205: Candy Button Paper

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Candy Button Paper
Nonrewriteable tape?
Title text: Nonrewriteable tape?

[edit] Explanation

This comic refers to Candy Buttons, a type of candy sold by Necco in the U.S. since 1980. Because they were glued to paper, each candy button would have some paper stuck to it. As said in the comic, some kids would carefully check each candy button to make sure they would accidentally eat paper, while some kids didn't care and ripped them off, eating large scraps of paper in the process.

Because of the resemblance of the strips of paper to the tape of a Turing Machine, a small minority of children (possibly only Randall or some of his friends) pretended to be a Turing Machine by creating rules and executing them upon the tape of candy exactly like a real Turing Machine would do.

The title text refers to the fact that, although it would be hypothetically possible to create a Turing Machine that can only delete symbols, the information density of the tape would be greatly reduced, and the original Turing Machine could read and write from the tape it operated on.

[edit] Transcript

When it came to eating strips of candy buttons, there were two main strategies. Some kids carefully removed each bead, checking closely for paper residue before eating.
[To the right, a small section of a strip of Candy Buttons paper is shown. 2 red buttons have been removed from the top of the strip.]
[To the left, a long strip is shown. It seems to be waving in the air.]
Others tore the candy off haphazardly, swallowing large scraps of paper as they ate.
Then there were the lonely few of us who moved back and forth on the strip, eating rows of beads here and there, pretending we were Turing machines.
[A strip is shown from bird's eye view. Many rows of buttons have already been eaten.]

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It is possible to run a Turing machine on a candy belt:

Marvin Minsky (1967), Computation: Finite and Infinite Machines, Prentice-Hall, Inc. Englewood Cliffs, N.J. In particular see p. 262ff (italics in original): "We can now demonstrate the remarkable fact, first shown by Wang [1957], that for any Turing machine T there is an equivalent Turing machine TN that never changes a once-written symbol! In fact, we will construct a two-symbol machine TN that can only change blank squares on its tape to 1's but can not change a 1 back to a blank." Minsky then offers a proof of this. -- Kopa Leo 16:01, 6 July 2013 (UTC)

In my opinion, intuitively, when writing is demanded, a turing machine just have to copy those symbols to a new location, minding the symbol that needs to be written. It can have a start-of-data mark so this would be transparent to other operations 05:45, 27 July 2014 (UTC)

so I'm the only one that put them in a loop, then moved it one button down on one side? (talk) (please sign your comments with ~~~~)

Candy button paper was around long before 1980. I remember it from the 1950s. 17:59, 2 October 2016 (UTC)

If candy buttons were two-sided, I would make it into a Möbius strip. 625571b7-aa66-4f98-ac5c-92464cfb4ed8 (talk) 14:28, 14 March 2017 (UTC)

Doesn't Randall mention three different strategies? The comic says two, however.

There are two main strategies (careful and fast) and one very uncommon strategy (Turing). 21:14, 3 August 2017 (UTC)
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