Hard disagree.
Lying is with intention to deceive.
Teaching is simplifying with the intention that they understand and get the correct intuition.
Math is not about lying, that's just silly.
> 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.
Nevertheless you don't have to lie to kids in any field, science, art or otherwise.
- 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
...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.
What exactly is the lie? 1/4 and 3/8 equals 5/8. Is there’s something more to that? Is that fundamentally wrong?
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_fraction...
[2] https://en.wikipedia.org/w/index.php?title=Field_of_fraction...
[3] https://en.wikipedia.org/w/index.php?title=Localization_(com...
Lies to children are like... time-reversal symmetry.
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_(com...
Nothing in your comment makes me want to go learn more theory, and I would argue that it's nonsense to anyone who is not a mathematician.
Imagine arguing that the only way to understand or appreciate basic set logic is to know all about infinite sets and ZF axioms... Most people, even mathematicians, will not understand all of that and have only heard about it in the most basics if at all.
A similar phenomenon happens with philosophy. Imagine arguing that simple logic is "stupid" and that one can only reason well if they have a total understanding of epistemology. I happen to think epistemology matters, and that people can benefit from at least being aware of it, but it is really a separate topic from actual mechanical logic and argumentation.
What a coincidence this came up today.
I'm not a mathematician. I minored in math, but even the undergrad work was honestly difficult for me.
For most people, this might be nonsense. But it doesnt have to be.
I'm trying to learn about Fast Fourier Transforms because they're relevant for an embedded device system I'm investigating. I'm also not an Electrical Engineer so it is mostly new to me.
To understand the language of FFTs, linear bases and the like, I've started working through Axler's Linear Algebra Done Right.
First, just learning more theory shows me we can learn and grow in our old age.
This week I worked through linear spaces. I'm actively asking myself questions and working with other fields besides the reals and complex numbers so I can understand coding theory in general more.
And the parent's comment about quotient rings is directly related to an active learning question I asked myself about whether the set with only the zero element is a linear space. I don't think it is a field if 0 is the multiplicative identity, 0 can't be 1, so it can't be a linear space, right?
But it works. I guess the set of the field for the scalar in a linear space is always assumed to contain more elements. It's a different set than the linear space. It seems like, duh, of course it is. But you don't see it until you work through it. And I'm guessing my experience can inform teaching others.
It's confusing to me, maybe because the notation is sparse in explicitly defining the set of the linear space and the set of the associated linear space.
But this helps me truly understand linear codes down the line, and Linear Feedback Shift Registers and FFTs. It's not just theory to me, I can now understand what my peers are saying and contribute my own thoughts.
Wouldn't that be great? If we could teach our kids that learning for the sake of learning is awesome? If only that was all this world was.
But you're right, you and the thousands of others posting, it's not. You have that voice, and the hundreds of online stories about college losing value have that political voice.
In the post-AI future I can imagine recreational mathematics being a socially approved past time. It helps with age-related cognitive decline, etc.
But I can also understand people in that post-AI future who had smart political ideas that were more important to them than smart math ideas.
Impactful ideas.
Just getting snapshots and puzzling out that post-AI future I don't know if we'll have the right space to encourage positive care for our mental and physical landscapes.
What a coincidence this came up today.
I'm not a mathematician. I minored in math, but even the undergrad work was honestly difficult for me.
For most people, this might be nonsense. But it doesnt have to be.
I'm trying to learn about Fast Fourier Transforms because they're relevant for an embedded device system I'm investigating. I'm also not an Electrical Engineer so it is mostly new to me.
To understand the language of FFTs, linear bases and the like, I've started working through Axler's Linear Algebra Done Right.
First, just learning more theory shows me we can learn and grow in our old age.
This week I worked through linear spaces. I'm actively asking myself questions and working with other fields besides the reals and complex numbers so I can understand coding theory in general more.
And the parent's comment about quotient fields and rings is directly related to a question I asked myself about the
You are free to ignore mathematics that is not completely trivial. I prefer (and would rather recommend) to understand it, and use this understanding to build a >1-billion-USD/EUR application out of it. :-)
OK there’s still no intent to deceive but almost all of the “rules” you learn have giant exceptions