Modern physics is full of references to “dimensions.” A mathematical term in use since who knows when, it became attached with quasi-mythical associations soon after Albert Einstein coined the term “raumzeit,” or spacetime in the early part of the 20th century. Actually Einstein drew the concept from two other mathematicians of his time, Poincaré and Minkowski, who first posed the use of time as a fourth dimension to clarify some of their mathematical formulae, but considered the resultant 4-dimensional construct as imaginary. Einstein instead made his “four-dimensional continuum” a central part of his Theory of General Relativity, published in 1915. For Einstein, space and time became parts of the real universe, even though neither has any real attributes that are discernable to the human sensory system.

As a young man, fascinated by science, and its literary counterpart, science fiction, I was enthralled by the notion of a mysterious fourth dimension, the idea of time travel, and possible movement into another universe through “wormholes” in spacetime, translation into a another dimension, and the like. Only later, when my education caught up with my fantasies, did I understand what was really meant by a dimension and began to question how one could be considered an actual entity in the real world. This is what I learned, and from it came a new understanding of how error can become institutionalized and almost a permanent part of our consciousness.

A dimension is nothing more or less than a descriptive term in language that refers to certain attributes of objects, events, and phenomena, the entities that make up the class of real elements in the world. As a descriptor in a language it is not real in the sense that it is discernable outside of our consciousness but occupies a level of abstraction higher than the real entities it describes. Dimensions are applied to measure, describe, communicate quantifiable attributes of objects, events, and phenomena, as in denoting the length of a line, the length and breadth of a planar object, or the length, breadth and height of a solid, what we call a 3-dimensional entity. For example, a rectilinear box can be described by stating the value of those three attributes of the object, in whatever dimensional units common to the location or region in which the object is located. Common units are, for instance, feet and inches in the U.S. and some other English language speaking countries, in meters, centimeters, etc. in those regions where the metric system is in use. But you can make up your own as long as you explain them to your audience.

For an object that has a form that is more complex that that of a rectilinear box, additional dimensions my be required to describe and measure its form and character. A toroidal form, for example, might require dimensions for its outside diameter, its cross sectional diameter, and the cross-section’s rotation through 360°, in this case still only three dimensions but different ones from the previous example. You can see, however, that different types of objects require different dimensions for their appropriate description. The dimensions described are the so-called spatial dimensions. Besides being used to denote the size and form of objects, there may be dimensions that locate an entity relative to other entities, either established reference points, as used by land surveyors, or separation distances between one entity and another.

In short, I think that it is apparent that there may be an unlimited number of so-called “dimensions”, but they are inseparably tied to the object, event, or phenomenon they describe; they do not exist as actual entities in and of themselves in some abstract region of the cosmos.

We use dimensions to describe events and phenomena as for instance, a storm system or hurricane. We describe it as being located so many miles from land, in a specific direction, as having winds of certain velocities at specific altitudes, as being of a certain size, as growing in intensity or weakening; each of these descriptive terms are quantifiable, and can be called dimensions.

In my fifty plus years as a practicing architect, I became intimately acquainted with the importance of dimensions. Without them, I could not communicate my desires and intentions to those who would implement my plans and turn them into useful products. I used them both to describe the products and their locations. And I used dimensions to describe other characteristics that had to be included in the final work. These included the capacity of heating and ventilating systems, the quantity of water to the plumbing systems, the voltage and current carrying capacity of electrical components. Each of these values was a “dimension.”

There is another set of dimensions of course, Loosely referenced in the discussion above, in talking about air, water, electricity, and in the storm example, there is the question of movement and its characteristics of velocity and acceleration. The calculation of these elements requires another dimension which we commonly refer to as time. Time is talked about by everyone and for centuries has escaped being understood. For our discussion here, it is important to understand that time, like space, exists only as a conceptual entity in our heads, not outside of them in some mysterious realm. Like space, you cannot reach out and grasp a handful or a cup full and examine it in your laboratory. Like space, you cannot bend it, curve it, break it slow it or speed it up. Its place in our quiver of descriptive tools is as a measure of the duration or persistence of objects, events, or phenomena. It is also nothing more than a descriptor, its units of measure derived from the observed regular periodicity of other events such as the recurrence of day and night, or the passage of earth around the sun. We use it in this way to calculate the velocity or acceleration of objects, events or phenomena or as a measure of their duration. The old joke is correct, “Time is just one damn thing after another”. It has no meaning or existence in and of itself except as it relates to the duration, the persistence of the real entities in the universe.

For the last hundred years or so, physicists have been guilty of misapprehension, misattribution, misrepresentation and downright misuse of the conceptual entities they call space and time, and what they have designated as the “dimensions” of those concepts. Einstein was not the first, only the most famous to propose a “four-dimensional” continuum (three spatial dimensions plus time) as a model for the cosmos, and to build a complex mansion of theories on that hypothetical ground. For the last thirty or so years people who call themselves theoretical physicists have built mighty dream palaces on that platform; string theory, SUSY, branes, multiverses, and the like, none of which are testable or can be the basis for predictive research or can be seen to have any relationship to the real world. I believe that this descent into unreality is the result of despair at trying to build something real on an unsupportable platform.

People ask, “How many dimensions are there?” The simple answer is, “There are as many as you need.” They have nothing to do with the structure of the universe, only as a way to measure, describe, and communicate our observations. The mathematicians have great fun playing with “multidimensional” worlds and concepts. These exist only in their heads, and, it seems, leave little room for real thinking. The math is not reality, it’s only one tool for describing it. But until we find a way to move physics back to its real original task, that of understanding and explaining reality, there is little hope of progress.

Charles,

Very good, but I’ve found also recursive ‘fractal’ gauges as important dimensions, closely related to chaos theory and Godels n-value logic. Also this; https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/#!

Now you’re retired I do hope you can read more of my papers and essays and give me a view?

Peter,

Thank you, The amplituhedron is truly beautiful. It makes me want to pick it up and turn it over in my hand, perhaps use it to adorn the throat of my beloved, but . . . it is still what they call a “mathematical object,” a contradiction in terms if I ever heard one. For me reality is made up of objects, events, and phenomena, things that stay the same when you look away then back. As Robert Heinlein said, “Reality is the stuff that when you stop believing in it, it doesn’t go away.” But I still love these constructions, one of my favorite capabilities of Wolfram’s “Mathematica.”