Are you seriously suggesting that I figure out how the Universal Turing Machine works and explain it in my own website or YouTube video?

Yes, I am!

I myself have not yet been able to figure out how the Universal Turing Machine works. However, if you have the time and the motivation to try it yourself, and if you do succeed in understanding how the Universal Turing Machine works, then that would be great. In that case, I would suggest that you create your own website or YouTube video in which you can present your explanation.

I think there would be some people who would be very interested in seeing what you have to say.

For one thing, an understanding of how the Universal Turing Machine works would show whether it really contains a Paper Town. (If you are wondering what a Paper Town is, you can ask that question at the bottom of this webpage.)

Of course, what I have in mind is a verbal explanation in English (or some other human language) of the ideas that were used when composing the Machine State Notation code for the Universal Turing Machine. In other words, a simple explanation of how the Universal Turing Machine works.

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Perhaps I should be a bit more explicit with what I am hoping for.

For example, if I were to explain how Sir Roger Penrose's UN+1 Turing Machine works, then I might say or write something like the following:

This program will take a string of 1's of any length and append a 1 at the end of the string. It will then display the string with the appended 1 as the answer.

For another example, if I were to explain how Sir Roger Penrose's EUC Turing Machine works, then I might say or write something like the following:

When this program starts running, it expects to have two strings of 1's, separated by one or more 0's, to the right of the Turing Machine's Read/Write Head.

It starts building a third string of 1's, to the left of the original two strings of 1's. For every 1 that it inserts into the new string, it removes a 1 from the beginning of each of the original strings. It keeps doing this until it removes all the 1's from the shorter string. What remains is the new string having the same length as the shorter string that was removed, and also what remains of the original longer string, which is now reduced in length by the length of the string that was removed.

So now again we have two strings of 1's separated by one or more 0's. So the Turing Machine again repeats the whole process, building a third string of 1's to the left of these two strings and eliminating the shorter string.

It keeps doing this over and over again until what's left is two strings of 1's of the same length. Then, the Turing Machine repeats the same process one last time. It builds a third string to the left of these two strings, and eliminates both of these two strings.

Finally, the Turing Machine has only one string of 1's on the tape, and it displays this as the answer by positioning its Read/Write Head to the right of this string.

Along with the above narrative, it might also be good to provide an explanation of how this method gives us the Greatest Common Divisor. It might be a verbal explanation, or maybe some diagram, or perhaps a flow chart similar to this one which appears on a Wikipedia page, or maybe a combination of all of these.

With the above narrative, anyone can then run the EUC Turing Machine, single-step through it, and clearly understand how the EUC algorithm works.

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It may happen that you put in a substantial amount of time studying the Universal Turing Machine and not figure out how it works. Yet, that time may not be completely wasted. By spending a lot of time on it, you may observe certain things that may give partial results that are worth knowing, or perhaps even discovering new ideas that nobody has yet imagined.

There have been moments in the history of mathematics (and also in science, in general) where someone was working on a specific problem and couldn't solve it, yet became inspired with a solution to another problem—perhaps one that is even more important, but everyone failed to notice.

The same may be true here. Just by thinking about how the Universal Turing Machine might work may inspire you to drift into areas of Artificial Intelligence and mathematics that may further lead you to make some very interesting, important, and amazing discoveries.

You won’t be inspired when doing nothing. You have to be thinking about something.

So, how about it! Give it a try!