the human experience is nonlinear

2025-08-07

"on a scale from 1 to 10..."

"what do you rate it on a scale from one to ten?" is a question that we all have heard at least once in our lives, likely more.

i have had a quixotic fixation with disliking this scale: why is it linear?!

so many facts of daily life from compound growth to getting out of bed and to the grocery store are all nonlinear experiences. yet, when communicating with each other, the de-facto scaling factor is always linear!

my understanding

for example, a common interpretation of this scale is that one (1) represents the worst thing one has ever experienced and ten (10) represents the best thing one has ever experienced in that context.

the best fish and chips you have ever experienced does not impact one's ability to rate the best birthday you have ever experienced.

in my opinion, these questions are simply trying to ascertain the following:

compared to your average experience, how many standard deviations from the mean does the following fall?

the linear 1-to-10 scale breaks down. if i am to take 5 as being my average experience; it only allows me to express that something was twice as good/bad as my average experience. however, i am sure that many individuals can think of ways to rate experiences that would easily break this domain. furthermore, each new experience informs the scale; that is to say that the average experience in a given taxonomy changes with respect to each new experience you may have.

my intuition

as a programmer, it seems more natural to think about these things in base-2. in an ideal world, the question would take the form:

what do you rate it on the scale?

there are two reasons for this particular choice in grammer:

1. the scale colloquially mentioned is almost always "one to ten" which means that there's room to compress the question.

2. leaving the scale unbounded means that there's room for a truly representative domain for the human experience.

semantics

i think it makes sense to use 1 as the natural description for an average experience. using the scale, i am limited by only my own experiences in ascribing scores to my experiences.

while my definition of "average" might differ from yours in a given taxonomy, it still communicates as "average." relatively scaling up or down is now meaningful across different experiences.

i don't need to understand what makes something +2^4 better for you, just that it is. we have other words to convey what things are; use them.

the domain expands from $[1,10]$ to $(-\infty ,+\infty )$, capturing the true breadth of every day life.

for any given experience $e\in E$, if my $Avg\left[E\right]$ is, by convention, equal to one, then any experience a half, fourth, or eighth as good can be indicated by the ratings 0.5, 0.25, 0.125.

now, i know what you are thinking: introducing reals is unrealistic!?

as an american that grew up on the inferior system of standard measurement that proliferated the concept of three-sixteenths of two-point-five-four centimenters, there exists room for reals.