The importance of math in the study of history

I'm currently reading William Shirer's The Rise and Fall of the Third Reich.  Several times during the course of his narrative, he mentioned the hundreds of tons of Nazi documents seized at the end of the war.  This just seems like such a vast amount of paper that I was having trouble wrapping my mind about it.

So I set out to try to translate it into something I can relate to.  Based on my experiences with the US postal system, I know that 5 sheets of paper is about an ounce*.  Multiplying this through by ounces per pound, pounds per ton, etc., yields the result that 100 tons of paper is approximately 16 million sheets.  A quick search at Google turns up the factoid that a sheet of 20-lb paper is 0.004 inches thick.  Multiplied through by 16 million sheets yields 64,000 inches, or 5,333 feet.  So a hundred tons of paper would require a little over a mile of filing cabinet spaces (at this scale, I feel pretty comfortable ignoring the thickness of the folders).  A quick search of an office supply shopping site turns up a 4-drawer, 26-1/2" deep filing cabinet for $170**.  Crunch the numbers and you'll need about 600 filing cabinets (at a total cost of just over $100,000) to store 100 tons of documents.  And the Allies had multiple hundreds of tons of Nazi documents to deal with - it's really kind of amazing.

Things like this are why I'm glad I had science-level training in math before switching over to history:  There's so much history that can be inadvertently glossed over if one doesn't know how to deal with the numbers, and one's experience of history is really the poorer for it.

*  I'm making the assumption here that any differences in the weight of a single sheet of paper between standard US office paper of today and German office paper of the 1930s and 1940s will be negligible enough over the course of hundreds to tons that I can still get a meaningful approximation.
**  Not necessarily the best deal, but it got 4.4 stars in customer reviews so should be adequate for our purposes here.

A reflection on the Boston Marathon bombing - lights in the darkness

As I followed the course of yesterday's events in Boston, I noted that we appear to have learned from September 11.  We haven't learned the lessons that the demagogues who tried to use September 11 as a hammer to try to force us to come around around to their way of thinking would have wanted to, but I think we have learned more important ones.  Here's are the lessons that I observed in action:

• Help the people who need help.  This was reflected not only in the people on the scene who rushed to the aid of the injured, but also in those who at a distance sought to find how they could best help.
• When you pass on information, make sure it's from a trustworthy source.  The New York Post found itself with egg on its face yesterday after announcing that the police had a suspect in custody.  The Boston Police Department, on the other hand, is deserving of massive kudos for the attention they paid to making sure people had accurate and relevant information.
• Don't let people use the tragedy for their own ends.  Every scammer who tried to work their way into the dialogue was quickly shut down.  Every demagogue who sought to use the bombing for their own ends (I'm looking at you, Alex Jones.*) was promptly shouted down.    And someone has already purchased the domain bostonmarathonconspiracy.com in order to keep it out of the hands of conspiracy theorists.
• There's no need to stay around and listen to  news coverage from people who don't know anything.  After 9/11, the news media filled the space between facts with the blathering of any talking head who was willing to sit in front of a camera, and people ate it up.  Yesterday the media once again brought out the talking heads, but people weren't having it.  They were turning the news off after they had the facts of the matter, or else ignoring the media entirely and getting their news directly from the source.

In short, even as I was witnessing some of the worst of human behavior, I was also witnessing some of the best.  To everyone who behaved like a decent, thoughtful, good human being yesterday:  My hat is off to you.  In a time of darkness, you managed to stand up for the best of what makes up human.

*  Please note that I am linking to the Wikipedia entry about Alex Jones, not to any of Jones' numerous conspiracy sites.  I want to provide information to those that need it, but not to provide Jones with any more links.

A game of thrones and books and movies...

After we finishing watching an episode of Game of Thrones the other night, my wife turned to me and asked  "Why do you like this? Everyone in this show is a dick!"  I knew this wasn't just a moment of Princess Bride-style exasperation ("Jesus, Grandpa, why'd you read me this thing?"), that she actually wanted to know.  And I was at a loss to tell her.  GoT has interesting characters, but other shows have that.  It has well-plotted stories, but other shows have that as well.  Ditto a well-crafted world with fascinating cultures.  But nothing I could think of that was only in GoT.

So I tried a different mental tack.  Maybe the reason that she wasn't loving it as much as I was, was that I had read the books and she hadn't.  Elements of back-story that were explained in the book were omitted from the movie.  Things were simplified.  The characters became, in some respects, caricatures of themselves, with a trait that manifested in a dozen small events in the books being shown by one larger event in the show.  But none of these are things that are unique to GoT.

Then yesterday when I was reading A Storm of Swords, I had a realization.  What makes GoT different from so many other fantasy novels is George R.R. Martin's use of point of view.  We don't just see the events with different characters' eyes, we think about them with different characters' brains, so a character who's one of the "good guys" when we're reading from one character's POV is a "bad guy" when viewed from another and a nonentity when viewed from yet another.  Rather than black and white, we're presented with dozens of constantly shifting shades of grey.  And consequently no one is really a "bad guy" except from a certain point of view*.

It's kind of a shame that the Serious Literary Critics will dismiss GoT as "just fantasy," because I think serious study of the books would do them good.  Martin has produced a truly postmodern novel.  Things happen.  People even cause things to happen.  And while there are stories, there's no one "story."  Each character is their own protagonist, facing their own challenges, confronting their own opponents.  And so we find ourselves in one chapter rooting for a character who we villify in another chapter.  Nobody thinks that they're the bad guy, and at least for a while we're forced to believe them.  That is what makes this series so fascinating to me.

*  This also means that no one is really a "good guy" except from a certain point of view.

Change your life: Fight the "Perfection"

On Single Dad Laughing (one of my favorite blogs), there's a post up today called "The Disease Called 'Perfection."  This is one of the most touching pieces of writing I've read in a long time.  You should go read it.  Go ahead - I'll wait.

Wasn't that good?  Don't you feel a little better knowing that you're not the only one who has problems they try to cover up?  And just think about all the energy we spend trying to cover up those problems - can't you think of much better things to do with that energy?

To get the ball rolling, I'm going to drop some of the shields I've been hiding behind.  I hope it helps somebody out there.

• I feel like a failure professionally.  Even though I have a graduate degree, even though I have a job (which is itself an accomplishment in this economy), even though I'm managing to keep a roof over my family's heads and food in our stomachs, I feel like a failure, because I feel like I should have done more in the past and should be doing more now.  I feel like I should be "exceptional" and the fact that I don't think I am just eats away the joy of anything I accomplish.
• I hate my body.  I'm about 75 pounds overweight and out of shape.  Even though I've bought a bicycle and go riding a couple of times a week, I feel like I'm not exercising enough.  Even though I try to eat healthy food and cut down on unhealthy food, I feel like I'm not really able to do it because the things I want to eat (candy, ice cream, pizza), just taste so good.
• I don't treat my wife and my kids as well as I'd like.  I don't hit them, or anything like that.  But I can be  overly critical.  I yell sometimes.  I don't always notice when someone needs my attention.  I know I should do better, but a lot of times it's easier not to.  A lot of times I'm just so wrapped up in myself that I don't notice what anyone else needs.
• Hell, I'm battling "Perfection" as I write this post.  Every word I type is having to force its way past an inner monologue yelling "You're faking it!  You're just confessing to these things so no one will suspect there are worse things hiding under there."

And maybe that inner voice is right.  But this isn't the final step anyway.  This is just the first step on the way to being "Real."

Screw April Fools

I wouldn't say April Fools Day is my least favorite event  on the calendar - that dubious honor belongs to the annual beginning and end of Daylight Savings Time - but it's certainly very near to that.  Thanks to my late diagnosis of Asperger Syndrome*, I had/have difficulty enough with communication and recognizing/dealing with joking on regular days, so when you throw in a day where people are even more likely to be untrustworthy, and I'm in hell.  Consequently I've taken to skipping any blog post dated April 1, as I'm all too likely to be baselessly excited or needlessly upset (depending on the content of the post in question) before I remember what day it is.  I also tend to not post on April 1, as I know that there's a good chance that someone will think that my post is a joke.**

I know I'm not the only one who feels this way - my son (who is autistic) is so upset by the very idea of April Fools that he's been dreading the day for over a month.  I was planning on keeping him home from school today, and was only saved from the necessity of doing so by the fact that his spring break carried over to tomorrow (by virtue of the fact that this year April Fools falls on the day after Easter).

Some people think puns are the lowest form of humor, but I think that the prank is much lower.  A pun is at least based on clever wordplay and can be enjoyed by both the teller and the listener, whereas a prank is nothing more than a lie with good PR and the "humor" from it is at the expense of the listener for falling for it.

*  For which it must be noted I hold my parents and doctors blameless, instead laying the blame on the lateness of translating Hans Asperger's writings into English.
**  For example, I think it's cute/interesting/amusing that my son has only 2 songs on his MP3 player, and has no desire for any more, the songs being REM's "It's the End of the World As We Know It" and Crazy Frog's version of "Axel F", but if I had written the post I originally planned to make about that, people would have thought it was an April Fools post (and not a particularly good one, at that).***
***  People would also expect that the links in the post would go to songs other than the ones they're identified as.  Which I suppose would be kind of funny, but getting people over the age of 10 to listen to Crazy Frog is quite humorous enough, without resorting to cheap tricks.

Game of Thrones: Postmodern escapism?

Today The Nation published an article by Michelle Dean called "Is 'Game of Thrones' Escapist Enough?"  Dean looks at Game of Thrones through the lens of our historically demonstrated appetite for escapist entertainment during bad times and, compared to past escapist utopias, finds it wanting.

And if you're looking for Great Depression-style, good-guys-in-white-hats, only happy endings fare, she's absolutely right.  But I don't think that sort of escape would have found many takers in today's world anyway.  Instead, I think Game of Thrones demonstrates a newer, postmodern sort of escapism that better resonates with people today.

Ned Stark, for example, is one of the characters people are more likely to want to identify with.  We get to hope that we would act as honorably as he does, while at the same time we imagine we could have handled the Westerosian politics more skillfully than he did and thus end up keeping our heads.  Likewise, Tyrion is a fascinating character because he is deficient in the martial virtues prized by his culture, yet he manages to make his way through the world more successfully than some characters who better embody the ideals of Westerosian manhood.  He is a dwarf among (sometimes literally) larger than life men, and yet he succeeds when he "should have" failed.

I think Tyrion, and also Arya (among others), demonstrate the escapist ideals of Game of Thrones:  By any rational analysis, these are characters who should have been completely crushed by the events of their world, but instead they're able not only to survive but to take action which significantly changes the world around them.  In a time when so many people feel helpless in trying to improve this situation, the power of this fantasy cannot be understated.

A tax on people who can't do math? Maybe, maybe not.

My friend Clay used to regale us all with tales of the fantastic things he had planned for when he won the lottery.  One day someone pointed out the fact that Clay never bought a ticket, an observation which he scoffed at.  "All that does," he said, "is increase your odds an infinitesimal amount."  He was right, of course, while also overlooking (for comedic effect) the qualitative difference between no chance and even the smallest non-zero chance.

That qualitative difference, not the actual odds, is what keeps people playing the various lottery games that have sprung up around the country.  After all, if you're working a minimum wage job, you've never heard of anyone like you who ever got rich by working, but every week or two you see on the news someone like you who got rich by winning the lottery.  Just last night, someone in New Jersey won $338 million in a Powerball drawing.  And besides the fact that you see people who win the jackpot, there's also the fact that every now and then you'll win a smaller prize.  This intermittent reinforcement has been determined by scientists to be the best way to train an animal* to exhibit a certain behavior.

Recognizing this, the people who run the lotteries have devised a variety of different games, with a variety of different reinforcement schedules, in order to provide maximal appeal to the maximum number of players.  Besides the big weekly and biweekly draws, there are smaller daily draws that can be placed for a little as 50 cents.  For people who'd rather not even wait for a daily draw, there are scratch-off games.  For people who don't even have time to wait to buy a scratch-off ticket from a cashier, there are vending machines that sell scratch-off tickets.  And finally, for people who want to "invest" larger amounts of money in the lottery, scratch-off tickets are now offered in multi-dollar denominations**.

Financial planners, libertarians, and other true believers in the capitalist system generally say that people shouldn't play the lottery, but should instead save and invest that money.  They might be right, from a strictly mathematical point of view.  But, interestingly, they're not right by a sufficiently noticeable margin that they don't feel the need to pad their numbers.

The effect of compound interest on investments funded by cutting out small, "frivolous" purchases has been dubbed "The Latte Factor" by author David Bach.  Bach has made a career out of this one idea, and latte factor calculators have sprung up all over the web.  The one that I used in writing this post sells the idea by urging people "just input $5 daily for fancy coffee over a period of 40 years at 10% and see what happens."  What happens, as it turns out, is that by cutting out this coffee you'd save just over $73 thousand in foregone spending and earn just under $890 thousand by investing these savings.  Of course,  the most expensive coffee on Starbuck's menu is only $4.25 and Warren Buffett, the most successful investor in the world, says says investors should expect a 7% return.  Plugging these numbers into the calculator yields savings of $62 thousand and earnings of $277 thousand.  Still nothing to sneeze at, but noticeably less than the fanciful example touted by the calculator.

But let's go back to our hypothetical lottery player.  They're going to be spending less than someone buying the most expensive drink at Starbucks every day, and hence saving less when they cut out this spending.  While some lottery players spend more, a fairly typical amount - and what I'll be using for my example here - would be $2 per week (one entry for each of that week's Powerball drawings).  Likewise, they're not going to be able to afford to invest in a mutual fund in order to get higher returns.  Once they save enough to move beyond hiding their money in their mattress, they'll probably be putting it in a saving account earning 1% interest.  Using these numbers, over a period of 40 years, would yield savings of $4159 and interest of $954.  Even if they do the math on this, our hypothetical lottery player is likely to decide that given the lower amount of effort involved in investing that $2 a week in the lottery rather than a saving account, coupled with the potential (however unlikely) for higher returns through playing the lottery, that they're better off with the lottery.

*  People are animals, my friend.
**  The largest of which I've ever seen is a $30 scratch-off game.  I'd never play it, but apparently I'm not the target audience.