118 karma · joined November 21, 2015
Usually, one says an element p of a general ring is prime if p|ab implies p|a or p|b. This property does not necessarily hold for the "smallest" divisor of a given element of your ring, as used in proof 1.
On the other hand, you might be interested in irreducible elements, i.e. those p for which a|p implies a = 1 or p, up to a unit (i.e. a divisor of 1). In fact, you can write any element of your ring as a product of irreducible elements, but not uniquely, not even uniquely up to units. In other words, you can have irreducible elements a, b, c, d, such that ab = cd, but none of them divides any of the others.
Here's where I think it cause problems: right now, if I feel like working from home on a given day, and I have no meetings, I just do it. If I was supposed to meet with my manager every single day, then now it's like I'm cancelling that meeting, so now I'm self-conscious that he thinks I'm slacking, and I would probably just not bother and drag myself in every day. Boom, reduced morale.
The reason business travel, and in general non-remote work, is worthwhile isn't necessarily the pre-planned meetings, it's also the familiarity developed by meeting somebody in person, shooting the shit over lunch, and being able to casually mention an idea or anecdote without the overhead of a "call."
I would also say the fact that Ginsberg is not a victim only bolsters his point. He really has nothing to gain by making these statements.
"Even while keeping funding for instruction relatively flat, universities increased the number of administrator positions by 60 percent between 1993 and 2009, 10 times the rate at which they added tenured positions. In the old days, different professors would take their turn as dean for this or that and then happily escape back to scholarship and teaching. Now the administration exists as an end in itself and a career path disconnected from the faculty and pursuit of knowledge. Writing a few years ago for this publication, the Johns Hopkins professor Benjamin Ginsberg described colleges and universities as now being “filled with armies of functionaries—vice presidents, associate vice presidents, assistant vice presidents, provosts, associate provosts, vice provosts, deans, deanlets, and deanlings, all of whom command staffers and assistants—who, more and more, direct the operations of every school.” So while college tuition surged from 2003 to 2013 by 94 percent at public institutions and 74 percent at private, nonprofit schools, and student debt has climbed to over $1.2 trillion, much of that money has been going to ensure higher pay for a burgeoning legion of bureaucrats."
I took these to prepare for first-job interviews coming out of grad school. Got an offer from a company frequently mentioned on this site, so I guess they helped.