# The Lumber Room

"Consign them to dust and damp by way of preserving them"

## 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 ${(x,y)}$ such that

$\displaystyle \frac12 < \left\lfloor \mathrm{mod} \left( \left\lfloor{\frac{y}{17}}\right\rfloor 2^{-17\lfloor x \rfloor - \mathrm{mod}(\lfloor y \rfloor, 17)}, 2 \right) \right\rfloor$

in the region

$\displaystyle 0 < x < 106$

$\displaystyle N < y < N+17$

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.

Written by S

Tue, 2011-04-12 at 13:05:20 +05:30

Posted in mathematics

Tagged with , , ,

## 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.

Written by S

Sat, 2007-12-08 at 05:53:25 +05:30

Posted in Uncategorized

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## 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.)

Written by S

Mon, 2007-11-26 at 01:16:42 +05:30

Posted in Uncategorized

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## Playful Pixar

with one comment

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…

Written by S

Sun, 2007-11-25 at 00:30:53 +05:30

Posted in entertainment

Tagged with , ,

## 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.]
Read the rest of this entry »

Written by S

Mon, 2007-10-22 at 04:30:59 +05:30

## The Microsoft Sound

with one comment

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.

Written by S

Sun, 2007-10-21 at 00:22:31 +05:30

Posted in Uncategorized