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> Lying is a core part of communicating mathematics. We lie to kindergarteners when explaining fractions. We lie to fourth graders when approaching limits... H

• Terr_ 16d ago
  Terry Pratchett, The Science of Discworld: > As humans, we have invented lots of useful kinds of lie. As well as lies-to-children ('as much as they can understand') there are lies-to-bosses ('as much as they need to know') lies-to-patients ('they won't worry about what they don't know') and, for all sorts of reasons, lies-to-ourselves. > Lies-to-children is simply a prevalent and necessary kind of lie. Universities are very familiar with bright, qualified school-leavers who arrive and then go into shock on finding that biology or physics isn't quite what they've been taught so far. 'Yes, but you needed to understand that,' they are told, 'so that now we can tell you why it isn't exactly true.' > Discworld teachers know this, and use it to demonstrate why universities are truly storehouses of knowledge: students arrive from school confident that they know very nearly everything, and they leave years later certain that they know practically nothing. Where did the knowledge go in the meantime? Into the university, of course, where it is carefully dried and stored.
  • amosj 16d ago
    Brilliant
  • bmacho 16d ago
    I don't get it? Nevertheless you don't have to lie to kids in any field, science, art or otherwise.
    • x-complexity 15d ago
      > Nevertheless you don't have to lie to kids in any field, science, art or otherwise. ...if and only if the kid in question has the mental capacity to take on the whole truth without confusion. Some kids have the potential to go hog wild on multivariable calculus, and they should be given the chance to handle it all. But they shan't be the benchmark that others with differing capabilities must hit to understand a concept.
    • photonemitter 16d ago
      the earth is round, but not really quite. Gravity is 10 m/s*2, but not quite, it’s the same everywhere on earth, but not really. A day is 24 hours, but not actually. A year is 365 days, except it’s not, and the leap years correct for the disparity, but not exactly. Light travels at c, but not across all distances, or through all mediums. There’s no sound in space, but there is wind, and it does sort of carry vibrations in a way that roughly is what we mean by sound Space is really really cold, but it’s not actually cold, hot/cold doesn’t measure the same way - it’s not about lying, that’s the wrong way to say it. We explain too simply. We lie by omission… The point of Pratchett is to make fun of how the university humbles the students, trading their self-assurance in their knowledge for actual knowledge that is dried inside its books
      • deleted 15d ago
        [deleted]
• bananamogul 16d ago
  I don’t remember us getting to fractions in kindergarten, but maybe the curriculum has radically changed since the early 70s. What exactly is the lie? 1/4 and 3/8 equals 5/8. Is there’s something more to that? Is that fundamentally wrong?
  • aleph_minus_one 16d ago
    > Is there’s something more to that? Yes: this is about building the quotient field (field of fractions) [1] for some integral domain, or more generally, building the localization ([2], [3]) of a commutative ring with respect to some given set that is closed under multiplication (the special case of the quotient field for a ring R is obtained when one chooses R\{0} as such a set). -- [1] https://en.wikipedia.org/w/index.php?title=Field_of_fractions&oldid=1372290847 https://en.wikipedia.org/w/index.php?title=Field_of_fraction... [2] https://en.wikipedia.org/w/index.php?title=Field_of_fractions&oldid=1372290847#Localization https://en.wikipedia.org/w/index.php?title=Field_of_fraction... [3] https://en.wikipedia.org/w/index.php?title=Localization_(commutative_algebra)&oldid=1371034380 https://en.wikipedia.org/w/index.php?title=Localization_(com...
    • wakawaka28 16d ago
      It's mighty pretentious to say that one needs all that theory to simply answer the question lol. For many questions, only the most rudimentary theory is plenty to get an answer, that is exactly the same answer as a more elaborate theory would yield.
      • aleph_minus_one 16d ago
        If you just want to do some stupid computations: sure. But this is not what mathematics is centrally about. The central point is the kind of thinking about the respective topics (and understanding it) which these more abstract definitions encode. Understanding the topic just enough to do some elementary computations does not give you the kind of thinking that is often near a transcendental experience. Just to give one example: the reason why the localization of a commutative ring (a generalization of the field of fractions) is introduced is that many properties of ring hold if and only if they hold for all of its local rings; see for example [1]. This means to understand some property of a commutative ring R, we "just" have to understand its (simpler) local rings. This is an example why one wants to study such ideas; on the other hand, I can imagine sooo many more exciting things to do with my life than dividing numbers by each others to form fractions. :-) [1] https://en.wikipedia.org/w/index.php?title=Localization_(commutative_algebra)&oldid=1371034380#Localization_at_primes https://en.wikipedia.org/w/index.php?title=Localization_(com...
• cheesecakegood 16d ago
  Now chemistry on the other hand… OK there’s still no intent to deceive but almost all of the “rules” you learn have giant exceptions