RAMBLES IN PHYSICS
by John T. Bennett
THE UNIVERSE IS "DIMENSIONLESS" or "DIMENSIONMORE"
So I got to thinking, as is sometimes the case, about the nature of our Universe, whether it is expanding, contracting, what shape it is, etcetera. Firstly let us lay down a few principles for the sake of this argument. Principle number one is that mathematics is a language. A language is a series of symbols, gestures, and expressions to help describe something. A language, therefore, while pointing to the truth, cannot actually be considered "the truth". In essence what this boils down to is a flaw in reasoning that because a mathematical equation, theory, what-have-you, is logically sound and consistent, it constitutes actual truth.
Let's give a brief example. Einstein can be attributed for the inclusion of a fourth dimension (time), where math had previously only been concerned with three. One of his peers whose name I've forgotten (starts with a 'K' I think) offered up a beautifully written piece describing the universe in five dimensions. When you worked in five dimensions the math allowed for special and general relativity and Maxwell's electromagnetic laws (field theory).
String Theory uses the same trick. Each time you insist upon a new law of nature, you can try to wrangle it and force it into the pre-existing framework like a puzzle piece that doesn't want to fit OR you can simply add another dimension which you assume must be folded up within the original three/four dimensions, and the math comes out smooth as a cucumber--though I assume incredibly complicated.
Now, this raises questions. How many dimensions are there in the Universe? It is easy to convince someone that there are three. We can go forward, up/down, and "through", so there you have x, y, and z. Pretty simple. But can you prove it? Mathematics has shown that the Universe can be worded different ways. A 2 dimensional universe can be conceived as a 3 dimensional universe all wrapped up like a tight ball, and it is just as sound and consistent. So if this is the case, how could you prove which one is true?
Physics does not like ambiguities, at least not classical mechanics. A system must be able to be traced back in time, and with the ability to "wrap up" dimensions, it would be impossible to know at any given point whether you were a 2 dimensional universe, or an 11 dimensional universe, and they cannot both be true. Well, they could, but that's another argument for later.
I would suggest, by pointing out the obvious, that neither is true. Dimensions are an abstract concept used in mathematics, which we have already decided is a language. If I am trying to communicate I do so in a variety of ways, but one is by adding complexity to simplify speech. For example perhaps I am talking about a kitchen and have come up with the term shelf. It would become complicated to keep talking about the kitchen if shelf were the only term I had.
"Put the milk on the shelf."
"Put the cup on the shelf. No, not the same shelf as the milk. A different shelf."
"Put the pancake mix on the shelf, but neither the shelf used by the milk or the cup."
"Put the plate on the shelf, using the same shelf as the cup unless there will then be not enough room for other cups, in which case the plate should go on another shelf that is definitely not the same shelf used for pancake mix or milk."
"I would like to specify that the milk should go on the shelf that is kept cold. So for future reference I will call it the shelf that is kept cold, and we will call the pancake mix shelf the shelf that is..."
The term shelf is great, but communicating with one term, or let's just call it a simple term, becomes complicated over time. In a kitchen with only one shelf there would be no reason to have more than one term, but language evolves along with the kitchen. We invent terms which are usually more than one syllable long, and we will call those terms complex terms. Complex terms possess much more information than the number of bits contained within them. For example, let is take a simple term, like shelf, and compare it to a complex term, like refridgerator.
What information does shelf tell us? Well we know that shelves are flat and that they are generally mounted to a surface, and used for putting things on. That is roughly all that the word shelf will tell us. For any more in depth information you would require other words, such as big shelf, or small shelf, or 3 ' by 4' shelf, etcetera.
What does the word refridgerator tell us? A refridgerator tells us to look for an object with a door, inside of which will be several shelves, and probably at least one drawer, and inside the temperature is kept cooler than outside, though only if "powered" by some means whether than be electricity or natural (such as a cold storage--namely that it is conceivable that a 'fridge could be powered by some other means and retain all the other functions). The word refridgerator becomes a specific location without having to specify the location. If I go to almost any house in the world and someone tells me to put something in the refridgerator, the only information I require to find the refridgerator is where the space they use for a "kitchen" is. Kitchen, of course, is also a complex term, meaning simply that it is one word with many other words "wrapped up" as it were.
I am using the term complex term. You could exchange complex term for concept but for the nature of this argument, I am going to simply continue to speak in terms of complexity. Complexity, according to information theory, also adds depth, and it also generates entropy, and we will come to that later.
So, what are dimensions? Mathematically speaking, dimensions can be seen as simply complex terms. More complicated bits of language that in fact make communication much simpler. It is irrelevant, therefore, to speak of how many dimensions the universe has. That is like asking how many words does it take to describe an elephant? By definition you could narrow it down to, let's say 10, and everyone agree that an elephant can be described in no less than 10 words, but that would never be true. An elephant could be described in one complex word (concept) that automatically contains those other 10 words. This is true of language, as an elephant is a complex term describing an animal of a specific size (very large) and generally colour (usually grey, to describe an elephant of another colour, you would have to include a separate word--if you say elephant it is grey, if you want to talk about a pink elephant you have to use the word pink), weight (very heavy), physical features (large trunk), fears (scared of mice) and so on and so on. The word elephant conjures up many words to your mind. The definition of a complex term is one that when you think about it and write down your thoughts, you will unravel a long list of thoughts. Simple terms, like blue, are a much shorter list. Blue really only describes the "blueness" of an object, and nothing else. For any more information, you require more words, like navy, to get more specifity.
So long story short, it is a flaw in reasoning to assume that the universe possesses a set number of dimensions as dimensions are an abstract concept of a language used to communicate about the universe. When we talk about something, the something does not automatically get captured in our speech like a soul was believed to be captured by a photo. The something we are talking about is independant of our language to describe it.
The Universe, therefore, has exactly as many dimensions as are useful in making communication simpler. If it is just as easy to speak of the universe in four dimensions, then it has four. If it is easier to speak of it in five dimensions, it should have five. The Universe could have any number of dimensions, all of which are indeterminable. Again, it would be like trying to work out exactly how much information is in the word elephant. The amount of information in a word is relative to the amount of information in the mind of the receiver. If I say elephant to a zoologist, the word will contain much more information than if I say elephant to a secretary (unless the secretary used to be a zoologist). Words that are abundant in information can also possess no information, as in the example that I say the word elephant to someone that does not know what an elephant is. In this case, I must manually unravel the word in order to explain it to the person, at which point, elephant will become a word that will from then on mean all of those things (or at least the ones that person remembers).
Dimensions are the same thing. Describing the universe in fourteen dimensions is great. It is however useless if you do not take the time to explain to "outsiders" what those extra ten dimensions stand for. And does the Universe have fourteen dimensions? Yes. Obviously. If I can prove that elephant includes the word "grey", then I can prove that the universe has those dimensions as long as it is consistent and logically sound. Elephant does not include the word abyss, for example, because elephants are not composed of abysses (that we know of). If I can describe something with language, it is assumed that the thing I am describing has those qualities. Even fictitious objects possess the qualities I imbue them with, and are subject to the same laws.
Take the word "life" for example. As the various fields of science, philosophy, theology, etcetera all expand their reasoning, life becomes a much more complicated term. Life now includes words such as organism, which themselves are complex terms. Therefore you have complex terms wrapped up in more complex terms, ad infinitum. The Universe is the same way, and for this reason I will eventually get around to my HARD DRIVE UNIVERSE theory, which is not so much a theory as simply a way of perceiving things that I think is handy.
So the Universe must have fourteen dimensions if you can describe it using fourteen dimensions. But the underlying point is that the universe, (or let us just say reality) always has more dimensions than we are describing. Using the term elephant for example, fails to accurately describe even the simplest of elephants, namely one sketched by a two year old with no talent. The complex term is a tool for communication. The barrier of any language will be its ability to completely describe anything that it is talking about, and math is no exception.
So, in conclusion, if you view the varying types of mathematics as grammatical rules to make describing a system more simple, than mathematics is no truer than the word elephant. The goal of math is to create the best term for description and nothing more. Mathematical "proofs" are not true in and of themselves, they are only consistent within their own language framework.
This point leads into my next point, but for now I will stop here as I have other things to do today.
