Headlines from a Mathematically Literate World

Our World: Market Rebounds after Assurances from Fed Chair
Mathematically Literate World: Market Rebounds without Clear Causal Explanation

Our WorldFirm’s Meteoric Rise Explained by Daring Strategy, Bold Leadership
Mathematically Literate WorldFirm’s Meteoric Rise Explained by Good Luck, Selection Bias

Our WorldGas Prices Hit Record High (Unadjusted for Inflation)
Mathematically Literate WorldGas Prices Hit Record High (In a Vacuous, Meaningless Sense)

Our WorldPsychologists Tout Surprising New Findings
Mathematically Literate WorldPsychologists Promise to Replicate Surprising New Findings Before Touting Them

Our WorldAfter Switch in Standardized Tests, Scores Drop
Mathematically Literate WorldAfter Switch in Standardized Tests, Scores No Longer Directly Comparable

Our World: Controversial Program Would Cost $50 Million in Taxpayer Money
Mathematically Literate World: Controversial Program Would Cost 0.001% of Taxpayer Money

Our World: Proposal Would Tax $250,000-Earners at 40%
Mathematically Literate World: Proposal Would Tax $250,000-Earners’ Very Last Dollar, and That Dollar Alone, at 40%

Our World: Poll Finds 2016 Candidates Neck and Neck
Mathematically Literate World: Poll Finds 2016 Predictions Futile, Absurd

Our World: One Dead in Shark Attack; See Tips for Shark Safety Inside
Mathematically Literate World: One Dead in Tragic, Highly Unlikely Event; See Tips for Something Useful Inside

Our World: Local Heat Wave Seen as Sign of Global Warming
Mathematically Literate World: Local Heat Wave Not Seen as Meaningful Indicator of Global Trends

Our World: Veteran Baseball Player Enjoys Breakout Month
Mathematically Literate World: Veteran Baseball Player Enjoys Transient Good Fortune

Our World: Market Share for Electric Cars Triples
Mathematically Literate World: Market Share for Electric Cars Rises to 0.4%

Our World: Still No Broad Agreement on Global Warming
Mathematically Literate World: Still 90% Agreement on Global Warming

Our WorldRates of Cancer Approach Historic High
Mathematically Literate WorldRates of Surviving Long Enough to Develop Cancer Approach Historic High

Our World: Hollywood Breaks Box Office Records with Explosions, Rising Stars
Mathematically Literate World: Hollywood Breaks Box Office Records with Inflation, Rising Population

Our World: Economist: “Eliminate Minimum Wage to Create Jobs, Improve Economy”
Mathematically Literate World: Economist: “Eliminate Minimum Wage, then Pray Our Model Has Some Empirical Basis in Reality”

Our World: Average Football Player Earns $3 Million, Lasts 4 Years in NFL
Mathematically Literate World: Average Football Player Earns $0 Million, Lasts 4 Years in High School

Our World: Politician Promises to Fund Math Education
Mathematically Literate World: Politician Promises to Fund, Meddle in Math Education

Our World: Illegal Downloaders Would Have Spent $300 Million to Obtain Same Music Legally
Mathematically Literate World: Illegal Downloaders Probably Would Not Have Bothered to Obtain Same Music Legally

Our World: Unemployment Rate Jumps from 7.6% to 7.8%
Mathematically Literate World: Unemployment Rate Probably a Little Under 8%; Maybe Rising, or Not, Can’t Really Tell

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Thanks for reading! (And thanks to readers who suggested improvements, some of which I’ve incorporated.) If you can tolerate my drawings (a big “if”), you might also enjoy A Math Professor Consults on a Hollywood Movie and the economic satire 20 Steps for Trading Up from a Paper Clip to a House.

You could also check out Fifty-Five Million, my new blog that aims to bring a math-literate perspective to education statistics. And I highly recommend Aaron Brown’s excellent critique of this post, delving more deeply into some key issues.

227 thoughts on “Headlines from a Mathematically Literate World

  1. Brilliant. A comedian once said about shark attacks that 95% of shark attacks happen away from shore. He was quick to point out that that should be pretty obvious as that is where most sharks live! Loved the post and the drawings weren’t too shabby either.

    1. As it happens, where and when shark attacks happen seem to be more driven by where and when there are people in the water than anything else. In the ocean, sharks are pretty ubiquitous,, bu the presence of a shark is only one of two requirements for a shark to interact with a person.

      And the comedian was wrong, most shark attacks happen very close to the shore. There are more people in the water at the beach than there ar in the middle of the ocean!

      (FWIW, David Baldridge’s book on shark attack is pretty out of date now, I guess, but it was my introduction to the concept of control data, and so I recommend it to anyone with an interest in shark attacks, or statistics!)

      1. I know. Comedian put 1 and 1 together and got 12. He thought more sharks= more attacks but without people this would be quite difficult. Perhaps that was part of his joke? He was pretty awful anyway.

  2. The remark about heat waves and global warming is misleading at best. I would liken that more to the question of whether a penny flip came up heads three times in a row. Not very interesting after-the-fact, but interesting if predicted beforehand. What makes heat waves interesting is that a high number of them was predicted beforehand and has come to pass, hence they may indeed be confirming evidence–perhaps not in isolation, but as part of a predicted trend. Of course you can make up a hypothetical heat wave about which this was not predicted, but you haven’t here, nor have you dismissed the fact that the prediction was for a statistically interesting number of deviations. No one of those will be “the one”, but that doesn’t mean there is no statistical meaning in the broader context, only that one by itself is not the complete information on the matter.

    The error here is akin to the grating phone message that says “Your phone call will be answered in the order received.” when order is a property of more than one call, yet surely there is an importance to that caller to know that there is some namable property of his call as part of a larger sequence, so you can’t say that it’s meaningless to talk about. It’s just badly worded.

    So while I applaud the general tenor of this page, I think the cheap shot on how easy it is to dismiss climate change arguments is both politically unwise and weakens the credibility of some of your other examples here by suggesting a desire for exactly the sensationalism you appear to be wanting to avoid.

    1. A LOCAL heat wave isn’t proof one way or the other of global warming. Repeated, careful measurement of the temperature from around the world over many years sure is, though. Global warming is obviously real, and the author even says “90% of scientists still agree”. He even draws a cartoon to point out how absurd calling this “conflict” is. Stop making me hate the people on my own side of these issues.

      1. Well, first a GLOBAL heat wave isn’t proof either. There are no proofs by specific example. But both are potentially relevant.

        Also, “local” is a super-vague term that might mean “my neighborhood” or “my continent” so that term is tricky to lean so subtle an argument on.

        And finally, the argument you make in your reply to me excludes the data point even before any math comes into play. So it’s not a very good use of math.

        I’m seeing a LOT of weather programs that are failing to take the opportunity to talk about heat waves in the context of a climate pattern. Their rationale appears to be exactly what you are saying. But that’s too narrow a reading of the math. The discussion we need to have is about what kinds of effects are predicted. We need to carefully say it doesn’t confirm a prediction, but still explain how it could be relevant.

        In my view, you would be better here referring to a snowstorm as not being a disproof. That’s a MUCH more important mathematical idea to get across because every time there is a snow storm the conversation shifts to a new ice age. And people need to see that snow storms are consistent with Climate Change in part because a prediction of a higher probability isn’t a prediction that something will always happen, and also because warming increases volatility and that changes wind patterns, moving storms that would have happened elsewhere to new locations. They need to understand that average temperatures are not the same as instantaneous temperatures. But the focus should be on what is a bad disproof, not what’s a bad proof. Proofs are generally hard, but there are a lot of disproofs running around that can be debunked.

        Finally, there’s no reason to be snarky about me on a personal level. That does no one any good. I am not criticizing you, I’m criticizing the example. I wouldn’t have taken the time to comment if I thought your approach was a bad one. I think this page is generally good stuff. I’m just trying to contribute to making a solid case, so you don’t end up lending accidental support for things you don’t mean to.

        1. I broached this topic, in a rather more abstract form, above, and would be interested in your thoughts on what I regarded as the more general question of the relationship between particular outcomes and the distributions from which they were drawn: when is a particular outcome evidence for a particular distribution, and when can a particular distribution explain some particular outcome? I don’t think these are trivial questions, and I don’t pretend to have final answers. But I think they are well worth thinking carefully about… (It starts off about cancer rates, but gets to other question…)

          (Here, I will note only that there are obvious outlier cases, where a particular outcome is only possible under a particular distribution, and is guaranteed by that particular distribution, and hence where that outcome can therefore be said both to provide knock-down evidence of that distribution, and that distribution can can be said to fully explain that outcome. Those are not common cases in the real world, alas.)

        1. 100% of scientists receive grants to prove SOMETHING.

          Are you saying all scientific proof is highly suspect, then?

    2. On the other hand, increases in hurricane frequency was also predicted. 2013 was in the bottom 5 years for hurricanes since 1960.

  3. A lot of these are pretty bad. The football one, for example, is just an over-literal reading of the first headline’s obvious implications, and the one about marginal tax rates at $250k is the same. Many of the politically tinged entries, such as minimum wage, are also pretty asinine and don’t really make sense as an example of an increase in mathematic literacy.

  4. “Poll: Candidate surges ahead 2%.”
    “Poll: Difference between candidates remains within margin of error.”

  5. Way cool!

    Though I disagree on climate. Some people might care if the sea rose 10 feet and drowned everyone in Bangaladesh. In fact, most would. But if preventing it required essentially an end to modern ways of life for the well off and a total halt to reduction in world poverty, we’d all agree with China and India and say “who cares? not me!”. That IS controversy.

    1. Really? If an average 🙂 human being’s body contains 6-8 pints of blood, then his/her weight should change upon removal of the head. The accompanying blood loss would affect the weight, would it not?

  6. A UK national technology agency claimed pupils with computer at home did better in GCSE so all children should have computers at home. Probably pupils in homes with expensive cars on the drive also do better in GCSE so buy each kid a Rolls Royce and watch their brains grow 😉

  7. Pretty funny.

    So, is math part of any science dept?

    Bc, and this is the funniest, “90% of scientistific consensus”……….uummmmmm….. and what is “scientific consensus”(?)…….and did your maths apply any rigor to the figure?

    Anyway, before and after that trip in this exercise it is pretty good…..that one trip allows us to see that you have not applied any statistical analysis to the MODELS which froth over their own alarming predictions and yet have no value in REALITY. But keep on, even if subliminally, pushing your scare meme.

  8. Our World: Still No Scientific Consensus on Global Warming
    Mathematically Literate World: Still 90% Scientific Consensus on Global Warming

    In general, loved the content. But, a math professor should know that
    “Scientific Consensus” is meaningless. Remember: Make a statement and offer a
    repeatable experiment to support it. Math is based on a huge pile of “Proofs”, each
    one repeatable by the interested student.

    There is no science in the collected works of Gore, Mann, and Hansen. Faith would
    be a better description.


  9. While reading the article below, all I could think about was this posting when I ran across the sentence, “We found that nearly half of the co-educational state-funded schools we looked are actually doing worse than average.” This sentence refers to how the “male” disciplines of math, physics, etc. are receiving less attention from girls when compared to the “female” disciplines, English, psychology, etc.

    If half of the schools are doing worse than the average (a confusing concept) perhaps a new title is in order:

    Our World: State schools ‘making gender bias worse’

    Mathematically Literate World: State schools ‘largely on track to reinforce gender biases’


  10. Our World: Poll Finds 2016 Candidates Neck and Neck
    Mathematically Literate World: Poll Finds 2016 Predictions Futile, Absurd
    Although you may be right about how the media reports polling results, it should be noted that, in politics, polls are not used as a predictive tool, (at least, among political operatives who know what they are doing polls are not so used), but rather as a snapshot of where things stand NOW, as data for deciding how to allocate campaign resources to get from point where-we-are-now A to point where-we-want-to-be B. A series of polls can show a trend, but even there have little predictive value.

    Reporters (or their editors) don;t seem to understand this — those folks working in campaigns mostly do.

  11. OK, OK, I’m going to post one more time then shut up (hopefully) before becoming a nuisance — so on the way out of the replies to this, I’ll just wonder if the drawings on “Conflict?” might be more of an encouragement for people to accept arguments based on the Bandwagon Fallacy than a helpful step towards math literacy…

  12. In the 2010s inflation-adjusted gas price finally overtook the peak of 1980. Significant news at that point at least.

    You have to be careful to not use “inflation” and “per capita” as a method to kill all arguments. Instead, see what the adjusted values are and confirm or deny the headline/argument.

  13. Our World: Average Football Player Earns $3 Million, Lasts 4 Years in NFL
    Mathematically Literate World: Average Football Player Earns $0 Million, Lasts 4 Years in High School

    I think this is the Median Football Player.
    With 14.5k HS football teams
    800 College Football teams.
    32 NFL teams
    Assumption A: that each HS player on the squad lasts 4 years
    Assumption B: Each HS and college team is similar in size to an NFL 53 man squad.
    If we ignore Canada, Practice Squad, Preseason, and Arena (Due to no statistics, maybe this is balanced by A and B, logically not though)
    The Average Football Player plays 2 college games (and one quarter), and makes 34 cents.

  14. Hey! These are hilarious, I would definitely like to see more 🙂

    The one thing I disagree with is:

    Our World: Controversial Program Would Cost $50 Million in Taxpayer Money
    Mathematically Literate World: Controversial Program Would Cost 0.001% of Taxpayer Money

    I think you might reverse these. I think percentages say a lot less about what is actually going on than the actual money spent. $50 Million is $50 Million, and can go to projects that would yield that much good.

    Other than that, these are brilliant. Thank you!!

  15. Compare: “Our World: Economist: ‘Eliminate Minimum Wage to Create Jobs, Improve Economy’
    Mathematically Literate World: Economist: ‘Eliminate Minimum Wage, then Pray Our Model Has Some Empirical Basis in Reality'”

    To: “Our World: Climatologist: ‘Reduce Carbon Emissions to Fight Global Warming, Reduce Environmental Damage’
    Mathematically Literate World: Climatologist: ‘Reduce Carbon Emissions, then Pray Our Model Has Some Empirical Basis in Reality'”

    This was the only headline that accused a relevant expert of mathematical illiteracy and not just a journalist. To me that sounds like we’ve left Mathematically Literate World and entered Ben Orlin World (not that I question your math skills).

  16. I just wish more people would think about what is being touted as ‘news’ before they felt they had an understanding of topics. I watch the news, read the papers or listen to the radio and find i have MORE questions than I had before ‘the complete’ story was told.

  17. Backwards on minimum wage. Against has always been an argument to common sense (raise price, sell less). For needs to do highly questionable empirical studies* to counter arguments to common sense. A certain lawyer who pretends to be an economist on TV short-circuits this problem neatly by asserting that there are reams of studies that aren’t questionable at all and they most certainly prove beyond any reasonable doubt that raising the minimum wage has no unhappy effect on entry-level employment and he’s very surprised those questioning him haven’t heard of them.

    *questionable just when you just consider the measurement problem for a couple of minutes. Common sense may be wrong, but it’s a hell of lot easier to deal with.

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