Is it just me or are we horrible at teaching advanced math? Where are the examples (with actual numbers)? Where is the motivation? Where are the pictures?
That’s a pretty good bar and I wonder if we could just cut to that chase earlier. But I also believe that people need enough math to see when they’re being cheated, and I feel like you could just tell middle schoolers that and they would pay attention. Maybe even primary school.
You told Billy he could have three apples, and now there are two left. Did Billy take more apples than he should have?
It’s always how do you share your cookies fairly with your friends and if they’re my cookies why do I have to share them at all? Screw “fairly” I’m keeping the extras at least. That sort of sharing is a socially advanced concept they don’t entirely get just yet.
Actually being able to do stuff with Bayes law by hand is going to be not only hard to teach, but probably impossible to remember for those of us who don't actually do math in real life. People forget stuff after a few months or years.
I highly doubt the average person is interested in checking the math on a science paper, so if you want the general public to understand statistics you... have to show us all a reason to, and also teach us all of the related skills needed to make it useful. Or else.... we will all just forget, even with the best teacher in the world.
Most of us aren't doing random game engines as a hobby project or testing things on bacteria cultures.
Maybe they should teach it in context of how to understand a scientific paper, since that's one of the more relevant things for non-pros. If you just teach statistics alone people will say
"Ok, now I know that it's easy to lie to yourself if you don't use any numbers but I don't have collections of large numbers of data points in my life to actually analyze"
If you have a way to fix this, you would be set for life, going around playing a sort of corduroy jacketed Robin Hood, keeping the rich from stealing from the poor.
In upper-level undergraduate math, I made a game of seeing how many pages I would go before seeing 7 printed anywhere. It was usually 10 pages, if I included the page numbers.
Here's an example:
https://en.wikipedia.org/wiki/Homology_(mathematics)
It has motivation, examples, and even actual numbers (though they're really just 0 and 1. most of the time). In my opinion, it's very good and clear exposition, for an encyclopedic article. However, I strongly suspect that people without enough mathematical knowledge (and "enough" in this case is something in the neighborhood of "enough to obtain an undergraduate degree in Mathematics") will simply not get anything about it beyond "it's about number of holes" (and that's not even remotely close to the whole picture: homology theories are important and useful in context of things with no "holes" to speak of). If you think otherwise, but not know what a quotient group is, you're just fooling yourself.
This is something I observe on HN a lot: people don't understand advanced mathematics, and are dumbfounded by the fact, trying to blame weird notation mathematicians insist on, or lack of motivation/examples/pictures etc. I never see people here do the same with advanced physics ("if the Standard Model is so standard, why can't they briefly and clearly describe what it is" is not something I ever see), molecular biology, or material science. People seem to know their limits and understand that really grokking these fields requires many years of deep study.
I think it's because many people on HN have good experience learning mathematics at school: it was something they always grasped really easily, and were easily able to figure out how to calculate derivatives, integrals, get matrices into normal forms etc. I don't want to rain on anyone's parade, because these things are still relatively difficult, and it does require more intellectual ability and effort that probably 3/4ths of the population aren't capable of. However, relative to advanced mathematics, undergraduate calculus is really rather trivial stuff.
Point is, if you don't understand modern advanced mathematics, you shouldn't get any more disappointed than you are about not being able to play violin. These things just don't come easy.
