How does Tupper’s self-referential formula work?

[I write this post with a certain degree of embarrassment, because in the end it turns out (1) to be more simple than I anticipated, and (2) already done before, as I could have found if I had internet access when I did this. :-)]

The so-called “Tupper’s self-referential formula” is the following, due to Jeff Tupper.

Graph the set of all points such that

in the region

where N is the following 544-digit integer:
48584506361897134235820959624942020445814005879832445494830930850619
34704708809928450644769865524364849997247024915119110411605739177407
85691975432657185544205721044573588368182982375413963433822519945219
16512843483329051311931999535024137587652392648746133949068701305622
95813219481113685339535565290850023875092856892694555974281546386510
73004910672305893358605254409666435126534936364395712556569593681518
43348576052669401612512669514215505395545191537854575257565907405401
57929001765967965480064427829131488548259914721248506352686630476300

The result is the following graph:

Figure 1: The graph of the formula, in some obscure region, is a picture of the formula itself.

Whoa. How does this work?

At first sight this is rather too incredible for words.

But after a few moments we can begin to guess what is going on, and see that—while clever—this is perhaps not so extraordinary after all. So let us calmly try to reverse-engineer this feat.

Wikipedia’s logo

has several errors.

Here’s the image:

and although I had seen it thousands of times, I hadn’t really noticed it until I saw it for a moment in Lessig’s corruption video. The errors in the Devanagari and Kannada scripts are immediately obvious; the New York Times ran an article about the error (they knew of only the Devanagari and a Japanese error).

Apparently, the original author has lost his source files, and no one knows how to fix it (seriously), so they have been either simply giving up, or using the ingenious argument that the logo is appropriate, as the existence of errors is characteristic of Wikipedia.

Edit [2010-05-13]: With the new Wikipedia logo, the errors are finally fixed, after seven years.

Bertrand Russell in Bollywood

This is for real: Bertrand Russell featured in a Hindi film.

Wikipedia confirms it:

Russell made a cameo appearance playing himself in the anti-war Bollywood film “Aman” which was released in India in 1967. This was Russell’s only appearance in a feature film.

as does IMDB page for Aman (1967):

Bertrand Russell … Himself.

And without this movie, Bertrand Russell might not have had the finite Erdős–Bacon number that he does. His Bacon number is four, going through this sole tenuous link:

Bertrand Russell was in Aman (1967) with Brahm Bhardwaj
Brahm Bhardwaj was in Kaalia (1981) with Ranjit Chowdhry
Ranjit Chowdhry was in I’m Not Rappaport (1996) with Marin Hinkle
Marin Hinkle was in Rails & Ties (2007) with Kevin Bacon

or

Bertrand Russell was in Aman (1967) with Om Prakash (I)
who was in Ghar Ho To Aisa (1990) with Saeed Jaffrey
who was in Sphinx (1981) with Frank Langella
who was in Frost/Nixon (2008) with Kevin Bacon

or

Kevin Bacon was in New York, I Love You (2008) with Irrfan Khan
who was in Dhund: The Fog (2003) with Gulshan Grover
who was in Patthar (1991) with Sunder (I)
who was in Aman (1967) with Bertrand Russell

Surprisingly though, establishing an Erdős number for Bertrand Russell is even harder! He rarely collaborated, except with Whitehead, who collaborated rarely as well. There is a publication path, but it goes through non-mathematical work: the Russell-Einstein Manifesto of 1955, titled Texts of scientists’ appeal for abolition of war, which gives him an Erdos number of 3, through A. Einstein — E. Straus — P. ErdösErdős. (That publication also gives Erdős numbers to many others including Max Born, F. Joliot-Curie, and Linus Pauling.)

Playful Pixar

Pixar’s 4-minute short film Red’s Dream (1987) has credits at the end that roll by inconspicuously, but if you take a second glance at the disclaimers, you’ll find they actually say:

All characters and events are fictitious. Any resemblance to actual persons or appliances, living or dead, is purely coincidental. The FBI investigates crimes. Mark Leather wrote a paint system but his name is really here just to impress girls. No portion of this movie, including the soundtrack, may be reproduced in any manner. Always wear a helmet.

Their 1988 short Tin Toy says:

Any resemblance to actual toys or children is unintentional. To open, press down while turning cap. Pixar and RenderMan are registered trademarks of Pixar. Seatbelts save lives. No portion of this movie, including its sound track, may be reproduced in any manner or we won’t be your friends anymore. This bag is not a toy. Keep out of reach of children.

It also has a “Babies John looked at a lot” section in the credits.
Several of the movies seem to have a “very very special thanks to Steve Jobs” and the like…

Film I saw

The LSC plays movies every weekend, to which I get free admission, and I usually watch all the films, no matter how bad I expect them to be :-)

Yesterday I saw 1408. It is a horror film based on a Stephen King short story. (It is about room 1408 of the Dolphin Hotel, where…)

The movie isn’t bad at all. It even has a happy ending. (The director’s cut apparently doesn’t.)

I saw a poster that said it

ranks with The Shining as one of the best Stephen King adaptations ever.

Obviously, the guy forgot about The Shawshank Redemption.

One might argue that Shawshank wasn’t a horror movie, but then again, neither was The Shining.
Really: Watch the trailer, it’s hilarious:
[Created by Robert Ryang. A contest-winning entry.]

The Microsoft Sound

The Microsoft Sound from Windows 95.
Actually evokes some sort of nostalgia :D

Made by composer Brian Eno, who describes it thus:

The idea came up at the time when I was completely bereft of ideas. I’d been working on my own music for a while and was quite lost, actually. And I really appreciated someone coming along and saying, “Here’s a specific problem – solve it.”

The thing from the agency said, “We want a piece of music that is inspiring, universal, blah-blah, da-da-da, optimistic, futuristic, sentimental, emotional,” this whole list of adjectives, and then at the bottom it said “and it must be 3¼ seconds long.”

I thought this was so funny and an amazing thought to actually try to make a little piece of music. It’s like making a tiny little jewel.

In fact, I made 84 pieces. I got completely into this world of tiny, tiny little pieces of music. I was so sensitive to microseconds at the end of this that it really broke a logjam in my own work. Then when I’d finished that and I went back to working with pieces that were like three minutes long, it seemed like oceans of time.

There are many compilation videos on Youtube, such as this one.

Probably the most interesting blog I’ve seen

I’m afraid to look at it, because I expect I’ll get tempted into spending hours and hours reading all the old posts: Strange Maps

Random quote

To be nobody but yourself, in a world which is doing its best to make you everybody else, means to fight the hardest battle which any human being can fight, and never stop fighting.

— e.e. cummings

BTW the typography was a marketing thing, not his own idea.

Al Gore has NOT joined George Bernard Shaw

I want to be pedantic here.

George Bernard Shaw used to be the only person to have both a Nobel (Literature) and an Oscar (Screenplay). Now Al Gore, who had earlier allegedly won an Oscar (Best Documentary), has won a Nobel (Peace). And unlike Shaw, he’s won an Emmy as well. And been vice-president, and almost-president.

An impressive list of achievements, no doubt, but the first part isn’t true: Al Gore didn’t personally win an Oscar; the film featuring him did (it won two, actually). The director called him on stage during the acceptance speech and Gore even spoke; that’s probably the reason for the confusion.
Full details:

• The 2006 Academy Award for Documentary Feature was awarded to “An Inconvenient Truth directed by Davis Guggenheim”.
• The 2007 Outstanding Creative Achievement in Interactive Television Primetime Emmy Award was Awarded to Current TV
• “The Nobel Peace Prize for 2007 is to be shared, in two equal parts, between the Intergovernmental Panel on Climate Change (IPCC) and Albert Arnold (Al) Gore Jr. for their efforts to build up and disseminate greater knowledge about man-made climate change, and to lay the foundations for the measures that are needed to counteract such change.”

(BTW: An Inconvenient Truth also won the Academy Award for Best Original Song: “I Need to Wake Up” – An Inconvenient Truth Music and lyrics: Melissa Etheridge. Apparently, it is the first documentary to win 2 Oscars, and the first to win a best original song Oscar.)

As for Shaw:

• The 1925 Nobel Prize in Literature was awarded to George Bernard Shaw “for his work which is marked by both idealism and humanity, its stimulating satire often being infused with a singular poetic beauty.”
• The 1938 Academy Award for Writing Adapted Screenplay was awarded to Pygmalion – Ian Dalrymple, Cecil Lewis, W.P. Lipscomb, George Bernard Shaw from the play by George Bernard Shaw.

Note that this is a 1938 film, not My Fair Lady. (That one was nominated in 1964 but didn’t win, and Shaw was dead by then and had nothing to do with the film. He had forbidden any of his plays from becoming musicals, so the musical My Fair Lady could be made in 1956 only after he had died in 1950.)

Biovisions at Harvard: The Inner Life of a Cell

Old news, but I was just digging up old files (specifically, I was going through my music collection, and found this mp3 file I had ripped from):
This stunning, breathtaking, enchanting animation (or here). The music is great too, but I have not been able to find out what it is see below.

The animation was created by a company called XVIVO, commissioned by Harvard University’s Department of Molecular and Cellular Biology. (Look here.) Also look at XVIVO’s site, for stuff like this.

An article here. An interview here:

We had to figure out how to take a cell that is so packed with molecules and to edit out visually about 90 to 95 percent of those molecules.

The entire video depicts what goes on inside one white blood cell

a cellular-motility theme and what happens to a white blood cell patrolling the capillary when there’s an inflammation outside the capillary

The full 8-minute video, with explanation, is here. Scroll down on the main page and look at some other (less polished) animations too.

Oh, and David Bolinsky, one of the founders of XVIVO, gave a talk at TED.

Update: I finally know what the music is, thanks to (of all places) a YouTube comment. It was composed by the company Massive Productions, specifically Matt Berkey. This music won an award (no surprise), a 2006 Telly award for Best Music Composition for a Non-Broadcast Film or Video. (Click here and scroll down, or look here.) Further Google-searching after knowing this led to this guy, who has been similarly interested. There’s a link on that post to here, which has a ripped-from-Youtube version of it. He contacted the composer and got a response (the music was available for $25), and an ad-filled mp3 of the song, and, in one of the comments, a higher-quality rip.

Canon

“No Woman, No Cry” by Bob Marley
“Sk8ter boy” by Avril Lavigne
“Torn” by Natalie Imbruglia
“With or without you” by U2

They all have Pachelbel’s Canon in them?

From watching (Rob Paravonian’s Pachelbel rant.

Che: the icon

A BBC article, and an old nytimes article on the icon. The BBC pictures are nice.

Neither of them mentions Maddox or Che Wearing Che T-shirt T-shirt. :-)

Postfix operators we learnt in kindergarten

I don’t know about your school, but in our school we kids went through several years without ever realising what the multiplication table we were saying actually said. As a result, we were all familiar with at least one postfix operator — the postfix multiplication operator “zar” (pronounced “zawr”). As we recited our “tables”:

Two one zar two,
Two two zar four,
Two three zar six,

and so on (always ending with a singsong, triumphant, “two ten zar twenty”.)

“Zar” was routinely treated as an operator (“what is six seven zar?”), and it was quite an epiphany to me (in class seven I think) when I suddenly realised what had been going on; I suspect many of my classmates still haven’t caught on. (BTW, what is the technical name for this, where “ones are” → “one zar”? Closest I know is Allomorph.)

Also, our “into” (for multiplication) is used for division in the US (at least), so our “five into twenty is hundred”, but their “five into twenty goes four [times]”. And the “by” — “thirty by forty is 0.75”, but a thirty-by-forty site is 30 × 40.

More to ponder — which parts of India say “by” in fractions and which say “over”? (Is “3/4” “three by four” or “three over four”? Of course it’s “three-fourths”…) Which ones say “aitch” and which ones say “hetch”? We always learnt it with the aspirated “h”, and that’s the way it seems to be in Chennai too.

“Pronunciation /heɪtʃ/ (and hence spelling haitch) is […] standard in Hiberno-English. In Northern Ireland it is a shibboleth as Protestant schools teach aitch and Catholics haitch.”

Meanwhile, I’ve always wanted to slaughter the (incorrect) Hindi-inspired “give exam” speakers, but it looks like the battle is being lost (in CMI, it had spread to even proper Bangalore/Chennai types). Maybe I should also find and resurrect my old zedzee and emptyset-not-phi rants while I’m in the mood…

“On the internet, nobody knows you’re a dog”

The popular phrase, and an article about it. The image can be found easily, here for example.