I Got The Thrilling Adventures Of Lovelace And Babbage For Free From Thriftbooks (after Much Fussing

His Famous Last Words: Billy Joel’s River of Dreams

From the first few chords of “No Man’s Land” to the fade-out at the end of “Famous Last Words”, this album is entirely unlike anything else I’ve ever heard. Heck, it’s unlike Billy Joel. He made a name for himself as the Piano Man—twenty years after that iconic breakout single, he made an album with barely a hint of piano on it and pretty much disappeared so that he could give new musicians a chance to be heard. And he didn’t come back until he had a truly worthwhile song to share.

Now, he’d seen his share of style changes over the years—look at Glass Houses or even The Bridge. But if those albums were a slow shuffle away from his piano-oriented roots, River of Dreams was a flying leap as he traded his trademark baby grand for overdriven guitars. But under this grittier rock sound, it really still feels like a Billy Joel album.

In my mind, no song handles better this fusion of the new sound with Billy’s signature lyrical style and themes than “No Man’s Land”. Despite its obviously rock sound, it is in many ways a thematic successor to The Stranger’s opening track, “Movin’ Out (Anthony’s Song)”. The two songs handle the a very similar sense of disillusionment and uncertainty, as well as the idea that you shouldn’t take what you’re told at face value. To the average listener, this is a shockingly punk rock sentiment to hear from a pop-oriented singer-songwriter, especially as blatant as it is in “No Man’s Land”. But I feel like this theme returning is a wonderful way to close the book on his career as a (probably unintentional) callback.

But that’s just it—this is his final album. He stepped back from music after River of Dreams. This whole album has a sense of finality about it; Billy has always been a storyteller more than just about any songwriter I’ve ever seen, and he seems to have done everything in his power to make his last big story (at least for now) great. For that reason, I find this album thematically akin to Turnstiles. Both deal with moving on and change, though in very different ways. That’s why—to me, anyway—this album seems so fitting as a goodbye. The drastically different styles present here fit and compliment the overall theme of change.

This is all pulled together by the final track, “Famous Last Words”. It’s a slow-paced, easygoing song exploring the prospect of change through the shift from summer into fall, ultimately using this as a metaphor for the end of Billy’s musical career. But it looks to this uncertain future with a feeling of safety and contentment, secure in the knowledge that good things must be somewhere up the road. It’s similar to “Vienna” in that way, as it’s also about accepting the future not with dread but with a willingness to go at your own speed and enjoy the scenery while you’re there.

I’d consider “Famous Last Words” to be among the greatest closing tracks ever—probably topped only by “The Long One” on the Beatles’ Abbey Road. It closes the record with every bit of strength with which “No Man’s Land” opened it, though in an entirely different way. With a track like this as his last true song for so many years, I think “Turn the Lights Back On” wasn’t the perfect single to release; it was the only one that could follow this song in theme, quality, and lyrics. In fact, I would count “Turn the Lights Back On” as almost a coda to River of Dreams because of this.

In the end, though, I think what River of Dreams represents most to me is an artist who wanted to leave a good legacy in terms of his work. From start to finish, it feels like Billy gave this record his all, and I have nothing but respect for any musician who decides to step back when they feel they have nothing left to say at the moment. Not to mention the fact that his decision to stop making new albums every few years most likely gave him time to really buckle down and get to breaking that record for longest residency at Madison Square Garden. Between the aforementioned residency and the clear care and effort put into both River of Dreams and “Turn the Lights Back On”, it seems that Billy Joel has a level of dedication to both his music and his fans that I greatly respect. If he were to make another full-length record, this precedent is enough to show me that it would very likely be a worthwhile one.

Today on the blog I start a new project: where do numbers come from?

By which I mean, mathematicians deal with lots of weird kinds of numbers. Real numbers, complex numbers, p-adic numbers, quaternions, surreal numbers, and more. And if you try to describe the more abstract types of "numbers" you sound completely incomprehensible.

But these numbers all come from somewhere. So I'm going to take you through a fictional history of numbers. Not the real history of the actual people who developed these concepts, but the way they could have developed them, cleaned up and organized. So in the end you can see how you, too, could have developed all these seemingly strange and abstract concepts.

This week in part 1, we cover the most sensible numbers. We start with the basic ability to count, and invent negative numbers, fractions, square roots, and more.

But that will still leave some important questions open—like, what is π? So we'll have to come back for that in part 2.

Why do we use the symbol for partial derivatives as the symbol for boundaries of manifolds?

he's like a stress ball to me.

So I recently stumbled on the Wikipedia article for the Grothendieck-Riemann-Roch theorem, which is an algebraic geometry thing that I'll hopefully learn some day once I actually have the prerequisite knowledge =w= But at the top of the article was this letter, which I thought was a wild thing to have at the top of a Wikipedia article about a niche abstract math thing - here's a translation:

Witches' Kitchen 1971 Riemann-Rochian Theorem: the latest craze*: the diagram

is commutatif**! To give this statement about f: X->Y some approximative meaning, I had to abuse the listeners' patience for nearly two hours. In black and white (in Springer's Lecture Notes) it seems like it will take up to about 400, 500 pages. A gripping example of how our thirst for knowledge and discovery indulges itself more and more in a(n il?)logical delirium far removed from life, while life itself is going to hell in thousandfold ways - and is threatened with absolute annihilation. High time to change our course! (6.12.1971) Alexander Grothendiek

* "der letzte Schrei" is a reasonably common German idiom meaning "the latest craze", but here it could alternatively be translated non-idiomatically as something like "the last cry". I think its more fun to imagine he means the idiom. ** I'm assuming this is a weird old-timey spelling probably taken from french but googling it I can find no examples of anybody using this spelling in German besides this letter

Note that this is 20 years before all of this happens:

(Gordon ramsay chewing out a restaurant owner over his old expired ingredients) And where the fuck does this door lead? If I see a- (there is a hallway miles long, with ashen black walls and no end in sight)¹

1. oh for fucks sake

In Defense of Tolkien’s Mountains

At tor.com, Alex Acks asserts that the mountain ranges of northwestern Middle-earth are geologically implausible. But I think a fair reconstruction of Middle-earth tectonic history can be made. This is a long post, so I’m putting it behind a read-more:

Keep reading

I have a new post up on my blog, continuing the Fictional History of Numbers series. In part 1 we built on the natural numbers using algebraic operations, and got the algebraic numbers. In part 2 and part 3 we used geometric and analytic arguments to build up the real numbers.

These two sets of numbers overlap, but aren't the same; there are real numbers that aren't algebraic (as we saw in part 3) but also algebraic numbers that aren't real. So what happens if we combine the two? We get the complex numbers, which are complete and also algebraically closed. But proving this is a little tricky, and touches on the deep strangeness of complex analysis.

And in the process of adding algebraic closure to the real numbers, we lose the ability to order them, which has its own consequences.

people trying to insist a fandom is tiny when it /only/ has a few thousand works on ao3 meanwhile my current fandom is a sixteen book series and has several hundred fewer works than goncharov, a movie that, and i cannot stress this enough, doesn’t even exist

fields of mathematics

number theory: The Queen of Mathematics, in that it takes a lot from other fields and provides little in return, and people are weirdly sentimental about it.

combinatorics: Somehow simultaneously the kind of people who get really excited about Martin Gardner puzzles and very serious no-nonsense types who don’t care about understanding why something is true as long as they can prove that it’s true.

algebraic geometry: Here’s an interesting metaphor, and here’s several thousand pages of work fleshing it out.

differential geometry: There’s a lot of really cool stuff built on top of a lot of boring technical details, but they frequently fill entire textbooks or courses full of just the boring stuff, and they seem to think students will find this interesting in itself rather than as a necessary prerequisite to something better. So there’s definitely something wrong with them.

category theory: They don’t really seem to understand that the point of generalizing a result is so that you can apply it to other situations.

differential equations: physicists

real analysis: What if we took the most boring parts of a proof and just spent all our time studying those?

point-set topology: See real analysis, but less relevant to the real world.

complex analysis: Sorcery. I thought it seemed like sorcery because I didn’t know much about it, but then I learned more, and now the stuff I learned just seems like sorcery that I know how to do.

algebraic topology: Some of them are part of a conspiracy with category theorists to take over mathematics. I’m pretty sure that most algebraic topologists aren’t involved in that, but I don’t really know what else they’re up to.

functional analysis: Like real analysis but with category theorists’ generalization fetish.

group theory: Probably masochists? It’s hard to imagine how else someone could be motivated to read a thousand-page paper, let alone write one.

operator algebras: Seems cool but I can’t understand a word of it, so I can’t be sure they’re not just bullshitting the whole thing.

commutative/homological algebra: Diagram chases are of the devil, and these people are his worshipers.