What exactly is an idea? A common definition states that an idea is a new way of thinking about, seeing, or doing things that arises mentally, either spontaneously or through a controlled process of brainstorming. While this definition captures the functional essence of an idea's initial creation, it fails to completely explain how ideas can be communicated, refined, or assessed: once it is communicated, an idea already exists – it is no longer novel and it is no longer the property of one mind. This distinction is particularly poignant when one discusses ideas that have already seen implementation, in such phrases as “Whoever thought up Wikipedia was brilliant! What a great idea!” The new way of thinking that brought us Wikipedia may at one point have been a novel concept within the mind of Jimbo Wales, but what Wikipedia is most certainly is not, as the idea has been exposed to the world, spread, and transmuted.

So if this definition fails to suffice, what will? Well, for one thing, an idea need not be the product of an exclusively human endeavor. For example, it is indeed possible to stand in awe of the concept of transforming sunlight into usable energy, despite the fact that this process happens in both plants and photovoltaic solar cells. We can say that this idea has spread, given both the number of plants and the number of solar cells in use, and we can in fact state that this idea was built upon, since solar cells were built upon the concepts that plants pioneered (just as airplanes built upon the flight of birds), with newer cells in turn building upon older cells to increase efficiency. The practical application of such ideas is known as technology; we'll call the process of tangibly applying ideas in this manner implementation.

Ideas such as this one were pioneered by nature and entered the human consciousness fairly early in our history. Nevertheless, it is important to emphasize that even once we are able to apply such concepts and create functionally similar technology, we do not completely understand the idea or its ramifications. For example, we cannot create solar cells with 100% efficiency, and even though it is intuitive that we probably cannot (that pesky second law of thermodynamics), we certainly don't know what an optimal solar cell's efficiency would be. We can only reason in this way when we know all of a system's rules and can deductively prove that certain properties would lead to inconsistencies that would render the entire system invalid, such as in pure mathematics. However, this generally requires long and rigorous proofs, for which a moment's intuition is not a proper substitute; rigorously proving 1+1 = 2, perhaps the most obvious of axioms, occupies pages of discourse and derivation. However, even in an artificially constructed system with an infinite amount of paper and time, such an approach is still doomed to fail: a mathematician named Kurt Gödel proved, in the famous 1931 result now known as Gödel's Incompleteness Theorem, that any system powerful enough to describe the natural numbers (and thus, through a process known as Gödel numbering, which assigns numbers to logical statements, itself) must contain statements that cannot be proven true or false. As powerful as this idea is, the intuition behind it is rather simple: such a system is capable of expressing paradoxical statements such as “this statement is false”, whose truth would assert its own falsehood, and vice versa. All of this is to say that whatever an idea is, we're very bad at assessing its consequences because we simply cannot know everything, even when we know all of the system's rules.

Gradually, we are beginning to develop the fragments of a definition that will form the primary motivation of this essay. Whatever an idea is, we know it doesn't have to be novel, it doesn't have to be man-made, it doesn't have to belong to a single mind, it can take tangible form through the process of implementation, and it is rather difficult to circumscribe. The remainder of these sections will explore the nature and consequences of one of the fundamental building blocks of reality: the idea.