One day, when I was still in grade school, I was sitting at the dining room table and working on my homework when my father came over and took a look at what I was doing. He saw the right triangles that I drew and my computations next to each one, and then he asked me "Are you learning how to use the Pythagorean Theorem?" I answered "Yes." He then proceeded to tell me the story that after Pythagoras discovered why this method always works, he had a huge party to which he invited all his friends. At this party he sacrificed a hundred oxen in thanksgiving to those Greek gods and goddesses that inspired him to make this great discovery.
I was fascinated by this story, and I thought to myself, that if I should ever be fortunate enough to accomplish anything that worthwhile, then I too would like to do something similar. Of course, being a Roman Catholic, my thanks would not go to the ancient Greek gods and goddesses, but rather to God or maybe one of His saints or angels. Also, I didn't think that I would want to sacrifice a hundred oxen, but rather express my thanksgiving in some other dramatic and public way, although I was not sure exactly how.
In the years that followed, I decided to pursue the study of mathematics and even received a Ph. D. in it. Yet, in all of my readings that came with this studying, I never came across the story that my father told me and started wondering if it was even true. Then, in the 1970's, I happened to watch the episode of the documentary series The Ascent of Man in which Jacob Bronowski told the story of how Pythagoras sacrificed a hundred oxen to the ancient Greek deities. (I saw this documentary series for the first time on CBC. Over the next few years, it was shown several times on PBS.)
I came across the same story again many years later. I found it on pages 4 and 23 of the book A History of Mathematics by Florian Cajori who wrote that Pythagoras sacrificed a hecatomb to the Muses who inspired him. (I saw this book many times sitting on the shelf of the library at St. Thomas High School in Detroit, which I attended. Each time I saw it, I promised myself that I would read it someday when I had the time. I finally found the time to read it when I retired.)
I was born in Siedlątków, Poland. The most remarkable building in this small village is the church of St. Mark the Evangelist that has been there for hundreds of years. Behind and above its main altar is the famous painting of Our Lady of Siedlątków. There are many fascinating legends associated with this painting.
For those of you who know Polish, there are two very good YouTube videos about this church and Our Lady of Siedlątków, which you can watch by clicking here or here.
My parents and I immigrated to America before I was two years old, so I didn't remember anything from Poland. I did, however, overhear my parents mention the church from time to time in their everyday conversations. I particularly remember one day in 1957, when they received a letter from Poland with the sad news that there was a fire in the church causing considerable damage. The painting of Our Lady of Siedlątków was damaged as well. They were stunned by this news, and as they sat at the kitchen table talking about the letter, they recalled some of the old legends. My father remembered that at one time the church had a collection of canes, crutches, and other articles donated by people who were miraculously cured after they prayed to Our Lady of Siedlątków. There was also the story about how the painting was moved from the church to a chapel in a neighboring cemetery, and then during the night, it somehow miraculously moved itself back to the church, where it remains to this very day.
Perhaps the most fascinating legend had to do with a wedding that did not happen because the team of horses pulling a very ornate carriage refused to move. The people then believed that it was Our Lady of Siedlątków who intervened and prevented what would have been a very unhappy marriage. That is as much as I heard of that legend that day, because both of my parents were familiar with the story, so that they didn't think it necessary to repeat the whole story to each other. Today, I regret that I didn't ask them to tell me the whole legend. (For centuries, rich noblemen would choose to vacation in Siedlątków because it was known as a place for excellent hunting and fishing. I can only imagine that it may have been a very rich and powerful Polish nobleman who came to visit Siedlątków, became attracted to a girl from that village, and decided to marry her, even if it was against her will. However, if this legend took place after the Second Partition of Poland in 1793, then it was probably a very rich and powerful Prussian nobleman. On the other hand, if it happened after the establishment of the Duchy of Warsaw in 1807, then it may have been a very rich and powerful French nobleman, or maybe even a very rich and powerful Saxon nobleman. Or, if it took place after the Congress of Vienna in 1815, then it was probably a very rich and powerful Russian nobleman.)
The damaged painting of Our Lady of Siedlątków was restored within a year after the church fire, as were also other things in the church that were damaged. In 1965, right after my high school graduation, my mother, my brother Witold, and I visited our family in Siedlątków for a few weeks, and I had a chance to meet my grandmother and my uncles, aunts, and cousins. We attended Mass at St. Mark's Church every Sunday, and I had the opportunity to see the legendary painting of Our Lady of Siedlątków for myself.
The picture of the painting of Our Lady of Siedlątków that you see on this page was taken by my niece Lydia Jakovski (Witold's daughter) with her cell phone, when she and her husband visited Siedlątków in October, 2019.
I retired several years ago, and that finally gave me some time to read many of the books that I always promised myself that I would read once I had the time. One of these books was The Emperor's New Mind by Sir Roger Penrose.
Chapter 2 of this book is entitled “Algorithms and Turing Machines”. It is in this chapter that Sir Roger Penrose explains in detail how Turing Machines work, and even provides some specific examples of Turing Machines. I received my Ph.D. in Mathematics a long time ago, and became familiar with Turing Machines even before then, but Turing Machines were not my area of specialization. So, I myself learned a lot about Turing Machines by reading Chapter 2 of this book.
I tried to work through the examples very carefully using pencil and paper. Going through Roger Penrose’s simplest example wasn’t too bad, but when I tried anything more complicated than that, then I would make mistakes, have to backtrack to see where I made the mistake, then I forgot where I was and had to start over, and then I made more mistakes. It was horrible!
Then I had an idea. Since I had a laptop at home with Microsoft Excel on it, and since I still remembered some of the VBA programming that I did before I retired, I decided to put together some quick VBA procedures, just for my own use. I tried using them with some of the examples in the book, and they worked beautifully!!!
Sir Roger Penrose gave six examples in his book. His sixth and last example is the Universal Turing Machine. The Universal Turing Machine is a Turing Machine that does whatever any other Turing Machine in the whole world can do. Penrose did not explain how his Universal Turing Machine works, but he did give the Turing Machine Number for his Universal Turing Machine. (Every Turing Machine has a Turing Machine Number associated with it.) Sir Roger Penrose wrote the Turing Machine Number for his Universal Turing Machine on page 74 of his book. It takes up the whole page and is 1,654 digits long. (When you consider that the estimated number of atoms in the universe is at most an 83-digit number, then you begin to realize that this is one heck of a huge number!)
I scanned the page with the 1,654-digit number. I found some free character recognition software online that created a Word file for me with the same text. After writing some VBA procedures that read the Word file and wrote all the digits, one digit per cell, into an Excel file, I wrote a few more VBA procedures and used them to construct a real Universal Turing Machine from its Turing Machine Number.
Then, I used this Universal Turing Machine on the examples in the book, as well as some additional examples I made up myself, and they all worked beautifully! I knew I had something really good here!!
It took me some time and effort to do what I've done so far, and I started thinking that maybe it would be good to share what I developed thus far with other people who are also interested in Turing Machines. The more I thought about it, the more I liked the idea.
Of course, I knew that I would have to reconstruct everything into one Excel file that could be used in some user-friendly way. That meant I needed to learn a lot more about VBA and Excel Userforms than I already knew. It also meant that I would have to have a website from which the Excel file could be downloaded. The website could also have some links across the top. One of these could be FAQ's, and these could be the first questions that might come to mind of most people as they want to learn something about Turing Machines. In that sense, this website would then also be a valuable educational site for the general public.
I knew that this would take a lot of work, and never having built a website before, I also knew that I had a lot to learn. Nevertheless, I felt it might be worth the effort, and estimated that if I took this project on as a new hobby, where I would spend an hour or two on it every day, then I should probably have a nice website ready in a few months. (Boy! Was I ever wrong on this estimate! It actually took me a few years.)
As I started constructing the Excel file, I was also learning more about what I needed to know about VBA, mostly from watching YouTube Tutorials. Then, when I started building the website, I found out that I needed to learn HTML5, CSS3, Dreamweaver, and Camtasia. I did this by reading Dummies books, and mostly by watching more YouTube Tutorials. (I only learned enough of each just to get by. I certainly do not consider myself an expert on any of them.)
Sadly, I was not happy with my first design. Nor my second, nor my third design. Each time that I had a partially working website with a partially working Excel file, I would pretend I was someone else using it for the first time, and then mumble to myself "No human on earth will like this!" (It reminded me of Charlton Heston as Michelangelo in the movie The Agony and the Ecstasy saying "If the wine is sour, throw it out!" and then going to destroy everything he painted on the ceiling of the Sistine Chapel.) Each time I was unhappy, I would scrap the whole thing and start over again. It was during one of these redesigns that I decided to have a separate Excel file do all of the necessary conversions of the different numerical notations, rather than stubbornly stick with my first design of the Excel file that would take care of everything, but also force the user to answer too many confusing questions. (Actually, it's not as bad as it sounds. Each time I scrapped the whole project and started over, I was able to reuse much of what I had already done.)
Surprisingly, all of this was not what took up most of my time. Most of my time was taken up in doing the FAQ's, which at first I thought would be easy.
Doing the FAQ's turned out to be difficult, but also very interesting and rewarding. It involved doing a lot of research on the internet, and sometimes purchasing and reading books. Almost every FAQ led to additional FAQ's that I thought were important and interesting enough to include in this website. For one thing, I came to the realization that I didn't know as much about Turing Machines as I thought I did.
The most interesting FAQ turned out to be Is the human brain a Turing Machine? For me, this is a very thought-provoking FAQ. (Is all of human thinking completely done in the brain, with the brain working just like a very sophisticated computer? Or, is there more to human thinking than just following an algorithm?) If this FAQ alone can someday inspire some brilliant geniuses to make scientific discoveries that can help explain how human thinking works, then this web site will certainly be worth the effort. (Can mathematics, or quantum theory, or perhaps some other science give us a glimpse of the world where human thinking takes place, where space and time is not as we know it.)
When I first read the book The Emperor's New Mind in 2014, I was already a cancer survivor and had suffered with chronic back pains for many years. Yet, I felt healthy enough and confident enough that I could easily finish my new hobby in just a few months. In the years that followed, however, my physical health started deteriorating rather rapidly in many ways. What was particularly bothersome was that I noticed that my mental abilities were diminishing as well. (I could only work on my hobby for so long before my brain stopped functioning completely, and all I could do was take a nap.)
By the year 2020, I felt I was only about half done with the web site I started to build. The Excel files were completely finished, but I still had plans to continue adding many more FAQ's. Furthermore, I wanted to revisit many of the FAQ's that I already did, and reorganize them and improve them.
2020 is also the year that the Coronavirus came to America. With my age and health, I knew that my chances of surviving it were slim. Unless I could somehow finish my website quickly, there's a good chance that all the work of my past few years would be wasted.
Actually, even before 2020, I was thinking about releasing a Version 1.0 of the web site, and then upgrading it from time to time with the parts I already planned. However, I also wanted to make sure that whatever I decided to release would at least look like a finished product.
The problem was, that I still had to record most of the videos, and I knew that would take a lot of time. Right now, I only had place holders for the videos. I was toying with the idea of having a screen come up with the words UNDER CONSTRUCTION when you clicked on the box that said Help Video, but I really didn't want to do that.
I decided that I'll do all the videos, plus anything else that will make the web site look like a finished product, and then, God willing, release Version 1.0.
After that, I can keep adding to the web site and improving it, each time updating the version number, for as long as God will allow me.
Throughout my life, I sometimes said a prayer to Our Lady of Siedlątków in time of need. When I started working on this web site, I did as well, asking that some people may think it's a good thing and find it useful. As I worked on it, I also thought about how Pythagoras thanked the Muses, and decided that, if I finish this website, then I should also thank Our Lady of Siedlątków in some comparable way.
Of course, I didn't think that inviting many people to a party at which I would sacrifice a hundred oxen would go over very well in this day and age. (Not only that, but I don't think I could afford a hundred oxen. I don't think I could afford even one ox.) Besides, I really didn't think that Our Lady of Siedlątków really wanted me to sacrifice a hundred oxen.
Instead, I thought of the idea of having an entire page in the website with the sole purpose of thanking Our Lady of Siedlątków. That in itself would be almost as dramatic as sacrificing a hundred oxen. (I don't know of too many people who do that when they create a website.) Furthermore, I don't know how many people were invited to the party that Pythagoras arranged, but the internet is accessible to many more people, so there's a good chance that more people may read this page than attended Pythagoras' party.
My dear reader, please do not misunderstand me. I do not in any way mean to imply that my accomplishment is in any way comparable to that of Pythagoras. The Pythagorean Theorem is truly a great achievement in the history of mathematics. Jacob Bronowski seemed to imply that it was in fact a great step in The Ascent of Man because it also had a great influence on man's new way of thinking for all generations to come. Meanwhile, all I did was build an Excel file by following the directions in a book and encasing it in this website.
On the other hand, my abilities are in no way comparable to those of Pythagoras, nor to any of the other famous people mentioned throughout this website. In that sense then, perhaps my accomplishment in building this website is as great an accomplishment for me as the Pythagorean Theorem was for Pythagoras. In any case, Our Lady of Siedlątków is at least as deserving of a "Thank You" from me as the Muses were from Pythagoras.
So, I made a promise to Our Lady of Siedlątków, that if the first version of this website makes it to the internet, then it will also have a page with a thank you to her for everyone to see. (I was also inadvertently making a deal with Our Lady of Siedlątków. If I don't finish this website, then nobody will see this page honoring Our Lady of Siedlątków.)
Dearest Lady of Siedlątków,
I thank you very much!
My dear reader, if you are reading this right now, then Our Lady of Siedlątków kept her part of the deal, and I kept my promise.
Version 1.0 -- August 10, 2021