A sense of where you are

The New York Times just put out a story titled “Overdose Deaths Exceeded Half a Million in 2014”. As so very often on reading something in the Times, I said to myself “that’s wrong.” Because it had to be wrong – off the top of my head I knew that less than three million died from any reason each year in the US: pop of ~300 million, three score and ten, population growth, QED. No way that big a fraction died from overdoses, and of course it was wrong: the real number is something like 50k, mostly prescription drugs.

Nobody at the Times noticed it at first. I don’t know that they ever did notice it by themselves- likely some reader brought it to their attention. But this happens all the time, because very few people have a picture of the world in their head that includes any numbers. Mostly they don’t even have a rough idea of relative size.

In much the same way, back in the 1980s,lots of writers were talking about 90,000 women a year dying of anorexia nervosa, another impossible number. Then there was the great scare about 1,000,000 kids being kidnapped in the US each year – also impossible and wrong. Practically all the talking classes bought into it.

You might think that the people at the top are different – but with a few exceptions, they’re just as clueless.

I’m not even counting all the falsehoods that you’re supposed to believe in.

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114 Responses to A sense of where you are

  1. JayMan says:

    Innumeracy seems to be a big part of the problem with a lot of things in society, from inability to recognize the threat of terrorism posed by Muslims to freaking out about supposedly unhealthy food.

    • Michael says:

      Shouldn’t numeracy lead me to conclude that Islamic terrorism is statistically insignificant?
      Shouldn’t we be far more concerned about potential danger, numerically speaking, from Russia, where they can send nukes? Or they from us?

      • Little spoon says:

        I was wondering the same thing. Islamic terrorism is on one hand a very very unlikely cause of death for Americans, even when compared to other deaths from violence. But on the other, Muslims are some 5000% more likely to be terrorists than non Muslims in the U.S.

      • Jim says:

        The danger to Europe is being overrun by massive Moslem immigration. Of course once the Moslem population in Western Europe becomes large enough there will be massive violence.

    • peppermint says:

      Islamic terrorism isn’t the real threat posted by Muslims in the West, except in the sense that if the state loses its monopoly on violence, then it is no longer the state.

      The real threat is that little Western girls will be groomed and trafficked by organized gangs involving Muslims of all ages and both sexes. By now it is likely that this has happened to a significant fraction of the English girls. Their brothers, fathers, and future husbands and children will be or are führious, and not just at the Muslims, but the state that allowed it.

      …Police went to a house outside which a father was demanding the release of his daughter, who was inside with a group of British Pakistani adults. Officers found the girl, 14, who had been drugged, under a bed. The father and his daughter were arrested for racial harassment and assault respectively…

      …A 13-year-old girl was found at 3am with disrupted clothing in a house with a large group of Asian men who had fed her vodka. A neighbour reported the girl’s screams. Police arrested the child for being drunk and disorderly but did not question the men…

      …one young white girl, known by social services to have been sexually abused by Asian men from the age of 12, was offered language lessons in Urdu and Punjabi by Rotherham council. The aim was ‘to engage’ her in education…

  2. Andrew says:

    The problem with people on the top is they are surrounded by people who think like themselves. They are no doubt college educated and probably know higher math. But their education has conditioned them to think ideologically and have not been burned by reality enough to be analytical. College is suppose to teach intellectual rigor and it does in some areas but not most If it did fewer would go to college ( I recall my logic class that started 30 students and ended with 4 ).

    • JayMan says:

      Actually, it doesn’t appear that education influences ideology.

    • gcochran9 says:

      Very few know any higher math. But the main problem, more than innumeracy, is not knowing many facts.

      • Anonymous says:

        I think the lacking knowledge tends to be a matter of kennen rather than wissen. The problem is knowing how to NAVIGATE facts. The problem isn’t no landmarks, it’s no sense of direction.

        • Anonymous says:

          This isn’t a g-factor thing (though it clearly helps). London cab drivers know how to get around London not because they have high g, but because they’ve journeyed the length and breadth of the territory again and again and again. Facts are a territory that most people don’t bother to chart.

          • Steve Sailer says:

            They get tested on it.

          • Anonymous says:

            Yeah, damn good thing too. I was referring to the time they spend studying to become a licensed cab driver in the first place — it’s pretty strenuous.

          • Jim says:

            Yes, people are often good at the things they need to know for their daily life. But in a modern democracy they are supposed to be able to base their votes on judgements about all kinds of things on which they are totally clueless.

      • Jacob says:

        Our educational/social system is set up to reward people who are fairly bright, very eager to please, and never make the mistake of knowing something they’re not supposed to know. The easiest way to fulfill the last item is not knowing much of anything.

        I think this is related to why we have such a cultural monoculture (ie, something like Harry Potter or Star Wars will take over and drive everything else out for a while, because everyone gets the message that here at last is something they are allowed to know something about), but obviously there’s more going on there.

        • Anonymous says:

          It’s not so much that you get punished for thinking individual thoughts (though you do), you just don’t get rewarded. The incentive in society is to “know” things other people “know”, not to know things other people don’t know.

    • peter connor says:

      In my experience, the people at the top know a little math, but seldom have ANY knowledge or understanding of higher math or the simple estimation skills discussed in this post….

      • Andrew says:

        Perhaps I should have said they were schooled in higher math with higher math meaning Calculus or Statistics. Of course they forget a lot after college.

        Estimation skills is spot on. I call it probabilistic thinking as demonstrated in this post by Cochran recognizing the outlier in the NYT article.

  3. Pincher Martin says:

    One of the comments the Mark Zuckerberg character says in the opening scene of The Social Network to identify himself as smart:

    “Did you know there are more people with genius IQ’s living in China than there are people of any kind living in the United States?”

    For some things you don’t even need to do the figuring to know they’re wrong. A little basic background knowledge is enough, and mathematical intuition will do the rest.

    • Rosenmop says:

      Besides which it doesn’t matter how smart people in China are as long as it has high corruption and low trust.


    • Jim says:

      I’m sure a lot of Americans couldn’t give you estimates of either the population of China or of the US.

      • Pincher Martin says:


        I’m sure that’s true. A lot of Americans don’t know a lot of things.

        But I would expect even a moderately intelligent American lad – the kind of boy who might later grow up to become a NYT journalist or Hollywood script writer – could give you estimates for those figures that were roughly accurate.

        And isn’t that the group we’re talking about here? The kind of people who not only produce these factoids, but eagerly consume them?

        • Jim says:

          I hope so but my faith in journalists is steadily sinking. As for Hollywood script writers they are about the last place I would look to for rational understanding of reality. Fantasy is their job. They probably actually believe that a 90 pound women could beat up a 250 pound man.

          • Pincher Martin says:

            Ideological motivations are surely to blame for a lot, but what ideology is causing a scriptwriter to think that one-fifth of China’s population are geniuses?

          • Pincher Martin says:

            And even if the screenwriter is an ignoramus, you would have expected one of the numerous people who read the script early in production to have been skeptical of that opening line in what is supposed to be a loosely biographical flick.

            Surely, Mark Zuckerberg is too smart to have actually said that line which the movie has his character saying.

      • Jim says:

        I wonder how accurate the official population figure for China actually is.

        • ursiform says:

          I’ve never heard of that being one of the Chinese statistics that was questionable. And, unlike some countries, they have a pretty good idea of their population, because they’ve been very worried about it for years, plus they like to keep track of people.

  4. ursiform says:

    I recall listening to a radio report of the shocking news that one-sixth of children were well below average on something or other. But it appeared the study had defined well below average as more than one standard deviation below the mean. In other words, one-sixth of children were in the bottom sixth. Pretty sure there is no solution to that problem …

  5. Jim says:

    500,000 would exceed the war deaths in any year of the Civil War.

  6. Jim says:

    I’m surprised it’s even 50,000. Aren’t total accidental deaths in the US roughly 100k?

  7. Jim says:

    It’s not just that most people don’t have a picture of the world that includes numbers, a lot of them don’t seem to have any picture of the world at all. How many Americans know the difference between Iran and Iraq or could find either on a globe? How many could find the Pacific Ocean on a globe?

  8. I would not assume that most of these elites ever had all that much math. They are likely to be higher SATV than SATM. They would have had to pass Algebra II/Trig to get into good colleges. Those good colleges sometimes, but not always have a mathematics requirement for graduation, but almost nowhere demands that all its Art History and French Literature majors complete a second semester of calc.

    Yet even that is not the problem. People who don’t use numbers in context quickly revert to hearing all Big Numbers as the same after the first few digits. “Thousand,” they can sort of do, because of experiencing dollars in their everyday lives. But million, billion, and trillion all feel similar to them. It’s just Big Number. Therefore, important numbers do not stick in their heads, so they can’t do estimates or back-of-the-estimate calculations of things. i remember when US Senators asserted that oil companies were keeping the price of gas low in order to elect Bush. Americans use 130B gallons a year. A ten-cent a gallon subsidy targeted toward election time would still mean a few billion bucks in gifts. And ten-cents may not give you the emotional charge in the electorate you’re looking for. You might have to go to 30-40 cents. A rational manipulative industry would just give to the campaigns at a fraction of the cost.

    But that would involve keeping big numbers in your head.

  9. MawBTS says:

    I once heard of a teacher who asked his class to (without thinking too hard or looking up any figures) provide their gut-instinct guess for various numbers: such as how fast a pitcher throws a baseball.

    Said gut-instinct guesses were usually an order of magnitude wrong in one direction or another.

    Most people are terrible with numbers.

    • Jim says:

      If people are asked to guess the number of say bubblegum pieces in a fairly large bin or container they usually guess way too low.

    • albatross says:

      I think the problem is neither lack of mathematical instruction nor lack of facts–it’s a lack of the habit of thinking through numbers for plausibility. You can’t just wait for some magic light to come on in your brain and tell you some number is wrong, you have to think “wait, what would that mean if it were true?”

  10. j says:

    Even “more than 50,000” is meaningless. Given the population’s growing lack of numeracy, these days the media tends to avoid figures. The NYT should emulate the Pirahã language that contains no words for discrete numbers and only three that approximate some notion of quantity—hói, a “small size or amount,” hoí, a “somewhat larger size or amount,” and baágiso, which can mean “a bunch.” But then there would be no material for Prof. Cochran to make fun of …

  11. Steve Sailer says:

    A really useful round number to keep in your head is 4 million: there are about 4 million people per year born in America, 4 million first graders, 4 million 18 year olds, etc.

  12. dearieme says:

    I once did one of those top-of-the-head estimations for a young woman. She squealed: “Ooh, you’re one of those people who can do that! So can my Dad.”

  13. Flemur says:

    The NYT even messed up their correction.

  14. I estimate that you’ve all covered that one.

  15. Fourth doorman of the apocalypse says:

    How can we determine whether the people at the top are largely ignorant or simply telling ‘noble’ falsehoods?

  16. half the people in India live in a one room house

    • ursiform says:

      That’s a lot of people to crowd into one room!

      • That is only my second most favorite ridiculous numerical factoid I read in a bad newspaper. My all time favorite one is for every 100,000 people hit by a bolt of lightening 1 person gets hit by a meteor. I seriously doubt if the reporter or anyone was counting, 99,998 crack, 99,999 crack, 100,000 thud, 1 crack, 2 crack….you get the picture. Anyway this factoid was made even more delightful by the story of the poor soul hit by the meteor. Wouldn’t you know it, poetic justice here, a fat lady lying in her bed in a trailer park in Texas got walloped in the side by a meteor. She lived but the hot rock left a nasty mark and then proceeded to demolish her clock radio.

        • Jim says:

          The number of people hit every year by lighting strikes is order of magnitude about 100k so there should be according to that factoid about one or two people hit by a meteor every year. But apparently there is only one documented case.

          • Steve Sailer says:

            A lady in the midwest was badly bruised by a meteorite in the late 1950s. I think there may have been more cases since then, but it’s clearly a few a century. In contrast, lightning strikes are common enough that celebrities get hit, such as golfer Lee Trevino and two other tour pros in 1975.

          • Jacob says:

            Since “Stars Fell in Alabama” was referring to an 1833 meteor shower, is there anything about any individual location on Earth that makes it more likely to be hit? Alabama isn’t that far from the KT impact crater, either, I guess.

          • Yep, it was Alabama and not Texas that the fat lady got clobbered by a meteor. I should have checked wiki instead of trusting my memory. It was 1954 and there have been other instances but it seems to be a once a generation thing.

        • iffen says:

          “individual location on Earth that makes it more likely to be hit? Alabama isn’t that far from the KT impact crater, either”

          God doesn’t like us but he has a bad aim?

  17. IC says:


    Media? What media? There is no media.

  18. RCB says:

    “Very few know any higher math. But the main problem, more than innumeracy, is not knowing many facts.”

    Facts are hard. Unfortunately I’ve fallen into a bad habit of believing that mere facts (“trivia”) are beneath me; theory is where it’s at. I like being able to derive results from basic principles on my own, rather than looking something up – more fun that way. But on the whole it just means that I know fewer things, and I spend a lot of time figuring out something that could have just been googled. So I’m probably more susceptible to believing stupid hearsay than others. Trying to work on this.

    To that end, I wonder what Cochran (and others here) believe are the most important facts. Think of it this way: if you were to design an n-year education curriculum, what would it include? Assume that your audience can learn whatever you teach them, given a reasonable timeframe. I seem to recall that Cochran homeschooled at least one of his kids, so presumably he can draw from experience.

  19. linsee says:

    Douglas Hofstadter has told a story about teaching math to an adult class — nurses, I think it was — in a room that had a view of the Empire State building. He asked them how tall it was, and got answers ranging from 50 feet to a mile. (Being New Yorkers, they’d all knew it had 100 stories.)

  20. Pingback: Reality Management | The Eyes of the Owl

  21. Steve Sailer says:

    Back in the 1980s, it was widely rumored that Microsoft job interviews were full of questions to test your estimation skills. But then I did a day-long interview in Redmond in 1987 and didn’t get a single such question. Instead, they were all of the “Where do you see yourself being in 5 years?” ilk.

  22. Pingback: Most useful data to memorize | Aeoli Pera

  23. melendwyr says:

    Innumeracy isn’t the problem. The problem is that people just don’t care about what the truth is, or what the numbers are. Numbers can’t be used in any way that produces a result they care about – if they want to motivate or scare people, they can do better with made-up facts than real ones. The only risk is being exposed as wrong, and if the people they’re talking to don’t truly care about reality either…

    • You are right, people just don’t care to learn more about the world around them. It isn’t incomprehension of numbers, it is a greater problem. People do care about reality but what is the payback for Joe Average with an IQ of 100 to struggle with the task of reading books he barely understands. Joe Average is threatened and confused by the complex world around him. He literally doesn’t know what the fuck is going on. Very bright people consistently babble nonsense about the world around them, what chance does Joe have to figure it out. He hides behind simple answers to complex questions. He really doesn’t have any choice.

      It is fun to read if you are smart just like it is fun to play basketball if you can dunk. But the reality is that we are all placed at a certain location of the bell shaped curve of human intelligence and if you need mind glasses to see the world with the clarity Cochran is talking about and you flat out can’t, well…it is what it is.

  24. mapman says:

    My favorite unappreciated number is that deaths from hospital-induced sepsis exceeds the number of deaths from traffic accidents. We hear a lot and endlessly about auto safety but how frequently do we hear about basic competence of nurses that take care of you?

    • melendwyr says:

      People want to believe that doctors and nurses will make them better. They don’t want to hear that the medical system does more harm than good.

      • IC says:

        It is about risk/benefit ratio as anything in life.

        Any thing in the world has both pro and con. Looking at thing on both sides is hard for many people to handle. They just want simple black/white answer.

        • melendwyr says:

          Ah, but that is NOT the case. If people cared about risk/benefit, they’d want to accurately know both so as to determine the ratio. In my experience, people want to discount one and credulously accept the other – but which one is which varies wildly and seems to depend on their prior assumptions.

          • IC says:

            Try it on people who barely finished elementary education or IQ below 90. See how they handle issue with risk/benefit ratio.

            As a physician, I know how they become, only further confused. They just said:” Doc, just tell me this gonna be good or bad for me.

            I usually ask them whether they have friends with college degree. Either consult with them or seek additional opinion. It is complicated.

          • melendwyr says:

            Doctors aren’t much different when dealing with issues that engage them emotionally. That’s when people stop testing hypotheses and seek out confirmation of their biases, or even merely what they would prefer to believe.

          • IC says:

            If you truly believe the medical system does more harm than good</>, then it is your decision.

            If you have bleeding trauma or cancer growing in your body, I sincerely hope you change your opinion. Your life might be lost due to your belief.

            • melendwyr says:

              What a foolish sentiment. My position is either right or wrong – and offering examples of specific cases in which the medical establishment would presumably be doing good has nothing whatsoever to do with my claim, which is about the ratio of benefit to harm.

          • IC says:

            I mistake your original sentence as broad rejection of entire health care. In your last comment, you seems not endorsing such attitude in general. Maybe my mistake again due to my foolish brain.

            We always respect patients decision whatever it is. Certainly it is your final judgment to accept or reject particular form of treatment. You are the boss of your own healthcare. Doctors only serve as helpers or advisers here. That is why there is informed consent.

            But broad rejection of health care is quite common. Here is some sentiment and belief are quite entertaining. This blog is dealing with such attitude.


    • Fourth doorman of the apocalypse says:

      Hmmm, so this page:


      estimates 99,000 deaths a year from hospital acquired infections.

      This page:


      shows 32,000 or so deaths in 2013.

      So, I guess that the claim looks reasonably correct.

  25. melendwyr says:

    The ways in which people distort factual data – whether through intention or accidentally – are the most important things a person can know. ‘Facts’ can be looked up, but if you don’t understand the ways those ‘facts’ are likely to not correspond with reality, you’re lost.

    Generalizing and metaphorizing, the most important things to know about maps is how the territory is likely to differ from them. If you know how to doubt and disbelieve the map, you can likely use it effectively (assuming it contains any useful information at all, of course). If you take the map for granted, its errors will lead you astray.

    One useful subset of this category is the Latin names for logical fallacies – not because the names themselves are important, but because of the list itself, which is far from complete but far superior to trying to identify them all yourself. Don’t reinvent the wheel without need.

  26. HL says:

    My favorite factoid that puts things in perspective is that for every hour worked in America we spend roughly $12.00 on healthcare. ($3 trillion/250 billion hours worked)

  27. Johanus de Morgateroyde says:

    I had a budding actuary for an office mate for a while.

    When I said, “The only tricky part of using a slide rule is moving the decimal point in your head.”

    He responded, “The problem is, most people don’t have a decimal point in their head.”

  28. Hmmmmmm. http://www.nature.com/neuro/journal/vaop/ncurrent/full/nn.4205.html

    Journal article on genetic determinants of intelligence. I kinda figured something was up, is this why the normally very cautious Greg Cochran talked about a breakthrough in understanding the underlying genetic elements in human intelligence in a year or two back in his Ionian Mission blog post.

  29. Dave says:


    Summary: An ex-Amish woman tries to drive a 60,000-pound truck across a 6-ton bridge because she “didn’t know how many pounds are in six tons”. But we mustn’t refuse to hire women or minorities who can’t do math because that’s “discrimination”!

    • Fourth doorman of the apocalypse says:

      Who would be dumb enough to think that truck weighs no more than 6 tons?

      Those tractors and trailers are rated for five tons per axle if I am not mistaken.

    • Stary Wylk says:

      How about that she was actually four times OVER the weight limit?

  30. MEH 0910 says:

    OT: http://arstechnica.com/science/2015/12/new-type-of-contagious-cancer-spreading-among-tasmanian-devils/
    “This week, scientists report finding a new type of transmissible tumor in Tasmanian devils, the famous marsupials of the Australian island state. It’s the second type of infectious cancer seen in devils and the fourth type overall. The finding, published in the Proceedings of the National Academy of Sciences, has left the study authors questioning whether infectious cancer cells are more common than expected or if there’s something about Tasmanian devils that makes them uniquely susceptible to catching deadly tumors—or maybe both.”

  31. Greying Wanderer says:

    “Neolithic and Bronze Age migration to Ireland and establishment of the insular Atlantic genome”


    “These include those coding for lactase persistence, blue eye color, Y chromosome R1b haplotypes, and the hemochromatosis C282Y allele; to our knowledge, the first detection of a known Mendelian disease variant in prehistory. ”

    milk has very little iron

    Apparently hemochromatosis C282Y allele retains iron to the extent it is a health risk – heart attacks and such. I don’t know for sure but I’m assuming this is only the case when a person has a reasonable amount of iron in their diet? For people with a low iron diet might C282Y have been beneficial and selected for?

    Would that mean milk drinkers with C282Y should drink lots of milk but leave out the oats (lots of iron) while milk drinkers without C282Y should make sure to include the oats?


    Personally i think there’ll be hundreds of these – adaptations to a shortage of some nutrient in a particular local diet in the past which means people from that area eating a modern diet can now OD on that nutrient.

  32. Steven C. says:

    Reminds me of the made-up statistic, widely reported in the US news media a few decades ago, that 85 million American women were abused by their male partners. They reacted with annoyance to those, probably misogynistic, critics who dared to point out that this would be about 115% of American women in relationships with men.

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