In Avengers EndgameTony Stark tries to make one Time Machine Reach the Infinity Stones before Thanos and avoid the devastating effect of his photo. Scientist behind iron man Explores several possibilities, one of which is Reverse Möbius strip. The truth is, in this case, science fiction has more fiction than science, because a lot of what we know about this mathematical phenomenon has to be twisted so that it can be related to time travel. But it is true that the Möbius strip is a concept that has been widely studied by mathematicians. In 1977 A problem has been proposed that has not yet been solved.
It was proposed by mathematicians Charles Weaver and Benjamin Halpern And at first it was apparently simple. A Möbius strip Can be produced easily, take a piece of paper, rotate it 180º and join its ends. Even a small child can do it. But these two scientists were amazed at how small they could make it without cutting it. They suggested that the question might be the relationship between its length and width. Above √3. This is roughly over 1.73. But since they could not prove it, they raised it.
However, another mathematician was now called upon Richard Schwartz We were able to do calculations that proved that number. It should be noted that the published study is still in its infancy Preprint. In other words, it doesn’t get peer review from scientists outside of its research, which would help make sure everything was done right. This indicates that the data should be read with caution. However, mathematicians who have already reviewed it informally agree. Will you be there too? Tony Stark?
What is a Möbius strip?
The Möbius strip was first described in 1858 by the German August Ferdinand Möbius and Johann Benedict List. Both performed their interpretation independently, but with the same results. It is believed that like other mathematicians before Carl Friedrich GaussAlthough the existence of this structure had already been studied, it was not described as Möbius and Listing did.
They described how it can be made from paper tape and what are its basic properties. These are very simple and can be easily understood by building a Möbius strip at home. Chief among these characteristics is There is only one face. If we take our piece of paper and start painting, we can finish without lifting the pencil from the paper or going through the edges that separate one face from another. The second characteristic is that It has only one edge. It can be proved in the same way. We can follow the edge with a finger or pencil without lifting it and when we reach the starting point we have everything covered.
It is very important to remember that this is a Möbius strip It is an orientationless surface. To explain this better, A Imaginary experiment with ants. Imagine some ants starting to walk in one of these settings. If you start from what we have assumed above, when you reach the starting point, you will be at the bottom. If the surface is oriented, they will be at the top because it is the same point, but it cannot be oriented. You cannot differentiate between inside and outside. Basically, in this case the terms “go up” and “go up” can be used.
A problem Iron Man didn’t solve, but Richard Schwartz did
In reports Scientific American, Schwartz explains the keys to the problem he solved. The first thing to keep in mind is that at the time, Weaver and Halpern proposed it The ribbons are sunk rather than embedded. But what does this mean?
“This means that they are not mutually interpenetrating or self-interlocking. Imagine that the Möbius strip is actually a hologram, a kind of ghostly graphic projection in three-dimensional space. Many sheets can overlap each other, like a ghost walking on a wall, but for an embedded band, such an overlap No.”
Richard Schwartz, a mathematician at Brown University
The example of the hologram is interesting because this is how Tony Stark teaches his companions. Möbius strip He is investigating that.
As Halpern and Weaver 1977 pointed out, the problem they present is simpler if there are self-intersections. So, his question is how much space will be required Avoid those encounters.
As soon as Schwartz became aware of the problem, he tried to solve it. did First approach in 2021. But, this did not materialize. At first he let it go, but recently decided to go over his calculations, convinced that there would be one small mistake that would change everything. He found it. When considering a piece of paper in 2 dimensions, it is not a parallelogram in which all its opposite sides are parallel to each other, but rather A trapeze, with two parallel sides.
By making this small change, all the calculations added up and reached the expected √3, which his predecessors could not prove.
Could these calculations have been useful to Iron Man in his research? Probably not, because getting a time machine would take more than just improving the size of the Möbius pieces. But surely he would have liked to know the solution to the problem. After all, science outside of fiction may seem less impressive, but is actually quite fascinating. Basically, because it’s real.
