Thinking About Infinity. Check My Math.

I have been thinking about infinity.

I was never good at math in school but I have always been fascinated by numbers. Here is what I have been running through my thoughts. Check my math.

infinity + 1 = infinity, which makes it seem like that 1 is a zero – no effect.

What about infinity minus 1? It has to be less than infinity. Right? So, what is the answer?

infinity + infinity = infinity

But infinity – infinity = 0

Two things inspired this infinitely frustrating thought experiment. First, I watched the film A Trip to Infinity (on Netflix). This 2022 documentary explores the concept of infinity through interviews with mathematicians and physicists.

The second inspiration was the much lighter sitcom Young Sheldon. In a recent episode, the precocious and young genius Sheldon comes to doubt the existence of zero. He is tutoring his not-very-bright neighbor Billy in math. During the session, Billy naively asks how zero can simultaneously exist as something but be nothing. The question causes Sheldon to have a kind of existential crisis. He turns to the two professors he works with and they can’t really answer the question and have some mathematical doubts too. It’s not unlike the physicist and mathematicians in the infinity film who have answers about defining infinity but don’t really agree or even seem very confident.

Sheldon rejects religion and God which is very important to his very Christian mother. Somewhat incongruously, when Sheldon talks with Billy again, Billy suggests they just pretend zero exists. Sheldon interprets this as an act of faith and that restores him.

It’s not that you can’t find a definition of “infinity.” It is that which is boundless, endless, or larger than any natural number. The ancient Greeks discussed the philosophical nature of infinity. In the 17th century, we get the infinity symbol and infinitesimal calculus. Working in the foundations of calculus, it was unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done.

By the end of the 19th century, people were studying infinite sets and infinite numbers, and infinity was clearly a mathematical concept. In physics and cosmology, whether the Universe is infinite is still an open question.

There is a section of the film that I rewatched and it still doesn’t make sense. One physicist says that if you place an apple in a box it will decay into mush and then dust. Then, it becomes microscopic particles and then it becomes one with the universe. Whoa. Give it enough time, and it will become an apple again. What?

I think the connection between the film and the TV episode is the futility of wrestling with paradoxes. You probably will end up accepting that with all of our knowledge we will likely never explain or comprehend the greater existential realities of the universe.

Aristotle said that the more you know, the more you realize how much you don’t know. Not that we shouldn’t think about these things. Just don’t expect an answer.

The Euphoria of Expressionism

I haven’t watched the HBO series Euphoria but I keep seeing raves about it on social media. It is an American adaptation of the Israeli show of the same name. The second season hit this year. The reviews I had seen initially described it as a “teen” show since it follows a troubled 17-year-old who is “a drug addict just out of rehab and likely to end up back in rehab, and her high school friends.

It gets a majority of positive reviews, with praise for its cinematography, plot, score, and performances. The subject matter is mature and somewhat controversial for its nudity and sexual content. Some critics found the nudity and sexual content excessive considering the characters’ ages.

From the German Expressionist silent film The Cabinet of Dr. Caligari (1920)

What caught my attention this past week was the video (below) discussing the visual style of German Expressionism and its influence on later films and TV including Euphoria.

German Expressionism in films was a movement that used distorted sets and sharp contrasts of light and dark. The movement was initially confined to Germany due to the isolation the country experienced during World War I. In 1916, the government had banned foreign films so with supply down, demand went up for german films. . The demand from theaters to generate films led to an increase in domestic film production from 24 films in 1914 to 130 films in 1918. In American films, it was influential in what in a later movement we call “film noir.” In all instances, it is highly stylized, sometimes surreal, and not a style we often see used today. (Though there are “neo-noir” films.)

Many film historians consider German silent cinema to be far ahead of Hollywood films of that time when it comes to innovations and style. Alfred Hitchcock was influenced by the movement from the very beginning. In 1924, he worked as an assistant director and art director at Babelsberg Studios near Berlin on the film The Blackguard. His set designs for that film are expressionistic. It is also seen in his directing, especially in some of his early, less well-known films. In his third film, The Lodger, Hitchcock used styles that the studio did not want used, such as Expressionist set designs, high contrast lighting, and trick camera work. One example of the latter is a shot of a man walking across a glass floor that is shot from below,

Another classic German Expressionist film is Nosferatu: A Symphony of Horror (German: Nosferatu – Eine Symphonie des Grauens), an early vampire film that is an unauthorized and unofficial adaptation of Bram Stoker’s 1897 novel Dracula. This 1922 silent horror film is directed by F. W. Murnau.

Count Orlok’s shadow on a staircase in Nosferatu

Though not all Expressionist films are horror, most have at least elements of the thriller and suspense, either physical or mental. One later American example is The Night of the Hunter. This 1955 American thriller film is directed by Charles Laughton. The critical reaction to the film at its release was so strong that it is the only film Laughton directed. It stars Robert Mitchum, Shelley Winters, and Lillian Gish. It is the story of a corrupt minister-turned-serial killer who attempts to charm an unsuspecting widow and steal money hidden by her executed husband.

Expressionist lighting by Laughton puts Gish in silhouette and Mitchum lit in the background

It is a dark film based on a real serial killer. It was a commercial and critical flop at its release, but in the decades since its release, the film has been listed as one of the best American films. It often makes the list close to Citizen Kane, another classic that has an Expressionist style in many ways. The director of photography on The Night of the Hunter was Stanley Cortez, who also shot Orson Welles’ followup to Kane, the 1942 film The Magnificent Ambersons.

Euphoria is not the only example we see today. The new Joel Coen interpretation of The Tragedy of Macbeth and Guillermo del Toro’s Nightmare Alley have definite Expressionist elements.

Euphoria is Expressionist in its style of sets and cinematography, but not in its plot.

Here is the short video that inspired me to look back on Expressionism. And it might get me to check out Euphoria.

A short film by Thomas Flight that shows Expressionist influences

Teachers on the Screen

This past week, a friend who is in the education world asked me if I could recommend a movie that shows some teacher:student engagement or student:student interaction.  I came up with these titles first: Dead Poets Society, Freedom Writers, The Emperor’s Club, and Dangerous Minds.

I also came up with a few that are not as serious and not always as positive – but are funnier: Teachers, Fast Times at Ridgemont High, and Rushmore.

I taught for four decades and in that time saw plenty of depictions of teachers and classrooms on screens big and small that were unrealistic and often downright insulting.

I crowdsourced the request via email to a few fellow educators and was surprised at how quickly they responded and how many I had not thought of right away.  Here’s the list we collected with a few comments and clips. What did we miss? Add a comment.

Dead Poets Society
Freedom Writers
The Emperor’s Club
Dangerous Minds
The Paper Chase

Professor Kingsfield on the Socratic Method of teaching

Mona Lisa Smile
The Miracle Worker
Teachers
Stand and deliver
October Sky
Rushmore
The Wonder Years (TV Series)

Boston Public (TV)
To Sir With Love
Mr. Corman
Fast Times at Ridgemont High
Animal House

School of Rock
Bad Teacher (hmmm…)
The Breakfast Club (more for student:student)
numerous Hogwarts scenes from the Harry Potter film series
The Karate Kid

BONUS CLIPS
Comedy is a good teaching tool.

Jerry Seinfeld plays a history teacher having problems teaching WWII

from Key and Peele – the substitute teacher

Dispatches From Elsewhere

Dispatches from Elsewhere is an American drama television series that was created by and stars Jason Segel. It premiered in March 2020 on AMC just as we were all locking down, sheltering at home and social distancing.

Jason Segel has said the series is structured somewhat like The Wizard of Oz and that is not a bad way to view the episodes which are all quite different and certainly a journey to a fantastical land.

Fantastical is a good adjective though it is no fantasy. I watched each of the ten episodes week to week, and in between, I did some research on Segel and the series. Currently, you can watch all the episodes on .amc.com.

The mystery-game-art-project that the series is about actually occurred in “real life.” Segel had seen a documentary about it by Spencer McCall called The Institute.  The game took place in San Francisco and Oakland over three years starting in 2008 to 2011. I haven’t seen the documentary but it seems to be like the game and the series deliberately mysterious. A puzzle to decipher.

Some people will like that (I did) and some people will be frustrated (my wife) and not want to figure things out. Some people may think that the game and the revelations are pretentious (I did not). Of course, those are all things that characters in the series also feel.

So much of television content is simple and easy to digest that I need to mix in some complex things.

They announced the series in 2018 with Jason Segel starring and later they added Richard E. Grant, Sally Field, Eve Lindley and Andre Benjamin to the cast. It would be shot in Philadelphia, a city with a lot of public murals and artwork that works into the story.

In the first few episodes, each of the main characters gets a full episode that focuses on their story. We are told each time that we (the viewers) are like that character. Siegel has compared the series to the Wizard of Oz and in both stories we are similar to each of the main characters.

Jason Segel is Peter, a kind of programmer who works at music service. It’s monotonous but safe. But he does want to find meaning in his life. He is on a team with the other characters trying to solving the game they all get in involved in playing. Though they’re not sure it is a game.

Andre Benjamin plays Fredwynn, a very intense, intelligent and very paranoid man.

Eve Lindley is Simone, a trans woman who is trying to figure out how she fits in.

Sally Field is Janice Foster, the optimistic, the older member,  with a very sick husband at home who is also trying to fire out who she will be.

Richard E. Grant plays Octavio Coleman, Esq., He is the head of the Jejune Institute that has created and is controlling the game. But for what purpose?

The Institute documentary tells us how the Jejune Institute created the alternate reality game. In those three years, it took in more than 10,000 players. Each had responded to enigmatic flyers posted in San Francisco that told you to go to the Institute for their “induction.”

People may be surprised that Segel created this series. He is best known for the sitcom How I Met Your Mother which he was in for all nine seasons. Prior to that he starred in two cultish series, Freaks and Geeks and Undeclared. H e has also done a  bunch of films. The one most people would point to is Forgetting Sarah Marshall which he wrote and starred in.

Two lesser-known films he did that I liked and that gave me a different take on Jason are Jeff, Who Lives at Home and The End of the Tour.  In the first, he is Jeff, a 30-year-old unemployed stoner living in his mother’s basement. The film has some of the follow-the-clues and find-the-meaning aspects of the new series.

In The End of the Tour, a magazine writer who interviewed the real life novelist David Foster Wallace (Segel) recalls the days that he followed the author for the article after he hears that Wallace has committed suicide.

Wallace’s novel Infinite Jest is a novel that I have been trying to finish for years. The novel was highly praised, an international bestseller, and very meaningful for many readers. If I finish the novel, it will merit a post here.

This is not a spoiler but in the final episode of the series, the story and the series is explained. Sort of explained. Jason Segel the actor emerges. In a flashback, a boy who would become the performer known as the Clown-Faced Boy, tells his parents that he wants to become an actor. His stage act runs for many performances but becomes stale. The boy wants change. Is he Segel or Peter? Cut to a support group meeting that includes Jason Segel (a version of the actor played by himself) who also wants a new direction in life.

Real life crosses over. Simone (or is it Eve?) invites Jason to her Barn of Beautiful Things and hands him a postcard to Elsewhere which sends the actor on a city journey and inspires him to write a script for a series titled “Dispatches from Elsewhere.”

The ending reminds me of a Fellini film where all of the cast shows up as characters and as actors. Jason meets the Clown-Faced Boy and realizes that he is his own career struggles personified and Jason asks for help making the series. The circle comes around when we see Jason watching the series with Janice, Simone, and Fredwynn. They like it but find the ending self-indulgent. Even viewers get a chance to be part of the ending.

I’m going to watch it again. Even knowing all the spoilers, there are still things that will surprise me. That’s always a good thing.

A Light Buffet of Ideas

As I work my way through the week, reading online and offline, listening, and looking around me, I collect things that I might want to write about here. Sometimes those notes lead to deeper searching, sometimes research, and sometimes they lead no further. Friday night is my start to the weekend and I usually post my shortest posts then.

Here are three things that are what they are and not anything more. A light buffet of ideas. Sample. Maybe you’ll like something enough to go further yourself.

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For example, I heard someone on the radio (actually, it was a podcast, but I still think of them as radio) ask if the interviewer knew what industry was worth $28 billion. That is more than the NFL, the NBA and MLB together. Answer: the book publishing industry. And I thought books were becoming a thing of the past. The statistic makes me feel better about books, bookstores and libraries – good places full of good things.

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In 1938, television was an idea being developed. No sets in homes. No programs. People didn’t know quite what could be done with it. When Edison was playing around with film, he wrongly was thinking of nickelodeon style viewing machines where you plunked in a coin and watch your little show. he was wrong, and rather quickly movies were projected for groups of people on a larger screen.

The same thinking was around with television. I came across this odd little device from a British company called the “Television Monocle.” It had a tiny screen, measuring just 1.5 inches by 1 inch, for a personal viewing experience. It looks a bit like the viewfinder on a video camera.

As with film, the path would lead to broadcasting to big audiences. Then again, since so many of us are watching TV and films on small screens again, maybe we are actually go backwards.

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Theobroma cacao. Theobroma, the genus name, is from the Greek and translates to “food of the gods”

Halloween is coming next week, so lots of chocolate will be bought and consumed. It is a historical and ancient food, though much of what we call chocolate today is far from what it once looked and tasted like.

It comes from the cultivated cacao tree (Theobroma cacao). Cacao domestication and chocolate have long been seen as emerging from Central America and Mexico where it was found mentioned in texts and there is archaeological evidence of it being consumed. It was in the form of a drink that was more gruel than modern hot cocoa.

It was once considered a food of the gods. It only showed up in the American Southwest about 1,000 years ago, but it was believed that cacao domestication and chocolate production originated in Mesoamerica less than 4,000 years ago.

But some newer research by a multidisciplinary team makes a case for chocolate use going back almost 5,500 years. They find evidence not in Mexico or Central America, but in the upper Amazon of South America.

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Triton, Neptune’s largest moon – Credit: NASA/JPL

It is late October. It is autumn here on the top half of the planet, but there are days that feel like summer and nights and mornings that feel like winter. I like the change of seasons. I’m not sure how I would feel about living in a place that is all one or two seasons. On a wintry day when I’m dealing with ice and snow, that kind of place sounds very appealing, but I suspect it would be boring.

We don’t think of seasons in outer space. So, it surprised me to read about the seasons of Triton.

Triton is Neptune’s largest moon. It has been gathering frost on its surface.  We have been observing the accumulation of the frost for 20 years and that frost continues to travel northward from the southern polar cap of Triton.

The frost comes from the sun heating and sublimating volatile material before it travels northward.

But something else that I read made me think that Ray Bradbury could have written a story about this. Triton’s frost varies over the world’s full season. The season lasts 84 years.

In Bradbury’ story “All Summer in a Day,” a class of students on Venus wait for one special day. Bradbury’s Venus is a world of constant rainstorms. The Sun is visible for only one hour every seven years. When I taught that story, I knew that my students couldn’t really imagine what it would be like to have only one day of summer every seven years. I can’t really imagine it myself.

What would it be like to have a Triton season of 84 years that might last your entire lifetime?  I can’t go any further with that thought either.

1950s Interactive TV

The 1950s in America was TV time. In 1949, only 2 percent of American households had a television set. By 1955, 64 percent of American households had a TV set.

It would take about a decade before educators and some of the public would start to complain that television was ruining children’s brains.

TV stations did have a problem filling up air time. Remember there was no way to record shows, so once a show was broadcast that was it. No reruns. (A few shows did get filmed with movie cameras right off a screen. They were known as a kinescope.) Most shows were live. There were old vaudeville acts, shows adapted from radio programs, travelogues, kiddie shows, shows for housewives, quiz and game shows. Most of what you saw was “local programming.” Sports entered the scene, and baseball and boxing were most popular.

Stations soon discovered that using old films from travelogues to features was a good way to get content that could be repeated because it was already “prerecorded.”

Though I am really a child of the 60s, I toddled my way through the second half of the 1950s and certainly watched TV. One movie showcase that I remember ran in the New York metropolitan area was on WOR-TV (Channel 9 for us) and was called “Million Dollar Movie.”

I read online that it ran in various formats for three decades. It was the HBO of the time as it ran the same film all week long, sometimes two times a night. The idea was that you could watch it at your convenience, but for the station, it filled a lot of hours. Younger readers will not remember that stations “signed off” at night and in those early decades of television, there was nothing to watch overnight.

The opening credits for the show used “Tara’s Theme” from my mother’s favorite film, Gone With the Wind. The films shown were often features that had been in theaters a few years before with “million dollar” budgets (a big deal back then), but it also ran some low-budget films. I got my early film education watching Astaire and Rogers dance across our tiny screen and plenty of westerns. I probably watched King Kong and Mighty Joe Young a half dozen times.

There was nothing educational or interactive about TV. It was passive and that was why we loved it.  We gathered around the “cool fire” of the television hearth as a family to watch and “chill out.” We made popcorn as if we were in our own movie theater.  Eventually, we convinced my mom to get frozen “TV dinners” (which were pretty dreadful) for us to eat while watching a show as a special treat.

In 1961, Newton Minow, FCC chairman, called television a “vast empty wasteland.” It got nicknamed the “boob tube” which was not a reference to breasts but to the idiots (“boobs” meant that too) that watched and maybe those that made TV.

Literary critics, educators, government and religious leaders would all blame TV for destroying the habits and the moral fiber of the American family. No one was reading. Kids weren’t go outside to play. Hollywood and theaters blamed it for a drop in their attendance and dollars (though they would later embrace it).

But the program that I was thinking about when I started this article was an odd littel show from the 1950s that was actually interactive.  It was on CBS and it was titled Winky Dink and You. It was a kids show that encouraged you to draw on the TV screen with crayons as you watched to interact with the characters. If the cartoon characters needed a bridge to cross a river, you were supposed to draw it there for them.

Of course, you were also supposed to buy a “magic screen” cover for your TV from the producers of the show. I suspect there were kids who drew on the actual TV set a few times.

The show first aired on Saturday mornings in 1953 and was carried live by about 175 stations around the country during its first year.

The technology was really crude and the stories were pretty dumb, but it was like nothing else on television at the time. My mom bought the screen for my sister to use. It came with some crayons in various colors. Of course, if you didn’t draw that bridge, the characters still went over the river. At first, I tried to make the bridge or road or whatever do other things too, somehow imagining I had some control over he program.

There was human host, Jack Barry, who told viewers what to do to help Winky Dink, the child-like animated character, who got into lots of trouble and we had to help him out. You traced Barry’s finger on the screen with your crayon to draw. No artistic talent required.

I found online that the actual magic screen set (available from the show originally) cost $1.98, and 2 million Winky Dink magic screen sets had been sold by February of 1955.

It was a great marketing idea, but there was also the idea that kids wouldn’t just be passively watch a show.

Winky Dink ran until 1957 and there were a few attempts to revive it or something like it all the way into the 1960s. The show was revived in syndication for 65 episodes, beginning in 1969 and ending in 1973. In the 1990s, a new “Winky Dink Kit” was sold, containing a screen, crayons, and all-new digitized Winky Dink and You episodes, but by then “educational television” had turned into a more passive talk-at-you approach.

When I was getting a graduate degree in media, I recall reading about the show and attempts at interactivity in the big 3-volume reference book, TV in the USA: A History of Icons, Idols, and Ideas. Bill Gates said it was “the first interactive TV show.” I suppose the most interactive we ever got with the TV screen wasn’t with any shows but with videogames. Maybe it’s time to revisit interactive TV in this age of artificial intelligence and many types of screens.