“The proof, as Scholze and Stix describe it, involves viewing the volumes of the two sets as living inside two different copies of the real numbers, which are then represented as part of a circle of six different copies of the real numbers, together with mappings that explain how each copy relates to its neighbors along the circle. To keep track of how the volumes of sets relate to one another, it’s necessary to understand how volume measurements in one copy relate to measurements in the other copies, Stix said.
“If you have an inequality of two things but the measuring stick is sort of shrunk by a factor which you don’t control, then you lose control over what the inequality actually means,” Stix said.”
As I have explained so far, IUT theory tries to do three things:
transport information between different theaters, reconstruct them, and then calculate the distortion.
Hence the title of this section is “transportation, reconstruction, and distortion”.
Let’s recall the difference between IUT theory and traditional mathematics again.
Traditional mathematics was restricted to a single theater.
Of course we have gotten to know a lot within it.
However, IUT theory is unique in a sense that it considers multiple theaters, that goes beyond our common sense and gives a new kind of flexibility.
What is important here is, even by making use of IUT theory, we expect to prove equalities/inequalities in our usual senses.
Traditionally, we have been trying it in a single theater.
However, perhaps there may be something we can’t do in one theater.
Considering multiple theaters may make us take a detour, but IUT theory tries to prove the inequality by taking advantage of the new flexibility.
So, what is a “theater”?
I showed this before: this is a normal world where you can do addition and multiplication at the same time, but we consider another theater.
Oh, what a fantastic notion. As long as you do this in simple operations, you keep what they call transportation symmetry. That’s what makes it work. If you try to do too much at once, it doesn’t work.
screen inside of a screen: I love this. It’s taking advantage of the holographic nature of mathematical operations. [actually it’s physics] So long as you don’t do too much, the operation be simultaneously applied at any level.
So you’re ONLY transporting the symmetries, NOT the objects.
I’m finally learning about that math theory that reports called “incomprehensible except to a few” and actually, it’s not that bad. This animation, which I saw on a video explaining Mochizuki’s notion of “theatres” to high school students – is a visual explaining what’s probably the most complicated part of the theory – which works mathematically, just, not in the same way standard mathematicians work.
Officially called “The Multiradial Representation of Inter-universal Teichmüller Theory”
It’s pretty if nothing else.
abc Conjecture and New Mathematics: English translation is here: https://www.youtube.com/watch?v=fNS7N04DLAQ&vl=en and it’s a LOT better than short news reports that talk about “conflict” when this theory is perfectly accepted in Japan as valid as they’ve been using it actively for decades now.
for posting about this. Inspired me to research and finally look into it.https://youtu.be/fNS7N04DLAQ?t=4562 1:16min This is the video in context of teaching high school students, complete with explanations. The English translation is in the closed captions.I opened a transcript to the side to read along.
Intuitively, I think it works because it keeps the indeterminites VERY very small and tightly controlled, like a quality control check at each step.
it’s funny how our expectations are set. We’re accustomed to other things such as youtube videos automatically coming in so we assume facebook will do it to itself, but it does not.
Yet, we keep expecting it to. We’re logical. Facebook is not.