In the Help Video, you said that when you ran the Universal Turing Machine on your first example, then it ran for a very long time, and then stopped with the error message that it couldn't finish because there weren't enough columns in the Excel file. Maybe there's nothing wrong. Do you think that if Excel files had more columns, then the Universal Turing Machine would have run to completion successfully?

Actually, I wondered if this might be the case myself, so I decided to investigate. What I found out is that if I ran the Universal Turing Machine (on Turing Machine Number 699), then on step 921 it steps into an infinite loop consisting of 11 steps and keeps repeating those same 11 steps forever. Each time it goes through this loop of 11 steps, it also moves one space further to the left on the paper tape. It continues doing this over and over until it runs out of paper tape (i.e., it runs out of Excel columns) at step 173,153.

What is also very interesting is that if I modify this Turing Machine (with Turing Machine Number 699) by adding a dummy instruction at the end (which is never executed) then I get a Turing Machine with Turing Machine Number 5,598. If I then run the Universal Turing Machine on this Turing Machine, then it runs without a problem and stops on step 1,374. It also gives the correct answer, which is 0.

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Having found one example of a Turing Machine for which the Universal Turing Machine does not work, I was able to find three other very similar examples that don't work either.

I tried running the Turing Machine whose Turing Machine Number is 315. This Turing Machine takes 3 steps and finishes with the correct answer of 0. However, running the Universal Turing Machine on this Turing Machine fails with the error message that there aren't enough columns in the Excel file to complete the run. Then, I added a dummy instruction at the end, thus giving me a Turing Machine with Turing Machine Number 2,526. This Turing Machine also takes only 3 steps and finishes with the correct answer of 0. Then, when I ran the Universal Turing Machine on this Turing Machine, it completed on step 1,322 with the correct answer of 0.

I tried running the Turing Machine whose Turing Machine Number is 1,259. This Turing Machine takes 3 steps and finishes with the correct answer of 1. However, running the Universal Turing Machine on this Turing Machine fails with the error message that there aren't enough columns in the Excel file to complete the run. Then, I added a dummy instruction at the end, thus giving me a Turing Machine with Turing Machine Number 10,078. This Turing Machine also takes only 3 steps and finishes with the correct answer of 1. Then, when I ran the Universal Turing Machine on this Turing Machine, it completed on step 1,438 with the correct answer of 1.

I tried running the Turing Machine whose Turing Machine Number is 2,795. This Turing Machine takes 3 steps and finishes with the correct answer of 1. However, running the Universal Turing Machine on this Turing Machine fails with the error message that there aren't enough columns in the Excel file to complete the run. Then, I added a dummy instruction at the end, thus giving me a Turing Machine with Turing Machine Number 22,366. This Turing Machine also takes only 3 steps and finishes with the correct answer of 1. Then, when I ran the Universal Turing Machine on this Turing Machine, it completed on step 1,492 with the correct answer of 1.

In all of the above examples, the data that was provided to the Turing Machines was always the single binary digit 1.

As a homework assignment, you can use the Notation Converter (which is the Excel file that you can download from the main page of this website) to convert each of the Turing Machine Numbers above into Machine State Notation to better see what these Turing Machines are. Also, you can run all of these Turing Machines (using the first Excel file that you can download from the main page of this website) to see if you get the same answers that I got.