You can learn vibes from a book but it has to be written a certain way, heavy on stories and concrete examples and pictures. The very best math textbooks do this: they switch back and forth between formal structured reasoning and motivating stories. The motivating stories give you, the math student, a muscle-memory sense of why the great theorems are true, and teach you how to discover new truths, i.e. how to do mathematical research. The formal reasoning teaches you how to check your intuition and when and why not to trust it.
A great example is David Bressoud's _A Radical Approach to Real Analysis_ which did more than any other book to teach me how to think like a mathematician. Now I am biased because I took the course from Professor Bressoud himself, and so maybe my vibe experience is confounded by that bit of apprenticeship. But at the very least I think a clever and motivated autodidact could have learned much-- maybe not all-- of the same vibe from self-study of the book. I would love to hear of someone trying it.
Theoretically, I agree with your conclusion—we need to bring heaven and hell together but that becomes impossible when both sides thrive on their differences. When the extreme voices control the dialog there will never be agreement. Unfortunately one party's ideology is based on hate, anger and resentment which is a huge impediment to the marriage of vibe and concept. xxxxx g di
You can learn vibes from a book but it has to be written a certain way, heavy on stories and concrete examples and pictures. The very best math textbooks do this: they switch back and forth between formal structured reasoning and motivating stories. The motivating stories give you, the math student, a muscle-memory sense of why the great theorems are true, and teach you how to discover new truths, i.e. how to do mathematical research. The formal reasoning teaches you how to check your intuition and when and why not to trust it.
A great example is David Bressoud's _A Radical Approach to Real Analysis_ which did more than any other book to teach me how to think like a mathematician. Now I am biased because I took the course from Professor Bressoud himself, and so maybe my vibe experience is confounded by that bit of apprenticeship. But at the very least I think a clever and motivated autodidact could have learned much-- maybe not all-- of the same vibe from self-study of the book. I would love to hear of someone trying it.
Theoretically, I agree with your conclusion—we need to bring heaven and hell together but that becomes impossible when both sides thrive on their differences. When the extreme voices control the dialog there will never be agreement. Unfortunately one party's ideology is based on hate, anger and resentment which is a huge impediment to the marriage of vibe and concept. xxxxx g di