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I’d like to see statistics taught in high school, perhaps in place of calculus. I was good at calculus in high school but haven’t used it since. Conversely, I encounter statistics in the media almost every day, and it took me quite a while to learn what to ignore or take with a grain of salt (practically all of it).

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You need calculus to really understand, at a deep level, statistics. However, I tend to agree with your proposal for high school- even a cursory understanding of stats would probably be relatively more useful for an average high school student than basic calculus.

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Bad statistics, in the press and many academic papers, is far far more common than bad calculus. It’s easier to know bad statistics if you know some. Every HS grad has some ideas about statistics, including wrong ideas. An intro to statistics class would be better than calculus, trigonometry, and maybe algebra 2.

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You can't really understand probability without calculus. Where do those tables and tests come from? Central limit to what?

Notice that while ideas about chances and likelihood have been worked on and gambled with since the dawn of civilization, calculus (pace Archimedes) was a product of the mid 17th century, and came long before work on normal distributions as extension of binomial logic, which came nearly a century later.

Euler's contributions (some before he turned 20!) were largely dependent on important results from calculus, and Gauss's work didn't come until 1823, and unlike calculus the basics of which can be sufficiently grasped by the numerately talented ten percent, most of the insights about probability are only genuinely cognitively accessible to a tiny fraction of the population. Try getting through half a page of E.T. Jaynes without reaching for some ibuprofen.

The point is that these kids wouldn't be learning to really understand the thing they are working with. It's the difference between learning how to use a word processor vs learning how to code the software.

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I’m talking about more basic stuff like sample size, standard deviation, longitudinal study vs sampling etc. Those should be the first question anyone asks when seeing a headline.

Also, that polling in general is junk.

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Ordinary people do NOT need to know how to code. They need to know how to use a word processor. Ordinary people do not need to know how to derive the central limit theorem--or even to know what it means. They need to know how statistics are used, and misused. Of course, they'll need some basics. But they don't need to know how to derive the binomial theorem. They need to see it, feel it. Have them test it by flipping coins and rolling dice. Run the course mostly as (real or made up) case studies. What is the "analyst" doing here? What is he trying to show? Should you be persuaded?

The more theoretical a statistics course is, the more high school students will forget it after it's over. Which makes it just a waste of time.

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I agree that statistics seems much harder to me than calculus.

I doubt a high school statistics requirement would be put to good purpose, and I doubt still more that there would be very many people capable of teaching it.

My longtime suggestion has been - since most people are not going to get far with math - to teach the history of math. The subject is pretty interesting and I think this would instill some, ah, intellectual humility. But also dignity - let us invite you in to this world that you will never be comfortable in, perhaps, but you can become comfortable with some concepts about how it came to be and its uses and wilder manifestations.

I wasn't bad at high school math, but had no creativity with it and I think it's fair to say I saw only the problem, not the whole (and I rarely did my homework) but I have gotten a lot more out of various popular treatments of math subjects, e.g. the Jordan Ellenberg book, another about incompleteness, Martin Gardner, etc.

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Conversely, I would however like to see more math in the humanities and history teaching.

For instance, wrt current events in Gaza - considering its current population - you're dealing with a people/problem that basically didn't exist 50-odd years ago.

Why is that?

That is so much more important to understand than whose ancient claim is stronger, or who did wrong to whom on more days during the Mandate, or how Palestinians came to be defrauded of the whole of their desert desserts if that is what they feel happened- by other Arabs first of all?

Food aid? Medicine? Ideology? - "told to" aggressively breed, an ethnicity that once had no trouble keeping its numbers in check? Is it urban life in their concrete boxes - nothing much for many of the men to do but stand around, so no reason to plan a life, which plan would include reproduction?

At the very least, the humble "intellectual" would keep alive in his mind that the 1970s worriers about population, might not be the utterly foolish clowns he must reflexively denounce them as. That concern about population had many strands ...

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100% same here. One year of algebra is the most you could need.

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This discussion raises a question of what in today's world a HS curriculum should be? Calculus for those looking for a career in STEM makes more sense than for others. To be an educated citizen, probability and statistics seems to make a great deal of sense.

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I can appreciate the sentiment but there always remains the questions of stagnant human nature. Perhaps teaching children decision science or the training the brain to make rational decisions may be a useful tool but one must also consider how that would inevitably generate the status game hierarchical imposition of society, particularly one that is exceedingly atomized seeking tribal collectivity. What I mean by this is, a step towards rational decision making becoming the norm or appearing so (humans exhibit irrational behaviors with post hoc rationalizations for the most part throughout decisions despite the reflections on training) which may just be an outgrowth of utilitarianism, one can begin to see how this will be extrapolated to a wider public and the coldness that this will effectively bring. Lasch's revolt of the elites comes to mind as a prelude prediction of this model at scale where the hyper rationalists trained decision makers will generate the conclusion that status is based on being naturally superior in intellect/conscientiousness therefore nobless oblige is merely an attack on meritocracy.

Some may suggest that it's going to happen anyway while others are going to say sympathy/empathy will be rational (remains to be seen but both sides will inevitably present these arguments regardless as they always do) but people who often try to introduce new ways to train children always happen to have blind spots to the trade offs and always happen to look for the bright side of things (optimism tends to have a bias towards advocating positive self interest on a general scale while often producing neglect/carelessness of trade offs) while ignoring the latent effects of such a policy while suffering from the exact problem you stated where ppl will seek to forward their model of policy/expertise for funding/recognition. It is a conundrum and interesting to think about but I think in the worship of novelty and desperation to break out of a funk, ppl will advocate for things that seem innovative and rational but often ignore the trade offs that will inevitably arise (trainers/policy proscribers often take the position that human nature can change if enough training will suffice because of course). Apologies for the long write up.

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your mention of Lasch reminds me that we are discussing that book at noon NY time on October 24 (today). Free for anyone, register here: https://libertyfund-org.zoom.us/webinar/register/WN_xIA06oSgRk2uq8K8JJG08Q#/registration

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Always be closing haha

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founding

Another mark of intellectual humility is a willingness to say, "I don't know."

In a democracy, a necessary corollary virtue of intellectual humility is *wise deference*. A tricky virtue, not to be confused with deference to experts or deference to authority.

Political competition, adversarial judicial systems, and bureaucratic spoils induce development of industries of rival experts.

I defer a lot to Arnold Kling about economics, thinking in bets, and finding one's sea legs during systemic shocks (e.g., the great recession, the pandemic, new regional wars that risk escalation into world wars).

But wise deference has its limits. To illustrate: Since I don't follow local politics (I have my head in the clouds), when the latest town election crept up on me, I asked a trusted, smart, wise friend, "Who should I vote for?" He replied: "I don't know. Wait. Let me ask my wife."

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I hope your readers will follow the link to Hamid's piece and make up their own mids about his perspective. Based on your snippet and comment above, they may be surprised to find that he begins the piece with the observation that Hamas "brutally massacred hundreds of civilians"

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Yes I did see that earlier post, and I understand that you hate Hamid more than you hate Hamas, but perhaps you have some readers who feel differently, and I would urge them to read his article before reaching a conclusion about his perspective.

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I would urge you to look at what Hamid omits. About 1948, for example, he makes it sound like the only thing that happened was that Israel decided to drive out lots of Arabs. He makes no mention of the fact that Arab states launched a war of extermination the day that Ben-Gurion declared a state. If there is a charitable interpretation of Hamid's article, I don't see it. Maybe other people will.

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He is describing what pro-Palestianian activists tend to emphasize, and he is doing so accurately. They certainly do not tend to emphasize the war that preceded the expulsions. Here is the exact quote:

"For their part, pro-Palestinian activists tend to emphasize an original set of injustices that occurred in 1948 when Israel was created — namely, the expulsion of Palestinians from their land and homes — and then the subsequent injustice of a never-ending occupation that began in 1967. Because these are the original sins, everything else can seem like a distraction from the core grievance. Even for Palestinian opponents of Hamas — and there are many — Hamas might be vile, but it is more a symptom of the conflict than a cause."

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It's behind a paywall. Please copy and paste the text here.

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Here's a link that bypasses the paywall: https://wapo.st/475NkNR

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Thanks for that. In another quote, he uses "while refusing to" instead of "but must not". Then he meta-meta-condemns the meta-condemning of his hedged condemnation.

"We can — and must — condemn Hamas’s heinous acts against Israeli civilians while refusing to forget that Israel has been a perpetrator of a brutal occupation against Palestinians. Some will condemn this as “bothsidesism,” but there are, quite literally, two primary parties to the Israeli-Palestinian conflict, each with competing — and, sadly, irreconcilable — narratives."

People can interpret that all for themselves. Personally, I feel no obligation to play dumb about a rhetorical pattern one has seen thousands of times which correlates almost perfectly with the intent to equivocate and excuse with the minimum amount of plausible deniability necessary to maintain respectability. The whole point of an immediate but / while following a perfunctory condemnation is precisely to soften the condemnation as not really that condemnable, if you think about it the right way. To convey that the inexcusable is in fact somewhat excusable, the unjustifiable somewhat justified, just enough at any rate so that people can pretend they don't have to be bothered and it's ok to stay loyal to the side that ecstatically celebrates this wicked stuff.

The irony is that he extols the duty of moral agency without succumbing to nihilistic relativism, but then eschews that very same obligation to make moral pronouncements in an unequivocal and unhedged manner. "While refusing to forget" is just another way of saying the infinitely flexible tribal moral calculus that gives a rationalized pass to my side, but never to the other side.

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If you think that Hamid's position is no different (or even worse) than that of Hamas itself, or of those who openly celebrated the atrocities (as Arnold seems to do) that's your perogative. Personally, I think it's an absurd and inhuman position that will continue to cost a lot of lives, Israeli and Palestinian.

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Templeton's track record of giving big grants in this area does not inspire much confidence. I know a little about Jeffrey Rosen's Constitution Center, and he is a great guy, but comes off as hopelessly naive when he assures the public with non-humble total confidence that "... separating their constitutional views from their political views, just like Supreme Court justices do ..." Dude, please. The whole problem of whatever they are trying to get at with humility cannot be addressed when one is non-humbly defining the bounds of respectable debate to exclude large segments of opinions. For the """conservative""" report on restoring the guardrails of democracy he commissioned ... Jonah Goldberg and David French, the most infamously fake conservatives around after Bill Kristol and Jennifer Rubin.

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"Of the hammers, I thought that Annie Duke’s was the most interesting. She wants to embed the techniques of decision science into the K-12 curriculum. These include probabilistic reasoning ... "

That's in some tension with the Null Hypothesis in Education. It's hard not to roll one's eyes whenever someone suggests that the answer is more education and more awareness, as if this was some kind of long-standing unsolved problem and millennia of our predecessors were somehow able to accomplish so much while being unable to make good choices and judgments because unschooled in decision science in their youth.

Most smart people I know who had formal university or professional training in probability, statistics, and rational decision-making are still not good at it even when (sometimes because) their own personal interests are on the line in scenarios of high stakes.

Sound and rigorous statistical reasoning is in practice very difficult, and Andrew Gelman's blog is a great resource for a depressing constant stream of top minds making loads of boneheaded errors, or easily slipping intentionally misleading analysis past an entire gauntlet of gatekeepers. I had a wise friend remark that giving the modern statistical suite of powerful tools and sophisticated techniques to anyone but an experienced mathematician was like handing a loaded revolver to a toddler and then letting them loose on a crowded playground.

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I agree, and half the time the commenters on Gelman's blog didn't seem in agreement. (I haven't read him in years; I at one time looked into his blog, hoping he would be my communicator on stats subjects but didn't find him as clear as I wanted him to be.) Some things may not be simplifiable. My feeling is they ought to be more so, if sound - but I have nothing to back that up except my ignorance on subjects that have prompted this thought!

On the other hand I am so muddled now, and my memory is so poor, perhaps the fact that nothing I learn in middle age can make a permanent impression in my brain bears no relation to what kids might be capable of.

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October 24, 2023
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There are still some analog clocks around. And the way they turn time into distance potentially opens the mind a bit to metaphor and math. An analog clock is just a different kind of graph.

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I should say we are arrived at Intellectual Humility when the self-appointed intellectuals who have colonised our institutions and are running our affairs - because we are too dumb to do so - on the principles of Marxist Socialism, recognise their intellectual vacuity.

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In other words, never.

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Richard Feynman had many meaningful things to say about "Intellectual Humility". E.g. "The first principle is that you must not fool yourself - and you are the easiest person to fool."

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It would be interesting to see "Intellectual Humility" compared and contrasted with 'high quality critical thinking'. Is there any difference?

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Might not we all be better off if the scribbler broke his pen?

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If I didn't think it'd be a waste of time, I could make several very novel grant applications to Templeton's intellectual humility project that wouldn't run afoul of sensibilities on areas of current controversy. But it seems to be they are most interested in leveraging the capabilities of people "in the arena" who already have plenty of experience in communicating to public audiences, TED talking, etc.

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I’m sure many of us would be interested in those thoughts. Maybe write up a couple “ideas with a paragraph” into comments?

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I know this post is not about hamas, But lately I have been thinking hamas is a feint. What if I ran has a nuke? what if hamas’ actions were meant to deplete the iron dome? What if the nuke is in hezbullah’s hands? What if the real goal is the nuke Israel?

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Some material for our nightmares.

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First, they have to have a nuke. Then they have to deliver it. Then they have to escape the consequences.

Nuclear weapons are not magic, automatically conferring victory to the user. The end of WW2 distorts our thinking. The Japanese had already lost the war. It was only a matter of time, and enormous casualties. Hiroshima and Nagasaki gave the Emperor a symbol of overwhelming might to which they could honorably surrender.

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You assume consequences.

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A single nuclear weapon would not destroy Israel. Israel has more than one.

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The scout and soldier analogy is good but I really like Tim Urban's thinking ladder. He has 4 groupings: scientist, sports fan, lawyer, and zealot. Don't get too caught up on these labels. The descriptions are better. I didn't read all of what's at this link but it seems to at least capture the intent of these four terms.

https://anthonydelaney.com/2023/04/28/how-can-we-think-at-a-higher-level/

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To gather those minds together to come up with a definition of the term “Intellectual Humility” seems like a massive waste.

Isn’t it like pornography- one knows it when one sees it?

Agree probabilistic thinking is important and should be taught at a young age. My kids went to an elementary school (private school overseas) that spent some time on this, which we thought was fantastic (except that they didn’t spend enough time on basic arithmetic and you can’t do probability without fractions and decimals, though playing dice games is a fun way to learn fractions and express them as decimals)

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They used to teach logic as part of the Trivium - logic, grammar, and rhetoric.

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