How to interpret analogy of Gaussian integral of Alien Copies in IUT theory by Mochizuki?

Question

In Mochizuki's paper, he refers to copy of Integral as 'Alien Copy', which is strange since the double integral is an extension of the surface of uni-dimensionnal integral due to Summation properties (linearity)...

Can anybody explain why 'Alien Copy' means in Gaussian integral computation ?

THE MATHEMATICS OF MUTUALLY ALIENCOPIES: FROM GAUSSIAN INTEGRALS TO INTER-UNIVERSAL TEICHMULLER THEORY

http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf

EDIT: To be precise, this is not very clear what can be considered as alien and as not-alien.

For example if we have :

I= Integral(gaussian(x) dx,-inf, inf)
J= Integral(gaussian(x/2) dx,-inf, inf)

are I and J are aliens ?

and what about

K= 2*Integral(gaussian(x) dx, 0, inf)  ?

Answer 1

You could always read the paper you linked a bit closer: he says, in the very first mention, that

common features that underlie these analogies may be summarized as follows:

• the introduction of two mutually alien copies of the object of interest;

• the computation of the effect — i.e., on the two mutually alien copies of the object of interest

• etc

he then continues to explain what he means:

Here, the intended sense of the descriptive “alien” is that of its original latin root, i.e., a sense of abstract, tautological “otherness”

So, in essence, he means that you introduce a copy of the thing that is "alien", as in that it is exactly the same but formally a different thing. Are you familiar with the calculation he refers to? It involves introducing the same integral once again but with another variable, making the two integrals "mutually alien".

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edit: I also found this quote from 1.3 of the paper relevant and quite entertaining:

Here, let us recall that our hypothetical high-school student was already in a mental state of extreme frustration as a result of the student’s intensive and heroic attempts in Step 2 which led only to an endless labyrinth of meaningless and increasingly complicated mathematical expressions. This experience left our hypothetical high-school student with the impression that the Gaussian integral was without question by far the most difficult integral that the student had ever encountered.

Step 3 evoked a reaction of intense indignation and distrust on the part of the student. That is to say, the idea that meaningful progress could be made in the computation of such an exceedingly difficult integral simply by considering two identical copies of the integral — i.e., as opposed to a single copy — struck the student as being utterly ludicrous.In light of this experience, the suggestion of