Monday, August 29, 2016

When is a mixture better than a middle?

We often optimize by looking for a nice middle partway along a spectrum:

  • Exercising means challenging your body enough to respond but not so much that you hurt yourself.
  • Astronomers look for potentially habitable planets in the"Goldilocks zones" around other stars, the bands where it's not too hot and not too cold.
  • It's appropriate to get to the airport not too late but also not too early.
  • Ordinary fruit juice tastes much better than straight-up concentrate does (oops), and also much better than plain water mixed with the tiny amount of juice left over from the last time you filled your glass.

This idea goes back at least to Aristotle, who claimed that virtues (like courage) are means between two opposite extreme vices (like cowardice and foolhardiness).

So when I read Nassim Taleb's The Black Swan, a book about how to prepare for the unexpectable, I was surprised to find that regarding the choice between high-risk high-growth investing and the low-risk low-growth options, he recommends not a middle ground, but a mixture: having some very dependable savings and some investments that are risky but full of potential. That way, you guard against catastrophe but stay open to good opportunities.

This got me wondering: When else is a mixture better than a middle? Another example would be a painting: a mixture of colors is much nicer than a canvas covered in a single average:

Pretend the left-hand side is a painting.
If I can spot the conditions that make a mixture better than a middle, maybe I can optimize in ways I'd never thought of before.

It certainly isn't always the case that a mixture of two extremes is preferable to a single middle: I'd rather be always courageous than sometimes cowardly and sometimes foolhardy. It's easy to see why a mean is better than the extremes in this case: the extremes are both bad! So that's one clue for when a middle is definitely better than a mixture: think whether the extremes are desirable or undesirable.

But just because the extremes are desirable doesn't mean a mixture of them will be. I like food either hot from the stove or cold from the fridge, but lose my desire to eat leftovers when I unevenly microwave them, leaving tongue-burning hot zones beside pockets of still-cold areas.

Or even worse, I like milk and I like orange juice, but mixing them produces a revolting curdled mess. (Thanks for that lesson, summer camp.) But orange cake with creamy icing is lovely, so sometimes it's the way you mix two things that makes the difference.

So a middle is better than a mixture of extremes when the extremes are both bad. And when the extremes are good, sometimes a mixture is worse than just sticking to one or the other. So when is a mixture the best way to go?

I think the answer resides in whether the extremes are alternatives or complements. Hot and cold are alternatives; you cannot heat and cool the same thing at the same time to enjoy the benefits of both. But opposite colors are complements: opposite colors can be sometimes be enjoyed even more side-by-side than alone. I caught on to this distinction a couple of weeks ago when my father-in-law mentioned growing morning glories and clematis on an arbor at their community garden. "Clematis takes longer to grow but is hardier, so it should be a good alternative—I mean complement—to the morning glories." Aha! A mixture can be better than a middle or extreme when you enjoy the extremes for qualities that aren't, in principle, mutually exclusive. Then you just have to find a way to combine them without destroying those qualities you like.

This explains Taleb's investing advice: the opposite approaches of high-risk/high-reward and low-risk/low-reward have complementary virtues, so a mixture makes more sense than a single medium.

Since I started working on this post, I've been thinking about what other areas of my life might benefit from mixtures as opposed to middles. For example, I like how personal tutoring is, and I love how many people an internet video can reach. I've often told myself that I'm aiming for a reasonable middle ground by teaching classes of 20 to 30 students, where I can interact with each one in some small way. But maybe it would be better if I instead worked more as a tutor and made more videos, to get more depth and breadth of interaction from a mixture of approaches than any single one would provide.

Here are my questions for you:

  • What are some more examples? What are some areas where you regularly use a mixture of more than one approach to get the best of multiple worlds? (Answers may involve food, exercise, relationships, chores, work, fun, finances—you name it!)
  • When is it hard to tell whether a mixture is better than a middle? I've mostly been focusing on cases where it's easy to tell, in order to try to get the principles down, but the next step would be to try to apply those principles to cases that are otherwise hard to analyze.

Thanks for reading!


  1. I think relationships are better as a mixture! The deep friendships, the fun classmate acquaintances, a casual neighborly hello, and the intensity of family, is nicer to me than knowing everyone just enough to call them friend but not enough to know them. I can't connect with everyone anyway, soI like appreciating both the simple and complex relationships for what they are.

    1. Yes! I think some of the times I have felt the loneliest were when I felt like I had lots of people around with whom I had friendly relations, but no real friends.

  2. Interesting -- and a great point. I wonder if I can call up my feduciary from IWA and adjust my strategy with the retirement savings. I went for a middle.

    I think one element of the challenge is when there aren't enough resources to go around. Perhaps my Mainstage Season at the school this year is an interesting example of a mixture rather than a middle.

    Normally, we have a budget that I spend on both the Fall Play, the Spring Musical, and improvements and equipment upgrades. Usually only what we NEED to spend on improvements, but that comes straight off the top and the two show budgets fall away from that price.

    Last year, we spent about 60/40 between the Spring Musical and the Fall Play. A middle, an average for each show.

    This year, because of other circumstances, we're compelled to spend little on a boutique performance on the Fall Play (two one-acts, no evening performances, $85 for the rights) and then are spending almost the entire budget putting on Shrek the Musical.

    I wouldn't want to do it this way every year, but it's an opportunity to do a show I would normally define as well outside our price range -- and oh my goodness, are the girls thrilled that we are doing Shrek!

    1. That does sound like a great opportunity for all involved! I'm curious to know how you'll feel about the "boutique" production afterward—might this be something you do intentionally in the future?—and whether it ends up being worth it to do something as recognizable as Shrek. Sounds like fun!


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