## Music 2011

It’s that time of the year again. Here is my favorite music list from 2011. I’m embarrassed by the top 2 since they are the top 2 on lots and lots of lists out there. It seems rather uninspired for me to not find something else. I’ve divided the list into three sections. The top 10, then the pretty good but not great set (in order of how much I like them), followed by the bottom part which I found to be sub-par.

1. Bon Iver – Bon Iver
2. James Blake – James Blake
3. Chris Merrit – Songs from Brokeland
4. Bjork – Biophilia
5. Incubus – If Not Now, When?
6. O’Death – Outside
7. Matt Nathanson – Modern Love
8. Moonface – Organ Music Not Vibraphone Like I’d Hoped
9. Loney Dear – Hall Music
10. Wilco – The Whole Love

The Chris Merrit album is a placeholder. About half way through this year I was so fed up with how boring and unoriginal all the music that was coming out was that I decided to go hunting for someone I wasn’t familiar with. I ran into Chris Merrit somehow. I spent the next 2 months slowly going through everything he had ever put out. I’m not sure I found a single song I didn’t like. I listened to no new music during this time period. My favorite album if you decide to check him out is Pixie and the Bear. Please check it out. You won’t regret it. My description of him is “Ben Folds … but good.” The album listed did come out this year, but it is only a demo so I’d wait until the full mastered album comes out next year.

I’ve written about everyone on this list with the exception of O’Death and Incubus, so I’ll try to keep this short. I’ve hated Bon Iver for the past two years. He put out my favorite album of 2008, but everything since then has been blah for me and I was about to give up hope. Instead he puts out this self-titled album that really is deserving of the number one spot.

Incubus is well-known from the early to mid 2000 time period for their singles “Drive,” “Pardon Me,” “Dig,” and “Oil and Water”. They were known as a mildly experimental, but mostly mainstream alternative rock band. I’m no expert on their history, but it seems they broke up around 2008 with no intention of recording anything together ever again. Good thing they did, because this is by far their most mature effort. It is incredibly subtle and restrained. The songs have a lot of emotion and energy behind them and they didn’t just let it out in a burst of rock. It is carefully constructed and beautiful at times. I’m honestly surprised this isn’t on any of the lists I’ve looked at.

O’Death could be considered “alternative country”. It is a really fun, creative, and often dark side to folk/Americana style music. Maybe you could call it a darker sounding Mumford and Sons. They liberally use banjo and other instruments that got them the name “country” but it never sounds like country at all. They sound more like a rock band with folk influence. I highly recommend it. To me it is the most successful attempt at such a fusion I’ve come across (much better than M&S).

Now onto the list of artist I found pretty good and enjoyable, but there were too many faults to call any of them honorable mentions like I usually do.

Grand Hallway, Florence + the Machine, Fleet Foxes, Death Cab for Cutie, Dodos, Bright Eyes, Elbow, Decemberists, Son Lux, and Wye Oak

Some of my favorite songs came off of these albums, but some of my least favorite songs came from here as well. Grand Hallway is a fantastic band from Seattle and if you ever get to see them live I recommend it. They pack tons of musicians on stage including violins, piano, bass, guitar, vocalists, slide guitar, drummers, and more. They have a great powerhouse sound that only comes across properly live. The only other thing I’d like to say is that Florence + the Machine is Adele done right. See my midway rankings for my complaints about Adele. If you want to know what I was talking about then listen to F+tM to see someone who fixes all those mistakes.

Now on to the bottom. These albums fell short in a major way.

Iron and Wine, Radiohead, and The Antlers have all been at the very, very top of my lists in the past. It was sad to have such disappointment in them. The Radiohead album is pretty horrible in my mind. They take all the things I love about them and remove all of those aspects to leave you with a shell of boring. I’ve liked Coldplay in the past, but this was worse than radio pop nonsense earning it the lowest ranking spot. The Cold War Kids also have put out some fantastic things in the past, but this was like an attempt to mimic the Kings of Leon style and the fresh originality of their old stuff got snuffed out.

Lastly, I got the Kate Bush album, but couldn’t fit it anywhere because it was weird enough and I haven’t listened to it enough to conclude whether or not it is nonsense or amazing. She reminds me of Tierney Sutton on this album who I used to love listening to, so there is a bit of nostalgia stuck in there muddling things.

As a concluding remark, this year turned out OK. I definitely listened to stuff not from this year more than any year in the past as I got bored with the current stuff. The finds from the past that I ended up loving involve things as diverse as Iceburn, Arvo Part, and My Bloody Valentine.

Please comment with things you’d think I’d like that I missed (aren’t on the list). I’ve already been informed I should check out the M83 album and the Destroyer album.

## Multiplication is Still Repeated Addition…yet again

Keith Devlin has posted yet another blog post on how multiplication is defined. I left a comment there, but it wasn’t as good as I hoped it would be. Now that I’ve gone back and read all the comments, I am completely convinced that I know exactly where the misunderstanding is occurring. I should maybe throw in that the comments have been turned off for that post. Maybe my blog doesn’t get enough traffic, but I can’t ever, ever see a reason to do that. You filter out a few comments that are off topic, but don’t shut down comments completely. It seems to go in blatant opposition to the idea of using a blog rather than just publishing somewhere. But that is a completely side issue.

Devlin wants to claim that the definition of multiplication is to define a function $f:\mathbb{N}\times \mathbb{N}\to \mathbb{N}$ in Peano arithmetic using recursion. Since the “definition” as repeated addition does not yield a function on the whole natural numbers it cannot possibly be the definition. In this strictest sense, the definition is not repeated addition because it is this other recursively defined function.

I’m with him on all of this. Of course that is true. Repeated addition only works for a finite stage and you must relying on something else to get the full function. The place we disagree is in what we mean by “definition”. Devlin wants to say that because it is necessarily the case that to define an honest multiplication function axiomatically in Peano arithmetic we must make some part of the definition that is not repeated addition, then we must say that the definition is not repeated addition.

That is a completely absurd idea. Devlin is conflating the two mathematical notions of definition and existence. You can make a definition of anything you want in math, but that doesn’t mean it exists. You then should prove that such a thing exists. I claim that the above “not repeated addition” definition of a function is actually the proof of the existence of a multiplication function and not a definition.

Recall that the context of this conversation is all about whether or not we should teach children that multiplication is repeated addition. The whole point of teaching children multiplication is precisely so that they can apply it to real world situations. The only sense in which multiplication can be applied to real world situations is if we know that it produces the same answer as repeated addition. I talk more about that in the original blog post. Even these strange analogies about stretching being a continuous rather than a discrete concept only makes sense after interpreting it as repeated addition.

Now that we’ve established the difference between definition and existence I’ll decompose what is going on to show that multiplication is repeated addition (by definition and hence ought to be taught to children because it isn’t incorrect). Recall that definitions in mathematics are technically biconditional statements. Definition: A function $m:\mathbb{N}\times\mathbb{N}\to \mathbb{N}$ is multiplication if and only if it satisfies $m(n,k)=k+k+\cdots +k$ repeated n times for any choice of $n,k$ in $\mathbb{N}$. Note that this is not only the definition that will tell us the multiplication function is useful, but a priori we don’t know that such a function exists.

Devlin’s post uses recursion to prove that such a function exists, but once these two notions are pulled apart we see that Devlin is actually incorrect. The (useful) definition is the one I give above. If we try to conflate the existence and definition as Devlin does, then we have no idea if the recursively defined $f$ can be used to compute something in reality. As I point out in the comments at that blog post, for all we know that nice recursive definition could yield $f(n,k)=2$ for all inputs. Are we going to call that multiplication? I think Devlin wrote that off as a flippant comment to be ignored, but I still think it illustrates the necessity of separating definition from existence perfectly and is precisely our point of disagreement.

Now to try to summarize briefly, it seems that when Devlin wants to use the phrase “multiplication is not defined to be repeated addition” he seems to mean that in order to have a function defined on $\mathbb{N}\times\mathbb{N}$ it must be defined recursively without reference to repeated addition. I agree completely. I just disagree that the definition of such a function should be consider the definition of multiplication (is the confusion that “definition” is used in reference to “defining a function” versus defining the term “multiplication”?). The actual definition should be the one I gave (otherwise we’ve made a useless function), and then the proof that such a function exists is what Devlin wants. I don’t see how Devlin could disagree with what I’ve written here, and hence I see no way to conclude anything other than multiplication is repeated addition…unless we are going to use some non-standard idea of what it means to “be” something.