The (Magnitude) Problem With No Name

As most of you know, I am a big fan of amusing myself by coining new names for various biases/numerical tomfoolery I see floating around on the internet. I have one that’s been bugging me for a little while now, but I can’t seem to find a good name for it. I tried it out on a bunch of people around Christmas (I am SUPER fun at parties guys), but while everyone got the phenomena, no one could think of a pithy name. Thus, I turn to the internet.

The problem I’m thinking of is a specific case of what I’ve previously called Number Blindness  or “The phenomena of becoming so consumed by an issue that your cease to see numbers as independent entities and view them only as props whose rightness or wrongness is determined solely by how well they fit your argument”. In this case though, it’s not just that people don’t care if their number is right or wrong, it’s that they seem oddly unmoved by the fact that the number they’re using isn’t even the right order of magnitude. It’s as though they think that any “big” number is essentially equal to any other big number, and therefore accuracy doesn’t matter any more.

For example, a few weeks ago Jenna Fischer (aka Pam from the Office) got herself in trouble by Tweeting out (inaccurately) that under the new tax bill teachers could no longer deduct their classroom expenses. She deleted it, but while I was scrolling through the replies I came across an exchange that went something like this:

Person 1: Well teachers wouldn’t have to buy their own supplies if schools stopped paying their football coaches $5 million a year

Person 2: What high school pays their coach $5 million a year?

Person 3: 28 coaches in Texas make over $120,000 a year.

Person 2: $120,000 is not $5 million.

Person 3: Well that’s part of an overall state budget of $20-25 million just for football coaches. (bs king’s note: I couldn’t find a source for this number, none was given in the Tweet)

Person 2: ….

Poor person 2.

Now clearly there was some number blindness here….person 1 and 3 only seemed to care about the idea that numbers could support their cause, not the accuracy of said numbers. But it was the stunning failure to recognize order of magnitude that took my breath away. How could you seriously reply to a comment about $5 million dollar salaries with an article about $120,000 dollar salaries and feel you’d proved a point? Or respond to a second query with an overall state budget, which is an order of magnitude higher than that? It’s like some sort of big number line got crossed, and now it’s all fair game.

I suspect this happens more often the bigger the numbers get….people probably drive astronomers nuts by equating things like a billion light years and a trillion light years away. Given that I’ve probably done this I won’t get too cocky here, but I would like a name for the phenomenon. Any thoughts are appreciated.

15 thoughts on “The (Magnitude) Problem With No Name

    • I’m liking this….it could be used to cover the opposite scenario as well, when someone quibbles with your numbers to an irrelevant level of granularity. Like “your point is invalid because you said 50 and the real number is 51”. Thanks!

      Liked by 1 person

  1. 120,000*28=3,360,000<20,000,000.

    Maybe "Pyrgopolynices' numbers". In the opening scene of Plautus' hilarious Braggart Soldier, the title character’s parasītus , or flatterer-slave, is repeating to his master said master’s supposed achievements on the battlefield:

    Arto. meminī: centum in Ciliciā/et quīnquāgintā, centum in Scytholatronia/trīgintā Sardōs, sexāgintā Mācedonēs./sunt hominēs quōs tū occidistī ūno diē.
    Pyrg.. quanta istaec hominum summast?
    Art. septem milia.
    Pyrg.: tantum esse oportet. rēctē ratiōnem tenēs.

    In English, that’s:
    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.
    PyrgopolynicesHow many men is that?
    Artotrogus: Seven thousand.
    Pyrgopolynices: It must be as much. [Thou] correctly hast the calculation.

    Liked by 1 person

  2. Something might be made using vertigo, or blindness, or threshold. We all likely have a threshold where it’s all just “Big Number” to us, though using large numbers in a context likely extends our range. In Watership Down, “hrair” meant anything above four.

    Ainslie, you are correct, but language changes, and that distinction is eroding. See also data, datum, which is farther along that line.

    Liked by 1 person

    • Good words, especially hrair.

      I toyed with versions of calling it the *something* line, but couldn’t find another word for that. I was discussing this with a few research folks I know, and we agreed that it’s somewhat similar to p-values….like once you cross a certain line it’s just “significant”.

      I also realized after writing this that my son is totally in a phase like this. He recently commented that he hated when I went on trips and left for “weeks and weeks”. I’ve never left him for more than 2 or 3 nights.

      Anyway, I appear to have much to chew on for name ideas here.

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      • Can’t believe I didn’t see this immediately. The Hrair Line: an arbitrary cutoff point after which all numbers seem equally big.

        This is coupled with the slightly more nefarious version The Receding Hrair Line” which is when this line changes based on topic, possibly to support your point over your opponents.

        (I still really like Mountain-Molehill Myopia and Pyrgopolynices’ numbers and will work on separate definitions for them as well)

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  3. My first thought is something along the lines of “numerical confirmation bias” but I don’t think that quite works. I also think person 2 could say that at $5 million per coach the $20-25 million would only cover 4-5 coaches. There are considerably more than 4-5 high school football coaches in Texas, so something is wrong with the numbers.

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    • Yeah, my best guess is that Person 1 actually just mixed up college coaches and high school coaches, and person 3 just decided not to back down.

      Also, I’m pretty sure the “teacher’s buying their own supplies” problem is not unique to Texas, and effects less football-fan-friendly states as well.

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  4. Pingback: Magnitude Problems, Now With Names | graph paper diaries

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