by Gabriel Just
duction to Hilbert Space
By Gabriel Just
Copyright © 2015 Gabriel Just
Professor Tinwin entered the biggest lecture hall at the Madonian institute of sentients’ past, present, and future. It could accommodate over 800 students, nevertheless it was completely silent when Tinwin walked to the front of the hall. This was to a small part because the professor was a highly respected scientist and to a much bigger part because only five students decided to attend his lecture today.
“Introduction to Hilbert Space” was a very important and fundamental topic, but for most students it was far too fundamental. Despite the low attendance the professor had to start his presentation. Like all Piki, he was too small to use the lectern in the intended way and like all proud Piki, he refused to use a smaller one. Instead he placed a tiny step ladder next to it and climbed on the step ladder first and on the lectern later, in order to use it as a pedestal, so that everyone could see him. This had the additional advantage that Tinwin could now also see all the students.
Two Piki were obviously impressed by his creative use of a lectern. Tinwin was certain that this must have been why they pointed at him and whispered. Also a Hironian was in the audience. He was so huge that he had to sit on two chairs simultaneously. Several broken chairs next to him suggested, that his previous attempts to sit on only one failed miserably. In the very last row Tinwin could make out a Skaren. Her scales currently had a bright green color. As an expert on most races of Hilbert Space and their body language, Tinwin knew that this meant that she was either extremely bored or in the final stage of the terminal Skaren flu. Of course Tinwin could rule out the first explanation, since he knew that his lectures were always very entertaining, so he felt a little bit sorry for her, because she might not survive to see the end of his lecture. The last student that Tinwin spotted was a Shey. He sat in a shady corner of the hall. A dark, hooded robe hid most of his face. Only a small, sharp beak peaked out.
The professor was rather content with his audience. Too often nobody showed up to his talks, or far worse, only a single person. With one single listener he was obliged to hold the lecture and the student was bound to endure it, making them both feel very uncomfortable and awkward. But five people was not bad at all for one of Tinwin’s talks, so he started the usual way.
“Welcome to ‘Introduction to Hilbert Space’. In this lecture we will learn about Hilbert Space, the region of space we live in. Technically, that is not true. Only you will learn something. I already know most of the things I teach. All of them, actually. But I am sure you are familiar with the whole concept of teaching. Where was I? Yes, Hilbert Space. Can anyone of you tell me what exactly Hilbert Space is?”
Tinwin looked around, but all the students tried to evade his look.
“Of course nobody of you can tell me that. This is why you are here. It is rather simple. Hilbert Space is only a small part of the observable universe, but truly the only part worth observing.”
“Why is that, Professor Tinwin?” one of the Piki students asked.
“I will come to that, please don’t interrupt my lecture by questions or any other irritating noise. Believe me, my talk is perfectly prepared for optimal understanding. Any deviation would make it more difficult, most likely even impossible, for you to grasp. And you are not only wasting my time, but also the time of your fellow students by asking questions. After all, they want to hear me talk, not you. So, where was I? Exactly, Hilbert Space is the only part of the universe worth observing. ‘Why is that?’ you might ask. Think of the universe as one giant planet. And on this planet there are many continents. All but one of them are barren and lifeless without much going on. Sometimes a small insect comes to existence there, but goes extinct only seconds later. But there is also one continent full of life, wonder and mystery. This continent is Hilbert Space. So, if you have the choice between observing this wonderful place and a barren wasteland, it is quite obvious what you should choose.”
“Why is Hilbert Space different?” the same student asked.
“Another question? Very well, I will generously answer it, if you promise to never interrupt me again.”
The Piki nodded excitedly and Tinwin tried to answer the question as best as he could.
“It all comes down to entropy. As you all know, globally the entropy of the universe constantly increases. Wait, you don’t know that yet. This is why I hate questions. They lead to you receiving information at a completely inappropriate time, just because you are impatient. Let us start again. As you hear for the first time, globally the entropy, which is something like a measure of disorder, constantly increases. This is quite intuitive. That broken chair over there for example had a low amount of entropy this morning. Now however, because of a spontaneous process, it is in disorder.”
“A spontaneous process? So it wasn’t my fault?” the Hironian next to the broken chair asked.
“Well, I would not go that far,” Tinwin answered. “Let’s just say that the universe favors processes where order is destroyed. The other direction however is quite unlikely. Sitting on a broken chair will not mend it by accident. So now you know why the universe is a dull place. Fundamental rules demand disorder. And this is exactly where Hilbert Space is slightly different than the rest of space. It is believed that Hilbert Space somehow radiates most of its entropy away to a distant part of the universe, which in turn becomes boring even faster. This region is called the CMB cold spot, which stands for ‘Center of Maximal Boredom’. Because of that, Hilbert Space can sometimes allow for spontaneous processes that lower entropy. This may be the creation of a new race, a planet that is exactly in the habitable zone of a star, or wormholes that allow for fast travel between systems. All these things are extremely rare in the rest of the universe, since they can happen only by pure chance. So you see, even though there is the possibility of an intelligent race outside Hilbert Space, sooner or later they will become extinct because of entropy, like the insect in our example. Also their existence must be extremely unpleasant, without anyone to talk to and no way to travel fast enough to ever reach anything noteworthy.”
All the students laughed, but for the first time in Tinwin’s career, with him and not about him. The scales of the Skaren even turned blue, which was a sign of amusement. And a sign that Tinwin’s inspiring lecture was so good that it even cured her of her terrible disease. Maybe answering questions was not the worst way to teach after all. Tinwin decided to try it once more.
“Any other questions?”
The Skaren student stood up and asked, “Why can all races in Hilbert Space live together. Why are we all so similar? Why do we breath the same gases? Why are we all of comparable height? Why do we all communicate via sound waves and light in a certain spectrum? Is there a deeper reason behind all of this?”
Tinwin smiled. “This is actually my main research field. It is called convergent devolution. And don’t listen to Professor Bonik. His theory of the humanoidothropic principle is rubbish. I would love to talk about this, but it really exceeds the scope of this lecture. I will, however give a talk about this topic later this week. You are of course all invited to listen to it.”
The Skaren nodded friendly and even scribbled something in her notebook. Tinwin couldn’t see what she wrote, but was flattered in any case.
“Well, where were we? I honestly can’t remember. But it doesn’t matter, there is no way I can hold the lecture in the usual way, not with all your questions interfering with my plan. Let’s try something different. What else do you want to know about Hilbert Space?”
“How big is it?” the Hironian shouted out.
“This is an interesting question. Today Hilbert Space consists
of hundreds of systems. However, it is constantly expanding. Not at a certain rate, but rather erratically. New inhabited systems and planets that could support life are discovered all the time. And if you work hard, you might also be able to find something new.”
“Did you ever find something new, Professor Tinwin?” one of the Piki students asked.
“Of course!” Tinwin answered. “All the time. However, I am more interested in the past, so I am even prouder if I discover something old. Like the one time, me and my assistant Kobb found this burial site on Kevar 7.”
Tinwin hesitated, since this lecture was called “Introduction to Hilbert Space” and not “Professor Tinwin Rambles About Past Adventures”. He came, however, to the conclusion that there was no better way to learn about Hilbert Space, than to listen to the stories that took place there. So Professor Tinwin decided to tell his story to the students, who listened eagerly.
It was a hot day on Kevar 7 as Tinwin arrived, mainly because all the days were hot days on a desert planet.
“Set us down right there, near that tent,” Tinwin ordered. His assistant Kobb, who piloted the shuttle, was unable to spot a tent on the surface.
“Which tent?” he asked.
“That one, next to that dune,” Tinwin