Bullshit is so dangerous because it could mean something. That VP could mean, it's time to look beyond the set of mature technologies we've been considering and look at newer technologies that we would normally ignore because they come with risks and rough edges and higher cost of ownership.

So it might be a substantive decision that affects how everybody in the room will do their jobs going forward. Or it could be a random stream of words chosen because they sound impressive, which everyone will nod respectfully at and then ignore. And like an LLM, he might have made it into his current position without needing to know the difference.

Most anime is either a guilty pleasure or a guilty displeasure for me. The stuff I like, I feel embarrassed of the part of me that likes it, and I feel embarrassed about what I'm willing to overlook to enjoy it. Then the stuff I don't like, I feel closed-minded about it, like what's wrong with me that I'm too stuffy to enjoy it or too dumb to get it. But I don't have friends or acquaintances who are into it, so it never comes up with other people, and I generally don't think about it.

Yeah, it took me a second, too. By "gaps" they mean numbers that can't be represented in a given construction. So irrational numbers are "gaps" in the rational numbers, and transcendental numbers are "gaps" in the algebraic numbers. Not the best spatial metaphor.

I just don't understand why this was disturbing. Prior to the construction of the reals, the existence of irrational and transcendental numbers was disturbing, because they showed that previous constructions (rational numbers and algebraic numbers) were incomplete. If those gaps were disturbing, a construction without gaps should have been satisfying, reassuring, a resolution of tension. Was there some philosophical or theological theory that required the existence of gaps, that claimed that a complete construction of the number line was mathematically impossible, because of some attribute of God or the cosmos?

I should have been more specific; I understand why it was a mathematical breakthrough. What I don't understand is why it would have triggered some kind of psychological horror or philosophical crisis. It was a new way of understanding numbers, but it didn't reveal numbers to be acting any differently than we had always assumed.

If anything, it seems like it would have been comforting to finally have mathematical constructions of the real numbers. It had been disturbing that our previous attempts, the rational and algebraic numbers, were known to be insufficient. The construction of the reals finally succeeded where previous attempts had failed.