Category Archives: offhand

Good math days

I have good math days and bad math days; we all do.  An outsider might think the good math days are the days when you have good ideas.  That’s not how it works, at least for me.  You have good ideas on the bad math days, too; but one at a time.  You have an idea, you try it, you make some progress, it doesn’t work, your mind says “too bad.”

On the good math days, you have an idea, you try it, it doesn’t work, you click over to the next idea, you get over the obstacle that was blocking you, then you’re stuck again, you ask your mind “What’s the next thing to do?” you get the next idea, you take another step, and you just keep going.

You don’t feel smarter on the good math days.  It’s not even momentum, exactly, because it’s not a feeling of speed.  More like:  the feeling of being a big, heavy, not very fast vehicle, with very large tires, that’s just going to keep on traveling, over a bump, across a ditch, through a river, continually and inexorably moving in a roughly fixed direction.

 

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How many books do I read in a year?

Data:

2006: 27

2007: 19

2008: 22

2009: 30

2010: 23

2011: 19

2012: 27

2013: 35

2014: 31

2015: 38

2016: 29

Don’t quite know what to make of this.  I’m sort of surprised there’s so much variation!  I’d have thought I’d have read less when my kids were infants, or when I was writing my own book, but it seems pretty random.   I do see that I’ve been clearly reading more books the last few years than I did in 2012 and before.

Lists, as always, are here (2011 on) and here (2006-2010.)

 

Multiple height zeta functions?

Idle speculation ensues.

Let X be a projective variety over a global field K, which is Fano — that is, its anticanonical bundle is ample.  Then we expect, and in lots of cases know, that X has lots of rational points over K.  We can put these points together into a height zeta function

\zeta_X(s) = \sum_{x \in X(K)} H(x)^{-s}

where H(x) is the height of x with respect to the given projective embedding.  The height zeta function organizes information about the distribution of the rational points of X, and which in favorable circumstances (e.g. if X is a homogeneous space) has the handsome analytic properties we have come to expect from something called a zeta function.  (Nice survey by Chambert-Loir.)

What if X is a variety with two (or more) natural ample line bundles, e.g. a variety that sits inside P^m x P^n?  Then there are two natural height functions H_1 and H_2 on X(K), and we can form a “multiple height zeta function”

\zeta_X(s,t) = \sum_{x \in X(K)} H_1(x)^{-s} H_2(x)^{-t}

There is a whole story of “multiple Dirichlet series” which studies functions like

\sum_{m,n} (\frac{m}{n}) m^{-s} n^{-t}

where (\frac{m}{n}) denotes the Legendre symbol.  These often have interesting analytic properties that you wouldn’t see if you fixed one variable and let the other move; for instance, they sometimes have finite groups of functional equations that commingle the s and the t!

So I just wonder:  are there situations where the multiple height zeta function is an “analytically interesting” multiple Dirichlet series?

Here’s a case to consider:  what if X is the subvariety of P^2 x P^2 cut out by the equation

x_0 y_0 + x_1 y_1 + x_2 y_2 = 0?

This has something to do with Eisenstein series on GL_3 but I am a bit confused about what exactly to say.

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What is the median length of homeownership?

Well, it’s longer than it used to be, per Conor Dougherty in the New York Times:

The median length of time people have owned their homes rose to 8.7 years in 2016, more than double what it had been 10 years earlier.

The accompanying chart shows that “median length of homeownership” used to hover at  just under 4 years.  That startled me!  Doesn’t 4 years seem like a pretty short length of time to own a house?

When I thought about this a little more, I realized I had no idea what this meant.  What is the “median length of homeownership” in 2017?  Does it mean you go around asking each owner-occupant how long they’ve lived in their house, and take the median of those numbers?  Probably not:  when people were asked that in 2008, the median answer was 10 years, and whatever the Times was measuring was about 3.7 years in 2008.

Does it mean you look at all house sales in 2017, subtract the time since last sale, and take the median of those numbers?

Suppose half of all houses changed hands every year, and the other half changed hands every thirty years.  Are the lengths of ownership we’re medianning half “one year” and half “30 years”, or “30/31 1 year” and 1/31 “30 years”?

There are about 75 million owner-occupied housing units in the US and 4-6 million homes sold per year, so the mean number of sales per unit per year is certainly way less than 1/4; of course, there’s no reason this mean should be close to the median of, well, whatever we’re taking the median of.

Basically I have no idea what’s being measured.  The Times doesn’t link to the Moody’s Analytics study it’s citing, and Dougherty says that study’s not public.  I did some Googling for “median length of homeownership” and as far as I can tell this isn’t a standard term of art with a consensus definition.

As papers run more data-heavy pieces I’d love to see a norm develop that there should be some way for the interested reader to figure out exactly what the numbers in the piece refer to.  Doesn’t even have to be in the main text.  Could be a linked sidebar.  I know not everybody cares about this stuff.  But I do!

 

 

 

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I guess Caffe 608 was in trouble

Eight years after I wondered whether the arthouse cinema / cafe in Hilldale could really make a go of it, Sundance 608 is getting bought out by AMC.  I have really come to like this weird little sort-of-arthouse and hope it doesn’t change too much under new management.  It’s a sign of my age, I guess, that I still think of “movie at the mall” as an entertainment option I want to exist.  It’s my Lindy Hop, my vaudeville, my Show of Shows.

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Fitchburg facts

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Tweet, repeat

Messing around a bit with lexical analysis of my tweets (of which there are about 10,000).  It’s interesting to see which tweets I’ve essentially duplicated (I mean, after @-mentions, etc. are removed.)  Some of the top duplicates:

  • Thanks (8 times)
  • thanks (6 times)
  • Yep (6 times)
  • Yes (5 times)
  • yep (5 times)
  • Thanks so much (5 times)
  • RT (5 times)
  • I know right (4 times)

More detailed tweet analysis later.

 

 

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AB for President

AB was talking about being President this morning.

Me:  I think you could be a really good candidate; you’re funny, and you get along with almost everybody.

AB:  And I have great hair!

She gets it.

Mark Metcalf

Have you ever heard of this guy?  I hadn’t.  Or thought I hadn’t.  But: he was Niedermeyer in Animal House

and the dad in Twisted Sister’s “We’re Not Gonna Take It” video

and the Master, the Big Bad of Buffy the Vampire Slayer season 1.

That’s a hell of a career! Plus: he lived in suburban Milwaukee until three years ago! And he used to go out with Glenn Close and Carrie Fisher! OK. Now I’ve heard of Mark Metcalf and so have you.

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Robin laid a gun

OK here’s a weird piece of kid culture AB brought home:

Jingle bells, Batman smells

Robin laid a gun

Shot a tree and made it pee in 1981

This dates back at least to 2007 apparently.

It scans and rhymes very nicely but makes so sense at all.  What can it mean?

It seems like we are witnessing a kind of cultural hybrid; the “Jingle bells / Batman smells” of my childhood has here combined with a “Jingle bells / shotgun shells” tradition I was unaware of until now, which is actually older than the Batman version.  A lot of the “shotgun shells” versions found online involve Santa meeting his death in a hail of bullets, but “shot a tree and made it pee” is not uncommon.  I wonder how many utterly nonsensical kids rhymes we know are actually hybrids of different songs, each of which at some point sort of made sense?

 

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