IN Avengers: EndgameTony Stark is trying to do Time Machine get to the Infinity Stones before Thanos and avoid the devastating effects of his snap. The scientist behind Hombre de Hierro explores several possibilities, including inverted Möbius strip. The reality is that in this case, science fiction is more fantasy than science, since what we know about this mathematical phenomenon would have to be greatly distorted in order for it to be associated with time travel. But it is true that the Möbius strip is a concept widely studied by mathematicians, especially since in 1977 A problem was proposed that has not yet been solved.
This was suggested by mathematicians Charles Weaver and Benjamin Halpern and at first it was seemingly simple. A Möbius strip can be made simply by taking a strip of paper, rotating it 180° and connecting the ends. Even a small child can do this. But the two scientists wondered how small they could make it without intersecting. They suggested that the issue might be the relationship between its length and width. more than √3. This is approximately higher than 1.73. But they only brought it up because they couldn’t prove it.
However, now another mathematician named Richard Schwartz was able to make calculations confirming this figure. It should be noted that the published study is still in its infancy. pre-press preparation. That is, he did not receive peer review from scientists outside of his research to help confirm that everything was done correctly. This indicates that the data should be read with caution. However, mathematicians who have already looked at it informally seem to agree. You would too Tony Stark?
What is a Möbius strip?
The Möbius strip was first described in 1858 by the German Augustus. Ferdinand Möbius and Johann Benedict Listing. Both made their descriptions independently, but with the same results. It is believed that earlier other mathematicians, e.g. Carl Friedrich Gausshave already investigated the existence of this structure, but did not describe it, as Möbius and Listing did.
They described how it would be constructed from paper tape and what its main properties were. They are very simple and easy to understand if you build a Mobius strip at home. The first of these characteristics is that has only one face. If we take our strip of paper and start coloring it, we can finish without lifting the pencil from the paper or going through the edges that separate one edge from the other. The second feature is that it only has one edge. This can be demonstrated in the same way. We can follow the edge with our finger or pencil without lifting it, and when we reach the starting point we will cover everything.
It is also very important to keep in mind that the Möbius strip This is a non-orientable surface. To better explain this, A. imaginary experiment with ants. Let’s imagine ants that begin to walk along one of these structures. If you start with what we covered above, then when you reach the starting point, you will end up at the bottom. If the surface were orientable, they would be at the top, since they are the same point, but it cannot be orientated. You also cannot distinguish the internal from the external. In principle, the terms “go down up” and “go down up” could be used in this case.
The problem that Iron Man didn’t solve, but Richard Schwartz did
In statements to Scientific AmericanSchwartz explained the key to the problem he had just solved. The first thing to keep in mind is that at the time Weaver and Halpern proposed this tapes are submerged rather than embedded. But what does it mean?
“This means that they do not interpenetrate or self-connect. Imagine that the Mobius strip was actually a hologram, a kind of ghostly graphical projection in three-dimensional space. Several sheets can overlap each other, like a ghost passing through a wall, but for a built-in strip there is no such overlap.”
Richard Schwartz, mathematician at Brown University
The example of a hologram is interesting, because this is exactly how Tony Stark teaches his comrades The Mobius strip what he was investigating.
Halpern and Weaver noted in 1977 that the problem they posed would be simple if self-intersections existed. So his question was how much space would be required for Avoid these intersections.
As soon as Schwartz became aware of this problem, he set about solving it. Did first approach in 2021. However, this did not happen. He initially gave it up, but recently decided to go back to his calculations, convinced that it would be just one small mistake that would change everything. And he found it. It was something so simple that if you consider a strip of paper in two dimensions, it will not be a parallelogram in which all its opposite sides are parallel to each other, but trapezoid, with only two parallel sides.
As a result of this small change, all calculations were summed up to produce the expected value of √3, which his predecessors could not demonstrate.
Were these calculations useful to Iron Man for his research? Perhaps not, because creating a time machine will require much more than just optimizing the size of the Mobius strip. But, of course, he would like to know the solution to the problem. After all, science outside of fiction may seem less impressive, but in fact it is much more spectacular. Mainly because it’s real.
Source: Hiper Textual
