s guidelines for understanding mathematics. Change each part of what you know — sometimes the extreme cases — to see what happens. “What if we had 10 years to do this? What if we only had three days?” “What if only 5 people show up to our event? What about 50, or 500, or 5,000?” Most of these questions will be a waste of time but a few might completely change the way you’ve been thinking.

Readers: how do you find blind spots? What tools should I add to this list? Have you ever completely overlooked something that was obvious in retrospect?

Mathematical Decision-Making

Whenever you make a decision you have to consider a universe of facts. Suppose you’re trying to decide where to go on vacation.

First you might make a list of all the cities you would consider as a vacation spot and all the facts you know about them. These are the integers, and you can get pretty far with a few simple operations. You know that Paris has great museums and London has bad food and Berlin has great nightlife.

But there are also huge gaps in the facts you know. If I teach you division, you can turn the facts you know into a much larger set of facts you don’t know — the rational numbers. What are the museums like in London? How’s the food in Berlin and the nightlife in Paris? You can spend your whole life wandering around in the rational numbers, making pretty good decisions and really honing your long division skills.

But there’s a much larger infinity of things you’ve never thought of. Can you take a staycation, or take a cruise? Is that hand gesture you always make considered rude in any of these cities? These unknown unknowns are like irrational numbers. You need new, exotic operations to find them but once you learn how to look for them they’re everywhere you look — and there are so so many of them.

We spend so much time practicing our long division for 3, 4 and 5 digit numbers — staying in the known unknowns of the rational numbers — and not nearly enough time developing and using the new tools that will bring the unknown unknowns to our attention. This is one of the most important ideas you can have in your cognitive toolkit.