We Hold These Truths

This blog lives by a two-part creed:

  1. You can put a number on anything if you try hard enough (number quality not guaranteed, see store for details).
  2. Once you put a number on something, you improve your understanding and decision making (even if the number isn’t of prime quality).

At the core of this belief is the idea that the world we live in is made of math, however literally you decide to take that statement. Whenever a field of science achieves any useful knowledge of that world, it is usually in form of precise mathematical equations or careful statistics. Every science is an exact science, or trying to be. Darwin discovered evolution and himself had no doubt that the theory is true, but it’s the mathematical accuracy of results such as Price’s equation of natural selection that give it the predictive and explanatory power that make it an unassailable bedrock of life sciences. Even in soft fields like personality psychology, models like the Myers-Briggs and Big-5 Traits rise and fall on correlation tables and statistical measures of validity.

Biology can be seen as applied chemistry and physics, and the math that would be needed to describe all of it in detail is much more complex. As a result, the equations we currently have in each field gives rougher approximations in biology than in physics. Psychology can be seen as applied biology, with the same relationship. The life of real humans on this planet is applied psychology, biology, economics, linguistics… we can scarcely hope to arrive at bulletproof mathematical statements. And still, that’s the way truth lies. Quoth the sages: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”

In this world, “putting a number on it” doesn’t mean spelling out 10 digits of precision. Vague ranges, guesstimates and anecdata are all tools that can take us a few steps closer to the truth if wielded with appropriate care.

A demonstration in action is in order: let’s put a number on the value I place on my own left pinky finger.

I have spent three decades both enjoying the use of my finger and regularly placing it in harm’s way, wood shop classes and volleyball matches. Here’s one thing I haven’t tried yet:

knife game

Playing the knife game as fast as I could, I estimate a 10% chance of losing a finger permanently. I think I wouldn’t play if you paid me $100, but I definitely would if you paid me $1,000,000. This translates to a range of finger values between $1,000 (\frac{\$100}{10\%}) and $10,000,000 (\frac{\$1,000,000}{10\%}).

We can put the finger on a more precise amount by examining the components of my finger’s value, such as the economic benefit. My career involves programming and writing, it’s likely that at least for the next 20 years that would require typing on a physical keyboard. Losing my finger will impair my ability to work by 2%. My work is valued at my average salary over the next two decades, let’s round it off optimistically to $100,000. This rough guesstimate values my finger as an income generating asset at 20 \, years \times 100,000 \, \frac{\$}{year} \times 0.02 \, impairment = \$40,000.

Fortunately, losing a finger isn’t unfixable: I can get a snazzy looking bionic replacement for $70,000. I use my finger for more than typing and a digital digit isn’t as good (yet) as my original one, so I can adjust both numbers up a bit and appraise my left pinky at $200,000, give or take an order of magnitude. It’s amazing what a combination of Googling, calculation and sensible guessing can do! Email me privately for offers into acquiring my finger; serious inquiries only.

finger one

Even a facetious example like my little finger has utility in allowing me to make informed decisions about my life. The X-ray on the right is the state of my actual pinky after mistiming a jump for a rebound in a basketball game. And yet, I keep playing basketball since you’d have to pay me more to quit the game than the expected harm to my finger. On the other hand, I avoid boxing and tackle football even though I think I would enjoy both sports because the value I place on my brain and the concussion statistics present a compelling case against them.

People arrive at these two decisions by intuition alone, and yet many others refuse to play volleyball or basketball because of hand injury risk while a million Americans play high school football. Many football players have different assessments of risk and reward than I do, but I’d wager that many don’t even think to evaluate and compare the two. Our brains are often ridiculously horrible at giving correct or reasonable answers on questions that can be solved with a simple computation. Intelligence won’t help you. Reading about biases won’t help you.

“Does this outfit make my butt look fat?” is the one query the correct answer to which is not arrived at by mathematics. For all other questions (at least the ones that this blog will explore), putting a number on it makes you more objective and less biased, illuminates the errors in your thinking, and brings you closer to the truth.

Footnote 1

No, I don’t compute the net present value of brushing my teeth every day, and I didn’t mean to say that literally everything in life must be calculated. I believe that in general people apply actual numbers on such a tiny minority of occasions that encouraging everyone to do it more often is strictly helpful.

Footnote 2

This is such an excellent exploration of the same idea that I didn’t want to hide it in a text-embedded link: If it’s worth doing it’s worth doing with made up statistics.

15 thoughts on “We Hold These Truths

  1. I think there’s a nonlinear utility of money issue being ignored here. Trading a 10% chance of losing a pinky against $1M is not equivalent to trading certainty against $10M, because $10M is not 10x better than $1M (consider how few people would be indifferent to a 10% chance of $10M or a certainty of $1M).


    1. That’s very true, I hadn’t thought of that. In any case, this proves my larger point of gaining insight through numbers: you should demand a better risk/reward ratio for larger risks and rewards than for small ones, especially as the non-linearity is compounded by loss-aversion.

      It will still probably take only a 6 figure sum to part me with my pinky :)


  2. I wonder why you can’t answer the “does it make my butt look fat” question with statistics? It may take some experiments for a start to generate the numbers, but I imagine some may have been done already. E.g. optical illusions that can be used in clothes design (vertical stripes etc).


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