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For many students, it is not so simple to grasp the concept of an abstract vector space. They could be taking linear algebra as college freshmen, without having seen any formal algebraic structures before. Many are unfamiliar with the formal notion of a set (and certainly have not seen the actual axioms of a set before). Most linear algebra students are not actually math majors; they are typically studying engineering, computer science, or some other physical science. Examples of abstract vector spaces are most often function spaces of some form (for example, polynomials of at most a given degree). These examples are not so motivating for non-math students.

The main reason why people care about linear algebra is that it lets you solve linear systems of equations (and perform related operations, such as projections). A linear system of equations has an immediate correspondence with a matrix of coefficients, a right-hand side vector, and a solution vector. For this reason, it is very natural to first talk about matrices and vectors (they can be used to represent concretely a linear system of equations), and then introduce the concept of vector space in cases where the abstract view can be clarifying or help with understanding.

From my perspective, the "right" way to teach linear algebra depends on the mathematical maturity of the students. If they are honors math majors, they can easily handle the definition of an abstract vector space right away. If they have less mathematical maturity, the abstract viewpoint isn't helpful for them (at least not without first familiarizing themselves with the more concrete concepts). Think about it this way: we don't teach school children about natural numbers and arithmetic by first listing the Peano axioms.

Listening to audiobooks is included in the survey (but they also mention that most people who listen to audiobooks also read print books; you are likely an outlier in that regard).

Yes, agreed completely. You can get a lot (but not everything) from context. The text will be clearer if you look up unfamiliar terms (which they were allowed to do). But if you gloss over Lincoln's Inn Hall as "obviously some kind of inn", you won't have a full understanding of what follows.

Since other commenters seem to think that the passage is just the first paragraph of chapter 1 (the fact of which suggests its own meta-commentary on the content of the article), it's worth mentioning that the passage is the first seven paragraphs of chapter 1, in which there are definitely some challenging sections, particularly in the later paragraphs.

To understand the passage and what follows, it is actually important to know what "Lincoln's Inn Hall" is. And to be clear, it's not an "inn" in the standard modern usage of the term, but rather a rather a professional association for lawyers.

This was strange and disappointing thing to read. Why such a conspiratorial tone ("we are being lied to", "we have enemies", etc.)?

Since this is written by Marc Andreessen, I did a search for "crypto" and "web 3", but no results came up. Isn't that strange coming from someone who was so prominent in promoting and advocating for a crypto-based future? I guess that one didn't pan out…

"Our enemy is the ivory tower" is a bit rich coming from a billionaire who lives in one of the most exclusive California communities (and vociferously opposes any development in that community, despite loudly proselytizing to others that "it's time to build").

Looking at the "Patron Saints", after skipping the meme-posting pseudonymous Twitter accounts, I am pretty sure university professor is the most common profession. The ivory tower is the enemy indeed. And it does seem distasteful to use the names of dead scientists and intellectuals like John Von Neumann and Richard Feynman to burnish the image of this polemic.

> What information does Applite track?

> None.

Absolutely love this part of the page---we need more software with this philosophy. Kudos.

For git config, the --show-origin flag is really useful for this, e.g.

  git config --show-origin --list