The Power of Mathematical Forms.

The concept of the “inner images” in our mind derives from psychology and was introduced by brain researcher Gerald Hüther to describe “all that, which is hidden behind the external, visible and measurable living phenomena and guides and steers the reactions and actions of living beings.” There are images in you that help you to be a good citizen or a caring mother, or guide you in moving around in the world. Your inner images determine what you think of yourself and what you think of the world and of other people, and so they determine how you interact with the world. Everything that you can do, every step that you can take, is guided by an inner image. Since you can undertake nothing that isn’t first initiated and then allowed by an inner image, these images determine what is possible for you: They define your potential.

The inner images arise in your mind from a variety of sources. Some act through your consciousness, while others are hidden in your unconscious. Some of them are inborn. Others arise in activation patterns of neural networks that your personal experiences have created in your brain. And yet another group appears in your mind out of a nonpersonal and collective realm of forms with which we are all connected, as Swiss psychiatrist Carl Gustav Jung described in the last century. Whatever the source of the inner images in us may be, the fact is that behind the physiological processes of our brain, nonempirical forms are at work that control our actions and give meaning to our life. These forms aren’t visible to or measurable by brain scientists. They are true forms of potentiality, because they exist before they manifest themselves in the visible world by affecting your body and controlling its processes. You can think about the states of cosmic potentiality in the same way you think about the inner images of your mind. The cosmic potentiality is a field comparable to other fields spread throughout the universe, such as the gravitational field, except that cosmic potentiality doesn’t contain any matter or energy, just states of what is possible in the world.

What exactly do I mean by the states of what is possible in the world? We have to dig in deeper to get a clearer understanding, but it is worth it: Getting a grasp of potentiality is one of the most important things you can do for yourself in this life. To appreciate the answer that physics has given this question, we have to keep in mind that the states of potentiality are invisible, and nobody can give a definitive description of invisible things. Physics can only observe what comes out of these states and then work backward, extrapolating into the darkness of the unknown, and suggest what its states might be like.

So far, the best that physics has come up with is the suggestion that the states of the cosmic potentiality are forms, meaning mathematical forms or numerical patterns: not patterns of energy or matter, but just plain numbers. For the lack of anything better, we will accept such descriptions, but we must always keep in mind that we can’t really know what the nonempirical realm of the world is like. It can interact with our world in space and time, but we can’t even know that space and time apply to it, inside it. Perhaps the best way to think of the nonempirical realm of the world is like how many mystics have described their experience of God: Their experience wasn’t of anything that appeared to their senses— it wasn’t anything that they could feel, hear, or see— and yet it was real and powerful. It has often been said that the American legal system is a formalistic system in which the notion of justice has been lost. Right or wrong don’t matter, true or false don’t matter; the only thing that matters is to follow the letter— or form— of the law, and to do that in a formalistic way.

You can think of quantum physics in the same way: It wasn’t invented as an intuitive or visual description of the world, like you might expect, but as a formalistic description, and, even though nobody wanted that, in the process of developing this formalism, the notion of reality was lost. The first concern of the physicists was to find a formalism that fit the visible phenomena so that we could deal with them. Once that job was done, they could deal with the problem of what it all might mean for our understanding of the nature of reality. Interestingly, the physicists of the twentieth century weren’t the first to suggest that the world consists of numbers.

Already in the sixth century BCE, Pythagoras, one of the Greek founders of Western philosophy, claimed to have found irrefutable arguments for the thesis that “all things are number,” meaning that the essence of things isn’t found in some stuff, but in forms. And in the fourth century BCE, Plato, one of the most influential philosophers of all times, taught his students that atoms were mathematical forms. Contemporary physicists are, of course, not guided in any way by the arguments of historic philosophers, but they find that they need something such as the Pythagorean formalism or Platonic idealism to explain the visible world.

The English word image is usually understood to mean an image of something, presenting a likeness with an object or structure that it images. In a general way, the word image can also be understood as a graphical form or pattern not of something, but a formal motif or figure in its own right. An abstract painting in modern art, for example, can be such an image that an artist put down on canvas without having any specific thing in mind. In this sense, the states of the cosmic potentiality can be described as images: They are the inner images of the universe that guide its visible phenomena. The images in the cosmic potentiality are, of course, different from the images in our mind.

Nevertheless, you will not go very far from truth if you think that the cosmic potentiality is something like a mental domain of the universe whose inner images are found everywhere in the world. Human beings have a body and a mind because the universe has a body and a mind, so to speak, even though we never use such terms in connection with the universe. The intent of this choice of words isn’t to revive archaic descriptions of the universe, but to demystify the human mind: There is nothing special about its images. Its images are as physically real as the images or mathematical forms that exist in atoms and molecules and determine their physical and chemical possibilities. Chemical reactions depend on the inner forms of the molecules that participate in them. The inner forms of atoms determine what kind of molecules can form. The visible world is shot through with invisible images that define its future possibilities. The aspect that is so difficult to get used to is the power of the images: All visible things and phenomena need an underlying image, or they couldn’t have appeared in the visible world. Since this rule applies to the processes of the physical world as well as to the processes of our mind, it reveals an unexpected congruence of the physical and the mental that is typical for the new physics. In a metaphorical way, you could say that quantum physics is the psychology of the universe.