Magnitude Problems, Now With Names

In my last blog post, I put out a call for name ideas for a particular “potentially motivated failure to recognize that the magnitude of numbers matters” problem I was seeing, and man did you all come through! There were actually 3 suggestions that got me excited enough that I wanted to immediately come up with definitions for them, so I now have 3 (actually 4) new ways to describe my problem. A big thanks to J.D.P Robinson, Korora, and the Assistant Village Idiot for their suggestions.

Here are the new phrases:

Hrair Line: a somewhat arbitrary line past which all numbers seem equally large

Based on the book “Watership Down” where characters use the word “hrair” to mean “any number greater than 4”.  We all have a line like this when numbers get big enough….I doubt any of us truly registers the difference between a quadrillion and a sextillion unless we encounter those numbers in our work. Small children do this with time (anything other than “right now” is “a long time”), and I’d guess all but the richest of us do this with money (a yearly salary of $10 million and $11 million are both just “more than I make” to me). On it’s own, this is not necessarily a bad thing, but rather a human tendency to only wrap our heads around the number values that matter most to us. This tendency can be misused however, which is where we get….

The Receding Hrair Line: The tendency to move one’s hrair line based on the subject under discussion, or for one group and not another, normally to benefit your argument

Also known (in my head) as the Soros/Koch brothers problem. Occasionally you’ll see references to charitable gifts by those controversial figures, and it’s always a little funny to see how people perceive those numbers based on their pre-conceived feelings about Soros/Koch. I’ve seen grants of $5000 called “a small grant” or be credited with helping fund the whole organization. You could certainly defend either stance in many cases, but my concern is that people frequently seem to start from their Soros/Koch feelings and then bring the numbers along for the ride. They are not working from any sort of standard for what a $5000 grant means to a charity, but rather a standard for what a George Soros or Koch brothers gift means and working backwards. This can also lead too….

Mountain-Molehill Myopiathe tendency to get so fixated on an issue that major changes in magnitude of the numbers involved do not change your stance. Alternatively, being so fixated on an issue that you believe that any change to the number completely proves your point.

A close relative of number blindness, but particularly focused on the size of the numbers. Taking my previous Soros/Koch example, let’s say someone had defend the “a $5000 grant is not a big deal” stance. Now let’s say that there was a typo here, and it turned out that was a $50,000  or a $500 grant. For most people, this would cause you to stop and say “ok, given this new information, let me rethink my stance”. For those suffering from Mountain-Molehill Myopia however, this doesn’t happen. They keep going and act like all their previous logic still stands. This is particularly bizarre, given that most people would have no problem with you pausing to reassess given new information. All but the most dishonest arguers are going to hold you accountable for previous logic if new information comes up. The refusal to do so actually makes you more suspect.

The alternative case here is when someone decides that a small change to the numbers now means EVERYTHING has changed. For example, let’s say the $5000 turns out to be $4900 or $5100. That shouldn’t change anything (unless there are tax implications that kick in at some level of course), but sometimes people seriously overreact to this. You said $5000 and it turns out it was $4900, this means your whole argument is flawed and I automatically win.

There is clearly a sliding scale here, as some changes are more borderline. A $5000 grant vs a $2000 grant may be harder to sort through. For rule of thumb purposes, I’d say an order of magnitude change requires a reaction, and less than that is a nuanced change. YMMV.

Now, all of these errors can be annoying in a vacuum, but they get worse when onlookers start jumping in. This is where you get…..

Pyrgopolynices’ numbers: Numbers that are wrong or over-inflated, but that you believe because they are supported by those around you due to tribal affiliations rather than independent verification

Based on the opening scene of  Plautus’  Braggart Soldier, Korora provided me with the context for this one (slightly edited from the original comment):

…the title character’s parasītus , or flatterer-slave, is repeating to his master said master’s supposed achievements on the battlefield:

Artotrogus:. I remember: One hundred fifty in Cilicia. A hundred in Scytholatronia*, thirty Sardians, sixty Macedonians. Those are the men thou slewest in one day.
Pyrgopolynices: How many men is that?
Artotrogus: Seven thousand.
Pyrgopolynices: It must be as much. [Thou] correctly hast the calculation.

*there is no such place

After reading this I got the distinct feeling that we did away with flatterer-slaves, and replaced them with social media.

As someone who likes to correct others numbers, you’d think I’d be all about chiming in on Facebook/Twitter/whatever  conversations about numbers or stats, but I’m not. Starting about 3 years ago, I stopped correcting anyone publicly and started messaging people privately when I had concerns about things they posted. While private messages seemed to get an amiable response and a good discussion almost 90% of the time, correcting someone publicly seemed to drive people out of the woodwork to claim that those numbers were actually right. Rather than acknowledge the error as they would privately, my friends would then turn their stats claims in to Pyrgopolynices’ numbers….numbers that people believed because other people were telling them they were true. Of course those people were only telling them they were true because someone on “their side” had said them to begin with, so the sense of check and balances was entirely fictitious.

Over the long term, this can be a very dangerous issue as it means people can go years believing certain things are true without ever rechecking their math.

That wraps it up! Again, thank you to J.D.P Robinson for mountain-molehill myopia, AVI for throwing the word “hrair” out there, and Korora for the backstory on Pyrgopolynices’ numbers. In related news, I think I may have to start a “lexicon” page to keep track of all of these.

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