Is there a "pre-statistics" book that teaches the thinking skills and concepts needed to understand statistics?
Something related: I often feel like I'm doing math when I work with information, especially when drawing out concepts and their relationships. Like 3D Tetris, but with recursion. There are also patterns in categorization. One of my purposes in learning math is to be able to quantify relationships between concepts, and create models, etc. What would I need to know about in this case?
However I will say that, as you learn more math, the intuition and big picture thinking is way more important than details. I normally forget the specifics of how something works, but I know what I’m trying to do and what thing I need to look up to do it. There is very little need to memorize things besides having enough “RAM” for the moment. You always have pen and paper to write stuff down!
Regarding modeling, the sky is kind of the limit. The more math you know, the more abstractions you learn and start to see in the world. Dynamical systems is a good field to look at but I’m biased because it’s my main topic. Despite its usual applications in physical modeling, an algorithm is basically a time-discrete dynamical system: you recursively apply a function to a state and that gives you a new state. I have certainly seen algorithms analyzed from that perspective before.
Another area you might find interesting is Algebra. This isn’t like the algebra you took in school but more about looking at a space of objects that interact via some operation and characterizing what you know about the space given that operation. A classic example is that rotation operations form an algebraic structure known as a “group” due to the fact that any two rotations gives you a third, rotations are invertible (you can cancel a rotation by rotating in the opposite manner), and they follow the associative property. There’s a book I’ve been meaning to read about how to use this kind of algebra to design safer and more intuitive APIs by considering the data structures of the APIs as objects and functions / methods as operators on those objects.
Dynamical systems is a great new keyword! Algorithms are a perfect example. I am exploring system dynamics from a metacybernetic point of view (via the viable system model). My focus is the dynamics of humans in complex systems, how systems change human behavior and vice versa.
Does big picture thinking in math involve understanding/intuition of the implications of formulas, and how they interact with other formulas (or other mathematical entities, I don't know if formula is a general enough term for "group of math actions")?
Graph dynamical systems looks promising, because I draw similar pictures when showing relationships over time. Fractals are always good, drawing fractals taught me to think recursively.
Is this the definition of group in the algebra you mentioned? https://mathworld.wolfram.com/Group.html
I am also interested in the way models create understanding, and how technical models can be visually altered to aid in understanding. I have a background in visual psychology, and see many mistakes that cloud the meaning of what is being communicated.
You don't need much beyond basic calculus. Most suffer from some mental block they got installed at a young age akin those that say "I'm bad at math" because their teacher sucked. Dive in and you won't regret it.
I feel stats is has a somewhat similar effect even among those with math education. Several friends who have a degree in math recoil at the first mention of stats concepts.
It is actually even fashionable in non-english countries. Declaring "I'm bad at [my native language], I only use english anyway" makes you a better person somehow. And it's not rare in other areas either – in post-truth world it's trendy not to know things.
Not that he was bad at German, necessarily, but that it was overly complex vs English, so he and his significant other even used English at home when they both didn't have to.
This is just one example, of course.
I was actually surprised to hear him say that (though it may have been to thwart my attempts at speaking some German when we had a meeting. I don't know any German,lol).
In my country it's especially fashionable not to know a native language for a people in tech. "It's impossible to talk about tech anyway in native languages, so we all should use english anyway in future" is very common. I tried to fight with it localizing/translating software for many years, but I've given up for now.
I can learn math fairly well if I have the right written material and the right direction. However, I do not retain math skills: without active practice, I revert back to "how do fractions work?"
For example, I did extremely well in a college algebra course that was partially online (combined with Khan Academy to catch up). I could do my tests perfectly in pen, much to the amusement of the assistants. I could make connections and see the implications and applications of the math. Roughly three to six months later, I was back to forgetting fractions.
I can't learn these things over time, but I can learn them all at once. I'm collecting resources for my next math adventure.
Would you be OK with elaborating on this a bit more?
The injury was diagnosed via SPECT scan. Two of them: one after mental activity, one after physical relaxation. This also revealed that my brain relaxes with mental activity, and "lights up" with physical relaxation.
I always knew there was "something" wrong with me, so I jumped at the opportunity to get a brain scan. The clinic was a little suspect in that they claimed to be able to diagnose mental health issues via the scan, but they combined the scan with more traditional evaluations.
To quote pg, many conversations on the Internet:
Person 1: ∃x P(x)
Person 2: -(∀x P(x))!