Chapter 1: The Nature of Knowledge

The distinction between knowledge that is discovered and that which is invented is fundamental to our understanding of science and ideology.

Discovered knowledge is obtained through our observations of the universe. Notable figures like Newton and Einstein exemplify this, having unveiled concepts such as gravity and relativity. Science, in essence, is a collection of discoveries that expand our comprehension of natural laws.

Engineers leverage these natural principles to create technologies such as computers, smartphones, the internet, and spacecraft. These innovations are grounded in scientific laws, which must be experimentally verified to be accepted as such. The process of acquiring and refining knowledge is deeply rooted in logic, reasoning, hypothesis formulation, experimentation, and validation.

It is crucial to note that discovery does not operate on axioms, whereas invention does.

Axiom: a proposition that is widely accepted as true without proof.

In contrast, invented knowledge lacks a foundation in natural phenomena and is entirely based on axiomatic principles. For instance, language serves as a prime example of invented knowledge, along with philosophy, ideology, and religion. Mathematics, too, falls under this category, as does the metric system.

Consider this: one could author a five-hundred-page book based on the axiom that there exists a singular true deity, XYZ, and all others are false. The validity of the subsequent content hinges on the acceptance of that initial axiom.

As a believer, one can utilize logic and reasoning to support various arguments within the confines of that chosen axiom. This is why numerous religions, countless languages, and millions of works of fiction exist; creativity knows no bounds.

However, it is crucial to recognize that mathematical proofs cannot be applied to religious contexts. This inconsistency arises because they are founded on divergent axioms—similar to the challenge of communicating in Chinese with someone who speaks only English, given their distinct grammatical structures.

Nevertheless, discovered knowledge allows for cross-disciplinary consistency. For example, the principles of physics apply to biological entities, as all living matter comprises atoms and molecules.

Unlike the technologies birthed from discovered knowledge, such as computers and spacecraft, invented knowledge—like philosophies and ideologies—has largely produced an abundance of ideas and discussions without tangible advancements.

Nonetheless, certain forms of invented knowledge, such as languages and mathematics, have proven to be immensely beneficial to humanity. The rest have served primarily to entertain and engage us over countless generations.

Chapter 2: The Debate of Invention vs. Discovery

In this video, we explore the age-old question: Is math invented or discovered? This discussion highlights the ongoing scientific controversies surrounding the nature of mathematical knowledge.

The second video delves into the difference between "invent" and "discover," providing advanced English lessons that clarify these concepts and their implications.