The word dimension is, like the word time, also a word that often seems to get misused, and misunderstood.
A quick look at various dictionary definitions gives a wide range of definitions of the word dimension, including: – a measurement, a property (of space), scope, magnitude, parameters.
That’s quite an array of meanings. I have never seen any attempt by anyone writing about space and/or time to define precisely what they believe ‘dimension’ means.
I think a dimension is an abstract calibration and indexing model. And that is the definition I am sticking to here. So at least I am prepared to put down an anchor (I wish others would).
When we talk about Space having three dimensions, and then state them as height, width and depth, or something similar, we are not talking about a property of reality, we are inferring an overlay that provides calibration in three separate, right-angles vectors. What are we doing with these vectors? We are determining spatial position, that’s all…indexing and calibrating is what dimensions do.
Space (another word with multiple meanings) is, in this context, the dimension of spatial position. Space calibrates and indexes position. And (with the greatest respect to Prof. Einstein) it’s NOT three dimensions. Height, width and depth might be three separate dimensions individually, but merged together they form a single dimension – the dimension of spatial position. Space is one dimension calibrated in three right-angled vectors.
Temperature – the dimension of Heat.
As we’ve already noted, a dimension is an abstract framework that we use to calibrate and index an aspect of reality.
A good example is temperature. Temperature is the dimension of heat. Temperature calibrates and indexes heat. Temperature is abstract – it exists only in our collective minds. Heat is real.
I use this dimension of temperature referencing heat as a simple aide to differentiate between a dimension, which is the abstract overlay; and the underlying reality that is being calibrated. Know the difference between temperature and heat. One is abstract, one is real. Hint: temperature doesn’t burn. I think the abstract and the reality become confused in some of the discussion around dimensions.
The same relationship exists between time and change. Time is abstract, change is real. And between space and position. Space (in this context) is abstract, position is real. (not forgetting, the word Space also has multiple meanings as we discuss later).