He's just using it as a synonym for "Consider..." or "Assume we have...", which is a really common way to start. I didn't find this paper to read very differently from a contemporary paper in Physical Review Letters, except that there's no introduction that gives context within the rest of the literature.
Using the word "imagine" isn't that unusual. Here's some examples in just the past couples of years:
"We might then imagine other starting points which..."
To me it read more like a math text than a physics text, in which "let there be X...", "imagine Y...", and similar phrases, are usually found. Yet I agree, it seems the physics community has grown a slight alergy to that kind of writing, and it probably would be received with a bit of skpeticism/disdain nowadays.
Nothing special about the "imagine" portion; plenty of research in theoretical Computer Science takes an even more informal.approach in the introduction.
This is a key point, well said. However, we need more people who are proficient in both "worlds" or at least, as another user points out below, more people willing to collaborate.
And for people who are genuinely curious about how this segues into graphical models, NNs, and the autoencoder (maybe the most interesting part of modern NNs), there's
I doubt Gareth or Daniela (the primary authors of ISL) would mind my pointing you towards Hastie's archives since both of them were advised by Trevor Hastie during their PhDs.
Matloff is a great guy. The chapters on shrinkage and dimension reduction aren't yet written in his book, and since these are important topics, you should consider reading the others. These things are mostly of interest for people who want to draw inference about underlying processes that may be generating observed outcomes. If all you care about is prediction, fit a Random Forest or xgboost GBM or a DNN and be done with it. But if you're actually curious about how complex descriptions of rare events can be thoughtfully analyzed, this is the standard progression.
Matloff's book is a great introduction. I particularly like the example on page 204. /ducks
I thought the recent Onion article "Encouraging New Study Indicates Majority Of U.S. Students Can Now Recognize Math" was satire... but perhaps sadly it isn't as far-fetched as it seems.
by that logic - algebra is a word from arabic, al jabr, if you follow it to its ultimate conclusion of somebody with a racist myopic worldview, arabic = desert and camels and guys with swords = terrorism = ISIS
