Why not just ask Sir Roger Penrose on how the Universal Turing Machine works?

Actually, I had considered writing a letter to Sir Roger Penrose and asking him to explain to me the algorithm that was encoded into the instructions of the Universal Turing Machine. However, I refrained from doing so for a few reasons.

First of all, I'm sure that Sir Roger Penrose never heard of me. I suspect that he receives letters from people all over the world. I know his time is very valuable and can be better spent in many other ways--in ways that can merit a Nobel Prize, or any of the other many prizes he was awarded--in ways that are beyond the capabilities of most people.

I really do not know if Sir Roger Penrose would ignore my letter, but if he would, then I would certainly understand why, and I would not be offended.

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There is also another reason why I didn't contact Sir Roger Penrose.

On pages 92-93 of his book The Essential Turing (Oxford University Press, 2013), Jack Copeland tells the story of how Donald Davies studied the famous paper by Alan Turing in which Turing described what became known as the Turing Machine. Davies noticed a few things in the paper that he suspected were programming errors. Davies asked Turing about these details, and Turing became very annoyed with Davies and said that these details didn't matter because the paper was right in principle.

This same book also has, on pages 103-124, an article by Donald Davies entitled Corrections to Turing's Universal Computing Machine. The purpose of the article is to explain all the corrections that have to be made to the Universal Turing Machine before it can be programmed to run on a real computer. On the first page of this article, Davies tells that when he told Alan Turing about this, Turing became impatient and said that he was just wasting time with a worthless endeavor.

I myself don't think that I would receive the same reaction if I contacted Sir Roger Penrose. For one thing, his Universal Turing Machine may not have any problems. However, even if Penrose did feel a bit bothered by my request, then I would certainly understand why, and would not be offended.

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There is also another reason why I didn't contact Sir Roger Penrose, and I think this is the strongest one.

I am very curious to find out if there is anyone out there who can figure out how the Penrose Universal Turing Machine works.

If you can figure it out, then I would suggest that you publish your explanation in your own website or YouTube video. I think many people would be interested in seeing it.

Please allow me to explain why I am thinking this way. I myself tried to figure out how this Universal Turing Machine works, but have not been able to. Maybe it really isn't all that difficult to figure out, and maybe my mind is not as sharp as it used to be when I was younger. Nevertheless, Sir Roger Penrose did not explain how it works in his book The Emperor's New Mind, and I'm guessing that the reason is that such an explanation would take up several additional pages in his book, or maybe it was just too unwieldy to put into words.

If I am right, and if the Penrose Universal Turing Machine is indeed difficult to understand, then the efforts to understand it by many talented mathematicians and computer scientists could only lead to discoveries and further research that could become very worthwhile.

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Please allow me again to explain why I am thinking this way.

In 1637, Pierre de Fermat discovered what became known as Fermat's Last Theorem. Fermat wrote in the margin of a book that he had a truly marvelous proof of this theorem, but that the margin was too narrow to contain it.

For 357 years, mathematicians struggled to prove this theorem, and a correct proof was finally found by Sir Andrew Wiles in 1994. Yet, in those 357 years, the many failed attempts to prove this theorem led to some remarkable and useful discoveries in Abstract Algebra.

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If you are still reading this FAQ, then you may be thinking that my mind just drifted off into some silly daydreaming that goes way beyond the scope of this FAQ or even this website, and that the last part of this FAQ should not be taken seriously. And, you're probably right.

But, let me add just one more thing.

The proof that Pierre de Fermat had in mind could not have been the same that Sir Andrew Wiles discovered. But, wouldn't it be very, very interesting if Fermat had actually written his proof down somewhere, and that piece of paper was found just now, about almost 400 years later. Who knows! That proof may have actually been something quite simple, yet so very clever, that nobody else could have thought of it!