I run gpt-oss 120b model on ollama (the model is about 65 GB on disk) with 128k context size (the model is super optimized and only uses 4.8 GB of additional RAM for KV cache at this context size) on M4 Max 128 GB RAM Mac Studio and I get 65 tokens/s.
Coaching does not imply superiority. I doubt any sports coach could substitute any player in a competitive game, yet they can coach them to become better version of themselves.
What engineers usually struggle with as they grow into more senior roles is the transition from being primarily a technologist to being a leader. This is such a huge shift for a lot of engineers and requires soft skills and communication style adjustments. The more senior you are the more your focus shifts from coding to listening, networking, influencing, selling the technical vision, building trust relationships, understanding what other engineers need and want, to mentoring, to raising the quality of the team around you through influence to motivating others as well. Being able to influence the product direction, being able to express in business terms why something has to be done or should be a higher priority etc. Also, understanding the organization and becoming organizationally savvy is important.
All of these skills take time and practice to achieve, and good managers can guide their people through the journey.
In ZFC set theory, indexed family over a set (possibly uncountable or even bigger), is just syntactic sugar for a function.
So let's say you have a set U (possibly uncountable). To say let {u_i}, i in I (another set, possibly uncountable) is equivalent to asserting existence of function f:I -> U, such that f(i) = u_i. Note that this does not even require axiom of choice, since you are allowed to postulate that a function exists.
Of course if I is uncountable you can't list the elements of I, but that is not important in this case.
I prefer this test: "Imagine a ball resting on a table. A person walks up to the table and pushes the ball". Question for the test subject: "What will happen?"
Everyone answers correctly the ball will roll of the table and fall to the ground. But then ask them" "What was the color of the ball? What was the size of the ball? What was the gender of the person pushing the ball, what clothes were they wearing?"
People with aphantasia are usually stunned by the follow up questions. People who don't have aphantasia really have seen the table, the material its made of, imagined a ball of certain size/type color (e.g. multicolor beach ball, or basketball or what ever), and they saw an actual person pushing the ball, they saw the ball rolling on the table an falling to the ground and can answer details about their vision.
Later, I got Commodore 64, then 128, then Amiga 500 (http://en.wikipedia.org/wiki/Amiga_500) which was such a joy to program. This is where I got my first exposure to C programming (Aztec C http://en.wikipedia.org/wiki/Aztec_C) and VIM. VIM was in fact first developed for Amiga where it was known as VI iMitation (hece VIM), and later back ported to UNIX. In the 90s went to university to study math and computer science and that's where I got introduced to "big iron" UNIX (HPUX). In late 90s I did some Windows C++ development, but I now program for all kinds of platforms from Solaris, to AIX to HPUX to Linux to Windows and Mac OS X and in dozens of languages. We even make our own VI, awk compiler, Perl interpreter, std C lib for all kinds of platforms, POSIX APIs port to Windows and others, port of UNIX tools and shells to Windows and a multi million LOC ALM application suite.
But today's computing really can't be compared to the experience in the 80s, when you as a kid could master your CPU and know its complete instruction set, its registers and important memory locations and feel completely in control. I shudder when I see where general computing is headed with kids dreaming of owning iPads.
P complexity class
https://en.wikipedia.org/wiki/P_(complexity)
NP complexity class
https://en.wikipedia.org/wiki/NP_(complexity)
P vs NP question
https://en.wikipedia.org/wiki/P_versus_NP_problem