I think it's sort of strange to refer to comparative advantage, which is taught in every "Introduction to Macroeconomics" class/textbook in existence, as an "arcane" part of economics.
I think your source for the "game dev side" is odd-it's from 2009, a recession with markedly different characteristics than this one-and says nothing about the claim you've made about people losing jobs right now. Usually video game sales track the market, this time they're not doing that, which makes this more interesting. Do you have any links indicating that game developers have been losing jobs at an absurd pace?I haven't been able to find any.
They probably meant out of the platforms Apple competes with. Presumably I could find a platform with, say, 12 users and only 1 non-native app, and if that app followed native UI guidelines I could say it has 100% native UI adoption and thus the “highest” out of every platform ever, but that is a useless statement.
I'm not going to engage in some arcane debate about the particularities of random windows laptops vs. apple ones. The fact is that there are comparable windows laptops at this point when it comes to "bezels and ports," in particular, but also when it comes to most things that make a laptop nice to use.
Presumably the vast majority of people are not going to want to scale their 13-inch display so that everything is significantly harder to read for the sake of increased screen real estate. But I'm glad that the MacBook works well for your specific use case.
I currently work on a MacBook Pro 13 and I switched from a XPS 13 with a 4k display. They're largely comparable, and the only difference I notice or care about is the OS. It seems that is how it is for most people.
That's not really accurate; a similarly specced XPS 13 is several hundred dollars cheaper than my laptop. But Apple is certainly winning the touchpad game, you're right about that.
Yeah, but almost nobody opts for the super high resolution display because the screen is so small that the difference is basically unnoticeable. A similar configuration to my laptop is several hundred dollars cheaper, and that's a not insignificant difference.
Have you seen any Windows laptops in the past five years? Many Windows ultrabooks rival Apple's in terms of "ports and bezels." The XPS 13, for example, has significantly thinner bezels than the MacBook Pro I'm typing this on, at a much more reasonable price.
In terms of aptitude testing, going through some books like "How to Prove It" and working on rigorous proofs-based material (perhaps an introductory analysis book with lots of diagrams) will be helpful. As will brushing up on geometry-lots of people memorize a lot of geometry in middle school/high school, do well in their class, and forget it. Geometric concepts continue to appear throughout math and having a deep grasp of them is super helpful for your first "rigorous" math classes, where the secret to finishing a proof often lies in visualizing or drawing it correctly.
If you want to study applied math and go into the workforce, then my point still stands, going to Princeton vs. Michigan simply doesn't matter. If you want to go to graduate school, it's unclear if it matters all that much. Princeton tends to draw the most talented young mathematicians in the world, and has for decades. Presumably if a student of that caliber went to Michigan, they would do just as well, because Michigan also has talented mathematicians who do good research and can write good letters of recommendation for graduate school.