Lessons Learned from School About Math

Mathematics is a vast and intricate field that encompasses everything from basic arithmetic to advanced theories in algebra, calculus, and beyond. It serves as a foundational tool for understanding patterns, solving problems, and making predictions across various disciplines. The beauty of math lies in its logical structure and the way it can describe real-world phenomena, enabling us to model everything from physical laws to financial systems. Additionally, it fosters critical thinking and analytical skills, making it essential for both academic pursuits and everyday decision-making.

The Role of Mathematics in Logical Reasoning

Honestly, mathematics is pure logic. Using it, we can practice logical reasoning. This is an excellent skill to apply to any aspect of our lives, but combine this with a skeptical mind and statistical analytical skills, and you'll be able to wade through all the pseudoscience that litters the internet. You'll also be able to see through poor arguments, bad reasoning, and terrible ideas.

Beyond Traditional Mathematics: Emerging Concepts

Mathematics as we know it is not the ultimate form of mathematics. This is due to two reasons: the Kurt G?del's Theorem on Undecidability and my own research on emergent computation. G?del's theorem roughly says that each axiomatic system eventually arrives at statements which cannot be proven true or false. My research shows that there is something more beyond our standard logic systems, and this is being utilized within massively-parallel, emergent systems.

Emergent Computation and Cellular Automata

Emergent systems are fascinating because they can arise spontaneously from simple rules and interactions. For example, in a cellular automaton, like Conway's Game of Life (GoL), emergent behaviors can be observed, despite being deterministic. Injected errors into the evaluation process of these emergent systems can be tolerated if the system is error-resilient.

In one research publication, it was shown that we can construct emergents that can sustain 1 error during their evaluation process and continue their existence. This is called error-resilience. The process is based on massively-parallel computations and redundancy, as described in the research paper. However, such a high level of massively-parallelism, giving birth to emergents, is beyond the capability of any human brain to imagine, contrary to standard logic systems.

This highlights a significant challenge for anyone who wants to understand the root principles that are located at the foundations of the laws governing our universe. It opens up a discussion about the nature of reality and the limits of human understanding.

References:

[1] Kroc, J. (2019). Error-resilient emergents in cellular automata. Journal of Physics and Information Sciences, 13(2), pp. 1-10. DOI: 10.25045/jpis.v13.i2.02

Further Reading: