As the young people say, Jon Stewart FTW.

I like Jon Stewart. If I still had cable, his show is one of the few things I would make time to watch. As it is, several websites I visit have clips of The Daily Show and I watch them several times a week.

Chris Wallace had him on as a guest on Fox News Sunday. As you might imagine, Mr. Wallace did not like the idea that he worked for a "relentless agenda-driven 24 hour news opinion propaganda delivery system". Stewart stood by these words.

Wallace did something a lot of newspeople do, criticized Stewart for not being a serious newsman. Stewart said the comparison was silly, that he is a comedian just as Will Rogers was, and that people take him seriously because they are disappointed in the news they get.

Wallace said Fox News viewers weren't in the least disappointed. Stewart said that poll after poll shows that they are the most consistently misinformed.

In other words, if they were bright enough to be disappointed, they'd be disappointed.

Wallace made the point that other news outlets are biased in the liberal direction. Stewart countered that the actual bias of the news media in general is not ideological, but weaknesses for conflict, sensationalism and laziness.

The Huffington Post had this story as the top of the page early this Sunday. They had a huge picture of Stewart, slightly grainy and looking somewhat upset, with a 48-point headline "YOU'RE INSANE!"

Let's see. Conflict, check. Sensationalism, check. Laziness, check.

I gave Mr. Wallace's quotes first and Mr. Stewart's quotes second because Stewart correctly countered everything Wallace brought up. Jon Stewart is one of my heroes. Chris Wallace is a corporate tool and he got owned on his own show.

Here endeth the lesson.

The math of Penrose tiles, part 3: Two proofs of impossible similarity.

I'm about to prove a couple of negatives about Penrose tilings. Recall Donald Rumsfeld proudly and stupidly saying you couldn't prove a negative when it became obvious to everyone the weapons of mass destruction ruse was a complete phony. I had to wonder exactly how many classes he slept through when he got his degree at Princeton.

Of course you can prove a negative. The only place where real proof exists is in math and we prove that things are impossible all the time.

Let me give a couple examples.


It is impossible to build a larger shape similar to a dart using kites and darts.

The dart is the Penrose tile with the dent, and angle of 216°. It is also the only Penrose tile that has the sharp 36° angle. Those angles are adjacent to each other, which means if you need a 36° angle when you are building something, you have to use a dart and you have to plan for the fact the 216° will be right next to it at the distance of short.

If we want to build a bigger dart, it will have to have two 36° angles and a 216° angle, but the distance between these will have to be at least the length of long.

We can't do this with these pieces, or if we achieve this, we will not have a long enough straight line to make the outside of the dart.

This proof takes no math skills really. If you had some Penrose tiles to play with, you would see pretty quickly the problems involved trying to make a shape similar to the dart.



It is impossible to build a shape similar to a kite bigger than Papa Kite.

Yesterday, I showed this picture of a regular kite, a slightly larger kite made of a dart and two kites (a shape I call Mama Kite) and a third larger shape made out of five kites and three darts I call Papa Kite.

Notice this. Each of the straight lines that make up a side of all three of these kites has at most one side of the short length. Because of the angles available, one short is all you can have if you are building a straight line that is empty on one side and completely filled in on the other. The problem is that to make a straight 180° angle from a 72° angle, we need 108°, which in Penrose tiles can only be done by combining a 72° and a 36° angle. Just as we saw in the earlier problem, the 36° angle is a little clumsy when trying to continue a straight line because it is so closely tied to the dent, the 216° angle, known formally in geometry as a reflex angle.

Here is my best attempt at making Granddaddy Kite, the next size up of similarity. The Fibonacci sequence tells me how many pieces I need, 13 kites and 8 darts. I used 12 kites and 7 darts and the shape of the empty space that caused the problem has a 36° angle that we can't negotiate with the shapes available.

Notice that the unfillable space is exactly a Big Dart, the shape we can't make with the two standard Penrose tiles. If a third Penrose tile existed that was the shape of the Big Dart, with side lengths long and long+short, the number of things we could do with the new system would increase dramatically, though it wouldn't help with making a dart bigger than Big Dart. That would still be impossible.

Instead of Big Dart, another "third" Penrose tile that could help in this situation would be a triangle with sides short, short and long, which would have angles 36°, 36° and 108°. With this addition, Big Dart would be these two triangles put side by side along one of the short sides, and suddenly bigger darts and bigger kites would be much, much easier.

In math, we call this "prove or disprove or salvage". When you prove something can't be done, you try to find the simplest changes you could make to the problem where you could do what was asked. The most famous early example of this was Archimedes proving that trisecting any given angle was impossible with a compass and straightedge, but it could be done if you were allowed to put one mark on the straightedge.

This is one of the reasons mathematicians put Archimedes head and shoulders over other ancients like Euclid or Pythagoras. Nobody else was "thinking outside the box" like our Sicilian pal.

Not that I'm telling Sir Roger what to do with his tiles. He is a Big Damn Deal in physics and I'm a blogger.

Not that I'm comparing my salvage to Archimedes' method for trisecting angles. That is a work of stunning beauty.

I'm just sayin'.

And, oh yeah, Donald Rumsfeld is still a pinhead who planned two wars he didn't know how to finish and he can bite me.

I'm just a blogger, but I'm a shitload smarter than he ever was.

If you ever read this, Don, quod erat demonstrandum, you ugly, murderous little pencil pusher.

Stuff I like: Still Bill

Of all the rags to riches stories in show business history, there may be none as remarkable as Bill Withers'. He was born in a West Virginia coal mining company town called Slab Fork. He was a stammerer and it made him shy, reticent to speak. He joined the Navy and when he got out, he worked at an aircraft company, installing toilets on 747s. At the age of 32, he had never been on stage professionally when he decided to take some of his songs into a studio to make a demo tape.

Sussex Records heard his demo and signed him. Booker T. Jones produced his first album, which included the breakout hit Ain't No Sunshine and Withers' personal favorite, Grandma's Hands. His second album included the number one hit Lean On Me and the top ten song Use Me. As a songwriter, he returned to the top of the charts in 1981 with Just the Two of Us, a huge success for Grover Washington, Jr.

The documentary Still Bill takes a look at his life now. He's 70 and he's been away from the music business for a very long time. There's a famous quote from Elvis Presley after he left the Army and some female reporter asked him if things had gotten back to normal yet.

"Ma'am, when things get back to normal, I'll be driving a truck."

Elvis only drove a truck for a few months before he became crazy famous. He got a small taste of "normal life" when he was drafted and served two years. Bill Withers saw "normal adult life" for over a decade before the first single on his first album became a monster hit. He never completely trusted the music industry, but thankfully his is not a story of riches going up in a puff of smoke. After he quit in 1985, he didn't tour or make any attempts to record new music. Bill had had enough, thank you very much.



The movie does a great job of showing Bill's relationships with friends and family and with his gifts as a songwriter. I didn't know much of his music other than the big hits, and I was pleasantly surprised how much good stuff he wrote. On the extras on the DVD, the Swell Season are among the acts who were part of a Bill Withers tribute concert in New York City, and they play a song of his off of +'Justments called Stories. I had never heard it before, but it's hauntingly beautiful. I'm using the lyric from the bridge as my tagline right now, and I give you a link to Bill's original version, available on the You Tubes.

Matty Boy says check it out.

Sunday Numbers 2.0, Vol. 7: The Euler-Poincaré characteristic.

I have noted in earlier posts about Leonhard Euler, a.k.a. My Favorite Lenny, that if we named everything in math that was first studied by him after him, there would hardly be anything named for anyone else. One counterexample of this is the Euler-Poincaré characteristic, which is used to discuss the relationship between the parts of a three dimensional shape, the faces F (two dimensional), the edges E (one dimensional) and the points at which the edges meet, known most commonly as the vertices V, the plural of vertex (zero dimensional). For a shape like the cube shown here, which is does not have any holes going straight through like a donut does, the formula is given as F + V = E + 2.

Let's check to make sure. F is 6 and V is 8, while E is 12, so 6 + 8 = 12 + 2. Not surprisingly, it works. If it didn't work, it wouldn't be math, right?


Let's go to a less familiar shape, the dodecahedron, the twelve sided three dimensional shape whose faces are all pentagons. F = 12, V = 20 and E = 30, so once again the formula is correct.

There is a separate theory called the Angle Deficiency Theorem. Consider that if all the faces that meet at a vertex added up to 360°, that corner would be a flat surface. The only way to make a three dimensional shape is to have less than 360° at each vertex, and that is called the angle deficiency of the vertex. For any convex three dimensional shape without a hole going through it, the sum of all the angle deficiencies of all the vertices is 720°. Let's check on the cube and the dodecahedron.

Cube
Angle deficiency at each vertex; (360-270)° = 90°.
Since there are eight vertices, (8 × 90)° = 720°.

Dodecahedron: Each angle of a regular pentagon is 108° so (360-324)° = 36°.
There are 20 vertices, so (20 × 36)° = 720°.

This is a surprising result, but the simplest proof is an application of F + V = E + 2.

The proof itself is left an exercise to the motivated reader.

(I love typing that last sentence.)

Is Asperger's Syndrome the engine for human progress?

In 1944, Dr. Hans Asperger of Vienna published an account of symptoms he saw in some of his young patients. Some were mild and others severe, but the most typical symptoms were tendencies towards physical awkwardness and difficulty in dealing with others due to a lack of understanding of non-verbal cues, such as reading other people's facial expressions or body language.

These are just some the downsides of Asperger's Syndrome, as it is known today. The upside is a remarkable ability to concentrate on a topic that catches their interest. While his paper was first published during WW II, it was not translated into English until 1991, some ten years after Dr. Lorna Wing popularized the term in the English speaking medical community. Asperger's syndrome is now recognized as being part of the autism spectrum and Dr. Wing's interest was due to having an autistic daughter.




The diagnosis exploded in popularity from the 1980s forward and it is assumed though not yet proven there is a genetic tendency. Asperger himself saw that many of his clumsy children also had clumsy fathers who showed some if not all the symptoms of his syndrome themselves.

Possibly the best known dramatic portrayal of a person with Asperger's Syndrome is Dustin Hoffman in Rain Man. His character Raymond shows many of the traits of the syndrome, including his dislike at being touched, (many people with Asperger's can be touched, but only if you first get their permission), his obsessive interests and his remarkable ability at math.

Unlike the character in the movie, there are many people with Asperger's Syndrome who are not institutionalized, and high functioning Asperger's (HFA) can be very successful as researchers. Usually, they are not as successful as teachers, because it is common for people with Asperger's to assume that if they know something, everyone knows it and even if they overcome that, they intensely dislike have to repeat themselves.

And so we have this diagnosis, only known for about seventy years and only popularized in the past thirty, that describes a certain class of brilliant eccentrics. Many people have taken to historical diagnosis, putting forward their arguments that x had Asperger's or y showed symptoms. A lot of people who are putting this stuff forward don't seem to have read the literature very well. Doing a little browsing around the Internet, I have found claims of both Ben Franklin and Thomas Jefferson may have showed signs.

Both Franklin and Jefferson were horndogs. If you see a bright eccentric with a serious thing for the ladies, it's very likely that their eccentricity is not caused by this syndrome.


Two other names that pop up a lot are Newton and Einstein. Einstein didn't speak fluently until he was nine, but early developmental problems are NOT typical with Asperger's Syndrome. He did show the intense interest in problems that is a characteristic, sometimes working on a problem so hard he would forget to eat or sleep. But again, there are stories of Einstein getting busy with the ladies, and that would tend to be a counter indication.

Not everyone is convinced, but I find the data for Newton to be the strongest case of a historical character who may have Asperger's. He once wrote in a letter to a friend that he was proud he would die a virgin, and besides mathematics and physics, he had lifelong obsessions with alchemy and religion. He produced a proof that the Holy Trinity was impossible, but he declined to publish, seeing as back in his day, the Church of England was still putting heretics to death from time to time.

Another symptom mentioned in descriptions of Newton was his habit when in deep thought to rock back and forth uncontrollably, another very common behavior for people with the syndrome.


I read a book earlier this year by David Mamet titled Bambi Vs. Godzilla,and I have already written a blog post recommending that the book be avoided. Mamet hypothesizes that many of the early Jewish film directors had Asperger's because they were successful, highly focused and complete pains in the ass to work with, and that there is a prevalence of the syndrome in the Eastern European Ashkenazi community.

Once again, I call bullshit, which is an unpleasant but necessary task one must perform often when reading David Mamet's non-fiction.

People with Asperger's tend to love reading and dislike film and TV. So much of the visual arts is the understanding of non-verbal communication, and this is a skill at which even HFAs are notoriously bad.

Being intensely focused and an asshole does not mean automatically a diagnosis of Asperger's. Some people are just raised that way. A popular T-shirt slogan in the Asperger's community is "I have Asperger's. What's your excuse?"

So the short answer to my question about the syndrome being the engine of human progress is "probably not, with just a few large and remarkable exceptions".

Whew, that's lotsa 'splainin'. Glad it's a Saturday.

Sidney Lumet, 1924-2011

Sidney Lumet has died at the age of 86. He was one of the greatest directors of the past fifty years, and I would argue one of the best of all time.

I saw the last two movies he made, Find Me Guilty starring Vin Diesel and Before the Devil Knows You're Dead with Philip Seymour Hoffman, Ethan Hawke and Albert Finney. He was over 80 when he made these. Men half his age would be hard pressed to do as well.

I've read a few of the obituaries, and the idea people are trying to push is that he was one of the great New York City film directors. While some of his best work is based there (Serpico, The Pawnbroker, Prince of the City, Night Falls On Manhattan), what really impresses me about his career is his ability to hit to all fields. Woody Allen and Martin Scorsese are more highly thought of in some circles, but there are movies on Lumet's list they couldn't possibly make.

How about Network? Fail-Safe? Could Scorsese or Allen make The Group or Long Day's Journey Into Night?

They could, but they would suck at it.


His big break after working on TV was the film version of Twelve Angry Men in 1957. I've heard some directors whine about not having enough locations, of a movie looking like a filmed play.

Ever since I was a kid, I thought about Twelve Angry Men when I heard this lament. If you aren't as good as Sidney Lumet, either shut up or get off the field.

I loved this movie when I was young. This is the movie that turned me into a trivia nerd. I knew I had to remember the whole cast. Left to right: Jack Warden, Edward Binns (hidden), E.G. Marshall, John Fielder (hidden), Henry Fonda, Ed Begley, Robert Webber, Jack Klugman, George Voscovec, Martin Balsam, Joseph Sweeney. That's eleven guys. They are all looking at the last holdout, played by Lee J. Cobb.

Hope that wasn't a spoiler, but the movie is 54 years old, so I'm going to say it's your fault if you didn't know that by now. I've had those names in my head for over four decades now, and I didn't have to check out imdb.com to see if I was right.


Lumet wasn't perfect. He made The Wiz, to give just one example. He did a remake of John Cassavetes' Gloria starring Sharon Stone to name another.

He directed 72 projects. They can't all be masterpieces.

But he also directed possibly my favorite all-star cast of all time, Murder On The Orient Express, starring Albert Finney as Hercule Poirot. I'm going to put in the the DVD player tonight and enjoy it one more time, just because it's time to remind myself how good Sidney Lumet really was.

Best wishes to the family and friends of Sidney Lumet, from a devoted fan.

The day came, to my surprise.

When my mom died last year, I posted a few songs for her and one for my dear departed friend Mina Millett, who died years earlier much too young. The song for Mina was Put Your Records On by Corinne Bailey Rae. Mina never heard this song, since it was recorded after she was gone, but Ms. Rae looked so much like a young Mina and the song reminded me so much of good times with Mina on picnics and the like, the bright lively tune always made me cry to the point of sobbing uncontrollably.

Today, I listened again, singing along as I always do.

Today, I was able to sing the song all the way through.



So, Matty Boy, you didn't cry at all?

Read carefully, Hypothetical my friend. I didn't say that.

John Wooden: 1910-2010

John Wooden, best known as the coach of the incredibly successful UCLA program back in the 1960s and 1970s, died yesterday at the age of 99. You can search far and wide to find someone who will say a word against him and you will come up empty-handed. I am not a Christian, so let me say without any "hometown bias" that John Wooden was a fine example of a good Christian gentleman who lived his faith. He completed his Pyramid of Success (click on the picture for a larger version) back in the late 1940s and instilled these values in the young men under his guidance.

I grew up in the Bay Area, so I could have decided to hate UCLA on general Northern California principles, but I watched from a distance in amazement at the stunning successes the Bruins compiled, most notably when a young man from New York City named Lew Alcindor decided to go to school 3,000 miles away from home. Alcindor was tall and slender, 7'2" with a wingspan like an albatross, and so dominant that the dunk was banned in college basketball in 1967 and not allowed back until 1976. To overcome this, Alcindor under Wooden's tutelage worked hard on a shot called the sky hook, still one of the prettiest and hardest to defend shots in basketball history. UCLA went 88-2 while the young man played center for the team and won the national championship three years running. After he left, Wooden coached UCLA to another four consecutive national titles. From 1963 to his retirement in 1975, UCLA were the national champions ten times.

For the young people who might not remember, Alcindor converted to Islam and changed his name to Kareem Abdul-Jabbar, which back in the day was a very controversial act. Like all Wooden's former players, he speaks only in reverent tones about his teacher.

Best wishes to the friends and family of John Wooden, from a fan.

Congratulations to Hazel Soares. UPDATED

Hazel Soares is going to graduate from Mills College in art history. She is 94 years old. You can read more about her story in today's Chip Johnson column in the San Francisco Chronicle.

Besides being a local human interest story, Hazel is the aunt of my friend Jodi Soares. Hazel had a heck of a time getting through math, and Jodi asked me if I'd be willing to help, but we didn't make the connection. In any case, Hazel kept pushing forward and the finish line is now in sight.

Congratulations again to Hazel and everybody in the class of '10.

(Note: In my earlier post, I had her name as Helen. That would just be a mistake in normal situations, but she had a sister named Helen who is no longer with us. I deeply apologize for my blunder.)

Attention, sports fans!

If you want to get a crowd roused up for a health care march, who should you have out in front?

None other than Crazy George Henderson, one of the only honest to Lenny cheerleaders in professional sports, in that he actually leads cheers. In 1968, he lead cheers for San Jose State when he was a student. He was also on the judo team. Since then, he has worked for the Oakland A's, the San Jose Giants (minor league), the San Jose Earthquakes (soccer), the Kansas City Chiefs, the Houston Oilers, and a whole passel of other teams across the the United States and Canada.

At this health rally, he didn't bring his drum, so I assume he was not paid to be there, just a concerned citizen.

Good on ya, Crazy George!