I tried to disprove the existence of a higher infinity and produced these tables instead. Part 3

Large cardinals are levels of infinity that are so large that these levels of infinity cannot be proven in standard ZFC set theory. While we are unable to prove the existence of large cardinals, we may be able to falsify some of these large cardinal axioms. This is a visualization of the algebras obtained in an attempt to falsify the existence of rank-into-rank cardinals.
A rank-into rank embedding is an elementary embedding j:V_\alpha
ightarrow V_\alpha for some \alpha. Kunen's inconsistency result states that if j:V_\\alpha
ightarrow V_\alpha is a non-trivial rank-into-rank embedding, then \alpha=\lambda or \alpha=\lambda+1 where \lambda=\lim_{n
ightarrow\omega}j^n(crit(j)). In particular, \lambda is a strong limit cardinal of countable cofinality.
Let \lambda be a cardinal, and let E_\lambda be the set of all elementary embeddings j:V_\lambda
ightarrow V_\lambda. Then E_\lambda is endowed with an algebraic operation * defined by setting j*k=\bigcup_\alpha j(k|_{V_\alpha}). If \gamma is less than \lambda and \gamma is a limit ordinal, then define a congruence ~^\gamma on (E_\lambda,*) by setting
j~^\gamma k precisely when j(x)\cap V_\gamma)=k(x)\cap V_\gamma for each x\in V_\gamma.
The images in the animation are images of quotient algebras of two generator subalgebras of E_\lambda/~_\gamma under the assumption that the algebra is non-trivial.
We start off with the trivial 1 element self-distributive algebra, and from old algebras we produce new algebras recursively. If X is an algebra with generators x_0,x_1, let ssg(X,(x_0,x_1),0) denote the set of all (up-to-isomorphism) critically simple Laver-like algebras Y with generators y_0,y_1 where
1. |crit[Y]|=|crit[X]|+1,
2. there is a surjective homomorphism f from Y to X where f(y_i)=x_i for all i,
3. crit(y*x) is greater than or equal to crit((y*y)*x) for all x,y in Y, and
4. if x_{i_0}*...*x_{i_r}=1 and x_{i_0}*...*x_{i_s} is not 1 for s less than r, and if i_0=1, then y_{i_0}*...*y_{i_r}=1 as well. Equivalently, there exists some non-unit c in y with f(c)=1 and where y_1=c*y.
Our collection F of algebras is the smallest class of algebras containing the one element algebra and where if X belongs to F and |ssg(X,(x_0,x_1),i)|=1, then the element of ssg(X,(x_0,x_1),i) also belongs to F. If X belongs to F and |ssg(X,(x_0,x_1),i)|=0, then non-trivial rank-into-rank embeddings do not exist and we have obtained an inconsistency in the large cardinal hierarchy.
In this visualization, we show elements of the set F. In order to make the visualization have a reasonable length, we only include the critically simple algebras of size at most 70. I have already included these tables in a previous visualization, but now I have reordered the elements so that the tables look completely different but so that one can still see the structures in the tables and also the relation between different tables.
In the visualization, we set X to be {1,...,n} for some n in such a way so that elements that are similar to one another in X are near each other on the interval {1,...,n}. In the visualization, the generators are denoted using red and blue squares. The black squares are the points of the form (x,x*y), and the remaining squares are white.
I have so far not been able to prove that rank-into-rank embeddings exist. And I do not expect to obtain a proof that rank-into-rank embeddings exist not because my tests are weak. I have ran these tests about a million times and have not found an inconsistency, but I have found many near misses, and I have no explanation for these many near misses other than the existence of rank-into-rank embeddings (or at least their existence in a good model). This tells me that rank-into-rank embeddings are probably consistent.
The notion of a Laver-like algebra is my own. This test for the consistency of rank-into-rank embeddings is my own.
Unless otherwise stated, all algorithms featured on this channel are my own. You can go to github.com/spo... to support my research on machine learning algorithms. I am also available to consult on the use of safe and interpretable AI for your business. I am designing machine learning algorithms for AI safety such as LSRDRs. In particular, my algorithms are designed to be more predictable and understandable to humans than other machine learning algorithms, and my algorithms can be used to interpret more complex AI systems such as neural networks. With more understandable AI, we can ensure that AI systems will be used responsibly and that we will avoid catastrophic AI scenarios. There is currently nobody else who is working on LSRDRs, so your support will ensure a unique approach to AI safety.

[@TimRichardson1984]

i am very honored and privileged to be the first person in the world to watch this work of art

[@josephvanname3377]

I appreciate the enthusiasm. Perhaps this content can be played at airports or hotels or in the backgrounds of malls or in the background when people are listening to podcasts.

[@Pablo-cr1rr]

qr tables

[@josephvanname3377]

QR codes are not as interpretable though. And the QR decomposition of a matrix is not very interpretable either. If you want something looking more like QR codes, you should check out my visualizations about bent functions and Hadamard matrices.