Do you know of any moments in history when a failure led to some other success?

I'm sure that there are very many examples of this sort of thing throughout history. Let me just mention the first five that come to my mind.

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Ernst Eduard Kummer was a Prussian Mathematician in the 19th century, famous for his several discoveries in mathematics. One of his main goals in life was to prove Fermat's Last Theorem. He failed. The best he could do was to prove this theorem for many different special cases, but not in the full generality that was required.

However, during the years that he struggled to prove this theorem, he introduced the idea of an Ideal Number, which further led to the development of the theories of Ideals and Rings. These have become notable areas of study in Abstract Algebra.

Kummer was awarded the Grand Prize from the Paris Academy of Sciences for this work.

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For the longest time, even up till the beginning of the 20th century, mathematicians had a very strong feeling that mathematics, as a logical system, was complete. What this means is, that any true statement in mathematics can be proved as a theorem. Of course, there were statements, such as Fermat's Last Theorem which were probably true, but for which nobody has yet found a proof; but everyone felt that it was just a matter of time before someone would find a proof.

Mathematicians also felt that the completeness of mathematics should itself be proved as a theorem. If this could be done, then the very strong feeling that mathematics is complete would become absolute certainty that mathematics is complete.

Of course, in order to do something like this, mathematics would first have to be put on a very firm logical foundation. Two mathematicians, Alfred North Whitehead and Bertrand Russel decided to undertake this project by writing the book Principia Mathematica. This three-volume book was a truly monumental task, written between the years 1910 and 1913. It was a truly impressive piece of work, except that, if one of its goals was to prove the completeness of mathematics, then if failed in that respect.

Then, in 1931, Kurt Gödel, using the material in the book Principia Mathematica, proved that mathematics is not complete! What he did was construct a statement that the human mind could recognize as obviously true, and yet could not possibly be proved as a mathematical theorem.

So, was the book Principia Mathematica a failure? Well, it may have failed to prove that mathematics is complete. Yet, without this book, Kurt Gödel would not have been able to prove the much more astounding and surprising theorem that mathematics is not complete.

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Arno Allan Penzias and Robert Woodrow Wilson were employed by Bell Telephone Laboratories to study radio waves. In 1964, they built their most sensitive antenna/receiver system, yet it was detecting a very slight background noise that they did not expect. They speculated that it must be coming from some flaw in the equipment they were using. They tried very hard to find and fix this problem, but failed.

They finally figured out that this noise was not coming from their equipment, but rather was a remnant of the Big Bang. This was a theory proposed by a Catholic Belgian Priest Georges Lemaître back in the 1930's.

Penzias and Wilson failed to eliminate the noise in their equipment; but instead, they succeeded in showing scientific evidence for the Big Bang Theory. For this, they were awarded the Nobel Prize in Physics in 1978.

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Scientists believed in the existence of a luminiferous aether that permeated the entire universe and provided the necessary medium for light. After all, if light was a wave, then there had to be something from which the waves could be made, and this had to be the aether.

In 1887, Albert A. Michelson and Edward W. Morley carried out an experiment that would determine the speed and direction of the planet earth as it travelled through the aether. They designed their equipment in such a way so that as they rotated it, they would find the direction in which the speed of light was the slowest, and that would be the direction that the earth was moving through the aether.

This experiment was a complete failure! It showed that the speed of light was the same regardless of the direction of the beam of light!

However, this failed experiment allowed Albert Einstein to believe that there is no such thing as aether, that the speed of light is the same regardless of how fast or in which direction the observer is moving, and further inspired him to come up with his Special Theory of Relativity, along with its astounding notions of Length Contraction and Time Dilation!

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Christopher Columbus believed that the best way to get to India from Europe was by sailing west from Europe across a great ocean and around the globe.

Today, we know that he failed to do that. Yet, when he reached land on October 12, 1492, he didn't know he failed. He thought he succeeded. That's why the American Natives were called Indians.

So, Columbus really failed in what he hoped to do, and that is to find the best way to reach India. However, what he did succeed in doing was discover a new land that was beyond anyone's imagination at that time!

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There are probably many other examples such as these that you may recall.

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If you are reading this web page, then the previous FAQ that you read was Are you seriously suggesting that I figure out how the Universal Turing Machine works and explain it in my own website or YouTube video? There, in the fourth paragraph from the bottom I mentioned that there were moments in history when failures actually led to some great successes. You then asked what failures and successes I had in mind, and that's how you ended up on this web page.

In the paragraph just below that one, I mentioned that your attempts to understand how the Universal Turing Machine works may lead you to some interesting, important, and amazing discoveries. Were you perhaps wondering what interesting, important, and amazing discoveries I had in mind?

Well, let's think about this.

First of all, it may happen that you spend a lot of time studying the Universal Turing Machine and actually figure out how it works, so that you can explain it in a human language. If so, then I would encourge you to share it in your own website or YouTube video. If you also made some interesting, important, and amazing discoveries along the way, that's great! I would encourage you to share those too!

Or, it may happen that you spend some time trying to understand the Universal Turing Machine and get absolutely nowhere. That may happen. It happens all the time. It's a disappointment and I'm sure it wouldn't be the first one in your life.

However, you may not give up easily and start thinking about various novel ways on how you can study the Universal Turing Machine. Perhaps you'll develop some software tools to help you with your analysis. Perhaps you'll start thinking about what's possible and what's not possible. Will doing so lead you into certain areas of mathematics or Artificial Intelligence (or maybe even logic, philosophy, human understanding, human languages, psychology, and who knows what else)?

So, are you still wondering what interesting, important, and amazing discoveries I had in mind?

I have absolutely no idea. I don't think anybody knows.

That is something that you will have to find out for yourself.