• Down With Geometry!

    Sure, I guess. But who cares?

    Everything seems to be pretty calm in the political world these days, so let’s switch gears momentarily and talk instead about math education. According to the Wall Street Journal, Steven Levitt (of Freakonomics fame) is now the one-billionth person to propose that we change the high school math curriculum to include more “useful” subjects:

    Dr. Levitt’s proposal is simple: Condense three years of high-school math—typically Algebra I in ninth grade, Geometry in 10th grade and Algebra II in junior year—to two years. Then, devote the freed up time to more relevant learning, such as data science or financial literacy.

    I have a better idea: just get rid of plane geometry completely. It is entirely useless both on its own and as a steppingstone to further studies in math, which are almost all based on algebra and analytic geometry.

    But Kevin! Geometry is where we lean about axioms and proofs. Those are critical to understanding how math works.

    No, they aren’t. But if you really want everyone to learn about the foundations of math, then make it a one-month unit in Algebra II or something. You can use plane geometry as an example, or you can use arithmetic, which is probably a better bet. Or you can just skip it, since foundations is a fairly advanced subject that’s of no real use for anything at the high school or undergrad level.¹ As for proofs, those are already covered in a semi-intuitive way in Algebra I, and that’s plenty. Students will get plenty of proof workouts later on.

    This would have the added benefit of making Algebra I and Algebra II into consecutive courses, instead of giving students a full year to forget Algebra I before they take up their study of more advanced subjects. A condensed unit on trigonometry, which is semi-useful, could be folded into Algebra II, taking the place of worthless topics like synthetic division. This can be followed by either calculus or data science, depending on your druthers.

    Anyway, down with geometry! Who’s with me?

    ¹I say this as someone with a considerable fondness for the foundations of math. Why else would I have a cat named Hilbert?

  • Coronavirus Growth in Western Countries: November 10 Update

    Before we get to our regular set of COVID-19 charts, here’s a look at worldwide deaths:

    I don’t know how accurate the worldwide data is, but it’s an understatement if anything. We are already well above the April peak and still skyrocketing upward.

    In the US, we recorded over 1,400 deaths on Tuesday, one of our highest totals ever—and given our case counts and hospitalization rates there’s every reason to think this is going to keep going up for quite a while. There’s probably not a lot we can do about this now—it’s already baked in—but we could certainly reduce our future death rate by simply wearing masks everywhere at all times. Unfortunately, our current president will have none of it. He’s too busy with the important business of trying to convince his followers that the election was stolen from them.

    Here’s the coronavirus death toll through November 10. The raw data from Johns Hopkins is here.

  • It’s Not a Coup. Not Yet, Anyway.

    Ned T. Johnston/U.S. Air/Planet Pix via ZUMA

    Two polls, two results:

    Is the glass half empty or half full? Before you answer, keep this in mind:

    Why does Donald Trump suddenly want a bunch of loyalists in charge of the Pentagon? It’s a little hard to come up with benign answers, isn’t it?

  • Joe Biden Won. But Trumpism Didn’t Lose.

    Considering what the Trump team is up to right now I hate to interrupt with some bad news, but I’m seeing a fair amount of wishful thinking about Joe Biden’s victory that really needs to be corrected before it congeals into lefty conventional wisdom. It’s true that once all the votes are counted, Biden will have a nice popular vote win, and it’s also true that he’ll most likely win over 300 electoral votes.

    But in terms of the states everyone was watching this was not a big victory. The key states, as in 2016, were the “blue wall” of Pennsylvania, Michigan, and Wisconsin. And in those states, Biden’s aggregate winning margin was 1.4 percent of the total vote. In 2016, Trump won by 0.6 percent of the vote. That’s a switch of two percentage points.

    No matter how you spin it, that’s just not very much. In a closely divided country, it was enough to give Biden a victory, and in that sense it’s a lot. And Democrats did make gains in a few specific demographics. But in terms of how overall attitudes have changed, it’s only a tiny turnaround. After four years of watching Trump in action; suffering through a pandemic; and not having the hated Hillary Clinton on the ballot, hardly anyone changed their minds. Add to that a tiny increase in the popular vote; no pickups in state legislatures; a loss of half a dozen House seats; worrisome losses among Latinos; and (so far) only a single pickup in the Senate, and it’s just not possible to say that the Democratic Party demonstrated any sort of increased appeal to the broad electorate.

    Think about that: After four years of Donald Trump, only a tiny percentage of the American public switched their votes to the Democratic Party.

    At the moment, the evidence is too thin to draw any conclusions about why this is. And given the complete uselessness of the exit polls, it might well be months or years before we can really say what happened. One way or another, though, we shouldn’t fool ourselves: there’s no real evidence that the country showed any increased love for either the Democratic Party or the liberal agenda writ large. We need to figure out why that is.

  • Lunchtime Photo

    Yesterday I showed you a picture of the border fence near Jacumba Hot Springs. Today I have a picture of the end of the fence. There’s nothing photogenic about this, however. It’s purely photojournalism. As you can see, when the fence hits a hill, it just stops. There’s precisely nothing to prevent someone from walking up to this section of the fence and walking across.

    That is, there’s nothing except the Border Patrol, which is presumably keeping an eye on places like this. But there’s at least a mile or two of unprotected border that goes over this hill, so there’s a fair amount for the Border Patrol to watch. And I imagine there are lots of places just like this one.

    None of this means the fence is useless, but it does mean that it’s primarily guards and patrol officers who are responsible for preventing illegal crossings, not the fence itself. This has been true of border walls and fences throughout human history.

    September 26, 2020 — Near Jacumba Hot Springs, California
  • The Republican Party Needs To Be Razed and the Earth Salted Behind It

    Why do I think the Republican Party is beyond redemption? I view their policy positions as mostly appalling, but that’s not the reason. I’m going to disagree with pretty much any conservative party, after all. It’s more about the underlying nature of the party leadership and what it believes it has to do in order to win. Over just the past decade or so, the Republican Party:

    • Chose Donald Trump as its presidential nominee.
    • Has openly strategized about suppressing the Black vote because Black voters heavily favor Democrats.
    • Played footsie with insane conspiracy theories like QAnon.
    • Spent the entire Obama presidency ginning up fake scandals.
    • Lied relentlessly about its dedication to reducing the deficit.
    • Lied equally relentlessly about its dedication to passing a health care bill.
    • Lied (and lied and lied) about the impact of its tax bills on the rich.
    • Has killed untold thousands of people by making mask-wearing into a partisan football during a pandemic.
    • Has openly appealed to racial bigotry as a way of increasing its share of the white vote.
    • Denied the obvious reality of destructive climate change solely for partisan benefit.
    • Is currently doing its best to convince its base that the entire 2020 election was fraudulent.

    This is, needless to say, not an exhaustive list, and none of it has anything to do with conservative policy. It speaks solely to the moral judgments of the party’s leaders, and these moral judgements are now so ingrained that I see no hope they’ll ever be abandoned. Perhaps in a different media universe they would have already paid a price for this, but in a conservative media universe dominated by Fox News, talk radio, and the Wall Street Journal editorial page they can get away with almost anything. Most Republican voters probably don’t even know their party has sunk to this level.

    The key question is whether it’s possible to convince moderate conservatives to care about this kind of stuff. Or, like so many of us, are they willing to give it a pass as long as Republicans do the things they want them to do? It’s a discouraging thought.

  • Coronavirus Growth in Western Countries: November 9 Update

    Here’s the coronavirus death toll through November 9. The raw data from Johns Hopkins is here.