The Uncertainty Principle: When one plus one is measurably not two

by Roger D. Jones

I am writing a new book with my colleague John Casti entitled Eddies in the Stream. It is an arrogant project about what life is. No, I mean really what life is. How did life come about? Is it constrained to be chemistry-based? Can computer programs be alive? Can cities be alive? Is a society of universes possible? That sort of thing.

This series of blogs contains bits and pieces from the book as it is being written. I am writing the blog as a way to decompress. I am also creating paintings on the topics in the book as a way to decompress.

There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. – Hamlet (1.5.167-8), Hamlet to Horatio


A self-referential system with strange properties exists in nature. Logic and counting fail. The system goes by the name quantum mechanics and deals most commonly with very small things such as atoms. The world of atoms is very different from the macroscopic world we are accustomed to. The world cannot be separated into the observed and the observer because the instruments we use to measure the properties of atoms are themselves made of atoms, as we ourselves are. We have atoms studying atoms. This is quite self- referential.

Experiments were performed in the early twentieth century that

indicated that small objects like electrons were particles if certain experiments were done, but were waves if other experiments were done. The statement, “This electron is a particle.” can be both true and false. This is a failure of logic of the kind that Kurt Gödel was concerned with. However, this example goes beyond the parlor games of mathematicians. This failure of logic can be measured and occurs in nature. As we will see, this logical failure, is crucial for the formation of life.

There are other related logical failures in the land of atoms and electrons. For instance, if you know where an electron is, then you cannot know where and how fast it is going somewhere else. Conversely, if you know how fast and where an electron is going, then you do not know where it is. This is called the Uncertainty Principle. If you have a rough idea on where an electron is, then you have a rough idea of where it is going, and vice versa. The Uncertainty Principle, a natural consequence of the logical failure of a self-referential system, is crucial to the formation of chemistry-based life. The Figure illustrates the electron cloud around a proton. These clouds form the basis of chemistry. Schrödinger discovered the equation that determines the behavior of these clouds and quantum particles, in general. The stability of these clouds is important for the stability of chemistry-based life, one of our two conditions for something to be alive. We will go into this a little deeper later.


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