Symposium Space Travel & Science Fiction: Prof. Dr. Metin Tolan (Technische Universität, Dortmund)

Have you ever wondered why there are always eight columns, yes, then it is true. Everything is full again and you have to go to state three again, then. you have two electrons for magnesium and then you have the pi responsible here again and that's how the physicist plays it for you too. Physicists can at least count, yes, and here you see the 4s state and there are the four p states, but in. the 3 states there are still 10 forgotten states, so to speak, which can also be filled and that's what happens here, the states are called just one electron 23 etc. here in the 17 electrons in this state be there and so it continues, then continue with five five, yes, there you can again, the ps is also good and of course we have the corresponding ds again and then now with six there, you can complete it and then you're at 6, so. now you have to remember that these 4 also allow the so-called f states and here we are with our gadolinium, yes, one electron is in the 4f state, with lanthanum, yes, with about two electrons, etc., so it will be four electrons when they are all full.

We continue here with the Schmidt 14 f electron criterion and there you see the water eu there you have another fifth of an electron that is then placed here and so you see that the periodic table has a certain order Now we want to go to our gadolinium The question was, which is the Bertolini electron configuration? It's essentially quite simple and here you can see that carolinum should have 84 f electrons. We simply cited it like that and now it doesn't have them. You can also prove it with experiments. The electronic configuration of gadolinium is derived from this scheme.

Yes, here you have 74 electrons and already 1 5 electrons, that even comes from sick mechanical calculations. In fact, that was the hardest question I could ask about the periodic table of the elements. If you know it, yes, if you know it then you will work properly again. Yes, it's actually the hardest question, so it's interesting. Obviously someone has thought about gadolinium. You could have used any other item, but you asked how electronics work. The gadolinium configuration is the only element that really deviates from this scheme, as you will learn in the lecture. You can see that means we can also say that Bock is guaranteed to be the same again, yeah, and then we can start the movie.

You know that Mr. Spock is the same again and then the big one wants to say yes, we don't want to live in exile in Volkan now, we want to return to Earth and face justice there, they have committed the most serious thing. crimes, theft of the

space

ship and so on. Yes, it has to heal somehow and you want to face it, so you fly with this Klingon borba, you fly for years and in the flight you realize that something seems wrong. with the Earth and that's where we come in. Yes, you can see what's happening, that you arrive on Earth and these difficulties on Earth arise because a probe has flown to Earth, a particularly powerful probe that somehow you can't approach and which is obviously sending a message to the earth which is not understood and you have just found out that this message is not understood and for not taking into account that it is directed to the water and in the water this message sounds different and that It's also how sound

travel

s differently in water.

Here in the air and Doug in things was different: the speed of sound in water is about four times greater than in air. You may have already tried it when you wrote underwater. that sounds very strange if you made it go far, yes, in that sense, that is simply because they have a different speed of propagation, but under water they propagate much further, that is, to much greater distances and that is why the humpback whales can actually communicate with their sounds, that's what they did there or they took advantage of that and they described it to us but you see what you're planning to do, you're planning to

travel

in time and when it comes to time travel they are o the physical.

You already have two fundamentally different types of time travel, that is, you can travel to the future or you can travel to the past, very true. But that's physically a completely different thing with the future of order, in physics it actually wasn't that difficult for you. to take care of the future and travel relaxed. We simply do it with Albert Einstein's theory of relativity. Imagine that he is now sitting in his chair. This yellow reference frame is at rest. I passed it with the speed that the special theory. of relativity tells us that if we now compare our clocks, they look at each other while I am currently looking at the clock, we compare and the two clocks and it comes out to When I move less time passes, yes, that is what the special theory of relativity says that is a conclusion, which means, by the way, if you think about it, that each of you is in your own time, you may have already known it, but the final consequence is that.

But it only becomes relevant if the speeds at which they move are close to the speed of light and they are not usually that and the speeds at which we move, even the fastest cars or the fastest rockets are like that. Much slower than the speed of light, so it doesn't matter, yes, but in principle it is to make time slower for a moving observer and that also means, by the way, that is the real reason for the step which Japan gave in Star Trek because if they just moved, if they just moved quickly, they would always come out somewhere far away in the future and that's what you want to avoid with warp drive.

That's the $450 because otherwise, if you didn't have the mob engine, Kirk and Spock would fly somewhere, they. They would return and if so, when they return, the people who sent them have already been dead for 2000 years. That would be a realistic scenario, yes, but that shouldn't happen and that's why you take the raab. Time travel. Yes, for example, Alexander Gerst is also a time traveler if you do the math. Yes. He moved around the Earth at 28,000 kilometers per hour for 165 days. , it's still in five milliseconds, the world still looks like that now, but at least it's on the right, it's even in the Guinness Book of Records like the previous record time traveler: Russian Gennadi Padalka, who was in orbit at 28,000 kilometers. per hour for 8,178 days so far.

If you put that into the relativity theory formula, you get that it's 25 milliseconds in the future and so on. But not because the speeds mentioned here are very, very small compared to the. speed of light, so it doesn't play a big role, but in principle you can go to the future, yes, that's possible, that's not a problem either. So you're in the future, yeah, because my God, it's that bad. It won't be like that in the future of course, everything is different with time travel from the past to the past, there are problems, you have to ask yourself what you are doing, how I really do it, how I do wars.

Do that and the second thing you have to ask yourself is: isn't there maybe a problem with Star Trek? No, how do you time travel in Star Trek now? That's what we will be shown in the movie, so worries flew. to the past and ask. Now let's see what physics really says about this. I just told you about the future, physics says yes, just buy a

space

ship that can fly at 99.99 percent of the speed of light, that's right now. that's the problem, but then you can move on to the lies of the future, so the future is not a problem, that is, about the past.

Well, first of all it must be said that with trips to the past there are always logical problems that are always mentioned. so to speak, through the so-called grandfather paradox which curiously is always called grandfather paradox all this is not grandmother paradox yes it goes on like this all the time these are the good ones grandparents are also the ones who matter now they have children yes, that's father and mother and now they have a son and he's currently traveling yes, he's now increasing his time machine and he travels to a time when his grandparents were alive and he doesn't get along so well with his grandfather and he brings that grandfather he is dead if the grandfather is dead again then there can be no parents and then there can be no doubt then you cannot fly back and then he cannot kill his grandfather and here you see the paradox, which is, if you talk about traveling in time to the past, then something like that is out of the question, yes, those paradoxes are simply not learned, for example, if I decide in the future that we will now travel back in time to this place.

We have to enter the lottery numbers for this afternoon or next week. Then the door has to open and I have to go through there and then I have to wonder somehow. Yes, we should, but Wintel is allowed. Of course not. I didn't play either, but I think it was strange and I have to throw it away because if I played there would be a risk of not coming back from the past because I have achieved enough, yes, but you can actually build. The logical processes that are not like that. Paradoxes include that it works, that it is physically possible, there are other things you have to take into account, but in principle that is not necessarily a reason why you can't travel to the past.

Just have your grandpa take me there for some reason, yeah, but what about physics? Now we have to take the theory of relativity a little further and we have to go to the general theory of relativity. Albert Einstein not only discovered that space and time are connected, but that space and time are connected through mass and energy, as they say, being curved when we wonder what a curved space is, everyone knows it, In two-dimensional space, everyone can understand it, this is simply a sheet. of paper and what now you somehow enter the third dimension, well, we live in a three-dimensional curved space, when now you ask yes and in reality they are curves, then the third dimension cannot tell either, we cannot imagine it, but mathematicians if you can. calculate it exactly they can also 20 dimensional spaces no problem yes it works and time is also determined by the changes of mass and energy also with the complete four dimensional curved space it is crowned and this has also been shown by experiments that this is the case , the effects are very, very small but measurable and yes, they can be represented in a somewhat striking way, but the German mathematician Kurt Gödel already pointed out to Einstein if that is the case with this theory of relativity, then within this theory there are so many - called closed time loops that are the dream of closed time we are simply a closed loop of the place, you all know that they simply go around and come out again in the same place and that with the same time they do advance in time but they come out of new at a point before the closed time cycle and they are allowed in the theory of relativity, that does not mean they have to exist but they are allowed, that is what Kurt Gödel Einstein announced, adjustment discovered that it is not so good because you said In reality, it is illogical and, in fact, a good physical theory automatically excludes the impossible.

Yeah, well, that means there are closed time loops in the general theory of relativity and that's why several people have thought about it. Yes, how can you do that? I can tell you right away through very, let's say artificial arrangements, so put themImagine the following: you have a cylindrical object, yes, it has a mass several times that of our sun, wherever it comes from, the goal is there for me, the ratio of length to width is about ten to one, yes, and this object moves in a millisecond. A thousandth of a second revolves around itself. Yes, such a cylinder is called a Tippler cylinder.

There are very heavy objects in the universe that move around themselves in a millisecond. -called millisecond pulsars. They are objects that allow several suns to pass through. Do they really rotate once around their entire axis for a thousandth of a second? Yes, there is such a thing, but cylindrical objects, given their dimensions, don't have to. they should exist. So this cylinder rotates and if you are now close to this heavy Cylinders fly by yes, then according to Frank Stippler's calculations, they can actually enter such tight time loops. Yes, then they could actually enter his past. if such an object existed, but that still means they haven't done too badly with Patrick, so if you obviously want to time travel, you need a particularly heavy object and you have to fly close to it.

And that's what we do. Yes, they look for the sun and they fly very close to the solar cylinder and 2 and they don't spin as fast, but let's leave that there, there are details, yes, if you want to do time travel like that. so you should get very close to our sun, yes, if you want to do it with us, so yes. Well, now we are in the past. The company's crew is now divided into three parts, all of which are assigned special tasks. Spox searches, of course, the choices also find out which ones Lieutenant Uhura and Mr.

Chekov have to do. Searching for a power source where all power was lost during the time jump, they need energy to get them into place so they can fly. Again, yeah, that's the search for energy and then there's McCoy and Scotty who want to find a tank for the whales, come on. Let's talk about it in a moment, yeah,first let's see the energy, what kind of energy source. Do you find and the energy you find there is really enough to operate the warp drive? So, they're standing next to an Enterprise carrier and he's got it.

Actually, the USS Enterprise was a US Navy aircraft carrier, it was actually in service from 1961 to 2012. You can see the corresponding dimensions there, yeah, and you can take a look. Yes, what is the power of this ship? That's about 280 1000 hp. The turbines produce it and the autonomy. It's 13 years, which means that this is the nuclear fuel that is there, it was actually used by the state to operate this aircraft carrier with a nuclear reactor and from this you can now determine from these two data what energy it is, so to speak, energy times time we have how much energy is stored in things when you just put nuclear fuel in it when you do that, that comes from it on this aircraft carrier there are three times 10 a.m.

July 17 or 300 peter chou energy is a lot of style so yes, that's quite a bit. You could completely supply Dortmund or Düsseldorf with energy for six years, everything needed for heating, electricity, everything needed for six years. If you're looking for a power source, you're also looking for an aircraft carrier. It's not a bad plan. That's enough for the propulsion that no longer worked. First we just have to think about what it is. Also what operations are actually possible with Star Trek, the speed of faster than light, you will soon see what that means, you can't actually go faster than light, yes, you will see immediately what that means, without the time changes, without always coming out.

At some point in the future I already told him that's it. The real problem is when you move fast through the universe. Now Newton might say, for example, yeah, wait a minute when you accelerate that fast because inertia doesn't have a problem. , that is the force that pushes you into the seat, then you die. Not if you accelerate it that fast, says Mr. Okuda, responsible for technical things on Star Trek Next Generation, no, we have trick shock absorbers aboard the Enterprise, yes, we don't need the trick shock absorbers aboard the Enterprise, but we will see the same thing .

You were there, or I would put it that way, physics is sometimes even crazier than you can imagine. I was in the US here 99 years ago and then I came across this headline saying three funds at all, the BBC announced that's not the case, but BBC fake news has a good reputation, yes, and As a Star Trek fan, of course, you'll notice that too. hot and dry shake and then I dug a little bit and took a look and witnessed you need to know that and Rob leads it based on Albert Einstein's general theory of relativity, which I explained to him with this curvature of space and time through of mass and energy.

However, they need the necessary amount of energy for the place in the form of so-called negative energy. What is negative for energy? Maybe you're thinking of a room where everyone is arguing. Yes, there is unlikely to be much negative energy. I can say that is not true. In physics, everything is still positive, by negative energy you mean less energy than in a vacuum. Yes, imagine yourself in a vacuum. So logically you would say it's very vacuum, the energy content is 0, yes, do it and the negative energy is now less energy than in vacuum. How can that be?

It's very simple, our modern idea of ​​emptiness is. It's not that the vacuum is nothing more than boiling in the vacuum, it is also fluctuating, that all the time particles are created and destroyed back and forth, it just happens so fast that we don't notice it, we only see the average and that's what What we say is emptiness. But if you suppress these fluctuations, then you can even create areas of space that have less energy than what in physics is called the Casimir effect and was actually verified experimentally in 1985, the movie goes back to the present 86, so someone actually calculated a unit of words like that, yeah, what would it have to do with the theory of relativity to fly on a Wednesday like in Star Trek 1994?

That was a while ago, so of course people said, Well, actually it would have to be unstable and it would have to consume too much energy to be mature and that's also true when you looked at the energy balance, to fly with a WAP unit. This type would have required several billion times more energy. of what one suspects in the entire universe that is of course too much yes, it must be said to be fair and the headline that I came across was from 1999 by Chris van den Brock, who was a scientist at Leiden University and which made 20 years ago of its publication, it reduced the energy requirement for the word 3 passes and 194 was published by the incredible factor 10 to the power of 32, that's 10 32 9, yes, that's a really big improvement over this result, yes, and that's what I saw there.

However, you should not think that I will fill the tank from time to time, with discounts you still need approximately the energy for a return flight that is completely contained in our sun. Yes, remember. Our sun has been in the fourth for the four and a half billion years of its existence. Existence 0.3 per thousand of your total energy released so far. But you would need all the energy immediately and tenfold. You've got 10 suns around you somewhere all the time, they're standing there like briquettes, yeah, and the tingling in your eyes drives you. I would always say things like physical.

I can tell you that we physicists have solved the problem. Yes, now it is the turn of engineers and they have to implement it somehow in everyday practical life. Yes, in principle, in principle it works like that. How does it work? Here you can see again our general theory of relativity and the warp drive. Imagine what you want. go from A to B. This is again a two-dimensional model. Yes, of course, you can move there directly. That would be normal. You are limited by the speed of light. amount of energy, then the room curves towards them.

They step forward and push into the curved space behind them again. In principle it works, so if I want to go to the exit, I can go there for example. I'm limited by the speed of light, but I can also release as much energy here as I can, so that the space between me and the target curves so that the exit is in front of my nose. I take a step. forward and I push it into the tight area the space behind me it theoretically turns off I need a little power for that yes yes and then I don't move at all so I don't need any shock absorber tricks I haven't moved at all yes the supports can be removed again immediately no one needs it, we have it So it's like that and that's what the herald first posted about it, which in principle works, yes, that's how it works, so why does a star appear?

Aggravate it? It does not move on its own, but is dragged by the shaft and moves when driven. The company doesn't even feel dragged into space. It's already high. It should be noted that in a television series it is important that at least it can be physically plausible how I move, yes, and that is not just the spaceship through signals and the highlight of the matter is that everything works without you changing the time , just like it is with Star Trek, everyone is always at the same time, yeah, it's not worth noting that, that you have to drive more because Rob has introduced it and then you have two trips in Star Trek, when you fly slowly, you make up with normal rocket propulsion, impulse propulsion, yes, let's do the energy balance on such an aircraft carrier, we have already seen that it is something like 10 to 17 joules, so it is one with 17 0, you need ten times the total energy of this sun. like what is the energy of our sun 10 0 47 21 with 47 0 1 yes but if you say well yes 10 17 is really a lot it is really a lot but it is still missing You would need a little bit that is the same amount of energy to fly with warp, but at least That's how it was in the series or the movie.

One thing is clear: you need a lot of energy and you are looking for a great source of energy, but I leave that to your own discretion. if that is really enough yes, well the group finds so they find their energy source the second group with pill and with mr scott they are supposed to have a noisy farmer who wants to transport the whales to the ship and for that you need an aquarium yes and Then they find a company that could do it, but the materials from the 80s of the last century simply are not enough.

They seem transparent. Aluminum is obviously the material I need to build a point that is light enough. and of course so strong at the same time to retain water, well we want to think what properties this transparent aluminum should really have and we need an aquarium for our two humpback whales, but we also want to think if this specification is reasonable, 60 x 10 feet , obviously the panel yes, we should do it. The aquarium is 60 feet, or 18 meters, that's a compromise with the length of a humpback whale behind them, they're 15 meters, so that's good, yeah, and. 10 feet, that's about three meters high, well, and now we have to do a little calculation.

The volume must be 18 thousand cubic feet. That's what it says, 600 square feet times the width. Here we can immediately calculate the width from 18,000 to 600. take out 30 football nine meters that is also realistic then actually match two expected books side by side so all those are reasonable numbers that are mentioned there. The question now is whether it is also reasonable to have these six centimeters and the answer is yes, yes, we can calculate that with the so-called industrial plate formula. At the end of the 19th century and the beginning of the 20th century, the problem of the deflection of a plate was solved by this gentleman from Karl von Bach.

Yes, this is not any

science

. Here, it has been known for a long time and with the help of this formula the deviation can be calculated, usually it is assumed to be 2 percent. Yes, that is a parameter that must be taken from a table that is here for our purposes. 3p is the pressure in your plate, it is called height, yes that is the thickness and the first so-called modulus of elasticity of plexiglass is three kilos per square meter, so it depends on the material and if you really number the inserts it comes out 5.1 inches would be the thickness and in the movie is said six because of course people would install safety cushions to know it, so the number mentioned is very understandable, yes it is not only made up but quite reasonable if you only want one inch Then you have to insert an inch here and of course, all of this in this, he decided that after all it's a little bit of math again, yeah, that means that if the thickness is just one inch, this modulus of elasticity has to be six to the power of three because the thickness here goes to the third power times higher, so 216 was announced, that means we are looking for a material with this elastic modulus instead of three kilonewtons per square millimeter 650 and the material has been around for a long time, yes, I mean, this aluminum, this aluminum compound, yes. it is an aluminum oxide compound that is already transparent aluminum was manufactured in 2002 yes and you can see it, you can see that the material has exactly this elastic modulus, what I told you is that it has the corresponding hardness of steel, yes, but only At a third of the weight it is exactly what we have.

If you've seen the film, the material has the disadvantage of being relatively expensive. One square meter costs a lot, so in principle it is only used for military purposes, but in principle it is possible. The point is that it is surprising that transparent aluminum is still used in the 23rd century. Yes, because it is old material now. It has to be said, but hey, at least it's a sensible material with which these aquariums are built. Yes, so you built the aquariums and brought them to the company. You have the power source around it again, so everything was fine.

You also knew that the two products you wanted were in an aquarium, but these choices were released earlier. The sea was open and this election was now threatened by the fate that threatens many elections. They approached the whalers and the company will have these two whales to take with them into the future and we will see how the company works. saved these two as everyone knows, yes, Klingon warbirds use tanning devices, yes, and that's why we want to meet now. Let's talk about transmission. Yes, how can it be that an object is invisible and now we have to think about it again from the physical side? , what does that mean Invisible Yes, an object is invisible if it reflects the least amount of light possible.

Now they see me precisely because it is light that I reflect in their direction or if they direct the light around them, yes, yes, the light. , so to speak, what should come to me, was guided around me, I cannot return to it from me or whether it adapts perfectly to the environment. Of course, that could also be the case, we exclude the latter because the environment is always a little different, but in principle it's fine, of course. What does the term invisible mean? You have to remember that we have a whole spectrum of electromagnetic waves, which is what we call light, which is just this small section of the.

Electromagnetic waves of between 400 and 700 nanometers in wavelength, that is, billionths of the wavelength of a meter. Yes, at first it is verygeneral. A body cannot be made invisible to everyone, the entire spectrum of electromagnetic waves can be told by physical laws. This is only done for a part of the wavelength spectrum and we know it for certain parts, for example in the area of ​​radar waves, i.e. electromagnetic waves with long wavelengths in the range of centimeters and meters. This has already been achieved. They are stealth bombers, they are almost invisible to radar rays and this was done using the method of reducing the reflection of the radar rays of such an aircraft through this strange shape.

Reflection decreases through certain materials. If you look at it, it's a. aircraft with a length of 21 meters and a wingspan of 52 meters. Yes, and the reflected signal from this plane is as strong as the signal from a small bird. Yes, it is almost invisible for this area of ​​the electromagnetic spectrum. We know this, so now we're wondering, of course, that's only possible because these radar waves have relatively long wavelengths. That's what they would have to do to make it work at smaller wavelengths. Well, the wavelengths of light have wavelengths that are approximately. 100,000 times smaller. To do that, we can do it with this trick.

With radio waves you can't do it anymore, you can't reduce it that much, you can do something else, you can see what the device is. obviously used here, you can, so to speak, see through people how it works. Of course, it would be difficult to make a device now, so if we really wanted to make proud spaceships, then we have to imagine it like this, here. we have a Klingon Borberg, you already look there and say you see that somehow he didn't disperse if he had to. Now they have four lenses on the stem and that is no different and of course they always have to carry these lenses with them somehow so that if they were there the lenses would be seen by someone so yes it is somehow theoretically possible moving the light, yes, but with this story of lenses it doesn't work so well either, but it goes even further. definitely make it smaller if you use so-called metamaterials, which are materials with a negative refractive index, so you see in this interface here yes, there you see as if it is now bending in some way, that is the effect that ensures that this is not altogether. so that you have the feeling that this is deposited here the refractive index is a positive number that describes it effect now it is like this normal materials do not have a negative refractive index the refractive index has is for several reasons is the positive one must also be positive, yes, and then it looks like this when you somehow dip a pen into water with a negative refractive index.

Yes, but you can create artificial structures that have a negative refractive index. These are little floating circles that you need to rush. The structures have to be smaller than the corresponding wavelength of the electromagnetic radiation. Yes, that's why you can only do this with a microwave. But you've already come a long way to see that these are very small structures and if you put them. into something, then you could ensure that the corresponding electromagnetic world is guided around the object. Yes, you can imagine it like that. The wave comes from down here and you can see this object because it disturbs this wave in which the light is somehow. scattered, so to speak, and you see these punishing waves that ensure that you can see this object, so what is happening now?

I see that they are materials, so to speak, if now you have a material that you create this gray with. point that ensures that we reach the waves, then they will be disturbed, but behind the object the waves will gather together again normally, then you can use the object You can't see because you can't see the problem. You put your left hand there, so okay, yeah, and these materials really exist. They are called metamaterials. Here you can see the light source again. The light rays appear to run in a straight line. they're just like that rotated and then they continue straight back and that's why you couldn't see this object because it's actually done in three dimensions and now you could do your work in the Klingon where, so to speak.

This has been successful so far, even in the infrared, so you've got it done, that's because you have to produce these little structures, but at least up to the infrared, the heat radiation has almost reached the visible level. The forecast is not. It is not very bold now to say that in 200 years something like this can be done, that they can be turned into objects. Small objects can be provided with such structures so that they cannot be seen later. At first, by the way, you can also turn them on and off. Yes, what you saw there is quite realistic, but these metamaterials were not yet there in 1986.

A vision of physicists, so to speak, that only recently emerged. in the 2000s and people started thinking about it. Well, now we're almost done with the movie and then it ends successfully again. Yes, you see, we're putting it so that the sun is shining again and everything is on the audio stream of the movie. in the end captain kirk and his crew were also forgiven again one thing is just promises for the ball in the end the most important thing remains in the movie It's really not entirely clear where this special comes from and why he wants to talk to these whales hunchbacks?

What do you really want from them? Yes, that is not clear throughout the movie. Compugroup's roof is the humpback whale and then it is annoying. Yeah, in a way that's the whole plan of the movie. it's a book about the movies, there's a bit more to it, you can even get into the thought process of the investigation, yes it's quite interesting, but in the movie it remains unexplained, well maybe we'll get to an ending. Okay, we start with Mr. Spock and I would now like to show you at least one more scene where he can see that in Star Trek the numbers and what he did there, at least he thought about it.

He didn't just produce shit, yeah. , and that can be strictly different from many other things. They always tried to at least make it meaningful when you give a number, yes, and the example I gave at the time comes from perhaps the most popular episode. In general, they are. From the classic series, you know, triples, yes, thirds, they are such small and fluffy churches, yes, they are very voracious, they multiply like hell. The Enterprise is currently on a space station and is supposed to deliver grain to another planet. yes and now it is like this, these thirds have multiplied so much that you are afraid, maybe they have also penetrated the barn and Captain Kirk wants to check it, let's try to understand it.

Bock says one million 771 1551 this number. He relies on the assumption that a Fibonacci triple was the one who asked this question in 1202. A man holds a pair of rabbits in a place that is completely surrounded by a wall. Now we want to know how many pairs of them there can be. bred in one year yes nature has established that these rabbits give birth to another pair every month and this starts in the second month after their birth yes, if you want to solve the problem then you just have to do it by painting also yes because your rabbit in the second month will be sexually mature in the third.

In the fourth month is the next pair of rabbits, which of course are still there. In the fourth month there are a couple of rabbits that reach sexual maturity. the fifth month, etc. if you don't count the students in pairs they get the number sequence 1 123 50 it's here at the bottom yes 813 these are the so called Fibonacci numbers you always have to add two numbers and then get the next one then add the last two again and then you take out the next one and to solve the Fibonacci problem you have to do it twelve times, twelve hard months.

Does this now have to do with thirds? It is quite simple by approx. Yes, that means you can replace a couple of rabbits with a smoothie and then you can do the same calculation. Of course, we only need to know how much breeding cycle we have for the older ones in a period of three days and ten offspring every 2.4 hours. a triple comes out and then a total of 30 reproduction cycles yes and we do not have to remember that we have 31 cycles because the first third of the chair is given away the election was already pregnant yes that is why we have to include that in the cycle So we are looking for the Fibonacci number 31, we always add two numbers, not the total, we add the two previous numbers and so on.

If you do that, you get one million 346 1269. We have one, you would say not bad. because Charles dries up to the same magnitude, yes, but the blog would be measured with 400,000 triple error. I asked myself. That's not bad, so it's also worth watching, but maybe it's even better. Yes, because I just took the square root of this number. says I accidentally came across the square root button, yeah, and then I found out that the square root is 1300 30.99 6.331 and 1331. I knew that eleven times eleven times helps, that means the number Diesbrock calls is almost 11 x 11 x 11 x 11 x 11 x 11 then almost 11 6 and 11 6 could also be explained like this if they always had a title and they shoot a third has ten guys at a time and if they do it six times in a row then 11 56 triple comes out at the end then that could also be what it means, yes, but we don't have any, there will be six play cycles and the number is not quite correct either, well, let's listen to it in the original in English, ha, yes, what does it say here in the original in English?

Even the young band Schippel painted stay up becomes frequent and produces new generation Apple 12 hours in a period of three days in the English original speaks of exactly six playback cycles and speaks of a slightly different number, yes, and if we We look at the square root of the number called en in the original in English, exactly house 1333 in the original in English is called exactly Eleven to the power of 6 and means a triple that always comes out ten per toss. So this number makes sense. Only the people who synchronized it couldn't imagine it. Yes, from the beginning it was clear to me that Bock was not talking nonsense, but he always gave precise numbers.

The only thing left to figure out is how the l 560 can calculate quickly. Yes, but that gives eleven powers the trick of the 111 l. 221 11 to 13 31 How does this happen? You always have to freeze here. Add the two numbers and you get the middle and front ones. Write individually 11 4 is one and then 46 41 10 so you can reduce the increase to the power of. eleven to a sum of small numbers. You have to take the carry into account because there are 10 of them there, but you can really practice it to do it very quickly. This is how many multiplication tricks work.

It's really easy because the best mental calculator I know is the German Rüdiger Gamm. What he can do, you would say 11 6 can be solved, so 11 6 it's not even good warm-up program. Well, I'm ready, maybe with one last comment. The following is the following excerpt from the Enterprise series that I gave to my students in front of the club before the last exam, I can tell you that it is not that funny, but it is also good, okay, so if you want more of That's right, There are many, many more examples from the Star Trek series in this book.

Of course, everything I have shown here now costs 11 euros and if so, you buy the book, yes, I like the rampant advertising of this book. Because if you buy the book you don't support teachers in need, yes, but all the proceeds go to the alumni association of our physics students. These are non-

prof

it associations and do not sponsor scholarships for our physics students at the Technical University of Dortmund. in Düsseldorf, but I may later come to Düsseldorf to support the physics students at TU Dortmund and we have already sold almost 28,000 books like this, so a lot has already been achieved for our physics students, but we have many students in Dortmund and we also have a lot of good students and they are worth supporting, well maybe in the end these three gentlemen for technical assistance, Mr.

Kramer once told me, man, the sound is on, yeah, that's the boost , although in Dortmund we don't have astrophysics. Since something is happening in our building, it's strange. These are the sources. Of course, I only showed you excerpts from the original DVD of the 1 meter cable which, as you saw, was only licensed. government sites and of course now I wish you the same. This man also wants exactly that, thanks for his attention, no.