What is a Paper Town?

A long, long time ago, when I was still in Grade School, or maybe in High School, I remember reading somewhere, that someone spent years computing the value of ℼ to several hundreds or maybe thousands of digits and then published it in a book. However, when he copied it into the book, he changed one of the digits. He actually wrote the wrong value of ℼ, but he did it intentionally, so that in case anyone else would also publish those same digits in a book of their own and claim that they computed all the digits themselves, then he had a way of proving that they simply copied them from him.

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I never heard of a Paper Town until I saw the movie Paper Towns. It's based on a book by John Green, who explains very nicely what a Paper Town is in the first 2 minutes of a TED talk that he gave in 2015.

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When I was preparing a Help Video, I decided to show how I could build a very short and simple Turing Machine consisting of only three instructions. Can you imagine my surprise when I tried to emulate this Turing Machine with the Universal Turing Machine, and found out that it didn't work!

Prior to this, I had composed very many (maybe hundreds) of Turing Machines of my own, some simple, some very complicated, and they all worked! So, what happened here?

I knew that something was wrong somewhere. It occurred to me that there might be an error in the Universal Turing Machine, but I thought it was probably much more likely there was a problem with either of the two Excel files that I prepared for download from the main page of this website. I tried to see if I could find the error somewhere in the VBA code I wrote in these Excel files, but did not find anything wrong. I wished very much that I understood the logic that was used in the execution of the Universal Turing Machine, but I was not able to figure that out either.

While I was doing all this, I thought of something that I thought that I should dismiss as whimsical. Could Sir Roger Penrose have purposely planted a Paper Town in his Universal Turing Machine, and I just simply stumbled upon it?

The more I thought about it, the more it somehow appealed to me as very interesting. I seriously do not think there is a Paper Town in the Universal Turing Machine, but I thought I'd mention it in an FAQ anyway ---- just in case.

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In the reading above, I mentioned a Help Video. In case you're wondering how you can get to this Help Video yourselves so that you can watch it, here are the steps you should take:

Click on the picture in the main page of this website to download the Notation Converter Excel file (if you haven't done so already).

With the Notation Converter Excel file open to the Welcome sheet, click on the picture.

When it asks you "From which numerical notation will you be converting your number?" click on Machine State.

When it asks you "What Machine States shall we use?" click on I will provide my own Machine States.

When it asks you "How will you provide your Machine States?" click on I'd just like to type it in.

Then, in the Userform that pops up in the upper left corner of the screen, click on the box Help Video.

Then, just watch the video. Enjoy.