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It is harder every day to have a discussion about any public issue that does not slide quickly into anger over irreconcilable differences. This is partly due to massive, deliberate attempts to pollute our language with lies and conspiracy theories untethered to any notion of reality, a fog of misinformation applied mostly by the far right. But there are other, less obvious culprits. One of the big ones is not political, it’s mathematical. And diabolical.
It is one of the most pernicious concepts ever invented by mathematicians, the notion of the average — a concept that is virtually meaningless, that not only has nothing to offer our understanding of the world, but actively interferes with it.
The concept is best defined by an old trope: if you have one foot in a pail of freezing water, and the other foot is in a pail of boiling water, on average, you are comfortable. Not exactly news you can use. Google tells me that the average temperature where I live is 52 degrees F, but on any given day what I actually live through might be -15 degrees F or +100 degrees F, so what good is it to know the average?
If you put one millionaire and nine homeless people in a room, it can then be said that the average net worth of the people in the room is $100,000. This would insult the millionaire and bewilder the homeless people because it would have nothing to do with any of them.
Trivial? I don’t think so. When, for example, scientists announce that July was the hottest month ever experienced on Planet Earth, while July where I live was perfectly normal for summer, with 90-degree days and refreshing 60-degree nights, it’s hard to relate to the doomsayers, easy to suspect that someone is exaggerating the whole global warming thing.
The Biden administration is strenuously telling us that, on average, the country and its economy are in terrific shape. It insists, for example, that unemployment is, on average, at an all-time low, but when you and several people you know have recently been laid off, it’s hard to relate. Similarly, they insist that the cost of living isn’t going up as fast as it was (when we have already been priced out of our comfort zone), that hundreds of thousand of new jobs have been created (just none of them anywhere near where I live), that middle-class incomes are rising (when we are still running out of money before we run out of month).
When their claims, all of which are mathematically defensible, don’t reflect our actual experience any more than the average long term weather forecast, we tend to get cranky and suspicious that the government is lying to us.
What we’ve got here is a failure to communicate. The Biden people might be speaking in averages, but we are listening in real life, and what they are saying makes no sense to us. Either we have to stick one foot in ice water and the other in boiling water, and learn to live on average; or they have to learn to talk reality to us.
‘Numbers don’t lie’ and ‘A picture is worth a thousand words’ are both nonsensical sayings – at least outside of a few select disciplines, such as accounting and cartography. Yet there’s something about the phonic resonance of these adages that appeals to the human psyche.
Equally taken as gospel by so many are such tropes as ‘Beauty is only skin deep’ and ‘God helps those who help themselves’. Short, sweet and easily digested. But as an artist, I can assure you that, all thigs being more or less equal, beauty, as perceived by the human creature, is far more dependent on bone structure, musculature and fat distribution than on skin. And I’ve not seen any evidence that God takes sides where hard work is concerned.
We humans are so dependent on language – the most important quality that separates us from the rest of the animal kingdom – that we tend to believe that, if something ‘sounds’ good then it must be true. This fact is the basis for the art of rhetoric.
In other words, bogus math may only be a part of the problem. Language, on the other hand, is a powerful tool that can act as a double-edged sword, particularly in this day and age when communication is so pervasive and intrusive – so many voices screaming all at once.
‘The Fire Sign Theater’ accurately prophesized our current dilemma back in 1970 with their futuristic album, “I Think We’re All Bozos on this Bus”…Now there’s a truism, by gosh!
As Gregg says, “bogus math.”
Mathematics does not lie. It cannot lie. That’s why it is trusted.
That’s also why it is abused by every unscrupulous person with an agenda. But it’s not mathematics, it’s not science, it’s an abuse. It only looks like mathematics. It is counterfeit.
Unfortunately, everything about using mathematics is hard, and almost nobody learns enough to do it right. But everyone thinks that he can, just like everyone knows that he can think. So, as I used to say to my intro stats people, “Most numbers you read are either mistakes or deliberate lies.” I could have added, “Textbooks too.”
The mean, or arithmetical average, is an excellent example. For a continuous variable which is normally distributed, the mean is one of two statistics which describe the distribution. But when the variable is binary, the mean is worthless. It’s a matter of knowing about distributions and how to describe and use them – as a Ph.D. mathematician once said to me, “The use of statistics should be banned. It’s just too hard.”
Interestingly, tradesmen are one of the few exceptions. They measure lengths and angles and use them correctly. Accountants too. But they keep to a restricted situation and don’t venture outside.
Yep, as always, context is everything.
Making up numbers helps, too. Maybe inflation is 3%, but if the government said inflation is 6%, we’d believe it and think things were not going well.