This blog is still alive, just in semi-hibernation.
When I want to write something longer than a tweet about something other than math or sci-fi, here is where I'll write it.

Sunday, August 26, 2012

Sunday numbers, 8/26 part b:
The Senate races


Another week goes by and the polls show good news for the Republicans again.  As you can see, the movement from blue to purple was more than the movement from purple to red, which means this week was not quite as positive for the Republican cause as last week was.  The median result is 50 seats for the Democrats, 49 for the Republicans and Angus King of Maine as the semi-kingmaker, or more precisely, the compromise maker. The odds of 50 seats or better for the Dems before King makes his decision is now 69.2%

The major difference in the parties is that while some people are called moderate Republicans, like the retiring Olympia Snowe, when the Republicans want to filibuster something, they have forty votes come rain or shine.

Moderate Republicans are not as extinct as the passenger pigeon. They are now called moderate Democrats.

New numbers next week. Stay tuned.

Sunday numbers, 8/26, part a: Week two of Romney-Ryan

At the beginning of this week, the momentum towards Romney-Ryan continued as it did in the first week, but by midweek the polls started showing gains for Obama-Biden. Overall, the Republican ticket gained slightly but not nearly as much as they did in the first week. (From the Republican point of view in math, we would say the function gained but the first derivative shrunk, not unlike a plane coming in for a landing.)

Here is the state-by-state situation.

Solidly Republican.
AK 3 AL 9 AR 6 AZ 11 ID 4 KS 6 KY 8 LA 8 MS 6 OK 7 SC 9 TX 38 UT 6 WV 5 WY 3
MT 3 was leaning Republican
EV total = 132

===
Leaning Republican.
IN 11    0.9998
GA 16    0.9978
ND 3    0.9995
NE 5    0.9995
TN 11    0.9804
MO 10    0.9656
NC 15    0.8772
SD 3    0.9285
IA 6    0.6814
FL 29    0.5992
EV total = 109

===
Coin flips.
VA 13    .5000 was Leaning Democratic
EV total = 13

===
Leaning Democratic.
NV 6    0.7307
WI 10    0.7594 GOLD
NH 4    0.7659
OH 18    0.8149 was toss-up
CO 9    0.8247
MN 10    0.9362
MI 16    0.9397
NJ 14    0.9736
PA 20    0.9756
OR 7    0.9858
WA 12    0.9937
CT 7    0.9893
NM 5    0.9996 was solidly Democratic
EV total = 138

===
Solidly Democratic.
CA 55 DC 3 DE 3 HI 4 IL 20 MA 11 MD 10 ME 4 NY 29 RI 4 VT 3
EV total = 146


The changes in favor of the Republicans in New Mexico and Montana are minor. The big gain for Romney-Ryan was changing Virginia to toss-up and the big loss was having Ohio go from toss-up to Leaning Democratic. Other numbers changed, but they did not change categories.

The long and short of this in terms of the median result is Obama's total in the electoral college shrunk from 295 to 293.  It takes 270 to win, so the Republicans are looking for 24 more electoral votes right now.  No one contested state gets them over that mark.


Because of movement of some small states towards the Democrats, the probability of victory increased ever so slightly from 88.2% last Sunday to 88.9% this weekend.  My program takes the 24 states currently at less than 99.99% Confidence of Victory for either party and throws them into a mix, producing two to the twenty fourth different outcomes, which is16,777,216 results to tally.  I've been programming in C a long time, and I'm still a little startled how lickety-split my computer can do all these calculations, about six seconds. I could never do this work by hand, and making an Excel program to do this would be a huge waste of resources.

This week is the Republican convention.  The networks have realized what a ratings dog these pageants are and have cut back their coverage markedly.  I expect a Republican surge from this week and a Democratic surge from their convention next week.  More than that, the real ad blitz will start after Labor Day.

Stay tuned.

Wednesday, August 22, 2012

Wednesday Math, back from the dead:
The wackiness that is set theory.


As I have have told my students from time to time, "Math is NOT set up the way it is just to make you crazy.  That's a happy little bonus."

But there is part of math that made even mathematicians crazy in its infancy and is still reviled by some people who have no business doing mathematics at all, the fundamentalist Christians who insist on home schooling their children.

That part of math is set theory and the guy who did the most important early work is the fella in the picture, Georg Cantor.

A set is a collection of objects. So far, so good. The cardinality of a set is the number of objects in the set.  if two sets have the same cardinality, you can match them up in a one-to-one correspondence.  If you have twelve kids at a party and twelve party hats, you can give each kid a hat, no one has to share and there are no unused hats.

What could go wrong?

Infinity could go wrong.

There are some infinite sets that can be put into one-to-one correspondence with other infinite sets.  For example, the cardinality of the positive integers is the same as the cardinality of all integers, positive, negative and zero.  Here's the one-to-one mapping.

1 goes to 0
2 goes to 1
3 goes to -1
4 goes to 2
5 goes to -2

The rule is:
even numbers (2n) go to half the value (n)
odd numbers (2n + 1) go to the negative of half the even number just before them (-n) .

So while it "makes sense" that all the integers is twice as big + 1 as just the positive numbers, multiplying infinity by 2 or 3 or even squaring infinity doesn't make a bigger number.

But this first infinity is just the beginning.  There are some infinities bigger than others.  It would be hard to show the proofs on a blog, so I'll ask you to take my word for it. Cantor knew the stuff he was doing was goofy, and instead of using the regular alphabet to denote the infinities or even the Greek alphabet, regularly used in geometry and trig, he named the different infinities after the first letter in the Hebrew alphabet, aleph.  The smallest infinity is aleph nought or aleph0 and the next size up is aleph1, usually called the countable and the uncountable infinities respectively.  The rational numbers are aleph0. The real numbers have more, aleph1. There are infinitely many infinities, but only the first few are the cardinality of things mathematicians find useful.

Set theory created an amazing row. Great mathematicians like Henri Poincare hated it. Pretty good mathematicians like Leopold Kronecker hated it. Mathematically astute philosophers like Ludwig Wittgenstein hated it. But Cantor had his adherents as well, most notably David Hilbert, who in his day was the Biggest Damn Deal in mathematics. John Von Neumann, the greatest mathematician of the generation after Cantor, Hilbert and Poincare, came up with Class Theory to turn some of the messiest sets into classes. Classes followed different rules than sets and calmed down the people who were trying to make a new paradox every week. Pretty much, for all its oddities, mathematicians now are happy to have set theory as a basic concept of the field.

If you are wondering how much anti-Semitism is involved in the objections to Cantor's work, it should be noted that his critics Kronecker and Wittgenstein are Jewish and his great supporter Hilbert is not Jewish. His critic Poincare was not a Jew, but not an anti-Semite either.

Another favorite part of the Cantor story is he ended up in the nuthouse.  People who understand mental illness better now say his diagnosis looks like bi-polar disorder and was NOT brought on by the amazing level of criticism heaped upon his work by well-respected colleagues.
So why do people who write books for home schoolers hate set theory?  They believe in just one infinity, and that infinity is their One True God.

I only recently heard about the hatred from the people trying to keep their kids under their thumbs for the love of Jeebus, but this coincides with me thinking for the first time about the additive group R/Q, the real numbers with the rational numbers removed, which is to say an uncountable infinity with a countable infinity removed.  There are uncountably infinite elements of this group, but the only one we can name is 0.  The rest are infinitesimally close to zero. It's real Through The Looking Glass stuff, and it comes from one of my favorite parts of practical math that has its roots in theoretical math, group theory.

This is just one of the reasons when someone asks "What are you doing for fun?" I often answer "You really don't want to know."


Sunday, August 19, 2012

Sunday numbers 2012, 6b: The Senate Races


I wrote my precious C program, so now I'm ready for as many toss-up races as can be thrown my way in the Senate contests. The news this week was strongly in favor of the Republicans. As of today, the most likely and median event is the Democrats keeping 51 seats, when just seven days ago they were looking at 54 being most likely and under 50 being nigh impossible. A big part of this is a poll that gives Akin a big lead in Missouri over McCaskill, but this was before he said women who are "legitimately raped" have almost no chance of being impregnated because of "natural defenses" some doctor told him about.  He has kinda sorta recanted, but he's a Tea Party candidate and the onus is now on him to show he isn't a nutcase, not unlike it was on Christine O'Donnell and Sharron Angle in 2010, to name just two big losers from the shallow end of the Republican gene pool so beloved by the Sarah Palin wing of the party.

New results next week. Stay tuned.

Sunday numbers 2012, 6a:
Week 1 of Romney-Ryan

We are now a week into know the tickets on both sides. As expected Romney-Ryan got a bump up. It will take another week to tell us if it's a trend or a bounce. Here are this week's probabilities for each state and Washington D.C., along with what changed from last week. Every state is given a probability of at least 50%, where the number given represents the probability for the party favored in that race.

Solidly Republican.
AK 3 AL 9 AR 6 AZ 11 ID 4 KS 6 KY 8 LA 8 MS 6 OK 7 SC 9 TX 38 UT 6 WV 5 WY 3
EV total = 129
===

Leaning Republican.
IN 11 0.9998
ND 3 0.9995
NE 5 0.9995
GA 16 0.9978
MT 3 0.9820
TN 11 0.9804
SD 3 0.9285
NC 15 0.8772
IA 6 0.6814
MO 10 0.6012 down from .9905
FL 29 0.5992 was Leaning Democratic

EV total = 112

===
Coin flips.
OH 18 .5000 was Leaning Democratic 
EV total = 18

===
Leaning Democratic.
VA 13 0.6777 GOLD
NH 4 0.7659 down from .8147
CO 9 0.7747 was Coin Flip
NV 6 0.8747
WI 10 0.8948 down from .9898
PA 20 0.9170 was Solidly Democratic
MN 10 0.9362
MI 16 0.9560 up from .9397
NJ 14 0.9736
OR 7 0.9858
CT 7 0.9893
WA 12 0.9937
EV total = 128

===
Solidly Democratic.
CA 55 DC 3 DE 3 HI 4 IL 20 MA 11 MD 10 ME 4 NM 5 NY 29 RI 4 VT 3
EV total = 151


While there were improvements for both the Republicans and the Democrats, the overall change brings the median electoral vote count for Obama-Biden down to 295, down from 311 last week. As it stands, there is no one state outside the Solidly Democratic group that the Republicans can grab to get over 270.


As you might expect, the probability for victory has also gone down for the Democratic ticket, from a very comfortable 98.0% as of last Sunday to a less comfortable but still comfortable 88.2%.

We are still two weeks away from Labor Day, when an unprecedented amount of cash gets poured into the political races.  I'll be back next Sunday to see what the situation is just before the deluge.

Stay tuned.


Saturday, August 18, 2012

Dersu Uzala, the Hunter


Earlier this week, I wrote a review of Catch-22, a book I returned to some forty years after I first read and loved it, only to find my love had waned over time.

This weekend, I watched Dersu Uzala, the Hunter for the first time since the 1970s. It was shot in the Soviet Union and directed by Akira Kurosawa, the only film he ever shot in 70 mm. It tells the story of the friendship of a Siberian native named Dersu Uzala and a Russian captain of a surveying party in the early part of the 20th Century, portrayed by Maksim Munzuk and Yuri Solomin respectively, the two men seated in this black and white still from the picture. The vast majority of the film is in color, but there is a scene comprised of photos of the main characters, this being one of the photos.

The movie is based on the memoir of the captain, Vladimir Arseniev. The film is long and slow and very beautiful. I don't know if modern audiences would feel antsy watching it or not, but because it is a story of man against the elements, the slow pace and long shots make perfect sense. One of the joys of seeing a foreign film from an era I'm unfamiliar with is to see great actors completely inhabiting parts. My constantly cataloging brain isn't thinking "Oh, yeah, I saw Maksim Munzuk in ..." I never saw him play anything but Dersu Uzala. In my mind, he is Dersu Uzala.

One of the surprises for me is the incredible beauty of Siberia. In the general imagination, Siberia might as well be Antarctica, but in the Russian view it is the great untamed wilderness, the way Americans felt about The West in the 19th Century.  There are plenty of scenes in the cold, snow and ice, but we also see it in the spring, summer and autumn. The movie contains some of the best nature photography ever.

Some might complain that Dersu is too much the over-simplified "noble savage". To those people, let me say... bite me. If you don't love him as much as the captain did, I don't know what movie you were watching.

I saw it on DVD. The quality of some parts was a little scratchy. I hope someone somewhere is working to re-master this and put it on Blu-Ray, because it is one of the most beautiful films of all time.


Wednesday, August 15, 2012

The book of my adolescence.

A lot is being made of Paul Ryan's favorite author, Ayn Rand. In explaining himself, he says he loves Catholicism - Rand hated all of Christianity - but loved Rand's view of economics. It sounds to me that Ryan's true hero is Pat Buchanan, who believes in the Catholic faith without the annoying optional extra feature of compassion. But then, Buchanan forgot to put hot horny heroines in his books, so young Paul Ryan lost interest.

(Mitt Romney, as you might expect, is something of an Etch-a-Sketch when it comes to his favorite books.  In 2007, during his presidential run, he said his favorite book was Battlefield Earth by L. Ron Hubbard. During the current candidacy, he says he loves the Twilight books.)

When I was an adolescent, the book I loved was Catch-22.  It is the only book I read from cover to cover and then started over at the beginning immediately. As I have made clear, right now I am reading the novels of Patrick O'Brian obsessively, but between voyages with Jack Aubrey and Stephen Maturin, I have been reading books by other authors, so I thought I'd give Joseph Heller another read after nearly forty years away from it.

Truth to tell, it doesn't hold up very well for me.

It was interesting to read the essays that are included in the 50th anniversary edition. Heller admits that the book is really much more about Korea and the America of the 1950s than it is about World War II. Norman Mailer writes a critical essay, saying he put it down several times with no intention of completing it, but finally came back to it and considers it one of the best works of all his contemporaries.

Like Mailer, I almost didn't finish the book this time.  The world Yossarian inhabits is a Kafkaesque nightmare with every man for himself and God against all.  I get enough of that in real life. There are some vague sex scenes, which I'm sure I enjoyed as a sixteen year old virgin, but as a man in his fifties who has had sex, they didn't do that much for me. There are other funny books I've read that can make me laugh even on multiple readings, notably Thurber and Kurt Vonnegut Jr., who was a close personal friend of Heller's after both of them became successful. Heller's stuff didn't quite tickle my funny bone this time.

I didn't hate the book and I could see why I loved it as a teenager, but I very much doubt I'll be reading it a fourth time. Now I am back on the happy Surprise with Aubrey and Maturin, with brave, reliable Barret Bonden and disagreeably comic Preserved Killick.  They are much better company than the wretched crew of officers flying planes out of Pianosa, forced to fly more and more missions by the vicious colonels Cathcart and Korn.


Monday, August 13, 2012

Sunday numbers 2012, 5b:
The Senate races

There are a lot of Senate races for which there is no data yet but with the ones we know, the Democrats look like they would keep at least 50 seats if the election were held today and have a 97.5% of getting 51 seats, which would mean independent Angus King of Maine - who right now looks like a shoo-in - could not be the swing vote if this stay this way.

I'm still using Excel in these prognostications, but in my spare time this week I'll write a separate C program for the Senate numbers, not unlike what I did for the electoral college count this weekend.  Thanks again to Art Velasquez for making the suggestion that let me cross the last hurdle in programming, a simple solution I should have considered but I've been away from coding for so long that it didn't occur to me.  Way to go, buddy!


Sunday, August 12, 2012

Sunday Numbers 2012, 5a: The presidential race begins.

Now that Romney has announced his running mate, the race begins in earnest. Following the lead of one of the candidates, I'm going to go all Etch-A-Sketch and pretend the data I collected up until this time doesn't even matter. I use Excel to collect and sort data, but I've written a C program to get to a lot of important information. 

Here is the state of the presidential race according to recent polls as of August 12. Remember that any polling data information should be introduced with the phrase "If the election were held today". The two letter state abbreviation is followed by the number of electoral votes and then, if necessary, the four digit decimal representing the Confidence of Victory number, given as a probability greater than or equal to 0.5.

Solidly Republican.
AK 3
AL 9
AR 6
AZ 11
ID 4
KS 6
KY 8
LA 8
MS 6
OK 7
SC 9
TX 38
UT 6
WV 5
WY 3
EV total = 129

===
Leaning Republican.
IN 11    0.9998
ND 3    0.9995
NE 5    0.9995
GA 16    0.9978
MO 10    0.9905
TN 11    0.9804
SD 3    0.9285
MT 3    0.9820
NC 15    0.8772
IA 6    0.6814
EV total = 83

===
Coin flips.
CO 9    .5000
EV total = 9

===
Leaning Democratic.
FL 29    0.6190
VA 13    0.6777
NH 4    0.8147
NV 6    0.8747 GOLD
MN 10    0.9362
MI 16    0.9397
NJ 14    0.9736
OH 18    0.9839
OR 7    0.9858
CT 7    0.9893
WI 10    0.9898
WA 12    0.9937
EV total = 146

===
Solidly Democratic.
CA 55
DC 3
DE 3
HI 4
IL 20
MA 11
MD 10
ME 4
NM 5
NY 29
PA 20
RI 4
VT 3
EV total = 171

The Golden Spike is currently in Nevada, which means that if Obama can win Nevada and all the states easier than Nevada, he retains the presidency. The Confidence Of Victory number is currently at .8747 for Obama in Nevada, so as you might expect, Obama is currently the favorite to win.

Note: In North Carolina today, Romney said: "If we win North Carolina, we win the presidency." Instead of calling him a liar, I'll just say he's ignorant. Probably, he has some number cruncher like me in his camp who knows that claim is bullshit, because right now, Romney is a prohibitive favorite in North Carolina and he is still a massively prohibitive underdog nationally.
This first chart shows the median electoral college result as of today. The numbers are Obama 309, Romney 229. This is not the most likely result, but there is about a 50% chance Obama would hit this number or better if the election were held today, and Romney has a 50% change to be at 229 or worse. Since 270 is the winning number, Romney has his work cut out for him.

This big fat column shows the current probability of victory. Obama wins in 98% of the 8,388,608 possible simulations my program ran.

There will be new polls this next week and the numbers will change.  Romney faces long odds and has to wrest several swing states from Obama to have a chance, while not letting any of his swing states slip away. There very well may be a Paul Ryan bounce next week. After all, there was a Sarah Palin bounce in 2008, but it was short lived. Palin really was an outsider, but anyone worthy of the name "political junkie" knows Paul Ryan's record, and the Democrats are positively gleeful to tell the numerically accurate facts about Paul Ryan's budgets. The first big salvo is that under Ryan's plan, Mitt's federal tax rate would be less than 1%. Now, Romney gets to run away from his own record and Ryan's record at the same time.

While the margin of victory was not as lopsided, I thought McCain ran as bad or worse a campaign as McGovern, Mondale, Dukakis or Kerry.  Romney has a real chance at being a worse candidate than any of them.

And let me give some credit to Team Obama. I like Barack, though I think Michelle is a little scary in a Tiger Mom kind of way. The girls are adorable.

But the people who run Obama's campaigns are ruthless. Ever since they turned golden boy Jack Ryan into roadkill in the Illinois senate race by finding out his gorgeous actress wife Jeri divorced him because he was insistent about threesomes, they have turned opposition research into war the way General Sherman liked it. To quote Tracy Morgan's character on 30 Rock, for these people, every week is Shark Week.

We will see how the next week goes.


Friday, August 3, 2012

Unable to agree on reality.


As regular readers know, I'm being obsessive about polling data, just like I was in 2008.

For anyone considering an intervention, I ask you to reconsider.  I'm 56, and I think we know what stuff I obsess about by now. Do not expect it to change.

Two companies, Gallup and Rasmussen, are putting out daily tracking polls for the national presidential numbers. For anyone with memory loss, let me say that the national numbers are crap because the electoral vote count is what matters. Go to Wikipedia and look up the 2000 election if you are unclear on the concept.

Although we have two companies engaging in serious numerical work that is about as useful as doing an astronomically accurate horoscope, it does have some value in that it lets us compare the data gathering methods of the two companies. If you are an old timer like me, you might still think Gallup is the gold standard of polling companies, but they lag far behind new companies like Rasmussen and PPP, and even produce less polls than some universities, notably Quinnipiac.

What we can see is that Rasmussen gives Mitt Romney a lot more credit than Gallup does. In May, Gallup thought the race about even, while Rasmussen gave the nod to Romney.  In June, Gallup said the tide was moving in Obama's favor slightly, while Rasmussen thought it was going the other way significantly. In July, the difference increased dramatically, with Gallup showing the tide turning strongly for Obama while Rasmussen thought Romney might have slipped slightly but was solidly ahead.

Again, let me say that the national polls are meaningless. More than that, if we look at Rasmussen's polls in the battleground states, they still show an electoral college advantage for Obama. If we look at the odds on Intrade, the betting site has Obama's odds at about 58% to 42%. If my Confidence of Victory numbers are anywhere close to right, Obama's actually over a 90% favorite right now, so betting him at these numbers should be positive expentancy. (Before any benighted commenter wants to talk about "the wisdom of the markets", Intrade was skewed in 2008 by one gambling fool convinced that McCain would shock the world.)

The polls have been all over the place this year.  My best advice is to look at the median, ignoring the polls that are rosiest for either candidate. This is the first presidential election post-Citizens United, and no one knows how the needle will move after Labor Day when hundreds of millions of dollars will be spent on ads, possibly even adding up to more than a billion when both sides are tallied. Still, the most reliable numbers say Romney is trailing and needs a big boost, possibly a miraculous boost to win. He may have a better chance to win than Rafalca has to medal (still in the hunt but 30th of 32 qualifying horses after the preliminary), but I wouldn't put money on either of them right now.

Wednesday, August 1, 2012

Supporting the arts, one cartoonist at a time.


As regular readers already know, I got a nice windfall early this summer.  I'm not going nuts, but I am spending money on some stuff I might not have considered before.

There are a lot of cartoonists whose main outlets are the free weekly newspapers that many large cities support. The free weeklies are having the same problems as other newspapers - dwindling ad sales - so the cartoonists are getting squeezed. A couple of my favorites, Tom Tomorrow of This Modern World and Ruben Bolling of Tom the Dancing Bug, have set up a subscription plan, which gives the fans early access and some insights into the artistic process.

I really like this week's cartoon from Bolling. Click on it to make it larger and actually legible.

If you like Bolling's work, consider joining THE INNER HIVE. Tom Tomorrow has a similar subscription service available called SPARKY'S LIST. If you enjoy these artists, show 'em a little love and ten bucks for six months. Such a deal!